multixact.c

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/*-------------------------------------------------------------------------
 *
 * multixact.c
 *      PostgreSQL multi-transaction-log manager
 *
 * The pg_multixact manager is a pg_xact-like manager that stores an array of
 * MultiXactMember for each MultiXactId.  It is a fundamental part of the
 * shared-row-lock implementation.  Each MultiXactMember is comprised of a
 * TransactionId and a set of flag bits.  The name is a bit historical:
 * originally, a MultiXactId consisted of more than one TransactionId (except
 * in rare corner cases), hence "multi".  Nowadays, however, it's perfectly
 * legitimate to have MultiXactIds that only include a single Xid.
 *
 * The meaning of the flag bits is opaque to this module, but they are mostly
 * used in heapam.c to identify lock modes that each of the member transactions
 * is holding on any given tuple.  This module just contains support to store
 * and retrieve the arrays.
 *
 * We use two SLRU areas, one for storing the offsets at 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.)
 *
 * XLOG interactions: this module generates a record whenever a new OFFSETs or
 * MEMBERs page is initialized to zeroes, as well as an
 * XLOG_MULTIXACT_CREATE_ID record whenever a new MultiXactId is defined.
 * This module ignores the WAL rule "write xlog before data," because it
 * suffices that actions recording a MultiXactId in a heap xmax do follow that
 * rule.  The only way for the MXID to be referenced from any data page is for
 * heap_lock_tuple() or heap_update() to have put it there, and each generates
 * an XLOG record that must follow ours.  The normal LSN interlock between the
 * data page and that XLOG record will ensure that our XLOG record reaches
 * disk first.  If the SLRU members/offsets data reaches disk sooner than the
 * XLOG records, we do not care; after recovery, no xmax will refer to it.  On
 * the flip side, to ensure that all referenced entries _do_ reach disk, this
 * module's XLOG records completely rebuild the data entered since the last
 * checkpoint.  We flush and sync all dirty OFFSETs and MEMBERs pages to disk
 * before each checkpoint is considered complete.
 *
 * Like clog.c, and unlike subtrans.c, we have to preserve state across
 * crashes and ensure that MXID and offset numbering increases monotonically
 * across a crash.  We do this in the same way as it's done for transaction
 * IDs: the WAL record is guaranteed to contain evidence of every MXID we
 * could need to worry about, and we just make sure that at the end of
 * replay, the next-MXID and next-offset counters are at least as large as
 * anything we saw during replay.
 *
 * We are able to remove segments no longer necessary by carefully tracking
 * each table's used values: during vacuum, any multixact older than a certain
 * value is removed; the cutoff value is stored in pg_class.  The minimum value
 * across all tables in each database is stored in pg_database, and the global
 * minimum across all databases is part of pg_control and is kept in shared
 * memory.  Whenever that minimum is advanced, the SLRUs are truncated.
 *
 * When new multixactid values are to be created, care is taken that the
 * counter does not fall within the wraparound horizon considering the global
 * minimum value.
 *
 * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * src/backend/access/transam/multixact.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/multixact.h"
#include "access/slru.h"
#include "access/transam.h"
#include "access/twophase.h"
#include "access/twophase_rmgr.h"
#include "access/xact.h"
#include "access/xlog.h"
#include "access/xloginsert.h"
#include "catalog/pg_type.h"
#include "commands/dbcommands.h"
#include "funcapi.h"
#include "lib/ilist.h"
#include "miscadmin.h"
#include "pg_trace.h"
#include "postmaster/autovacuum.h"
#include "storage/lmgr.h"
#include "storage/pmsignal.h"
#include "storage/proc.h"
#include "storage/procarray.h"
#include "utils/builtins.h"
#include "utils/memutils.h"
#include "utils/snapmgr.h"


/*
 * Defines for MultiXactOffset page sizes.  A page is the same BLCKSZ as is
 * used everywhere else in Postgres.
 *
 * Note: because MultiXactOffsets are 32 bits and wrap around at 0xFFFFFFFF,
 * MultiXact page numbering also wraps around at
 * 0xFFFFFFFF/MULTIXACT_OFFSETS_PER_PAGE, and segment numbering at
 * 0xFFFFFFFF/MULTIXACT_OFFSETS_PER_PAGE/SLRU_PAGES_PER_SEGMENT.  We need
 * take no explicit notice of that fact in this module, except when comparing
 * segment and page numbers in TruncateMultiXact (see
 * MultiXactOffsetPagePrecedes).
 */

/* We need four bytes per offset */
#define MULTIXACT_OFFSETS_PER_PAGE (BLCKSZ / sizeof(MultiXactOffset))

#define MultiXactIdToOffsetPage(xid) \
    ((xid) / (MultiXactOffset) MULTIXACT_OFFSETS_PER_PAGE)
#define MultiXactIdToOffsetEntry(xid) \
    ((xid) % (MultiXactOffset) MULTIXACT_OFFSETS_PER_PAGE)
#define MultiXactIdToOffsetSegment(xid) (MultiXactIdToOffsetPage(xid) / SLRU_PAGES_PER_SEGMENT)

/*
 * The situation for members is a bit more complex: we store one byte of
 * additional flag bits for each TransactionId.  To do this without getting
 * into alignment issues, we store four bytes of flags, and then the
 * corresponding 4 Xids.  Each such 5-word (20-byte) set we call a "group", and
 * are stored as a whole in pages.  Thus, with 8kB BLCKSZ, we keep 409 groups
 * per page.  This wastes 12 bytes per page, but that's OK -- simplicity (and
 * performance) trumps space efficiency here.
 *
 * Note that the "offset" macros work with byte offset, not array indexes, so
 * arithmetic must be done using "char *" pointers.
 */
/* We need eight bits per xact, so one xact fits in a byte */
#define MXACT_MEMBER_BITS_PER_XACT          8
#define MXACT_MEMBER_FLAGS_PER_BYTE         1
#define MXACT_MEMBER_XACT_BITMASK   ((1 << MXACT_MEMBER_BITS_PER_XACT) - 1)

/* how many full bytes of flags are there in a group? */
#define MULTIXACT_FLAGBYTES_PER_GROUP       4
#define MULTIXACT_MEMBERS_PER_MEMBERGROUP   \
    (MULTIXACT_FLAGBYTES_PER_GROUP * MXACT_MEMBER_FLAGS_PER_BYTE)
/* size in bytes of a complete group */
#define MULTIXACT_MEMBERGROUP_SIZE \
    (sizeof(TransactionId) * MULTIXACT_MEMBERS_PER_MEMBERGROUP + MULTIXACT_FLAGBYTES_PER_GROUP)
#define MULTIXACT_MEMBERGROUPS_PER_PAGE (BLCKSZ / MULTIXACT_MEMBERGROUP_SIZE)
#define MULTIXACT_MEMBERS_PER_PAGE  \
    (MULTIXACT_MEMBERGROUPS_PER_PAGE * MULTIXACT_MEMBERS_PER_MEMBERGROUP)

/*
 * Because the number of items per page is not a divisor of the last item
 * number (member 0xFFFFFFFF), the last segment does not use the maximum number
 * of pages, and moreover the last used page therein does not use the same
 * number of items as previous pages.  (Another way to say it is that the
 * 0xFFFFFFFF member is somewhere in the middle of the last page, so the page
 * has some empty space after that item.)
 *
 * This constant is the number of members in the last page of the last segment.
 */
#define MAX_MEMBERS_IN_LAST_MEMBERS_PAGE \
        ((uint32) ((0xFFFFFFFF % MULTIXACT_MEMBERS_PER_PAGE) + 1))

/* page in which a member is to be found */
#define MXOffsetToMemberPage(xid) ((xid) / (TransactionId) MULTIXACT_MEMBERS_PER_PAGE)
#define MXOffsetToMemberSegment(xid) (MXOffsetToMemberPage(xid) / SLRU_PAGES_PER_SEGMENT)

/* Location (byte offset within page) of flag word for a given member */
#define MXOffsetToFlagsOffset(xid) \
    ((((xid) / (TransactionId) MULTIXACT_MEMBERS_PER_MEMBERGROUP) % \
      (TransactionId) MULTIXACT_MEMBERGROUPS_PER_PAGE) * \
     (TransactionId) MULTIXACT_MEMBERGROUP_SIZE)
#define MXOffsetToFlagsBitShift(xid) \
    (((xid) % (TransactionId) MULTIXACT_MEMBERS_PER_MEMBERGROUP) * \
     MXACT_MEMBER_BITS_PER_XACT)

/* Location (byte offset within page) of TransactionId of given member */
#define MXOffsetToMemberOffset(xid) \
    (MXOffsetToFlagsOffset(xid) + MULTIXACT_FLAGBYTES_PER_GROUP + \
     ((xid) % MULTIXACT_MEMBERS_PER_MEMBERGROUP) * sizeof(TransactionId))

/* Multixact members wraparound thresholds. */
#define MULTIXACT_MEMBER_SAFE_THRESHOLD     (MaxMultiXactOffset / 2)
#define MULTIXACT_MEMBER_DANGER_THRESHOLD   \
    (MaxMultiXactOffset - MaxMultiXactOffset / 4)

#define PreviousMultiXactId(xid) \
    ((xid) == FirstMultiXactId ? MaxMultiXactId : (xid) - 1)

/*
 * 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 MultiXactOffsetSLRULock and
 * MultiXactMemberSLRULock 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;

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

    /* Have we completed multixact startup? */
    bool        finishedStartup;

    /*
     * Oldest multixact that is still potentially referenced by a relation.
     * Anything older than this should not be consulted.  These values are
     * updated by vacuum.
     */
    MultiXactId oldestMultiXactId;
    Oid         oldestMultiXactDB;

    /*
     * Oldest multixact offset that is potentially referenced by a multixact
     * referenced by a relation.  We don't always know this value, so there's
     * a flag here to indicate whether or not we currently do.
     */
    MultiXactOffset oldestOffset;
    bool        oldestOffsetKnown;

    /* support for anti-wraparound measures */
    MultiXactId multiVacLimit;
    MultiXactId multiWarnLimit;
    MultiXactId multiStopLimit;
    MultiXactId multiWrapLimit;

    /* support for members anti-wraparound measures */
    MultiXactOffset offsetStopLimit;    /* known if oldestOffsetKnown */

    /*
     * Per-backend data starts here.  We have two arrays stored in the area
     * immediately following the MultiXactStateData struct. Each is indexed by
     * BackendId.
     *
     * In both arrays, there's a slot for all normal backends (1..MaxBackends)
     * followed by a slot for max_prepared_xacts prepared transactions. Valid
     * BackendIds start from 1; 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 oldest valid value among all of the OldestMemberMXactId[] and
     * OldestVisibleMXactId[] entries is considered by vacuum as the earliest
     * possible value still having any live member transaction.  Subtracting
     * vacuum_multixact_freeze_min_age from that value we obtain the freezing
     * point for multixacts for that table.  Any value older than that is
     * removed from tuple headers (or "frozen"; see FreezeMultiXactId.  Note
     * that multis that have member xids that are older than the cutoff point
     * for xids must also be frozen, even if the multis themselves are newer
     * than the multixid cutoff point).  Whenever a full table vacuum happens,
     * the freezing point so computed is used as the new pg_class.relminmxid
     * value.  The minimum of all those values in a database is stored as
     * pg_database.datminmxid.  In turn, the minimum of all of those values is
     * stored in pg_control and used as truncation point for pg_multixact.  At
     * checkpoint or restartpoint, unneeded segments are removed.
     */
    MultiXactId perBackendXactIds[FLEXIBLE_ARRAY_MEMBER];
} MultiXactStateData;

/*
 * Last element of OldestMemberMXactId and OldestVisibleMXactId arrays.
 * Valid elements are (1..MaxOldestSlot); element 0 is never used.
 */
#define MaxOldestSlot   (MaxBackends + max_prepared_xacts)

/* 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 every time.
 *
 * 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.  However, it's not clear what a
 * better policy for flushing old cache entries would be.)  FIXME actually
 * this is plain wrong now that multixact's may contain update Xids.
 *
 * 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
{
    MultiXactId multi;
    int         nmembers;
    dlist_node  node;
    MultiXactMember members[FLEXIBLE_ARRAY_MEMBER];
} mXactCacheEnt;

#define MAX_CACHE_ENTRIES   256
static dlist_head MXactCache = DLIST_STATIC_INIT(MXactCache);
static int  MXactCacheMembers = 0;
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)
#define debug_elog6(a,b,c,d,e,f) elog(a,b,c,d,e,f)
#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)
#define debug_elog6(a,b,c,d,e,f)
#endif

/* internal MultiXactId management */
static void MultiXactIdSetOldestVisible(void);
static void RecordNewMultiXact(MultiXactId multi, MultiXactOffset offset,
                               int nmembers, MultiXactMember *members);
static MultiXactId GetNewMultiXactId(int nmembers, MultiXactOffset *offset);

/* MultiXact cache management */
static int  mxactMemberComparator(const void *arg1, const void *arg2);
static MultiXactId mXactCacheGetBySet(int nmembers, MultiXactMember *members);
static int  mXactCacheGetById(MultiXactId multi, MultiXactMember **members);
static void mXactCachePut(MultiXactId multi, int nmembers,
                          MultiXactMember *members);

static char *mxstatus_to_string(MultiXactStatus status);

/* management of SLRU infrastructure */
static int  ZeroMultiXactOffsetPage(int pageno, bool writeXlog);
static int  ZeroMultiXactMemberPage(int pageno, bool writeXlog);
static bool MultiXactOffsetPagePrecedes(int page1, int page2);
static bool MultiXactMemberPagePrecedes(int page1, int page2);
static bool MultiXactOffsetPrecedes(MultiXactOffset offset1,
                                    MultiXactOffset offset2);
static void ExtendMultiXactOffset(MultiXactId multi);
static void ExtendMultiXactMember(MultiXactOffset offset, int nmembers);
static bool MultiXactOffsetWouldWrap(MultiXactOffset boundary,
                                     MultiXactOffset start, uint32 distance);
static bool SetOffsetVacuumLimit(bool is_startup);
static bool find_multixact_start(MultiXactId multi, MultiXactOffset *result);
static void WriteMZeroPageXlogRec(int pageno, uint8 info);
static void WriteMTruncateXlogRec(Oid oldestMultiDB,
                                  MultiXactId startTruncOff,
                                  MultiXactId endTruncOff,
                                  MultiXactOffset startTruncMemb,
                                  MultiXactOffset endTruncMemb);


/*
 * MultiXactIdCreate
 *      Construct a MultiXactId representing two TransactionIds.
 *
 * The two XIDs must be different, or be requesting different statuses.
 *
 * NB - we don't worry about our local MultiXactId cache here, because that
 * is handled by the lower-level routines.
 */
MultiXactId
MultiXactIdCreate(TransactionId xid1, MultiXactStatus status1,
                  TransactionId xid2, MultiXactStatus status2)
{
    MultiXactId newMulti;
    MultiXactMember members[2];

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

    Assert(!TransactionIdEquals(xid1, xid2) || (status1 != status2));

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

    /*
     * 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.
     */

    members[0].xid = xid1;
    members[0].status = status1;
    members[1].xid = xid2;
    members[1].status = status2;

    newMulti = MultiXactIdCreateFromMembers(2, members);

    debug_elog3(DEBUG2, "Create: %s",
                mxid_to_string(newMulti, 2, members));

    return newMulti;
}

/*
 * MultiXactIdExpand
 *      Add a TransactionId to a pre-existing MultiXactId.
 *
 * If the TransactionId is already a member of the passed MultiXactId with the
 * same status, 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 code trying to wait for one MultiXactId to finish;
 * see notes in heapam.c.
 *
 * NB - we don't worry about our local MultiXactId cache here, because that
 * is handled by the lower-level routines.
 *
 * Note: It is critical that MultiXactIds that come from an old cluster (i.e.
 * one upgraded by pg_upgrade from a cluster older than this feature) are not
 * passed in.
 */
MultiXactId
MultiXactIdExpand(MultiXactId multi, TransactionId xid, MultiXactStatus status)
{
    MultiXactId newMulti;
    MultiXactMember *members;
    MultiXactMember *newMembers;
    int         nmembers;
    int         i;
    int         j;

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

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

    debug_elog5(DEBUG2, "Expand: received multi %u, xid %u status %s",
                multi, xid, mxstatus_to_string(status));

    /*
     * Note: we don't allow for old multis here.  The reason is that the only
     * caller of this function does a check that the multixact is no longer
     * running.
     */
    nmembers = GetMultiXactIdMembers(multi, &members, false, false);

    if (nmembers < 0)
    {
        MultiXactMember member;

        /*
         * 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.
         */
        member.xid = xid;
        member.status = status;
        newMulti = MultiXactIdCreateFromMembers(1, &member);

        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 with the
     * same status, just return the existing MultiXactId.
     */
    for (i = 0; i < nmembers; i++)
    {
        if (TransactionIdEquals(members[i].xid, xid) &&
            (members[i].status == status))
        {
            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 of
     * interest. This is any running transaction, and also any transaction
     * that grabbed something stronger than just a lock and was committed. (An
     * update that aborted is of no interest here; and having more than one
     * update Xid in a multixact would cause errors elsewhere.)
     *
     * Removing dead members is not just an optimization: freezing of tuples
     * whose Xmax are multis depends on this behavior.
     *
     * Note we have the same race condition here as above: j could be 0 at the
     * end of the loop.
     */
    newMembers = (MultiXactMember *)
        palloc(sizeof(MultiXactMember) * (nmembers + 1));

    for (i = 0, j = 0; i < nmembers; i++)
    {
        if (TransactionIdIsInProgress(members[i].xid) ||
            (ISUPDATE_from_mxstatus(members[i].status) &&
             TransactionIdDidCommit(members[i].xid)))
        {
            newMembers[j].xid = members[i].xid;
            newMembers[j++].status = members[i].status;
        }
    }

    newMembers[j].xid = xid;
    newMembers[j++].status = status;
    newMulti = MultiXactIdCreateFromMembers(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.
 *
 * Caller is expected to have verified that the multixact does not come from
 * a pg_upgraded share-locked tuple.
 */
bool
MultiXactIdIsRunning(MultiXactId multi, bool isLockOnly)
{
    MultiXactMember *members;
    int         nmembers;
    int         i;

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

    /*
     * "false" here means we assume our callers have checked that the given
     * multi cannot possibly come from a pg_upgraded database.
     */
    nmembers = GetMultiXactIdMembers(multi, &members, false, isLockOnly);

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

    /*
     * Checking for myself is cheap compared to looking in shared memory;
     * return true if any live subtransaction of the current top-level
     * transaction is a member.
     *
     * This is not needed for correctness, it's just a fast path.
     */
    for (i = 0; i < nmembers; i++)
    {
        if (TransactionIdIsCurrentTransactionId(members[i].xid))
        {
            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].xid))
        {
            debug_elog4(DEBUG2, "IsRunning: member %d (%u) is running",
                        i, members[i].xid);
            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 do some operation that might require a MultiXactId (tuple lock,
 * update or delete).  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 doing any such possibly-MultiXactId-able operation.
 */
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.
         *
         * Note that a shared lock is sufficient, because it's enough to stop
         * someone from advancing nextMXact; and nobody else could be trying
         * to write to our OldestMember entry, only reading (and we assume
         * storing it is atomic.)
         */
        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 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 <= MaxOldestSlot; 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);
    }
}

/*
 * ReadNextMultiXactId
 *      Return the next MultiXactId to be assigned, but don't allocate it
 */
MultiXactId
ReadNextMultiXactId(void)
{
    MultiXactId mxid;

    /* XXX we could presumably do this without a lock. */
    LWLockAcquire(MultiXactGenLock, LW_SHARED);
    mxid = MultiXactState->nextMXact;
    LWLockRelease(MultiXactGenLock);

    if (mxid < FirstMultiXactId)
        mxid = FirstMultiXactId;

    return mxid;
}

/*
 * MultiXactIdCreateFromMembers
 *      Make a new MultiXactId from the specified set of members
 *
 * Make XLOG, SLRU and cache entries for a new MultiXactId, recording the
 * given TransactionIds as members.  Returns the newly created MultiXactId.
 *
 * NB: the passed members[] array will be sorted in-place.
 */
MultiXactId
MultiXactIdCreateFromMembers(int nmembers, MultiXactMember *members)
{
    MultiXactId multi;
    MultiXactOffset offset;
    xl_multixact_create xlrec;

    debug_elog3(DEBUG2, "Create: %s",
                mxid_to_string(InvalidMultiXactId, nmembers, members));

    /*
     * See if the same set of members 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(nmembers, members);
    if (MultiXactIdIsValid(multi))
    {
        debug_elog2(DEBUG2, "Create: in cache!");
        return multi;
    }

    /* Verify that there is a single update Xid among the given members. */
    {
        int         i;
        bool        has_update = false;

        for (i = 0; i < nmembers; i++)
        {
            if (ISUPDATE_from_mxstatus(members[i].status))
            {
                if (has_update)
                    elog(ERROR, "new multixact has more than one updating member");
                has_update = true;
            }
        }
    }

    /*
     * Assign the MXID and offsets range to use, and make sure there is space
     * in the OFFSETs and MEMBERs files.  NB: this routine does
     * START_CRIT_SECTION().
     *
     * Note: unlike MultiXactIdCreate and MultiXactIdExpand, we do not check
     * that we've called MultiXactIdSetOldestMember here.  This is because
     * this routine is used in some places to create new MultiXactIds of which
     * the current backend is not a member, notably during freezing of multis
     * in vacuum.  During vacuum, in particular, it would be unacceptable to
     * keep OldestMulti set, in case it runs for long.
     */
    multi = GetNewMultiXactId(nmembers, &offset);

    /* Make an XLOG entry describing the new MXID. */
    xlrec.mid = multi;
    xlrec.moff = offset;
    xlrec.nmembers = nmembers;

    /*
     * XXX Note: there's a lot of padding space in MultiXactMember.  We could
     * find a more compact representation of this Xlog record -- perhaps all
     * the status flags in one XLogRecData, then all the xids in another one?
     * Not clear that it's worth the trouble though.
     */
    XLogBeginInsert();
    XLogRegisterData((char *) (&xlrec), SizeOfMultiXactCreate);
    XLogRegisterData((char *) members, nmembers * sizeof(MultiXactMember));

    (void) XLogInsert(RM_MULTIXACT_ID, XLOG_MULTIXACT_CREATE_ID);

    /* Now enter the information into the OFFSETs and MEMBERs logs */
    RecordNewMultiXact(multi, offset, nmembers, members);

    /* Done with critical section */
    END_CRIT_SECTION();

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

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

    return multi;
}

/*
 * RecordNewMultiXact
 *      Write info about a new multixact into the offsets and members files
 *
 * This is broken out of MultiXactIdCreateFromMembers so that xlog replay can
 * use it.
 */
static void
RecordNewMultiXact(MultiXactId multi, MultiXactOffset offset,
                   int nmembers, MultiXactMember *members)
{
    int         pageno;
    int         prev_pageno;
    int         entryno;
    int         slotno;
    MultiXactOffset *offptr;
    int         i;

    LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

    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, true, multi);
    offptr = (MultiXactOffset *) MultiXactOffsetCtl->shared->page_buffer[slotno];
    offptr += entryno;

    *offptr = offset;

    MultiXactOffsetCtl->shared->page_dirty[slotno] = true;

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

    LWLockAcquire(MultiXactMemberSLRULock, LW_EXCLUSIVE);

    prev_pageno = -1;

    for (i = 0; i < nmembers; i++, offset++)
    {
        TransactionId *memberptr;
        uint32     *flagsptr;
        uint32      flagsval;
        int         bshift;
        int         flagsoff;
        int         memberoff;

        Assert(members[i].status <= MultiXactStatusUpdate);

        pageno = MXOffsetToMemberPage(offset);
        memberoff = MXOffsetToMemberOffset(offset);
        flagsoff = MXOffsetToFlagsOffset(offset);
        bshift = MXOffsetToFlagsBitShift(offset);

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

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

        *memberptr = members[i].xid;

        flagsptr = (uint32 *)
            (MultiXactMemberCtl->shared->page_buffer[slotno] + flagsoff);

        flagsval = *flagsptr;
        flagsval &= ~(((1 << MXACT_MEMBER_BITS_PER_XACT) - 1) << bshift);
        flagsval |= (members[i].status << bshift);
        *flagsptr = flagsval;

        MultiXactMemberCtl->shared->page_dirty[slotno] = true;
    }

    LWLockRelease(MultiXactMemberSLRULock);
}

/*
 * GetNewMultiXactId
 *      Get the next MultiXactId.
 *
 * Also, reserve the needed amount of space in the "members" area.  The
 * starting offset of the reserved space is returned in *offset.
 *
 * This may generate XLOG records for expansion of the offsets and/or members
 * files.  Unfortunately, we have to do that while holding MultiXactGenLock
 * to avoid race conditions --- the XLOG record for zeroing a page must appear
 * before any backend can possibly try to store data in that page!
 *
 * We start a critical section before advancing the shared counters.  The
 * caller must end the critical section after writing SLRU data.
 */
static MultiXactId
GetNewMultiXactId(int nmembers, MultiXactOffset *offset)
{
    MultiXactId result;
    MultiXactOffset nextOffset;

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

    /* safety check, we should never get this far in a HS standby */
    if (RecoveryInProgress())
        elog(ERROR, "cannot assign MultiXactIds during recovery");

    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);

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

    /* Assign the MXID */
    result = MultiXactState->nextMXact;

    /*----------
     * Check to see if it's safe to assign another MultiXactId.  This protects
     * against catastrophic data loss due to multixact wraparound.  The basic
     * rules are:
     *
     * If we're past multiVacLimit or the safe threshold for member storage
     * space, or we don't know what the safe threshold for member storage is,
     * start trying to force autovacuum cycles.
     * If we're past multiWarnLimit, start issuing warnings.
     * If we're past multiStopLimit, refuse to create new MultiXactIds.
     *
     * Note these are pretty much the same protections in GetNewTransactionId.
     *----------
     */
    if (!MultiXactIdPrecedes(result, MultiXactState->multiVacLimit))
    {
        /*
         * For safety's sake, we release MultiXactGenLock while sending
         * signals, warnings, etc.  This is not so much because we care about
         * preserving concurrency in this situation, as to avoid any
         * possibility of deadlock while doing get_database_name(). First,
         * copy all the shared values we'll need in this path.
         */
        MultiXactId multiWarnLimit = MultiXactState->multiWarnLimit;
        MultiXactId multiStopLimit = MultiXactState->multiStopLimit;
        MultiXactId multiWrapLimit = MultiXactState->multiWrapLimit;
        Oid         oldest_datoid = MultiXactState->oldestMultiXactDB;

        LWLockRelease(MultiXactGenLock);

        if (IsUnderPostmaster &&
            !MultiXactIdPrecedes(result, multiStopLimit))
        {
            char       *oldest_datname = get_database_name(oldest_datoid);

            /*
             * Immediately kick autovacuum into action as we're already in
             * ERROR territory.
             */
            SendPostmasterSignal(PMSIGNAL_START_AUTOVAC_LAUNCHER);

            /* complain even if that DB has disappeared */
            if (oldest_datname)
                ereport(ERROR,
                        (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                         errmsg("database is not accepting commands that generate new MultiXactIds to avoid wraparound data loss in database \"%s\"",
                                oldest_datname),
                         errhint("Execute a database-wide VACUUM in that database.\n"
                                 "You might also need to commit or roll back old prepared transactions, or drop stale replication slots.")));
            else
                ereport(ERROR,
                        (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                         errmsg("database is not accepting commands that generate new MultiXactIds to avoid wraparound data loss in database with OID %u",
                                oldest_datoid),
                         errhint("Execute a database-wide VACUUM in that database.\n"
                                 "You might also need to commit or roll back old prepared transactions, or drop stale replication slots.")));
        }

        /*
         * To avoid swamping the postmaster with signals, we issue the autovac
         * request only once per 64K multis generated.  This still gives
         * plenty of chances before we get into real trouble.
         */
        if (IsUnderPostmaster && (result % 65536) == 0)
            SendPostmasterSignal(PMSIGNAL_START_AUTOVAC_LAUNCHER);

        if (!MultiXactIdPrecedes(result, multiWarnLimit))
        {
            char       *oldest_datname = get_database_name(oldest_datoid);

            /* complain even if that DB has disappeared */
            if (oldest_datname)
                ereport(WARNING,
                        (errmsg_plural("database \"%s\" must be vacuumed before %u more MultiXactId is used",
                                       "database \"%s\" must be vacuumed before %u more MultiXactIds are used",
                                       multiWrapLimit - result,
                                       oldest_datname,
                                       multiWrapLimit - result),
                         errhint("Execute a database-wide VACUUM in that database.\n"
                                 "You might also need to commit or roll back old prepared transactions, or drop stale replication slots.")));
            else
                ereport(WARNING,
                        (errmsg_plural("database with OID %u must be vacuumed before %u more MultiXactId is used",
                                       "database with OID %u must be vacuumed before %u more MultiXactIds are used",
                                       multiWrapLimit - result,
                                       oldest_datoid,
                                       multiWrapLimit - result),
                         errhint("Execute a database-wide VACUUM in that database.\n"
                                 "You might also need to commit or roll back old prepared transactions, or drop stale replication slots.")));
        }

        /* Re-acquire lock and start over */
        LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
        result = MultiXactState->nextMXact;
        if (result < FirstMultiXactId)
            result = FirstMultiXactId;
    }

    /* Make sure there is room for the MXID in the file.  */
    ExtendMultiXactOffset(result);

    /*
     * Reserve the members space, similarly to above.  Also, be careful not to
     * return zero as the starting offset for any multixact. See
     * GetMultiXactIdMembers() for motivation.
     */
    nextOffset = MultiXactState->nextOffset;
    if (nextOffset == 0)
    {
        *offset = 1;
        nmembers++;             /* allocate member slot 0 too */
    }
    else
        *offset = nextOffset;

    /*----------
     * Protect against overrun of the members space as well, with the
     * following rules:
     *
     * If we're past offsetStopLimit, refuse to generate more multis.
     * If we're close to offsetStopLimit, emit a warning.
     *
     * Arbitrarily, we start emitting warnings when we're 20 segments or less
     * from offsetStopLimit.
     *
     * Note we haven't updated the shared state yet, so if we fail at this
     * point, the multixact ID we grabbed can still be used by the next guy.
     *
     * Note that there is no point in forcing autovacuum runs here: the
     * multixact freeze settings would have to be reduced for that to have any
     * effect.
     *----------
     */
#define OFFSET_WARN_SEGMENTS    20
    if (MultiXactState->oldestOffsetKnown &&
        MultiXactOffsetWouldWrap(MultiXactState->offsetStopLimit, nextOffset,
                                 nmembers))
    {
        /* see comment in the corresponding offsets wraparound case */
        SendPostmasterSignal(PMSIGNAL_START_AUTOVAC_LAUNCHER);

        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("multixact \"members\" limit exceeded"),
                 errdetail_plural("This command would create a multixact with %u members, but the remaining space is only enough for %u member.",
                                  "This command would create a multixact with %u members, but the remaining space is only enough for %u members.",
                                  MultiXactState->offsetStopLimit - nextOffset - 1,
                                  nmembers,
                                  MultiXactState->offsetStopLimit - nextOffset - 1),
                 errhint("Execute a database-wide VACUUM in database with OID %u with reduced vacuum_multixact_freeze_min_age and vacuum_multixact_freeze_table_age settings.",
                         MultiXactState->oldestMultiXactDB)));
    }

    /*
     * Check whether we should kick autovacuum into action, to prevent members
     * wraparound. NB we use a much larger window to trigger autovacuum than
     * just the warning limit. The warning is just a measure of last resort -
     * this is in line with GetNewTransactionId's behaviour.
     */
    if (!MultiXactState->oldestOffsetKnown ||
        (MultiXactState->nextOffset - MultiXactState->oldestOffset
         > MULTIXACT_MEMBER_SAFE_THRESHOLD))
    {
        /*
         * To avoid swamping the postmaster with signals, we issue the autovac
         * request only when crossing a segment boundary. With default
         * compilation settings that's roughly after 50k members.  This still
         * gives plenty of chances before we get into real trouble.
         */
        if ((MXOffsetToMemberPage(nextOffset) / SLRU_PAGES_PER_SEGMENT) !=
            (MXOffsetToMemberPage(nextOffset + nmembers) / SLRU_PAGES_PER_SEGMENT))
            SendPostmasterSignal(PMSIGNAL_START_AUTOVAC_LAUNCHER);
    }

    if (MultiXactState->oldestOffsetKnown &&
        MultiXactOffsetWouldWrap(MultiXactState->offsetStopLimit,
                                 nextOffset,
                                 nmembers + MULTIXACT_MEMBERS_PER_PAGE * SLRU_PAGES_PER_SEGMENT * OFFSET_WARN_SEGMENTS))
        ereport(WARNING,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg_plural("database with OID %u must be vacuumed before %d more multixact member is used",
                               "database with OID %u must be vacuumed before %d more multixact members are used",
                               MultiXactState->offsetStopLimit - nextOffset + nmembers,
                               MultiXactState->oldestMultiXactDB,
                               MultiXactState->offsetStopLimit - nextOffset + nmembers),
                 errhint("Execute a database-wide VACUUM in that database with reduced vacuum_multixact_freeze_min_age and vacuum_multixact_freeze_table_age settings.")));

    ExtendMultiXactMember(nextOffset, nmembers);

    /*
     * Critical section from here until caller has written the data into the
     * just-reserved SLRU space; we don't want to error out with a partly
     * written MultiXact structure.  (In particular, failing to write our
     * start offset after advancing nextMXact would effectively corrupt the
     * previous MultiXact.)
     */
    START_CRIT_SECTION();

    /*
     * Advance counters.  As in GetNewTransactionId(), this must not happen
     * until after file extension has succeeded!
     *
     * We don't care about MultiXactId wraparound here; it will be handled by
     * the next iteration.  But note that nextMXact may be InvalidMultiXactId
     * or the first value on a segment-beginning page after this routine
     * exits, so anyone else looking at the variable must be prepared to deal
     * with either case.  Similarly, nextOffset may be zero, but we won't use
     * that as the actual start offset of the next multixact.
     */
    (MultiXactState->nextMXact)++;

    MultiXactState->nextOffset += nmembers;

    LWLockRelease(MultiXactGenLock);

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

/*
 * GetMultiXactIdMembers
 *      Return the set of MultiXactMembers that make up a MultiXactId
 *
 * Return value is the number of members found, or -1 if there are none,
 * and *members is set to a newly palloc'ed array of members.  It's the
 * caller's responsibility to free it when done with it.
 *
 * from_pgupgrade must be passed as true if and only if only the multixact
 * corresponds to a value from a tuple that was locked in a 9.2-or-older
 * installation and later pg_upgrade'd (that is, the infomask is
 * HEAP_LOCKED_UPGRADED).  In this case, we know for certain that no members
 * can still be running, so we return -1 just like for an empty multixact
 * without any further checking.  It would be wrong to try to resolve such a
 * multixact: either the multixact is within the current valid multixact
 * range, in which case the returned result would be bogus, or outside that
 * range, in which case an error would be raised.
 *
 * In all other cases, the passed multixact must be within the known valid
 * range, that is, greater to or equal than oldestMultiXactId, and less than
 * nextMXact.  Otherwise, an error is raised.
 *
 * onlyLock must be set to true if caller is certain that the given multi
 * is used only to lock tuples; can be false without loss of correctness,
 * but passing a true means we can return quickly without checking for
 * old updates.
 */
int
GetMultiXactIdMembers(MultiXactId multi, MultiXactMember **members,
                      bool from_pgupgrade, bool onlyLock)
{
    int         pageno;
    int         prev_pageno;
    int         entryno;
    int         slotno;
    MultiXactOffset *offptr;
    MultiXactOffset offset;
    int         length;
    int         truelength;
    int         i;
    MultiXactId oldestMXact;
    MultiXactId nextMXact;
    MultiXactId tmpMXact;
    MultiXactOffset nextOffset;
    MultiXactMember *ptr;

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

    if (!MultiXactIdIsValid(multi) || from_pgupgrade)
        return -1;

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

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

    /*
     * If we know the multi is used only for locking and not for updates, then
     * we can skip checking if the value is older than our oldest visible
     * multi.  It cannot possibly still be running.
     */
    if (onlyLock &&
        MultiXactIdPrecedes(multi, OldestVisibleMXactId[MyBackendId]))
    {
        debug_elog2(DEBUG2, "GetMembers: a locker-only multi is too old");
        *members = NULL;
        return -1;
    }

    /*
     * We check known limits on MultiXact before resorting to the SLRU area.
     *
     * An ID older than MultiXactState->oldestMultiXactId cannot possibly be
     * useful; it has already been removed, or will be removed shortly, by
     * truncation.  If one is passed, an error is raised.
     *
     * Also, an ID >= nextMXact shouldn't ever be seen here; if it is seen, it
     * implies undetected ID wraparound has occurred.  This raises a hard
     * error.
     *
     * Shared lock is enough here since we aren't modifying any global state.
     * Acquire it just long enough to grab the current counter values.  We may
     * need both nextMXact and nextOffset; see below.
     */
    LWLockAcquire(MultiXactGenLock, LW_SHARED);

    oldestMXact = MultiXactState->oldestMultiXactId;
    nextMXact = MultiXactState->nextMXact;
    nextOffset = MultiXactState->nextOffset;

    LWLockRelease(MultiXactGenLock);

    if (MultiXactIdPrecedes(multi, oldestMXact))
    {
        ereport(ERROR,
                (errcode(ERRCODE_INTERNAL_ERROR),
                 errmsg("MultiXactId %u does no longer exist -- apparent wraparound",
                        multi)));
        return -1;
    }

    if (!MultiXactIdPrecedes(multi, nextMXact))
        ereport(ERROR,
                (errcode(ERRCODE_INTERNAL_ERROR),
                 errmsg("MultiXactId %u has not been created yet -- apparent wraparound",
                        multi)));

    /*
     * Find out the offset at which we need to start reading MultiXactMembers
     * and the number of members in the multixact.  We determine the latter as
     * the difference between this multixact's starting offset and the next
     * one's.  However, there are some corner cases to worry about:
     *
     * 1. This multixact may be the latest one created, in which case there is
     * no next one to look at.  In this case the nextOffset value we just
     * saved is the correct endpoint.
     *
     * 2. The next multixact may still be in process of being filled in: that
     * is, another process may have done GetNewMultiXactId but not yet written
     * the offset entry for that ID.  In that scenario, it is guaranteed that
     * the offset entry for that multixact exists (because GetNewMultiXactId
     * won't release MultiXactGenLock until it does) but contains zero
     * (because we are careful to pre-zero offset pages). Because
     * GetNewMultiXactId will never return zero as the starting offset for a
     * multixact, when we read zero as the next multixact's offset, we know we
     * have this case.  We sleep for a bit and try again.
     *
     * 3. Because GetNewMultiXactId increments offset zero to offset one to
     * handle case #2, there is an ambiguity near the point of offset
     * wraparound.  If we see next multixact's offset is one, is that our
     * multixact's actual endpoint, or did it end at zero with a subsequent
     * increment?  We handle this using the knowledge that if the zero'th
     * member slot wasn't filled, it'll contain zero, and zero isn't a valid
     * transaction ID so it can't be a multixact member.  Therefore, if we
     * read a zero from the members array, just ignore it.
     *
     * This is all pretty messy, but the mess occurs only in infrequent corner
     * cases, so it seems better than holding the MultiXactGenLock for a long
     * time on every multixact creation.
     */
retry:
    LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

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

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

    Assert(offset != 0);

    /*
     * Use the same increment rule as GetNewMultiXactId(), that is, don't
     * handle wraparound explicitly until needed.
     */
    tmpMXact = multi + 1;

    if (nextMXact == tmpMXact)
    {
        /* Corner case 1: there is no next multixact */
        length = nextOffset - offset;
    }
    else
    {
        MultiXactOffset nextMXOffset;

        /* 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, true, tmpMXact);

        offptr = (MultiXactOffset *) MultiXactOffsetCtl->shared->page_buffer[slotno];
        offptr += entryno;
        nextMXOffset = *offptr;

        if (nextMXOffset == 0)
        {
            /* Corner case 2: next multixact is still being filled in */
            LWLockRelease(MultiXactOffsetSLRULock);
            CHECK_FOR_INTERRUPTS();
            pg_usleep(1000L);
            goto retry;
        }

        length = nextMXOffset - offset;
    }

    LWLockRelease(MultiXactOffsetSLRULock);

    ptr = (MultiXactMember *) palloc(length * sizeof(MultiXactMember));
    *members = ptr;

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

    truelength = 0;
    prev_pageno = -1;
    for (i = 0; i < length; i++, offset++)
    {
        TransactionId *xactptr;
        uint32     *flagsptr;
        int         flagsoff;
        int         bshift;
        int         memberoff;

        pageno = MXOffsetToMemberPage(offset);
        memberoff = MXOffsetToMemberOffset(offset);

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

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

        if (!TransactionIdIsValid(*xactptr))
        {
            /* Corner case 3: we must be looking at unused slot zero */
            Assert(offset == 0);
            continue;
        }

        flagsoff = MXOffsetToFlagsOffset(offset);
        bshift = MXOffsetToFlagsBitShift(offset);
        flagsptr = (uint32 *) (MultiXactMemberCtl->shared->page_buffer[slotno] + flagsoff);

        ptr[truelength].xid = *xactptr;
        ptr[truelength].status = (*flagsptr >> bshift) & MXACT_MEMBER_XACT_BITMASK;
        truelength++;
    }

    LWLockRelease(MultiXactMemberSLRULock);

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

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

/*
 * mxactMemberComparator
 *      qsort comparison function for MultiXactMember
 *
 * We can't use wraparound comparison for XIDs because that does not respect
 * the triangle inequality!  Any old sort order will do.
 */
static int
mxactMemberComparator(const void *arg1, const void *arg2)
{
    MultiXactMember member1 = *(const MultiXactMember *) arg1;
    MultiXactMember member2 = *(const MultiXactMember *) arg2;

    if (member1.xid > member2.xid)
        return 1;
    if (member1.xid < member2.xid)
        return -1;
    if (member1.status > member2.status)
        return 1;
    if (member1.status < member2.status)
        return -1;
    return 0;
}

/*
 * 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 members array will be sorted in-place.
 */
static MultiXactId
mXactCacheGetBySet(int nmembers, MultiXactMember *members)
{
    dlist_iter  iter;

    debug_elog3(DEBUG2, "CacheGet: looking for %s",
                mxid_to_string(InvalidMultiXactId, nmembers, members));

    /* sort the array so comparison is easy */
    qsort(members, nmembers, sizeof(MultiXactMember), mxactMemberComparator);

    dlist_foreach(iter, &MXactCache)
    {
        mXactCacheEnt *entry = dlist_container(mXactCacheEnt, node, iter.cur);

        if (entry->nmembers != nmembers)
            continue;

        /*
         * We assume the cache entries are sorted, and that the unused bits in
         * "status" are zeroed.
         */
        if (memcmp(members, entry->members, nmembers * sizeof(MultiXactMember)) == 0)
        {
            debug_elog3(DEBUG2, "CacheGet: found %u", entry->multi);
            dlist_move_head(&MXactCache, iter.cur);
            return entry->multi;
        }
    }

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

/*
 * mXactCacheGetById
 *      returns the composing MultiXactMember 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
 * MultiXactMember set.  Return value is number of members, or -1 on failure.
 */
static int
mXactCacheGetById(MultiXactId multi, MultiXactMember **members)
{
    dlist_iter  iter;

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

    dlist_foreach(iter, &MXactCache)
    {
        mXactCacheEnt *entry = dlist_container(mXactCacheEnt, node, iter.cur);

        if (entry->multi == multi)
        {
            MultiXactMember *ptr;
            Size        size;

            size = sizeof(MultiXactMember) * entry->nmembers;
            ptr = (MultiXactMember *) palloc(size);
            *members = ptr;

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

            debug_elog3(DEBUG2, "CacheGet: found %s",
                        mxid_to_string(multi,
                                       entry->nmembers,
                                       entry->members));

            /*
             * Note we modify the list while not using a modifiable iterator.
             * This is acceptable only because we exit the iteration
             * immediately afterwards.
             */
            dlist_move_head(&MXactCache, iter.cur);

            return entry->nmembers;
        }
    }

    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 nmembers, MultiXactMember *members)
{
    mXactCacheEnt *entry;

    debug_elog3(DEBUG2, "CachePut: storing %s",
                mxid_to_string(multi, nmembers, members));

    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_SIZES);
    }

    entry = (mXactCacheEnt *)
        MemoryContextAlloc(MXactContext,
                           offsetof(mXactCacheEnt, members) +
                           nmembers * sizeof(MultiXactMember));

    entry->multi = multi;
    entry->nmembers = nmembers;
    memcpy(entry->members, members, nmembers * sizeof(MultiXactMember));

    /* mXactCacheGetBySet assumes the entries are sorted, so sort them */
    qsort(entry->members, nmembers, sizeof(MultiXactMember), mxactMemberComparator);

    dlist_push_head(&MXactCache, &entry->node);
    if (MXactCacheMembers++ >= MAX_CACHE_ENTRIES)
    {
        dlist_node *node;
        mXactCacheEnt *entry;

        node = dlist_tail_node(&MXactCache);
        dlist_delete(node);
        MXactCacheMembers--;

        entry = dlist_container(mXactCacheEnt, node, node);
        debug_elog3(DEBUG2, "CachePut: pruning cached multi %u",
                    entry->multi);

        pfree(entry);
    }
}

static char *
mxstatus_to_string(MultiXactStatus status)
{
    switch (status)
    {
        case MultiXactStatusForKeyShare:
            return "keysh";
        case MultiXactStatusForShare:
            return "sh";
        case MultiXactStatusForNoKeyUpdate:
            return "fornokeyupd";
        case MultiXactStatusForUpdate:
            return "forupd";
        case MultiXactStatusNoKeyUpdate:
            return "nokeyupd";
        case MultiXactStatusUpdate:
            return "upd";
        default:
            elog(ERROR, "unrecognized multixact status %d", status);
            return "";
    }
}

char *
mxid_to_string(MultiXactId multi, int nmembers, MultiXactMember *members)
{
    static char *str = NULL;
    StringInfoData buf;
    int         i;

    if (str != NULL)
        pfree(str);

    initStringInfo(&buf);

    appendStringInfo(&buf, "%u %d[%u (%s)", multi, nmembers, members[0].xid,
                     mxstatus_to_string(members[0].status));

    for (i = 1; i < nmembers; i++)
        appendStringInfo(&buf, ", %u (%s)", members[i].xid,
                         mxstatus_to_string(members[i].status));

    appendStringInfoChar(&buf, ']');
    str = MemoryContextStrdup(TopMemoryContext, buf.data);
    pfree(buf.data);
    return str;
}

/*
 * 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;
    dlist_init(&MXactCache);
    MXactCacheMembers = 0;
}

/*
 * AtPrepare_MultiXact
 *      Save multixact state at 2PC transaction prepare
 *
 * In this phase, we only store our OldestMemberMXactId value in the two-phase
 * state file.
 */
void
AtPrepare_MultiXact(void)
{
    MultiXactId myOldestMember = OldestMemberMXactId[MyBackendId];

    if (MultiXactIdIsValid(myOldestMember))
        RegisterTwoPhaseRecord(TWOPHASE_RM_MULTIXACT_ID, 0,
                               &myOldestMember, sizeof(MultiXactId));
}

/*
 * PostPrepare_MultiXact
 *      Clean up after successful PREPARE TRANSACTION
 */
void
PostPrepare_MultiXact(TransactionId xid)
{
    MultiXactId myOldestMember;

    /*
     * Transfer our OldestMemberMXactId value to the slot reserved for the
     * prepared transaction.
     */
    myOldestMember = OldestMemberMXactId[MyBackendId];
    if (MultiXactIdIsValid(myOldestMember))
    {
        BackendId   dummyBackendId = TwoPhaseGetDummyBackendId(xid, false);

        /*
         * Even though storing MultiXactId is atomic, acquire lock to make
         * sure others see both changes, not just the reset of the slot of the
         * current backend. Using a volatile pointer might suffice, but this
         * isn't a hot spot.
         */
        LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);

        OldestMemberMXactId[dummyBackendId] = myOldestMember;
        OldestMemberMXactId[MyBackendId] = InvalidMultiXactId;

        LWLockRelease(MultiXactGenLock);
    }

    /*
     * We don't need to transfer OldestVisibleMXactId value, because the
     * transaction is not going to be looking at any more multixacts once it's
     * prepared.
     *
     * We assume that storing a MultiXactId is atomic and so we need not take
     * MultiXactGenLock to do this.
     */
    OldestVisibleMXactId[MyBackendId] = InvalidMultiXactId;

    /*
     * Discard the local MultiXactId cache like in AtEOX_MultiXact
     */
    MXactContext = NULL;
    dlist_init(&MXactCache);
    MXactCacheMembers = 0;
}

/*
 * multixact_twophase_recover
 *      Recover the state of a prepared transaction at startup
 */
void
multixact_twophase_recover(TransactionId xid, uint16 info,
                           void *recdata, uint32 len)
{
    BackendId   dummyBackendId = TwoPhaseGetDummyBackendId(xid, false);
    MultiXactId oldestMember;

    /*
     * Get the oldest member XID from the state file record, and set it in the
     * OldestMemberMXactId slot reserved for this prepared transaction.
     */
    Assert(len == sizeof(MultiXactId));
    oldestMember = *((MultiXactId *) recdata);

    OldestMemberMXactId[dummyBackendId] = oldestMember;
}

/*
 * multixact_twophase_postcommit
 *      Similar to AtEOX_MultiXact but for COMMIT PREPARED
 */
void
multixact_twophase_postcommit(TransactionId xid, uint16 info,
                              void *recdata, uint32 len)
{
    BackendId   dummyBackendId = TwoPhaseGetDummyBackendId(xid, true);

    Assert(len == sizeof(MultiXactId));

    OldestMemberMXactId[dummyBackendId] = InvalidMultiXactId;
}

/*
 * multixact_twophase_postabort
 *      This is actually just the same as the COMMIT case.
 */
void
multixact_twophase_postabort(TransactionId xid, uint16 info,
                             void *recdata, uint32 len)
{
    multixact_twophase_postcommit(xid, info, recdata, len);
}

/*
 * 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).
 */
Size
MultiXactShmemSize(void)
{
    Size        size;

    /* We need 2*MaxOldestSlot + 1 perBackendXactIds[] entries */
#define SHARED_MULTIXACT_STATE_SIZE \
    add_size(offsetof(MultiXactStateData, perBackendXactIds) + sizeof(MultiXactId), \
             mul_size(sizeof(MultiXactId) * 2, MaxOldestSlot))

    size = SHARED_MULTIXACT_STATE_SIZE;
    size = add_size(size, SimpleLruShmemSize(NUM_MULTIXACTOFFSET_BUFFERS, 0));
    size = add_size(size, SimpleLruShmemSize(NUM_MULTIXACTMEMBER_BUFFERS, 0));

    return size;
}

void
MultiXactShmemInit(void)
{
    bool        found;

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

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

    SimpleLruInit(MultiXactOffsetCtl,
                  "MultiXactOffset", NUM_MULTIXACTOFFSET_BUFFERS, 0,
                  MultiXactOffsetSLRULock, "pg_multixact/offsets",
                  LWTRANCHE_MULTIXACTOFFSET_BUFFER);
    SimpleLruInit(MultiXactMemberCtl,
                  "MultiXactMember", NUM_MULTIXACTMEMBER_BUFFERS, 0,
                  MultiXactMemberSLRULock, "pg_multixact/members",
                  LWTRANCHE_MULTIXACTMEMBER_BUFFER);

    /* 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..MaxOldestSlot in each array.
     */
    OldestMemberMXactId = MultiXactState->perBackendXactIds;
    OldestVisibleMXactId = OldestMemberMXactId + MaxOldestSlot;
}

/*
 * 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.)
 */
void
BootStrapMultiXact(void)
{
    int         slotno;

    LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

    /* Create and zero the first page of the offsets log */
    slotno = ZeroMultiXactOffsetPage(0, false);

    /* Make sure it's written out */
    SimpleLruWritePage(MultiXactOffsetCtl, slotno);
    Assert(!MultiXactOffsetCtl->shared->page_dirty[slotno]);

    LWLockRelease(MultiXactOffsetSLRULock);

    LWLockAcquire(MultiXactMemberSLRULock, LW_EXCLUSIVE);

    /* Create and zero the first page of the members log */
    slotno = ZeroMultiXactMemberPage(0, false);

    /* Make sure it's written out */
    SimpleLruWritePage(MultiXactMemberCtl, slotno);
    Assert(!MultiXactMemberCtl->shared->page_dirty[slotno]);

    LWLockRelease(MultiXactMemberSLRULock);
}

/*
 * Initialize (or reinitialize) a page of MultiXactOffset to zeroes.
 * If writeXlog is true, also emit an XLOG record saying we did this.
 *
 * 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, bool writeXlog)
{
    int         slotno;

    slotno = SimpleLruZeroPage(MultiXactOffsetCtl, pageno);

    if (writeXlog)
        WriteMZeroPageXlogRec(pageno, XLOG_MULTIXACT_ZERO_OFF_PAGE);

    return slotno;
}

/*
 * Ditto, for MultiXactMember
 */
static int
ZeroMultiXactMemberPage(int pageno, bool writeXlog)
{
    int         slotno;

    slotno = SimpleLruZeroPage(MultiXactMemberCtl, pageno);

    if (writeXlog)
        WriteMZeroPageXlogRec(pageno, XLOG_MULTIXACT_ZERO_MEM_PAGE);

    return slotno;
}

/*
 * MaybeExtendOffsetSlru
 *      Extend the offsets SLRU area, if necessary
 *
 * After a binary upgrade from <= 9.2, the pg_multixact/offsets SLRU area might
 * contain files that are shorter than necessary; this would occur if the old
 * installation had used multixacts beyond the first page (files cannot be
 * copied, because the on-disk representation is different).  pg_upgrade would
 * update pg_control to set the next offset value to be at that position, so
 * that tuples marked as locked by such MultiXacts would be seen as visible
 * without having to consult multixact.  However, trying to create and use a
 * new MultiXactId would result in an error because the page on which the new
 * value would reside does not exist.  This routine is in charge of creating
 * such pages.
 */
static void
MaybeExtendOffsetSlru(void)
{
    int         pageno;

    pageno = MultiXactIdToOffsetPage(MultiXactState->nextMXact);

    LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

    if (!SimpleLruDoesPhysicalPageExist(MultiXactOffsetCtl, pageno))
    {
        int         slotno;

        /*
         * Fortunately for us, SimpleLruWritePage is already prepared to deal
         * with creating a new segment file even if the page we're writing is
         * not the first in it, so this is enough.
         */
        slotno = ZeroMultiXactOffsetPage(pageno, false);
        SimpleLruWritePage(MultiXactOffsetCtl, slotno);
    }

    LWLockRelease(MultiXactOffsetSLRULock);
}

/*
 * This must be called ONCE during postmaster or standalone-backend startup.
 *
 * StartupXLOG has already established nextMXact/nextOffset by calling
 * MultiXactSetNextMXact and/or MultiXactAdvanceNextMXact, and the oldestMulti
 * info from pg_control and/or MultiXactAdvanceOldest, but we haven't yet
 * replayed WAL.
 */
void
StartupMultiXact(void)
{
    MultiXactId multi = MultiXactState->nextMXact;
    MultiXactOffset offset = MultiXactState->nextOffset;
    int         pageno;

    /*
     * Initialize offset's idea of the latest page number.
     */
    pageno = MultiXactIdToOffsetPage(multi);
    MultiXactOffsetCtl->shared->latest_page_number = pageno;

    /*
     * Initialize member's idea of the latest page number.
     */
    pageno = MXOffsetToMemberPage(offset);
    MultiXactMemberCtl->shared->latest_page_number = pageno;
}

/*
 * This must be called ONCE at the end of startup/recovery.
 */
void
TrimMultiXact(void)
{
    MultiXactId nextMXact;
    MultiXactOffset offset;
    MultiXactId oldestMXact;
    Oid         oldestMXactDB;
    int         pageno;
    int         entryno;
    int         flagsoff;

    LWLockAcquire(MultiXactGenLock, LW_SHARED);
    nextMXact = MultiXactState->nextMXact;
    offset = MultiXactState->nextOffset;
    oldestMXact = MultiXactState->oldestMultiXactId;
    oldestMXactDB = MultiXactState->oldestMultiXactDB;
    LWLockRelease(MultiXactGenLock);

    /* Clean up offsets state */
    LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

    /*
     * (Re-)Initialize our idea of the latest page number for offsets.
     */
    pageno = MultiXactIdToOffsetPage(nextMXact);
    MultiXactOffsetCtl->shared->latest_page_number = pageno;

    /*
     * Zero out the remainder of the current offsets page.  See notes in
     * TrimCLOG() for background.  Unlike CLOG, some WAL record covers every
     * pg_multixact SLRU mutation.  Since, also unlike CLOG, we ignore the WAL
     * rule "write xlog before data," nextMXact successors may carry obsolete,
     * nonzero offset values.  Zero those so case 2 of GetMultiXactIdMembers()
     * operates normally.
     */
    entryno = MultiXactIdToOffsetEntry(nextMXact);
    if (entryno != 0)
    {
        int         slotno;
        MultiXactOffset *offptr;

        slotno = SimpleLruReadPage(MultiXactOffsetCtl, pageno, true, nextMXact);
        offptr = (MultiXactOffset *) MultiXactOffsetCtl->shared->page_buffer[slotno];
        offptr += entryno;

        MemSet(offptr, 0, BLCKSZ - (entryno * sizeof(MultiXactOffset)));

        MultiXactOffsetCtl->shared->page_dirty[slotno] = true;
    }

    LWLockRelease(MultiXactOffsetSLRULock);

    /* And the same for members */
    LWLockAcquire(MultiXactMemberSLRULock, LW_EXCLUSIVE);

    /*
     * (Re-)Initialize our idea of the latest page number for members.
     */
    pageno = MXOffsetToMemberPage(offset);
    MultiXactMemberCtl->shared->latest_page_number = pageno;

    /*
     * Zero out the remainder of the current members page.  See notes in
     * TrimCLOG() for motivation.
     */
    flagsoff = MXOffsetToFlagsOffset(offset);
    if (flagsoff != 0)
    {
        int         slotno;
        TransactionId *xidptr;
        int         memberoff;

        memberoff = MXOffsetToMemberOffset(offset);
        slotno = SimpleLruReadPage(MultiXactMemberCtl, pageno, true, offset);
        xidptr = (TransactionId *)
            (MultiXactMemberCtl->shared->page_buffer[slotno] + memberoff);

        MemSet(xidptr, 0, BLCKSZ - memberoff);

        /*
         * Note: we don't need to zero out the flag bits in the remaining
         * members of the current group, because they are always reset before
         * writing.
         */

        MultiXactMemberCtl->shared->page_dirty[slotno] = true;
    }

    LWLockRelease(MultiXactMemberSLRULock);

    /* signal that we're officially up */
    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
    MultiXactState->finishedStartup = true;
    LWLockRelease(MultiXactGenLock);

    /* Now compute how far away the next members wraparound is. */
    SetMultiXactIdLimit(oldestMXact, oldestMXactDB, true);
}

/*
 * This must be called ONCE during postmaster or standalone-backend shutdown
 */
void
ShutdownMultiXact(void)
{
    /* Flush dirty MultiXact pages to disk */
    TRACE_POSTGRESQL_MULTIXACT_CHECKPOINT_START(false);
    SimpleLruFlush(MultiXactOffsetCtl, false);
    SimpleLruFlush(MultiXactMemberCtl, false);
    TRACE_POSTGRESQL_MULTIXACT_CHECKPOINT_DONE(false);
}

/*
 * Get the MultiXact data to save in a checkpoint record
 */
void
MultiXactGetCheckptMulti(bool is_shutdown,
                         MultiXactId *nextMulti,
                         MultiXactOffset *nextMultiOffset,
                         MultiXactId *oldestMulti,
                         Oid *oldestMultiDB)
{
    LWLockAcquire(MultiXactGenLock, LW_SHARED);
    *nextMulti = MultiXactState->nextMXact;
    *nextMultiOffset = MultiXactState->nextOffset;
    *oldestMulti = MultiXactState->oldestMultiXactId;
    *oldestMultiDB = MultiXactState->oldestMultiXactDB;
    LWLockRelease(MultiXactGenLock);

    debug_elog6(DEBUG2,
                "MultiXact: checkpoint is nextMulti %u, nextOffset %u, oldestMulti %u in DB %u",
                *nextMulti, *nextMultiOffset, *oldestMulti, *oldestMultiDB);
}

/*
 * Perform a checkpoint --- either during shutdown, or on-the-fly
 */
void
CheckPointMultiXact(void)
{
    TRACE_POSTGRESQL_MULTIXACT_CHECKPOINT_START(true);

    /* Flush dirty MultiXact pages to disk */
    SimpleLruFlush(MultiXactOffsetCtl, true);
    SimpleLruFlush(MultiXactMemberCtl, true);

    TRACE_POSTGRESQL_MULTIXACT_CHECKPOINT_DONE(true);
}

/*
 * Set the next-to-be-assigned MultiXactId and offset
 *
 * This is used when we can determine the correct next ID/offset exactly
 * from a checkpoint record.  Although this is only called during bootstrap
 * and XLog replay, we take the lock in case any hot-standby backends are
 * examining the values.
 */
void
MultiXactSetNextMXact(MultiXactId nextMulti,
                      MultiXactOffset nextMultiOffset)
{
    debug_elog4(DEBUG2, "MultiXact: setting next multi to %u offset %u",
                nextMulti, nextMultiOffset);
    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
    MultiXactState->nextMXact = nextMulti;
    MultiXactState->nextOffset = nextMultiOffset;
    LWLockRelease(MultiXactGenLock);

    /*
     * During a binary upgrade, make sure that the offsets SLRU is large
     * enough to contain the next value that would be created.
     *
     * We need to do this pretty early during the first startup in binary
     * upgrade mode: before StartupMultiXact() in fact, because this routine
     * is called even before that by StartupXLOG().  And we can't do it
     * earlier than at this point, because during that first call of this
     * routine we determine the MultiXactState->nextMXact value that
     * MaybeExtendOffsetSlru needs.
     */
    if (IsBinaryUpgrade)
        MaybeExtendOffsetSlru();
}

/*
 * Determine the last safe MultiXactId to allocate given the currently oldest
 * datminmxid (ie, the oldest MultiXactId that might exist in any database
 * of our cluster), and the OID of the (or a) database with that value.
 *
 * is_startup is true when we are just starting the cluster, false when we
 * are updating state in a running cluster.  This only affects log messages.
 */
void
SetMultiXactIdLimit(MultiXactId oldest_datminmxid, Oid oldest_datoid,
                    bool is_startup)
{
    MultiXactId multiVacLimit;
    MultiXactId multiWarnLimit;
    MultiXactId multiStopLimit;
    MultiXactId multiWrapLimit;
    MultiXactId curMulti;
    bool        needs_offset_vacuum;

    Assert(MultiXactIdIsValid(oldest_datminmxid));

    /*
     * We pretend that a wrap will happen halfway through the multixact ID
     * space, but that's not really true, because multixacts wrap differently
     * from transaction IDs.  Note that, separately from any concern about
     * multixact IDs wrapping, we must ensure that multixact members do not
     * wrap.  Limits for that are set in SetOffsetVacuumLimit, not here.
     */
    multiWrapLimit = oldest_datminmxid + (MaxMultiXactId >> 1);
    if (multiWrapLimit < FirstMultiXactId)
        multiWrapLimit += FirstMultiXactId;

    /*
     * We'll refuse to continue assigning MultiXactIds once we get within 3M
     * multi of data loss.  See SetTransactionIdLimit.
     */
    multiStopLimit = multiWrapLimit - 3000000;
    if (multiStopLimit < FirstMultiXactId)
        multiStopLimit -= FirstMultiXactId;

    /*
     * We'll start complaining loudly when we get within 40M multis of data
     * loss.  This is kind of arbitrary, but if you let your gas gauge get
     * down to 2% of full, would you be looking for the next gas station?  We
     * need to be fairly liberal about this number because there are lots of
     * scenarios where most transactions are done by automatic clients that
     * won't pay attention to warnings.  (No, we're not gonna make this
     * configurable.  If you know enough to configure it, you know enough to
     * not get in this kind of trouble in the first place.)
     */
    multiWarnLimit = multiWrapLimit - 40000000;
    if (multiWarnLimit < FirstMultiXactId)
        multiWarnLimit -= FirstMultiXactId;

    /*
     * We'll start trying to force autovacuums when oldest_datminmxid gets to
     * be more than autovacuum_multixact_freeze_max_age mxids old.
     *
     * Note: autovacuum_multixact_freeze_max_age is a PGC_POSTMASTER parameter
     * so that we don't have to worry about dealing with on-the-fly changes in
     * its value.  See SetTransactionIdLimit.
     */
    multiVacLimit = oldest_datminmxid + autovacuum_multixact_freeze_max_age;
    if (multiVacLimit < FirstMultiXactId)
        multiVacLimit += FirstMultiXactId;

    /* Grab lock for just long enough to set the new limit values */
    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
    MultiXactState->oldestMultiXactId = oldest_datminmxid;
    MultiXactState->oldestMultiXactDB = oldest_datoid;
    MultiXactState->multiVacLimit = multiVacLimit;
    MultiXactState->multiWarnLimit = multiWarnLimit;
    MultiXactState->multiStopLimit = multiStopLimit;
    MultiXactState->multiWrapLimit = multiWrapLimit;
    curMulti = MultiXactState->nextMXact;
    LWLockRelease(MultiXactGenLock);

    /* Log the info */
    ereport(DEBUG1,
            (errmsg("MultiXactId wrap limit is %u, limited by database with OID %u",
                    multiWrapLimit, oldest_datoid)));

    /*
     * Computing the actual limits is only possible once the data directory is
     * in a consistent state. There's no need to compute the limits while
     * still replaying WAL - no decisions about new multis are made even
     * though multixact creations might be replayed. So we'll only do further
     * checks after TrimMultiXact() has been called.
     */
    if (!MultiXactState->finishedStartup)
        return;

    Assert(!InRecovery);

    /* Set limits for offset vacuum. */
    needs_offset_vacuum = SetOffsetVacuumLimit(is_startup);

    /*
     * If past the autovacuum force point, immediately signal an autovac
     * request.  The reason for this is that autovac only processes one
     * database per invocation.  Once it's finished cleaning up the oldest
     * database, it'll call here, and we'll signal the postmaster to start
     * another iteration immediately if there are still any old databases.
     */
    if ((MultiXactIdPrecedes(multiVacLimit, curMulti) ||
         needs_offset_vacuum) && IsUnderPostmaster)
        SendPostmasterSignal(PMSIGNAL_START_AUTOVAC_LAUNCHER);

    /* Give an immediate warning if past the wrap warn point */
    if (MultiXactIdPrecedes(multiWarnLimit, curMulti))
    {
        char       *oldest_datname;

        /*
         * We can be called when not inside a transaction, for example during
         * StartupXLOG().  In such a case we cannot do database access, so we
         * must just report the oldest DB's OID.
         *
         * Note: it's also possible that get_database_name fails and returns
         * NULL, for example because the database just got dropped.  We'll
         * still warn, even though the warning might now be unnecessary.
         */
        if (IsTransactionState())
            oldest_datname = get_database_name(oldest_datoid);
        else
            oldest_datname = NULL;

        if (oldest_datname)
            ereport(WARNING,
                    (errmsg_plural("database \"%s\" must be vacuumed before %u more MultiXactId is used",
                                   "database \"%s\" must be vacuumed before %u more MultiXactIds are used",
                                   multiWrapLimit - curMulti,
                                   oldest_datname,
                                   multiWrapLimit - curMulti),
                     errhint("To avoid a database shutdown, execute a database-wide VACUUM in that database.\n"
                             "You might also need to commit or roll back old prepared transactions, or drop stale replication slots.")));
        else
            ereport(WARNING,
                    (errmsg_plural("database with OID %u must be vacuumed before %u more MultiXactId is used",
                                   "database with OID %u must be vacuumed before %u more MultiXactIds are used",
                                   multiWrapLimit - curMulti,
                                   oldest_datoid,
                                   multiWrapLimit - curMulti),
                     errhint("To avoid a database shutdown, execute a database-wide VACUUM in that database.\n"
                             "You might also need to commit or roll back old prepared transactions, or drop stale replication slots.")));
    }
}

/*
 * Ensure the next-to-be-assigned MultiXactId is at least minMulti,
 * and similarly nextOffset is at least minMultiOffset.
 *
 * This is used when we can determine minimum safe values from an XLog
 * record (either an on-line checkpoint or an mxact creation log entry).
 * Although this is only called during XLog replay, we take the lock in case
 * any hot-standby backends are examining the values.
 */
void
MultiXactAdvanceNextMXact(MultiXactId minMulti,
                          MultiXactOffset minMultiOffset)
{
    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
    if (MultiXactIdPrecedes(MultiXactState->nextMXact, minMulti))
    {
        debug_elog3(DEBUG2, "MultiXact: setting next multi to %u", minMulti);
        MultiXactState->nextMXact = minMulti;
    }
    if (MultiXactOffsetPrecedes(MultiXactState->nextOffset, minMultiOffset))
    {
        debug_elog3(DEBUG2, "MultiXact: setting next offset to %u",
                    minMultiOffset);
        MultiXactState->nextOffset = minMultiOffset;
    }
    LWLockRelease(MultiXactGenLock);
}

/*
 * Update our oldestMultiXactId value, but only if it's more recent than what
 * we had.
 *
 * This may only be called during WAL replay.
 */
void
MultiXactAdvanceOldest(MultiXactId oldestMulti, Oid oldestMultiDB)
{
    Assert(InRecovery);

    if (MultiXactIdPrecedes(MultiXactState->oldestMultiXactId, oldestMulti))
        SetMultiXactIdLimit(oldestMulti, oldestMultiDB, false);
}

/*
 * Make sure that MultiXactOffset has room for a newly-allocated MultiXactId.
 *
 * NB: this is called while holding MultiXactGenLock.  We want it to be very
 * fast most of the time; even when it's not so fast, no actual I/O need
 * happen unless we're forced to write out a dirty log or xlog page to make
 * room in shared memory.
 */
static 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);

    LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

    /* Zero the page and make an XLOG entry about it */
    ZeroMultiXactOffsetPage(pageno, true);

    LWLockRelease(MultiXactOffsetSLRULock);
}

/*
 * Make sure that MultiXactMember has room for the members of a newly-
 * allocated MultiXactId.
 *
 * Like the above routine, this is called while holding MultiXactGenLock;
 * same comments apply.
 */
static void
ExtendMultiXactMember(MultiXactOffset offset, int nmembers)
{
    /*
     * It's possible that the members span more than one page of the members
     * file, so we loop to ensure we consider each page.  The coding is not
     * optimal if the members span several pages, but that seems unusual
     * enough to not worry much about.
     */
    while (nmembers > 0)
    {
        int         flagsoff;
        int         flagsbit;
        uint32      difference;

        /*
         * Only zero when at first entry of a page.
         */
        flagsoff = MXOffsetToFlagsOffset(offset);
        flagsbit = MXOffsetToFlagsBitShift(offset);
        if (flagsoff == 0 && flagsbit == 0)
        {
            int         pageno;

            pageno = MXOffsetToMemberPage(offset);

            LWLockAcquire(MultiXactMemberSLRULock, LW_EXCLUSIVE);

            /* Zero the page and make an XLOG entry about it */
            ZeroMultiXactMemberPage(pageno, true);

            LWLockRelease(MultiXactMemberSLRULock);
        }

        /*
         * Compute the number of items till end of current page.  Careful: if
         * addition of unsigned ints wraps around, we're at the last page of
         * the last segment; since that page holds a different number of items
         * than other pages, we need to do it differently.
         */
        if (offset + MAX_MEMBERS_IN_LAST_MEMBERS_PAGE < offset)
        {
            /*
             * This is the last page of the last segment; we can compute the
             * number of items left to allocate in it without modulo
             * arithmetic.
             */
            difference = MaxMultiXactOffset - offset + 1;
        }
        else
            difference = MULTIXACT_MEMBERS_PER_PAGE - offset % MULTIXACT_MEMBERS_PER_PAGE;

        /*
         * Advance to next page, taking care to properly handle the wraparound
         * case.  OK if nmembers goes negative.
         */
        nmembers -= difference;
        offset += difference;
    }
}

/*
 * GetOldestMultiXactId
 *
 * Return the oldest MultiXactId that's still possibly still seen as live by
 * any running transaction.  Older ones might still exist on disk, but they no
 * longer have any running member transaction.
 *
 * It's not safe to truncate MultiXact SLRU segments on the value returned by
 * this function; however, it can be used by a full-table vacuum to set the
 * point at which it will be possible to truncate SLRU for that table.
 */
MultiXactId
GetOldestMultiXactId(void)
{
    MultiXactId oldestMXact;
    MultiXactId nextMXact;
    int         i;

    /*
     * 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 <= MaxOldestSlot; 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;
    }

    LWLockRelease(MultiXactGenLock);

    return oldestMXact;
}

/*
 * Determine how aggressively we need to vacuum in order to prevent member
 * wraparound.
 *
 * To do so determine what's the oldest member offset and install the limit
 * info in MultiXactState, where it can be used to prevent overrun of old data
 * in the members SLRU area.
 *
 * The return value is true if emergency autovacuum is required and false
 * otherwise.
 */
static bool
SetOffsetVacuumLimit(bool is_startup)
{
    MultiXactId oldestMultiXactId;
    MultiXactId nextMXact;
    MultiXactOffset oldestOffset = 0;   /* placate compiler */
    MultiXactOffset prevOldestOffset;
    MultiXactOffset nextOffset;
    bool        oldestOffsetKnown = false;
    bool        prevOldestOffsetKnown;
    MultiXactOffset offsetStopLimit = 0;
    MultiXactOffset prevOffsetStopLimit;

    /*
     * NB: Have to prevent concurrent truncation, we might otherwise try to
     * lookup an oldestMulti that's concurrently getting truncated away.
     */
    LWLockAcquire(MultiXactTruncationLock, LW_SHARED);

    /* Read relevant fields from shared memory. */
    LWLockAcquire(MultiXactGenLock, LW_SHARED);
    oldestMultiXactId = MultiXactState->oldestMultiXactId;
    nextMXact = MultiXactState->nextMXact;
    nextOffset = MultiXactState->nextOffset;
    prevOldestOffsetKnown = MultiXactState->oldestOffsetKnown;
    prevOldestOffset = MultiXactState->oldestOffset;
    prevOffsetStopLimit = MultiXactState->offsetStopLimit;
    Assert(MultiXactState->finishedStartup);
    LWLockRelease(MultiXactGenLock);

    /*
     * Determine the offset of the oldest multixact.  Normally, we can read
     * the offset from the multixact itself, but there's an important special
     * case: if there are no multixacts in existence at all, oldestMXact
     * obviously can't point to one.  It will instead point to the multixact
     * ID that will be assigned the next time one is needed.
     */
    if (oldestMultiXactId == nextMXact)
    {
        /*
         * When the next multixact gets created, it will be stored at the next
         * offset.
         */
        oldestOffset = nextOffset;
        oldestOffsetKnown = true;
    }
    else
    {
        /*
         * Figure out where the oldest existing multixact's offsets are
         * stored. Due to bugs in early release of PostgreSQL 9.3.X and 9.4.X,
         * the supposedly-earliest multixact might not really exist.  We are
         * careful not to fail in that case.
         */
        oldestOffsetKnown =
            find_multixact_start(oldestMultiXactId, &oldestOffset);

        if (oldestOffsetKnown)
            ereport(DEBUG1,
                    (errmsg("oldest MultiXactId member is at offset %u",
                            oldestOffset)));
        else
            ereport(LOG,
                    (errmsg("MultiXact member wraparound protections are disabled because oldest checkpointed MultiXact %u does not exist on disk",
                            oldestMultiXactId)));
    }

    LWLockRelease(MultiXactTruncationLock);

    /*
     * If we can, compute limits (and install them MultiXactState) to prevent
     * overrun of old data in the members SLRU area. We can only do so if the
     * oldest offset is known though.
     */
    if (oldestOffsetKnown)
    {
        /* move back to start of the corresponding segment */
        offsetStopLimit = oldestOffset - (oldestOffset %
                                          (MULTIXACT_MEMBERS_PER_PAGE * SLRU_PAGES_PER_SEGMENT));

        /* always leave one segment before the wraparound point */
        offsetStopLimit -= (MULTIXACT_MEMBERS_PER_PAGE * SLRU_PAGES_PER_SEGMENT);

        if (!prevOldestOffsetKnown && !is_startup)
            ereport(LOG,
                    (errmsg("MultiXact member wraparound protections are now enabled")));

        ereport(DEBUG1,
                (errmsg("MultiXact member stop limit is now %u based on MultiXact %u",
                        offsetStopLimit, oldestMultiXactId)));
    }
    else if (prevOldestOffsetKnown)
    {
        /*
         * If we failed to get the oldest offset this time, but we have a
         * value from a previous pass through this function, use the old
         * values rather than automatically forcing an emergency autovacuum
         * cycle again.
         */
        oldestOffset = prevOldestOffset;
        oldestOffsetKnown = true;
        offsetStopLimit = prevOffsetStopLimit;
    }

    /* Install the computed values */
    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
    MultiXactState->oldestOffset = oldestOffset;
    MultiXactState->oldestOffsetKnown = oldestOffsetKnown;
    MultiXactState->offsetStopLimit = offsetStopLimit;
    LWLockRelease(MultiXactGenLock);

    /*
     * Do we need an emergency autovacuum?  If we're not sure, assume yes.
     */
    return !oldestOffsetKnown ||
        (nextOffset - oldestOffset > MULTIXACT_MEMBER_SAFE_THRESHOLD);
}

/*
 * Return whether adding "distance" to "start" would move past "boundary".
 *
 * We use this to determine whether the addition is "wrapping around" the
 * boundary point, hence the name.  The reason we don't want to use the regular
 * 2^31-modulo arithmetic here is that we want to be able to use the whole of
 * the 2^32-1 space here, allowing for more multixacts than would fit
 * otherwise.
 */
static bool
MultiXactOffsetWouldWrap(MultiXactOffset boundary, MultiXactOffset start,
                         uint32 distance)
{
    MultiXactOffset finish;

    /*
     * Note that offset number 0 is not used (see GetMultiXactIdMembers), so
     * if the addition wraps around the UINT_MAX boundary, skip that value.
     */
    finish = start + distance;
    if (finish < start)
        finish++;

    /*-----------------------------------------------------------------------
     * When the boundary is numerically greater than the starting point, any
     * value numerically between the two is not wrapped:
     *
     *  <----S----B---->
     *  [---)            = F wrapped past B (and UINT_MAX)
     *       [---)       = F not wrapped
     *            [----] = F wrapped past B
     *
     * When the boundary is numerically less than the starting point (i.e. the
     * UINT_MAX wraparound occurs somewhere in between) then all values in
     * between are wrapped:
     *
     *  <----B----S---->
     *  [---)            = F not wrapped past B (but wrapped past UINT_MAX)
     *       [---)       = F wrapped past B (and UINT_MAX)
     *            [----] = F not wrapped
     *-----------------------------------------------------------------------
     */
    if (start < boundary)
        return finish >= boundary || finish < start;
    else
        return finish >= boundary && finish < start;
}

/*
 * Find the starting offset of the given MultiXactId.
 *
 * Returns false if the file containing the multi does not exist on disk.
 * Otherwise, returns true and sets *result to the starting member offset.
 *
 * This function does not prevent concurrent truncation, so if that's
 * required, the caller has to protect against that.
 */
static bool
find_multixact_start(MultiXactId multi, MultiXactOffset *result)
{
    MultiXactOffset offset;
    int         pageno;
    int         entryno;
    int         slotno;
    MultiXactOffset *offptr;

    Assert(MultiXactState->finishedStartup);

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

    /*
     * Flush out dirty data, so PhysicalPageExists can work correctly.
     * SimpleLruFlush() is a pretty big hammer for that.  Alternatively we
     * could add an in-memory version of page exists, but find_multixact_start
     * is called infrequently, and it doesn't seem bad to flush buffers to
     * disk before truncation.
     */
    SimpleLruFlush(MultiXactOffsetCtl, true);
    SimpleLruFlush(MultiXactMemberCtl, true);

    if (!SimpleLruDoesPhysicalPageExist(MultiXactOffsetCtl, pageno))
        return false;

    /* lock is acquired by SimpleLruReadPage_ReadOnly */
    slotno = SimpleLruReadPage_ReadOnly(MultiXactOffsetCtl, pageno, multi);
    offptr = (MultiXactOffset *) MultiXactOffsetCtl->shared->page_buffer[slotno];
    offptr += entryno;
    offset = *offptr;
    LWLockRelease(MultiXactOffsetSLRULock);

    *result = offset;
    return true;
}

/*
 * Determine how many multixacts, and how many multixact members, currently
 * exist.  Return false if unable to determine.
 */
static bool
ReadMultiXactCounts(uint32 *multixacts, MultiXactOffset *members)
{
    MultiXactOffset nextOffset;
    MultiXactOffset oldestOffset;
    MultiXactId oldestMultiXactId;
    MultiXactId nextMultiXactId;
    bool        oldestOffsetKnown;

    LWLockAcquire(MultiXactGenLock, LW_SHARED);
    nextOffset = MultiXactState->nextOffset;
    oldestMultiXactId = MultiXactState->oldestMultiXactId;
    nextMultiXactId = MultiXactState->nextMXact;
    oldestOffset = MultiXactState->oldestOffset;
    oldestOffsetKnown = MultiXactState->oldestOffsetKnown;
    LWLockRelease(MultiXactGenLock);

    if (!oldestOffsetKnown)
        return false;

    *members = nextOffset - oldestOffset;
    *multixacts = nextMultiXactId - oldestMultiXactId;
    return true;
}

/*
 * Multixact members can be removed once the multixacts that refer to them
 * are older than every datminmxid.  autovacuum_multixact_freeze_max_age and
 * vacuum_multixact_freeze_table_age work together to make sure we never have
 * too many multixacts; we hope that, at least under normal circumstances,
 * this will also be sufficient to keep us from using too many offsets.
 * However, if the average multixact has many members, we might exhaust the
 * members space while still using few enough members that these limits fail
 * to trigger full table scans for relminmxid advancement.  At that point,
 * we'd have no choice but to start failing multixact-creating operations
 * with an error.
 *
 * To prevent that, if more than a threshold portion of the members space is
 * used, we effectively reduce autovacuum_multixact_freeze_max_age and
 * to a value just less than the number of multixacts in use.  We hope that
 * this will quickly trigger autovacuuming on the table or tables with the
 * oldest relminmxid, thus allowing datminmxid values to advance and removing
 * some members.
 *
 * As the fraction of the member space currently in use grows, we become
 * more aggressive in clamping this value.  That not only causes autovacuum
 * to ramp up, but also makes any manual vacuums the user issues more
 * aggressive.  This happens because vacuum_set_xid_limits() clamps the
 * freeze table and the minimum freeze age based on the effective
 * autovacuum_multixact_freeze_max_age this function returns.  In the worst
 * case, we'll claim the freeze_max_age to zero, and every vacuum of any
 * table will try to freeze every multixact.
 *
 * It's possible that these thresholds should be user-tunable, but for now
 * we keep it simple.
 */
int
MultiXactMemberFreezeThreshold(void)
{
    MultiXactOffset members;
    uint32      multixacts;
    uint32      victim_multixacts;
    double      fraction;

    /* If we can't determine member space utilization, assume the worst. */
    if (!ReadMultiXactCounts(&multixacts, &members))
        return 0;

    /* If member space utilization is low, no special action is required. */
    if (members <= MULTIXACT_MEMBER_SAFE_THRESHOLD)
        return autovacuum_multixact_freeze_max_age;

    /*
     * Compute a target for relminmxid advancement.  The number of multixacts
     * we try to eliminate from the system is based on how far we are past
     * MULTIXACT_MEMBER_SAFE_THRESHOLD.
     */
    fraction = (double) (members - MULTIXACT_MEMBER_SAFE_THRESHOLD) /
        (MULTIXACT_MEMBER_DANGER_THRESHOLD - MULTIXACT_MEMBER_SAFE_THRESHOLD);
    victim_multixacts = multixacts * fraction;

    /* fraction could be > 1.0, but lowest possible freeze age is zero */
    if (victim_multixacts > multixacts)
        return 0;
    return multixacts - victim_multixacts;
}

typedef struct mxtruncinfo
{
    int         earliestExistingPage;
} mxtruncinfo;

/*
 * SlruScanDirectory callback
 *      This callback determines the earliest existing page number.
 */
static bool
SlruScanDirCbFindEarliest(SlruCtl ctl, char *filename, int segpage, void *data)
{
    mxtruncinfo *trunc = (mxtruncinfo *) data;

    if (trunc->earliestExistingPage == -1 ||
        ctl->PagePrecedes(segpage, trunc->earliestExistingPage))
    {
        trunc->earliestExistingPage = segpage;
    }

    return false;               /* keep going */
}


/*
 * Delete members segments [oldest, newOldest)
 *
 * The members SLRU can, in contrast to the offsets one, be filled to almost
 * the full range at once. This means SimpleLruTruncate() can't trivially be
 * used - instead the to-be-deleted range is computed using the offsets
 * SLRU. C.f. TruncateMultiXact().
 */
static void
PerformMembersTruncation(MultiXactOffset oldestOffset, MultiXactOffset newOldestOffset)
{
    const int   maxsegment = MXOffsetToMemberSegment(MaxMultiXactOffset);
    int         startsegment = MXOffsetToMemberSegment(oldestOffset);
    int         endsegment = MXOffsetToMemberSegment(newOldestOffset);
    int         segment = startsegment;

    /*
     * Delete all the segments but the last one. The last segment can still
     * contain, possibly partially, valid data.
     */
    while (segment != endsegment)
    {
        elog(DEBUG2, "truncating multixact members segment %x", segment);
        SlruDeleteSegment(MultiXactMemberCtl, segment);

        /* move to next segment, handling wraparound correctly */
        if (segment == maxsegment)
            segment = 0;
        else
            segment += 1;
    }
}

/*
 * Delete offsets segments [oldest, newOldest)
 */
static void
PerformOffsetsTruncation(MultiXactId oldestMulti, MultiXactId newOldestMulti)
{
    /*
     * We step back one multixact to avoid passing a cutoff page that hasn't
     * been created yet in the rare case that oldestMulti would be the first
     * item on a page and oldestMulti == nextMulti.  In that case, if we
     * didn't subtract one, we'd trigger SimpleLruTruncate's wraparound
     * detection.
     */
    SimpleLruTruncate(MultiXactOffsetCtl,
                      MultiXactIdToOffsetPage(PreviousMultiXactId(newOldestMulti)));
}

/*
 * Remove all MultiXactOffset and MultiXactMember segments before the oldest
 * ones still of interest.
 *
 * This is only called on a primary as part of vacuum (via
 * vac_truncate_clog()). During recovery truncation is done by replaying
 * truncation WAL records logged here.
 *
 * newOldestMulti is the oldest currently required multixact, newOldestMultiDB
 * is one of the databases preventing newOldestMulti from increasing.
 */
void
TruncateMultiXact(MultiXactId newOldestMulti, Oid newOldestMultiDB)
{
    MultiXactId oldestMulti;
    MultiXactId nextMulti;
    MultiXactOffset newOldestOffset;
    MultiXactOffset oldestOffset;
    MultiXactOffset nextOffset;
    mxtruncinfo trunc;
    MultiXactId earliest;

    Assert(!RecoveryInProgress());
    Assert(MultiXactState->finishedStartup);

    /*
     * We can only allow one truncation to happen at once. Otherwise parts of
     * members might vanish while we're doing lookups or similar. There's no
     * need to have an interlock with creating new multis or such, since those
     * are constrained by the limits (which only grow, never shrink).
     */
    LWLockAcquire(MultiXactTruncationLock, LW_EXCLUSIVE);

    LWLockAcquire(MultiXactGenLock, LW_SHARED);
    nextMulti = MultiXactState->nextMXact;
    nextOffset = MultiXactState->nextOffset;
    oldestMulti = MultiXactState->oldestMultiXactId;
    LWLockRelease(MultiXactGenLock);
    Assert(MultiXactIdIsValid(oldestMulti));

    /*
     * Make sure to only attempt truncation if there's values to truncate
     * away. In normal processing values shouldn't go backwards, but there's
     * some corner cases (due to bugs) where that's possible.
     */
    if (MultiXactIdPrecedesOrEquals(newOldestMulti, oldestMulti))
    {
        LWLockRelease(MultiXactTruncationLock);
        return;
    }

    /*
     * Note we can't just plow ahead with the truncation; it's possible that
     * there are no segments to truncate, which is a problem because we are
     * going to attempt to read the offsets page to determine where to
     * truncate the members SLRU.  So we first scan the directory to determine
     * the earliest offsets page number that we can read without error.
     *
     * NB: It's also possible that the page that oldestMulti is on has already
     * been truncated away, and we crashed before updating oldestMulti.
     */
    trunc.earliestExistingPage = -1;
    SlruScanDirectory(MultiXactOffsetCtl, SlruScanDirCbFindEarliest, &trunc);
    earliest = trunc.earliestExistingPage * MULTIXACT_OFFSETS_PER_PAGE;
    if (earliest < FirstMultiXactId)
        earliest = FirstMultiXactId;

    /* If there's nothing to remove, we can bail out early. */
    if (MultiXactIdPrecedes(oldestMulti, earliest))
    {
        LWLockRelease(MultiXactTruncationLock);
        return;
    }

    /*
     * First, compute the safe truncation point for MultiXactMember. This is
     * the starting offset of the oldest multixact.
     *
     * Hopefully, find_multixact_start will always work here, because we've
     * already checked that it doesn't precede the earliest MultiXact on disk.
     * But if it fails, don't truncate anything, and log a message.
     */
    if (oldestMulti == nextMulti)
    {
        /* there are NO MultiXacts */
        oldestOffset = nextOffset;
    }
    else if (!find_multixact_start(oldestMulti, &oldestOffset))
    {
        ereport(LOG,
                (errmsg("oldest MultiXact %u not found, earliest MultiXact %u, skipping truncation",
                        oldestMulti, earliest)));
        LWLockRelease(MultiXactTruncationLock);
        return;
    }

    /*
     * Secondly compute up to where to truncate. Lookup the corresponding
     * member offset for newOldestMulti for that.
     */
    if (newOldestMulti == nextMulti)
    {
        /* there are NO MultiXacts */
        newOldestOffset = nextOffset;
    }
    else if (!find_multixact_start(newOldestMulti, &newOldestOffset))
    {
        ereport(LOG,
                (errmsg("cannot truncate up to MultiXact %u because it does not exist on disk, skipping truncation",
                        newOldestMulti)));
        LWLockRelease(MultiXactTruncationLock);
        return;
    }

    elog(DEBUG1, "performing multixact truncation: "
         "offsets [%u, %u), offsets segments [%x, %x), "
         "members [%u, %u), members segments [%x, %x)",
         oldestMulti, newOldestMulti,
         MultiXactIdToOffsetSegment(oldestMulti),
         MultiXactIdToOffsetSegment(newOldestMulti),
         oldestOffset, newOldestOffset,
         MXOffsetToMemberSegment(oldestOffset),
         MXOffsetToMemberSegment(newOldestOffset));

    /*
     * Do truncation, and the WAL logging of the truncation, in a critical
     * section. That way offsets/members cannot get out of sync anymore, i.e.
     * once consistent the newOldestMulti will always exist in members, even
     * if we crashed in the wrong moment.
     */
    START_CRIT_SECTION();

    /*
     * Prevent checkpoints from being scheduled concurrently. This is critical
     * because otherwise a truncation record might not be replayed after a
     * crash/basebackup, even though the state of the data directory would
     * require it.
     */
    Assert(!MyProc->delayChkpt);
    MyProc->delayChkpt = true;

    /* WAL log truncation */
    WriteMTruncateXlogRec(newOldestMultiDB,
                          oldestMulti, newOldestMulti,
                          oldestOffset, newOldestOffset);

    /*
     * Update in-memory limits before performing the truncation, while inside
     * the critical section: Have to do it before truncation, to prevent
     * concurrent lookups of those values. Has to be inside the critical
     * section as otherwise a future call to this function would error out,
     * while looking up the oldest member in offsets, if our caller crashes
     * before updating the limits.
     */
    LWLockAcquire(MultiXactGenLock, LW_EXCLUSIVE);
    MultiXactState->oldestMultiXactId = newOldestMulti;
    MultiXactState->oldestMultiXactDB = newOldestMultiDB;
    LWLockRelease(MultiXactGenLock);

    /* First truncate members */
    PerformMembersTruncation(oldestOffset, newOldestOffset);

    /* Then offsets */
    PerformOffsetsTruncation(oldestMulti, newOldestMulti);

    MyProc->delayChkpt = false;

    END_CRIT_SECTION();
    LWLockRelease(MultiXactTruncationLock);
}

/*
 * 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)
{
    MultiXactOffset offset1;
    MultiXactOffset offset2;

    offset1 = ((MultiXactOffset) page1) * MULTIXACT_MEMBERS_PER_PAGE;
    offset2 = ((MultiXactOffset) 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.)
 */
bool
MultiXactIdPrecedes(MultiXactId multi1, MultiXactId multi2)
{
    int32       diff = (int32) (multi1 - multi2);

    return (diff < 0);
}

/*
 * MultiXactIdPrecedesOrEquals -- is multi1 logically <= multi2?
 *
 * XXX do we need to do something special for InvalidMultiXactId?
 * (Doesn't look like it.)
 */
bool
MultiXactIdPrecedesOrEquals(MultiXactId multi1, MultiXactId multi2)
{
    int32       diff = (int32) (multi1 - multi2);

    return (diff <= 0);
}


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

    return (diff < 0);
}

/*
 * Write an xlog record reflecting the zeroing of either a MEMBERs or
 * OFFSETs page (info shows which)
 */
static void
WriteMZeroPageXlogRec(int pageno, uint8 info)
{
    XLogBeginInsert();
    XLogRegisterData((char *) (&pageno), sizeof(int));
    (void) XLogInsert(RM_MULTIXACT_ID, info);
}

/*
 * Write a TRUNCATE xlog record
 *
 * We must flush the xlog record to disk before returning --- see notes in
 * TruncateCLOG().
 */
static void
WriteMTruncateXlogRec(Oid oldestMultiDB,
                      MultiXactId startTruncOff, MultiXactId endTruncOff,
                      MultiXactOffset startTruncMemb, MultiXactOffset endTruncMemb)
{
    XLogRecPtr  recptr;
    xl_multixact_truncate xlrec;

    xlrec.oldestMultiDB = oldestMultiDB;

    xlrec.startTruncOff = startTruncOff;
    xlrec.endTruncOff = endTruncOff;

    xlrec.startTruncMemb = startTruncMemb;
    xlrec.endTruncMemb = endTruncMemb;

    XLogBeginInsert();
    XLogRegisterData((char *) (&xlrec), SizeOfMultiXactTruncate);
    recptr = XLogInsert(RM_MULTIXACT_ID, XLOG_MULTIXACT_TRUNCATE_ID);
    XLogFlush(recptr);
}

/*
 * MULTIXACT resource manager's routines
 */
void
multixact_redo(XLogReaderState *record)
{
    uint8       info = XLogRecGetInfo(record) & ~XLR_INFO_MASK;

    /* Backup blocks are not used in multixact records */
    Assert(!XLogRecHasAnyBlockRefs(record));

    if (info == XLOG_MULTIXACT_ZERO_OFF_PAGE)
    {
        int         pageno;
        int         slotno;

        memcpy(&pageno, XLogRecGetData(record), sizeof(int));

        LWLockAcquire(MultiXactOffsetSLRULock, LW_EXCLUSIVE);

        slotno = ZeroMultiXactOffsetPage(pageno, false);
        SimpleLruWritePage(MultiXactOffsetCtl, slotno);
        Assert(!MultiXactOffsetCtl->shared->page_dirty[slotno]);

        LWLockRelease(MultiXactOffsetSLRULock);
    }
    else if (info == XLOG_MULTIXACT_ZERO_MEM_PAGE)
    {
        int         pageno;
        int         slotno;

        memcpy(&pageno, XLogRecGetData(record), sizeof(int));

        LWLockAcquire(MultiXactMemberSLRULock, LW_EXCLUSIVE);

        slotno = ZeroMultiXactMemberPage(pageno, false);
        SimpleLruWritePage(MultiXactMemberCtl, slotno);
        Assert(!MultiXactMemberCtl->shared->page_dirty[slotno]);

        LWLockRelease(MultiXactMemberSLRULock);
    }
    else if (info == XLOG_MULTIXACT_CREATE_ID)
    {
        xl_multixact_create *xlrec =
        (xl_multixact_create *) XLogRecGetData(record);
        TransactionId max_xid;
        int         i;

        /* Store the data back into the SLRU files */
        RecordNewMultiXact(xlrec->mid, xlrec->moff, xlrec->nmembers,
                           xlrec->members);

        /* Make sure nextMXact/nextOffset are beyond what this record has */
        MultiXactAdvanceNextMXact(xlrec->mid + 1,
                                  xlrec->moff + xlrec->nmembers);

        /*
         * Make sure nextXid is beyond any XID mentioned in the record.
         * This should be unnecessary, since any XID found here ought to have
         * other evidence in the XLOG, but let's be safe.
         */
        max_xid = XLogRecGetXid(record);
        for (i = 0; i < xlrec->nmembers; i++)
        {
            if (TransactionIdPrecedes(max_xid, xlrec->members[i].xid))
                max_xid = xlrec->members[i].xid;
        }

        AdvanceNextFullTransactionIdPastXid(max_xid);
    }
    else if (info == XLOG_MULTIXACT_TRUNCATE_ID)
    {
        xl_multixact_truncate xlrec;
        int         pageno;

        memcpy(&xlrec, XLogRecGetData(record),
               SizeOfMultiXactTruncate);

        elog(DEBUG1, "replaying multixact truncation: "
             "offsets [%u, %u), offsets segments [%x, %x), "
             "members [%u, %u), members segments [%x, %x)",
             xlrec.startTruncOff, xlrec.endTruncOff,
             MultiXactIdToOffsetSegment(xlrec.startTruncOff),
             MultiXactIdToOffsetSegment(xlrec.endTruncOff),
             xlrec.startTruncMemb, xlrec.endTruncMemb,
             MXOffsetToMemberSegment(xlrec.startTruncMemb),
             MXOffsetToMemberSegment(xlrec.endTruncMemb));

        /* should not be required, but more than cheap enough */
        LWLockAcquire(MultiXactTruncationLock, LW_EXCLUSIVE);

        /*
         * Advance the horizon values, so they're current at the end of
         * recovery.
         */
        SetMultiXactIdLimit(xlrec.endTruncOff, xlrec.oldestMultiDB, false);

        PerformMembersTruncation(xlrec.startTruncMemb, xlrec.endTruncMemb);

        /*
         * During XLOG replay, latest_page_number isn't necessarily set up
         * yet; insert a suitable value to bypass the sanity test in
         * SimpleLruTruncate.
         */
        pageno = MultiXactIdToOffsetPage(xlrec.endTruncOff);
        MultiXactOffsetCtl->shared->latest_page_number = pageno;
        PerformOffsetsTruncation(xlrec.startTruncOff, xlrec.endTruncOff);

        LWLockRelease(MultiXactTruncationLock);
    }
    else
        elog(PANIC, "multixact_redo: unknown op code %u", info);
}

Datum
pg_get_multixact_members(PG_FUNCTION_ARGS)
{
    typedef struct
    {
        MultiXactMember *members;
        int         nmembers;
        int         iter;
    } mxact;
    MultiXactId mxid = PG_GETARG_UINT32(0);
    mxact      *multi;
    FuncCallContext *funccxt;

    if (mxid < FirstMultiXactId)
        ereport(ERROR,
                (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                 errmsg("invalid MultiXactId: %u", mxid)));

    if (SRF_IS_FIRSTCALL())
    {
        MemoryContext oldcxt;
        TupleDesc   tupdesc;

        funccxt = SRF_FIRSTCALL_INIT();
        oldcxt = MemoryContextSwitchTo(funccxt->multi_call_memory_ctx);

        multi = palloc(sizeof(mxact));
        /* no need to allow for old values here */
        multi->nmembers = GetMultiXactIdMembers(mxid, &multi->members, false,
                                                false);
        multi->iter = 0;

        tupdesc = CreateTemplateTupleDesc(2);
        TupleDescInitEntry(tupdesc, (AttrNumber) 1, "xid",
                           XIDOID, -1, 0);
        TupleDescInitEntry(tupdesc, (AttrNumber) 2, "mode",
                           TEXTOID, -1, 0);

        funccxt->attinmeta = TupleDescGetAttInMetadata(tupdesc);
        funccxt->user_fctx = multi;

        MemoryContextSwitchTo(oldcxt);
    }

    funccxt = SRF_PERCALL_SETUP();
    multi = (mxact *) funccxt->user_fctx;

    while (multi->iter < multi->nmembers)
    {
        HeapTuple   tuple;
        char       *values[2];

        values[0] = psprintf("%u", multi->members[multi->iter].xid);
        values[1] = mxstatus_to_string(multi->members[multi->iter].status);

        tuple = BuildTupleFromCStrings(funccxt->attinmeta, values);

        multi->iter++;
        pfree(values[0]);
        SRF_RETURN_NEXT(funccxt, HeapTupleGetDatum(tuple));
    }

    SRF_RETURN_DONE(funccxt);
}