spgutils.c

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/*-------------------------------------------------------------------------
 *
 * spgutils.c
 *    various support functions for SP-GiST
 *
 *
 * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *          src/backend/access/spgist/spgutils.c
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#include "access/amvalidate.h"
#include "access/htup_details.h"
#include "access/reloptions.h"
#include "access/spgist_private.h"
#include "access/transam.h"
#include "access/xact.h"
#include "catalog/pg_amop.h"
#include "commands/vacuum.h"
#include "storage/bufmgr.h"
#include "storage/indexfsm.h"
#include "storage/lmgr.h"
#include "utils/builtins.h"
#include "utils/catcache.h"
#include "utils/index_selfuncs.h"
#include "utils/lsyscache.h"
#include "utils/syscache.h"


/*
 * SP-GiST handler function: return IndexAmRoutine with access method parameters
 * and callbacks.
 */
Datum
spghandler(PG_FUNCTION_ARGS)
{
    IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);

    amroutine->amstrategies = 0;
    amroutine->amsupport = SPGISTNProc;
    amroutine->amoptsprocnum = SPGIST_OPTIONS_PROC;
    amroutine->amcanorder = false;
    amroutine->amcanorderbyop = true;
    amroutine->amcanbackward = false;
    amroutine->amcanunique = false;
    amroutine->amcanmulticol = false;
    amroutine->amoptionalkey = true;
    amroutine->amsearcharray = false;
    amroutine->amsearchnulls = true;
    amroutine->amstorage = false;
    amroutine->amclusterable = false;
    amroutine->ampredlocks = false;
    amroutine->amcanparallel = false;
    amroutine->amcaninclude = false;
    amroutine->amusemaintenanceworkmem = false;
    amroutine->amparallelvacuumoptions =
        VACUUM_OPTION_PARALLEL_BULKDEL | VACUUM_OPTION_PARALLEL_COND_CLEANUP;
    amroutine->amkeytype = InvalidOid;

    amroutine->ambuild = spgbuild;
    amroutine->ambuildempty = spgbuildempty;
    amroutine->aminsert = spginsert;
    amroutine->ambulkdelete = spgbulkdelete;
    amroutine->amvacuumcleanup = spgvacuumcleanup;
    amroutine->amcanreturn = spgcanreturn;
    amroutine->amcostestimate = spgcostestimate;
    amroutine->amoptions = spgoptions;
    amroutine->amproperty = spgproperty;
    amroutine->ambuildphasename = NULL;
    amroutine->amvalidate = spgvalidate;
    amroutine->amadjustmembers = spgadjustmembers;
    amroutine->ambeginscan = spgbeginscan;
    amroutine->amrescan = spgrescan;
    amroutine->amgettuple = spggettuple;
    amroutine->amgetbitmap = spggetbitmap;
    amroutine->amendscan = spgendscan;
    amroutine->ammarkpos = NULL;
    amroutine->amrestrpos = NULL;
    amroutine->amestimateparallelscan = NULL;
    amroutine->aminitparallelscan = NULL;
    amroutine->amparallelrescan = NULL;

    PG_RETURN_POINTER(amroutine);
}

/* Fill in a SpGistTypeDesc struct with info about the specified data type */
static void
fillTypeDesc(SpGistTypeDesc *desc, Oid type)
{
    desc->type = type;
    get_typlenbyval(type, &desc->attlen, &desc->attbyval);
}

/*
 * Fetch local cache of AM-specific info about the index, initializing it
 * if necessary
 */
SpGistCache *
spgGetCache(Relation index)
{
    SpGistCache *cache;

    if (index->rd_amcache == NULL)
    {
        Oid         atttype;
        spgConfigIn in;
        FmgrInfo   *procinfo;
        Buffer      metabuffer;
        SpGistMetaPageData *metadata;

        cache = MemoryContextAllocZero(index->rd_indexcxt,
                                       sizeof(SpGistCache));

        /* SPGiST doesn't support multi-column indexes */
        Assert(index->rd_att->natts == 1);

        /*
         * Get the actual data type of the indexed column from the index
         * tupdesc.  We pass this to the opclass config function so that
         * polymorphic opclasses are possible.
         */
        atttype = TupleDescAttr(index->rd_att, 0)->atttypid;

        /* Call the config function to get config info for the opclass */
        in.attType = atttype;

        procinfo = index_getprocinfo(index, 1, SPGIST_CONFIG_PROC);
        FunctionCall2Coll(procinfo,
                          index->rd_indcollation[0],
                          PointerGetDatum(&in),
                          PointerGetDatum(&cache->config));

        /* Get the information we need about each relevant datatype */
        fillTypeDesc(&cache->attType, atttype);

        if (OidIsValid(cache->config.leafType) &&
            cache->config.leafType != atttype)
        {
            if (!OidIsValid(index_getprocid(index, 1, SPGIST_COMPRESS_PROC)))
                ereport(ERROR,
                        (errcode(ERRCODE_INVALID_PARAMETER_VALUE),
                         errmsg("compress method must be defined when leaf type is different from input type")));

            fillTypeDesc(&cache->attLeafType, cache->config.leafType);
        }
        else
        {
            cache->attLeafType = cache->attType;
        }

        fillTypeDesc(&cache->attPrefixType, cache->config.prefixType);
        fillTypeDesc(&cache->attLabelType, cache->config.labelType);

        /* Last, get the lastUsedPages data from the metapage */
        metabuffer = ReadBuffer(index, SPGIST_METAPAGE_BLKNO);
        LockBuffer(metabuffer, BUFFER_LOCK_SHARE);

        metadata = SpGistPageGetMeta(BufferGetPage(metabuffer));

        if (metadata->magicNumber != SPGIST_MAGIC_NUMBER)
            elog(ERROR, "index \"%s\" is not an SP-GiST index",
                 RelationGetRelationName(index));

        cache->lastUsedPages = metadata->lastUsedPages;

        UnlockReleaseBuffer(metabuffer);

        index->rd_amcache = (void *) cache;
    }
    else
    {
        /* assume it's up to date */
        cache = (SpGistCache *) index->rd_amcache;
    }

    return cache;
}

/* Initialize SpGistState for working with the given index */
void
initSpGistState(SpGistState *state, Relation index)
{
    SpGistCache *cache;

    /* Get cached static information about index */
    cache = spgGetCache(index);

    state->config = cache->config;
    state->attType = cache->attType;
    state->attLeafType = cache->attLeafType;
    state->attPrefixType = cache->attPrefixType;
    state->attLabelType = cache->attLabelType;

    /* Make workspace for constructing dead tuples */
    state->deadTupleStorage = palloc0(SGDTSIZE);

    /* Set XID to use in redirection tuples */
    state->myXid = GetTopTransactionIdIfAny();

    /* Assume we're not in an index build (spgbuild will override) */
    state->isBuild = false;
}

/*
 * Allocate a new page (either by recycling, or by extending the index file).
 *
 * The returned buffer is already pinned and exclusive-locked.
 * Caller is responsible for initializing the page by calling SpGistInitBuffer.
 */
Buffer
SpGistNewBuffer(Relation index)
{
    Buffer      buffer;
    bool        needLock;

    /* First, try to get a page from FSM */
    for (;;)
    {
        BlockNumber blkno = GetFreeIndexPage(index);

        if (blkno == InvalidBlockNumber)
            break;              /* nothing known to FSM */

        /*
         * The fixed pages shouldn't ever be listed in FSM, but just in case
         * one is, ignore it.
         */
        if (SpGistBlockIsFixed(blkno))
            continue;

        buffer = ReadBuffer(index, blkno);

        /*
         * We have to guard against the possibility that someone else already
         * recycled this page; the buffer may be locked if so.
         */
        if (ConditionalLockBuffer(buffer))
        {
            Page        page = BufferGetPage(buffer);

            if (PageIsNew(page))
                return buffer;  /* OK to use, if never initialized */

            if (SpGistPageIsDeleted(page) || PageIsEmpty(page))
                return buffer;  /* OK to use */

            LockBuffer(buffer, BUFFER_LOCK_UNLOCK);
        }

        /* Can't use it, so release buffer and try again */
        ReleaseBuffer(buffer);
    }

    /* Must extend the file */
    needLock = !RELATION_IS_LOCAL(index);
    if (needLock)
        LockRelationForExtension(index, ExclusiveLock);

    buffer = ReadBuffer(index, P_NEW);
    LockBuffer(buffer, BUFFER_LOCK_EXCLUSIVE);

    if (needLock)
        UnlockRelationForExtension(index, ExclusiveLock);

    return buffer;
}

/*
 * Update index metapage's lastUsedPages info from local cache, if possible
 *
 * Updating meta page isn't critical for index working, so
 * 1 use ConditionalLockBuffer to improve concurrency
 * 2 don't WAL-log metabuffer changes to decrease WAL traffic
 */
void
SpGistUpdateMetaPage(Relation index)
{
    SpGistCache *cache = (SpGistCache *) index->rd_amcache;

    if (cache != NULL)
    {
        Buffer      metabuffer;

        metabuffer = ReadBuffer(index, SPGIST_METAPAGE_BLKNO);

        if (ConditionalLockBuffer(metabuffer))
        {
            Page        metapage = BufferGetPage(metabuffer);
            SpGistMetaPageData *metadata = SpGistPageGetMeta(metapage);

            metadata->lastUsedPages = cache->lastUsedPages;

            /*
             * Set pd_lower just past the end of the metadata.  This is
             * essential, because without doing so, metadata will be lost if
             * xlog.c compresses the page.  (We must do this here because
             * pre-v11 versions of PG did not set the metapage's pd_lower
             * correctly, so a pg_upgraded index might contain the wrong
             * value.)
             */
            ((PageHeader) metapage)->pd_lower =
                ((char *) metadata + sizeof(SpGistMetaPageData)) - (char *) metapage;

            MarkBufferDirty(metabuffer);
            UnlockReleaseBuffer(metabuffer);
        }
        else
        {
            ReleaseBuffer(metabuffer);
        }
    }
}

/* Macro to select proper element of lastUsedPages cache depending on flags */
/* Masking flags with SPGIST_CACHED_PAGES is just for paranoia's sake */
#define GET_LUP(c, f)  (&(c)->lastUsedPages.cachedPage[((unsigned int) (f)) % SPGIST_CACHED_PAGES])

/*
 * Allocate and initialize a new buffer of the type and parity specified by
 * flags.  The returned buffer is already pinned and exclusive-locked.
 *
 * When requesting an inner page, if we get one with the wrong parity,
 * we just release the buffer and try again.  We will get a different page
 * because GetFreeIndexPage will have marked the page used in FSM.  The page
 * is entered in our local lastUsedPages cache, so there's some hope of
 * making use of it later in this session, but otherwise we rely on VACUUM
 * to eventually re-enter the page in FSM, making it available for recycling.
 * Note that such a page does not get marked dirty here, so unless it's used
 * fairly soon, the buffer will just get discarded and the page will remain
 * as it was on disk.
 *
 * When we return a buffer to the caller, the page is *not* entered into
 * the lastUsedPages cache; we expect the caller will do so after it's taken
 * whatever space it will use.  This is because after the caller has used up
 * some space, the page might have less space than whatever was cached already
 * so we'd rather not trash the old cache entry.
 */
static Buffer
allocNewBuffer(Relation index, int flags)
{
    SpGistCache *cache = spgGetCache(index);
    uint16      pageflags = 0;

    if (GBUF_REQ_LEAF(flags))
        pageflags |= SPGIST_LEAF;
    if (GBUF_REQ_NULLS(flags))
        pageflags |= SPGIST_NULLS;

    for (;;)
    {
        Buffer      buffer;

        buffer = SpGistNewBuffer(index);
        SpGistInitBuffer(buffer, pageflags);

        if (pageflags & SPGIST_LEAF)
        {
            /* Leaf pages have no parity concerns, so just use it */
            return buffer;
        }
        else
        {
            BlockNumber blkno = BufferGetBlockNumber(buffer);
            int         blkFlags = GBUF_INNER_PARITY(blkno);

            if ((flags & GBUF_PARITY_MASK) == blkFlags)
            {
                /* Page has right parity, use it */
                return buffer;
            }
            else
            {
                /* Page has wrong parity, record it in cache and try again */
                if (pageflags & SPGIST_NULLS)
                    blkFlags |= GBUF_NULLS;
                cache->lastUsedPages.cachedPage[blkFlags].blkno = blkno;
                cache->lastUsedPages.cachedPage[blkFlags].freeSpace =
                    PageGetExactFreeSpace(BufferGetPage(buffer));
                UnlockReleaseBuffer(buffer);
            }
        }
    }
}

/*
 * Get a buffer of the type and parity specified by flags, having at least
 * as much free space as indicated by needSpace.  We use the lastUsedPages
 * cache to assign the same buffer previously requested when possible.
 * The returned buffer is already pinned and exclusive-locked.
 *
 * *isNew is set true if the page was initialized here, false if it was
 * already valid.
 */
Buffer
SpGistGetBuffer(Relation index, int flags, int needSpace, bool *isNew)
{
    SpGistCache *cache = spgGetCache(index);
    SpGistLastUsedPage *lup;

    /* Bail out if even an empty page wouldn't meet the demand */
    if (needSpace > SPGIST_PAGE_CAPACITY)
        elog(ERROR, "desired SPGiST tuple size is too big");

    /*
     * If possible, increase the space request to include relation's
     * fillfactor.  This ensures that when we add unrelated tuples to a page,
     * we try to keep 100-fillfactor% available for adding tuples that are
     * related to the ones already on it.  But fillfactor mustn't cause an
     * error for requests that would otherwise be legal.
     */
    needSpace += SpGistGetTargetPageFreeSpace(index);
    needSpace = Min(needSpace, SPGIST_PAGE_CAPACITY);

    /* Get the cache entry for this flags setting */
    lup = GET_LUP(cache, flags);

    /* If we have nothing cached, just turn it over to allocNewBuffer */
    if (lup->blkno == InvalidBlockNumber)
    {
        *isNew = true;
        return allocNewBuffer(index, flags);
    }

    /* fixed pages should never be in cache */
    Assert(!SpGistBlockIsFixed(lup->blkno));

    /* If cached freeSpace isn't enough, don't bother looking at the page */
    if (lup->freeSpace >= needSpace)
    {
        Buffer      buffer;
        Page        page;

        buffer = ReadBuffer(index, lup->blkno);

        if (!ConditionalLockBuffer(buffer))
        {
            /*
             * buffer is locked by another process, so return a new buffer
             */
            ReleaseBuffer(buffer);
            *isNew = true;
            return allocNewBuffer(index, flags);
        }

        page = BufferGetPage(buffer);

        if (PageIsNew(page) || SpGistPageIsDeleted(page) || PageIsEmpty(page))
        {
            /* OK to initialize the page */
            uint16      pageflags = 0;

            if (GBUF_REQ_LEAF(flags))
                pageflags |= SPGIST_LEAF;
            if (GBUF_REQ_NULLS(flags))
                pageflags |= SPGIST_NULLS;
            SpGistInitBuffer(buffer, pageflags);
            lup->freeSpace = PageGetExactFreeSpace(page) - needSpace;
            *isNew = true;
            return buffer;
        }

        /*
         * Check that page is of right type and has enough space.  We must
         * recheck this since our cache isn't necessarily up to date.
         */
        if ((GBUF_REQ_LEAF(flags) ? SpGistPageIsLeaf(page) : !SpGistPageIsLeaf(page)) &&
            (GBUF_REQ_NULLS(flags) ? SpGistPageStoresNulls(page) : !SpGistPageStoresNulls(page)))
        {
            int         freeSpace = PageGetExactFreeSpace(page);

            if (freeSpace >= needSpace)
            {
                /* Success, update freespace info and return the buffer */
                lup->freeSpace = freeSpace - needSpace;
                *isNew = false;
                return buffer;
            }
        }

        /*
         * fallback to allocation of new buffer
         */
        UnlockReleaseBuffer(buffer);
    }

    /* No success with cache, so return a new buffer */
    *isNew = true;
    return allocNewBuffer(index, flags);
}

/*
 * Update lastUsedPages cache when done modifying a page.
 *
 * We update the appropriate cache entry if it already contained this page
 * (its freeSpace is likely obsolete), or if this page has more space than
 * whatever we had cached.
 */
void
SpGistSetLastUsedPage(Relation index, Buffer buffer)
{
    SpGistCache *cache = spgGetCache(index);
    SpGistLastUsedPage *lup;
    int         freeSpace;
    Page        page = BufferGetPage(buffer);
    BlockNumber blkno = BufferGetBlockNumber(buffer);
    int         flags;

    /* Never enter fixed pages (root pages) in cache, though */
    if (SpGistBlockIsFixed(blkno))
        return;

    if (SpGistPageIsLeaf(page))
        flags = GBUF_LEAF;
    else
        flags = GBUF_INNER_PARITY(blkno);
    if (SpGistPageStoresNulls(page))
        flags |= GBUF_NULLS;

    lup = GET_LUP(cache, flags);

    freeSpace = PageGetExactFreeSpace(page);
    if (lup->blkno == InvalidBlockNumber || lup->blkno == blkno ||
        lup->freeSpace < freeSpace)
    {
        lup->blkno = blkno;
        lup->freeSpace = freeSpace;
    }
}

/*
 * Initialize an SPGiST page to empty, with specified flags
 */
void
SpGistInitPage(Page page, uint16 f)
{
    SpGistPageOpaque opaque;

    PageInit(page, BLCKSZ, MAXALIGN(sizeof(SpGistPageOpaqueData)));
    opaque = SpGistPageGetOpaque(page);
    memset(opaque, 0, sizeof(SpGistPageOpaqueData));
    opaque->flags = f;
    opaque->spgist_page_id = SPGIST_PAGE_ID;
}

/*
 * Initialize a buffer's page to empty, with specified flags
 */
void
SpGistInitBuffer(Buffer b, uint16 f)
{
    Assert(BufferGetPageSize(b) == BLCKSZ);
    SpGistInitPage(BufferGetPage(b), f);
}

/*
 * Initialize metadata page
 */
void
SpGistInitMetapage(Page page)
{
    SpGistMetaPageData *metadata;
    int         i;

    SpGistInitPage(page, SPGIST_META);
    metadata = SpGistPageGetMeta(page);
    memset(metadata, 0, sizeof(SpGistMetaPageData));
    metadata->magicNumber = SPGIST_MAGIC_NUMBER;

    /* initialize last-used-page cache to empty */
    for (i = 0; i < SPGIST_CACHED_PAGES; i++)
        metadata->lastUsedPages.cachedPage[i].blkno = InvalidBlockNumber;

    /*
     * Set pd_lower just past the end of the metadata.  This is essential,
     * because without doing so, metadata will be lost if xlog.c compresses
     * the page.
     */
    ((PageHeader) page)->pd_lower =
        ((char *) metadata + sizeof(SpGistMetaPageData)) - (char *) page;
}

/*
 * reloptions processing for SPGiST
 */
bytea *
spgoptions(Datum reloptions, bool validate)
{
    static const relopt_parse_elt tab[] = {
        {"fillfactor", RELOPT_TYPE_INT, offsetof(SpGistOptions, fillfactor)},
    };

    return (bytea *) build_reloptions(reloptions, validate,
                                      RELOPT_KIND_SPGIST,
                                      sizeof(SpGistOptions),
                                      tab, lengthof(tab));

}

/*
 * Get the space needed to store a non-null datum of the indicated type.
 * Note the result is already rounded up to a MAXALIGN boundary.
 * Also, we follow the SPGiST convention that pass-by-val types are
 * just stored in their Datum representation (compare memcpyDatum).
 */
unsigned int
SpGistGetTypeSize(SpGistTypeDesc *att, Datum datum)
{
    unsigned int size;

    if (att->attbyval)
        size = sizeof(Datum);
    else if (att->attlen > 0)
        size = att->attlen;
    else
        size = VARSIZE_ANY(datum);

    return MAXALIGN(size);
}

/*
 * Copy the given non-null datum to *target
 */
static void
memcpyDatum(void *target, SpGistTypeDesc *att, Datum datum)
{
    unsigned int size;

    if (att->attbyval)
    {
        memcpy(target, &datum, sizeof(Datum));
    }
    else
    {
        size = (att->attlen > 0) ? att->attlen : VARSIZE_ANY(datum);
        memcpy(target, DatumGetPointer(datum), size);
    }
}

/*
 * Construct a leaf tuple containing the given heap TID and datum value
 */
SpGistLeafTuple
spgFormLeafTuple(SpGistState *state, ItemPointer heapPtr,
                 Datum datum, bool isnull)
{
    SpGistLeafTuple tup;
    unsigned int size;

    /* compute space needed (note result is already maxaligned) */
    size = SGLTHDRSZ;
    if (!isnull)
        size += SpGistGetTypeSize(&state->attLeafType, datum);

    /*
     * Ensure that we can replace the tuple with a dead tuple later.  This
     * test is unnecessary when !isnull, but let's be safe.
     */
    if (size < SGDTSIZE)
        size = SGDTSIZE;

    /* OK, form the tuple */
    tup = (SpGistLeafTuple) palloc0(size);

    tup->size = size;
    tup->nextOffset = InvalidOffsetNumber;
    tup->heapPtr = *heapPtr;
    if (!isnull)
        memcpyDatum(SGLTDATAPTR(tup), &state->attLeafType, datum);

    return tup;
}

/*
 * Construct a node (to go into an inner tuple) containing the given label
 *
 * Note that the node's downlink is just set invalid here.  Caller will fill
 * it in later.
 */
SpGistNodeTuple
spgFormNodeTuple(SpGistState *state, Datum label, bool isnull)
{
    SpGistNodeTuple tup;
    unsigned int size;
    unsigned short infomask = 0;

    /* compute space needed (note result is already maxaligned) */
    size = SGNTHDRSZ;
    if (!isnull)
        size += SpGistGetTypeSize(&state->attLabelType, label);

    /*
     * Here we make sure that the size will fit in the field reserved for it
     * in t_info.
     */
    if ((size & INDEX_SIZE_MASK) != size)
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("index row requires %zu bytes, maximum size is %zu",
                        (Size) size, (Size) INDEX_SIZE_MASK)));

    tup = (SpGistNodeTuple) palloc0(size);

    if (isnull)
        infomask |= INDEX_NULL_MASK;
    /* we don't bother setting the INDEX_VAR_MASK bit */
    infomask |= size;
    tup->t_info = infomask;

    /* The TID field will be filled in later */
    ItemPointerSetInvalid(&tup->t_tid);

    if (!isnull)
        memcpyDatum(SGNTDATAPTR(tup), &state->attLabelType, label);

    return tup;
}

/*
 * Construct an inner tuple containing the given prefix and node array
 */
SpGistInnerTuple
spgFormInnerTuple(SpGistState *state, bool hasPrefix, Datum prefix,
                  int nNodes, SpGistNodeTuple *nodes)
{
    SpGistInnerTuple tup;
    unsigned int size;
    unsigned int prefixSize;
    int         i;
    char       *ptr;

    /* Compute size needed */
    if (hasPrefix)
        prefixSize = SpGistGetTypeSize(&state->attPrefixType, prefix);
    else
        prefixSize = 0;

    size = SGITHDRSZ + prefixSize;

    /* Note: we rely on node tuple sizes to be maxaligned already */
    for (i = 0; i < nNodes; i++)
        size += IndexTupleSize(nodes[i]);

    /*
     * Ensure that we can replace the tuple with a dead tuple later.  This
     * test is unnecessary given current tuple layouts, but let's be safe.
     */
    if (size < SGDTSIZE)
        size = SGDTSIZE;

    /*
     * Inner tuple should be small enough to fit on a page
     */
    if (size > SPGIST_PAGE_CAPACITY - sizeof(ItemIdData))
        ereport(ERROR,
                (errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
                 errmsg("SP-GiST inner tuple size %zu exceeds maximum %zu",
                        (Size) size,
                        SPGIST_PAGE_CAPACITY - sizeof(ItemIdData)),
                 errhint("Values larger than a buffer page cannot be indexed.")));

    /*
     * Check for overflow of header fields --- probably can't fail if the
     * above succeeded, but let's be paranoid
     */
    if (size > SGITMAXSIZE ||
        prefixSize > SGITMAXPREFIXSIZE ||
        nNodes > SGITMAXNNODES)
        elog(ERROR, "SPGiST inner tuple header field is too small");

    /* OK, form the tuple */
    tup = (SpGistInnerTuple) palloc0(size);

    tup->nNodes = nNodes;
    tup->prefixSize = prefixSize;
    tup->size = size;

    if (hasPrefix)
        memcpyDatum(SGITDATAPTR(tup), &state->attPrefixType, prefix);

    ptr = (char *) SGITNODEPTR(tup);

    for (i = 0; i < nNodes; i++)
    {
        SpGistNodeTuple node = nodes[i];

        memcpy(ptr, node, IndexTupleSize(node));
        ptr += IndexTupleSize(node);
    }

    return tup;
}

/*
 * Construct a "dead" tuple to replace a tuple being deleted.
 *
 * The state can be SPGIST_REDIRECT, SPGIST_DEAD, or SPGIST_PLACEHOLDER.
 * For a REDIRECT tuple, a pointer (blkno+offset) must be supplied, and
 * the xid field is filled in automatically.
 *
 * This is called in critical sections, so we don't use palloc; the tuple
 * is built in preallocated storage.  It should be copied before another
 * call with different parameters can occur.
 */
SpGistDeadTuple
spgFormDeadTuple(SpGistState *state, int tupstate,
                 BlockNumber blkno, OffsetNumber offnum)
{
    SpGistDeadTuple tuple = (SpGistDeadTuple) state->deadTupleStorage;

    tuple->tupstate = tupstate;
    tuple->size = SGDTSIZE;
    tuple->nextOffset = InvalidOffsetNumber;

    if (tupstate == SPGIST_REDIRECT)
    {
        ItemPointerSet(&tuple->pointer, blkno, offnum);
        Assert(TransactionIdIsValid(state->myXid));
        tuple->xid = state->myXid;
    }
    else
    {
        ItemPointerSetInvalid(&tuple->pointer);
        tuple->xid = InvalidTransactionId;
    }

    return tuple;
}

/*
 * Extract the label datums of the nodes within innerTuple
 *
 * Returns NULL if label datums are NULLs
 */
Datum *
spgExtractNodeLabels(SpGistState *state, SpGistInnerTuple innerTuple)
{
    Datum      *nodeLabels;
    int         i;
    SpGistNodeTuple node;

    /* Either all the labels must be NULL, or none. */
    node = SGITNODEPTR(innerTuple);
    if (IndexTupleHasNulls(node))
    {
        SGITITERATE(innerTuple, i, node)
        {
            if (!IndexTupleHasNulls(node))
                elog(ERROR, "some but not all node labels are null in SPGiST inner tuple");
        }
        /* They're all null, so just return NULL */
        return NULL;
    }
    else
    {
        nodeLabels = (Datum *) palloc(sizeof(Datum) * innerTuple->nNodes);
        SGITITERATE(innerTuple, i, node)
        {
            if (IndexTupleHasNulls(node))
                elog(ERROR, "some but not all node labels are null in SPGiST inner tuple");
            nodeLabels[i] = SGNTDATUM(node, state);
        }
        return nodeLabels;
    }
}

/*
 * Add a new item to the page, replacing a PLACEHOLDER item if possible.
 * Return the location it's inserted at, or InvalidOffsetNumber on failure.
 *
 * If startOffset isn't NULL, we start searching for placeholders at
 * *startOffset, and update that to the next place to search.  This is just
 * an optimization for repeated insertions.
 *
 * If errorOK is false, we throw error when there's not enough room,
 * rather than returning InvalidOffsetNumber.
 */
OffsetNumber
SpGistPageAddNewItem(SpGistState *state, Page page, Item item, Size size,
                     OffsetNumber *startOffset, bool errorOK)
{
    SpGistPageOpaque opaque = SpGistPageGetOpaque(page);
    OffsetNumber i,
                maxoff,
                offnum;

    if (opaque->nPlaceholder > 0 &&
        PageGetExactFreeSpace(page) + SGDTSIZE >= MAXALIGN(size))
    {
        /* Try to replace a placeholder */
        maxoff = PageGetMaxOffsetNumber(page);
        offnum = InvalidOffsetNumber;

        for (;;)
        {
            if (startOffset && *startOffset != InvalidOffsetNumber)
                i = *startOffset;
            else
                i = FirstOffsetNumber;
            for (; i <= maxoff; i++)
            {
                SpGistDeadTuple it = (SpGistDeadTuple) PageGetItem(page,
                                                                   PageGetItemId(page, i));

                if (it->tupstate == SPGIST_PLACEHOLDER)
                {
                    offnum = i;
                    break;
                }
            }

            /* Done if we found a placeholder */
            if (offnum != InvalidOffsetNumber)
                break;

            if (startOffset && *startOffset != InvalidOffsetNumber)
            {
                /* Hint was no good, re-search from beginning */
                *startOffset = InvalidOffsetNumber;
                continue;
            }

            /* Hmm, no placeholder found? */
            opaque->nPlaceholder = 0;
            break;
        }

        if (offnum != InvalidOffsetNumber)
        {
            /* Replace the placeholder tuple */
            PageIndexTupleDelete(page, offnum);

            offnum = PageAddItem(page, item, size, offnum, false, false);

            /*
             * We should not have failed given the size check at the top of
             * the function, but test anyway.  If we did fail, we must PANIC
             * because we've already deleted the placeholder tuple, and
             * there's no other way to keep the damage from getting to disk.
             */
            if (offnum != InvalidOffsetNumber)
            {
                Assert(opaque->nPlaceholder > 0);
                opaque->nPlaceholder--;
                if (startOffset)
                    *startOffset = offnum + 1;
            }
            else
                elog(PANIC, "failed to add item of size %u to SPGiST index page",
                     (int) size);

            return offnum;
        }
    }

    /* No luck in replacing a placeholder, so just add it to the page */
    offnum = PageAddItem(page, item, size,
                         InvalidOffsetNumber, false, false);

    if (offnum == InvalidOffsetNumber && !errorOK)
        elog(ERROR, "failed to add item of size %u to SPGiST index page",
             (int) size);

    return offnum;
}

/*
 *  spgproperty() -- Check boolean properties of indexes.
 *
 * This is optional for most AMs, but is required for SP-GiST because the core
 * property code doesn't support AMPROP_DISTANCE_ORDERABLE.
 */
bool
spgproperty(Oid index_oid, int attno,
            IndexAMProperty prop, const char *propname,
            bool *res, bool *isnull)
{
    Oid         opclass,
                opfamily,
                opcintype;
    CatCList   *catlist;
    int         i;

    /* Only answer column-level inquiries */
    if (attno == 0)
        return false;

    switch (prop)
    {
        case AMPROP_DISTANCE_ORDERABLE:
            break;
        default:
            return false;
    }

    /*
     * Currently, SP-GiST distance-ordered scans require that there be a
     * distance operator in the opclass with the default types. So we assume
     * that if such a operator exists, then there's a reason for it.
     */

    /* First we need to know the column's opclass. */
    opclass = get_index_column_opclass(index_oid, attno);
    if (!OidIsValid(opclass))
    {
        *isnull = true;
        return true;
    }

    /* Now look up the opclass family and input datatype. */
    if (!get_opclass_opfamily_and_input_type(opclass, &opfamily, &opcintype))
    {
        *isnull = true;
        return true;
    }

    /* And now we can check whether the operator is provided. */
    catlist = SearchSysCacheList1(AMOPSTRATEGY,
                                  ObjectIdGetDatum(opfamily));

    *res = false;

    for (i = 0; i < catlist->n_members; i++)
    {
        HeapTuple   amoptup = &catlist->members[i]->tuple;
        Form_pg_amop amopform = (Form_pg_amop) GETSTRUCT(amoptup);

        if (amopform->amoppurpose == AMOP_ORDER &&
            (amopform->amoplefttype == opcintype ||
             amopform->amoprighttype == opcintype) &&
            opfamily_can_sort_type(amopform->amopsortfamily,
                                   get_op_rettype(amopform->amopopr)))
        {
            *res = true;
            break;
        }
    }

    ReleaseSysCacheList(catlist);

    *isnull = false;

    return true;
}