bufpage.c

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/*-------------------------------------------------------------------------
 *
 * bufpage.c
 *    POSTGRES standard buffer page code.
 *
 * Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 *
 * IDENTIFICATION
 *    src/backend/storage/page/bufpage.c
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"
 
#include "access/htup_details.h"
#include "access/itup.h"
#include "access/xlog.h"
#include "pgstat.h"
#include "storage/checksum.h"
#include "utils/memdebug.h"
#include "utils/memutils.h"
 
 
/* GUC variable */
bool        ignore_checksum_failure = false;
 
 
/* ----------------------------------------------------------------
 *                      Page support functions
 * ----------------------------------------------------------------
 */
 
/*
 * PageInit
 *      Initializes the contents of a page.
 *      Note that we don't calculate an initial checksum here; that's not done
 *      until it's time to write.
 */
void
PageInit(Page page, Size pageSize, Size specialSize)
{
    PageHeader  p = (PageHeader) page;
 
    specialSize = MAXALIGN(specialSize);
 
    Assert(pageSize == BLCKSZ);
    Assert(pageSize > specialSize + SizeOfPageHeaderData);
 
    /* Make sure all fields of page are zero, as well as unused space */
    MemSet(p, 0, pageSize);
 
    p->pd_flags = 0;
    p->pd_lower = SizeOfPageHeaderData;
    p->pd_upper = pageSize - specialSize;
    p->pd_special = pageSize - specialSize;
    PageSetPageSizeAndVersion(page, pageSize, PG_PAGE_LAYOUT_VERSION);
    /* p->pd_prune_xid = InvalidTransactionId;      done by above MemSet */
}
 
 
/*
 * PageIsVerifiedExtended
 *      Check that the page header and checksum (if any) appear valid.
 *
 * This is called when a page has just been read in from disk.  The idea is
 * to cheaply detect trashed pages before we go nuts following bogus line
 * pointers, testing invalid transaction identifiers, etc.
 *
 * It turns out to be necessary to allow zeroed pages here too.  Even though
 * this routine is *not* called when deliberately adding a page to a relation,
 * there are scenarios in which a zeroed page might be found in a table.
 * (Example: a backend extends a relation, then crashes before it can write
 * any WAL entry about the new page.  The kernel will already have the
 * zeroed page in the file, and it will stay that way after restart.)  So we
 * allow zeroed pages here, and are careful that the page access macros
 * treat such a page as empty and without free space.  Eventually, VACUUM
 * will clean up such a page and make it usable.
 *
 * If flag PIV_LOG_WARNING is set, a WARNING is logged in the event of
 * a checksum failure.
 *
 * If flag PIV_REPORT_STAT is set, a checksum failure is reported directly
 * to pgstat.
 */
bool
PageIsVerifiedExtended(Page page, BlockNumber blkno, int flags)
{
    PageHeader  p = (PageHeader) page;
    size_t     *pagebytes;
    int         i;
    bool        checksum_failure = false;
    bool        header_sane = false;
    bool        all_zeroes = false;
    uint16      checksum = 0;
 
    /*
     * Don't verify page data unless the page passes basic non-zero test
     */
    if (!PageIsNew(page))
    {
        if (DataChecksumsEnabled())
        {
            checksum = pg_checksum_page((char *) page, blkno);
 
            if (checksum != p->pd_checksum)
                checksum_failure = true;
        }
 
        /*
         * The following checks don't prove the header is correct, only that
         * it looks sane enough to allow into the buffer pool. Later usage of
         * the block can still reveal problems, which is why we offer the
         * checksum option.
         */
        if ((p->pd_flags & ~PD_VALID_FLAG_BITS) == 0 &&
            p->pd_lower <= p->pd_upper &&
            p->pd_upper <= p->pd_special &&
            p->pd_special <= BLCKSZ &&
            p->pd_special == MAXALIGN(p->pd_special))
            header_sane = true;
 
        if (header_sane && !checksum_failure)
            return true;
    }
 
    /* Check all-zeroes case */
    all_zeroes = true;
    pagebytes = (size_t *) page;
    for (i = 0; i < (BLCKSZ / sizeof(size_t)); i++)
    {
        if (pagebytes[i] != 0)
        {
            all_zeroes = false;
            break;
        }
    }
 
    if (all_zeroes)
        return true;
 
    /*
     * Throw a WARNING if the checksum fails, but only after we've checked for
     * the all-zeroes case.
     */
    if (checksum_failure)
    {
        if ((flags & PIV_LOG_WARNING) != 0)
            ereport(WARNING,
                    (errcode(ERRCODE_DATA_CORRUPTED),
                     errmsg("page verification failed, calculated checksum %u but expected %u",
                            checksum, p->pd_checksum)));
 
        if ((flags & PIV_REPORT_STAT) != 0)
            pgstat_report_checksum_failure();
 
        if (header_sane && ignore_checksum_failure)
            return true;
    }
 
    return false;
}
 
 
/*
 *  PageAddItemExtended
 *
 *  Add an item to a page.  Return value is the offset at which it was
 *  inserted, or InvalidOffsetNumber if the item is not inserted for any
 *  reason.  A WARNING is issued indicating the reason for the refusal.
 *
 *  offsetNumber must be either InvalidOffsetNumber to specify finding a
 *  free line pointer, or a value between FirstOffsetNumber and one past
 *  the last existing item, to specify using that particular line pointer.
 *
 *  If offsetNumber is valid and flag PAI_OVERWRITE is set, we just store
 *  the item at the specified offsetNumber, which must be either a
 *  currently-unused line pointer, or one past the last existing item.
 *
 *  If offsetNumber is valid and flag PAI_OVERWRITE is not set, insert
 *  the item at the specified offsetNumber, moving existing items later
 *  in the array to make room.
 *
 *  If offsetNumber is not valid, then assign a slot by finding the first
 *  one that is both unused and deallocated.
 *
 *  If flag PAI_IS_HEAP is set, we enforce that there can't be more than
 *  MaxHeapTuplesPerPage line pointers on the page.
 *
 *  !!! EREPORT(ERROR) IS DISALLOWED HERE !!!
 */
OffsetNumber
PageAddItemExtended(Page page,
                    Item item,
                    Size size,
                    OffsetNumber offsetNumber,
                    int flags)
{
    PageHeader  phdr = (PageHeader) page;
    Size        alignedSize;
    int         lower;
    int         upper;
    ItemId      itemId;
    OffsetNumber limit;
    bool        needshuffle = false;
 
    /*
     * Be wary about corrupted page pointers
     */
    if (phdr->pd_lower < SizeOfPageHeaderData ||
        phdr->pd_lower > phdr->pd_upper ||
        phdr->pd_upper > phdr->pd_special ||
        phdr->pd_special > BLCKSZ)
        ereport(PANIC,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted page pointers: lower = %u, upper = %u, special = %u",
                        phdr->pd_lower, phdr->pd_upper, phdr->pd_special)));
 
    /*
     * Select offsetNumber to place the new item at
     */
    limit = OffsetNumberNext(PageGetMaxOffsetNumber(page));
 
    /* was offsetNumber passed in? */
    if (OffsetNumberIsValid(offsetNumber))
    {
        /* yes, check it */
        if ((flags & PAI_OVERWRITE) != 0)
        {
            if (offsetNumber < limit)
            {
                itemId = PageGetItemId(page, offsetNumber);
                if (ItemIdIsUsed(itemId) || ItemIdHasStorage(itemId))
                {
                    elog(WARNING, "will not overwrite a used ItemId");
                    return InvalidOffsetNumber;
                }
            }
        }
        else
        {
            if (offsetNumber < limit)
                needshuffle = true; /* need to move existing linp's */
        }
    }
    else
    {
        /* offsetNumber was not passed in, so find a free slot */
        /* if no free slot, we'll put it at limit (1st open slot) */
        if (PageHasFreeLinePointers(page))
        {
            /*
             * Scan line pointer array to locate a "recyclable" (unused)
             * ItemId.
             *
             * Always use earlier items first.  PageTruncateLinePointerArray
             * can only truncate unused items when they appear as a contiguous
             * group at the end of the line pointer array.
             */
            for (offsetNumber = FirstOffsetNumber;
                 offsetNumber < limit;  /* limit is maxoff+1 */
                 offsetNumber++)
            {
                itemId = PageGetItemId(page, offsetNumber);
 
                /*
                 * We check for no storage as well, just to be paranoid;
                 * unused items should never have storage.  Assert() that the
                 * invariant is respected too.
                 */
                Assert(ItemIdIsUsed(itemId) || !ItemIdHasStorage(itemId));
 
                if (!ItemIdIsUsed(itemId) && !ItemIdHasStorage(itemId))
                    break;
            }
            if (offsetNumber >= limit)
            {
                /* the hint is wrong, so reset it */
                PageClearHasFreeLinePointers(page);
            }
        }
        else
        {
            /* don't bother searching if hint says there's no free slot */
            offsetNumber = limit;
        }
    }
 
    /* Reject placing items beyond the first unused line pointer */
    if (offsetNumber > limit)
    {
        elog(WARNING, "specified item offset is too large");
        return InvalidOffsetNumber;
    }
 
    /* Reject placing items beyond heap boundary, if heap */
    if ((flags & PAI_IS_HEAP) != 0 && offsetNumber > MaxHeapTuplesPerPage)
    {
        elog(WARNING, "can't put more than MaxHeapTuplesPerPage items in a heap page");
        return InvalidOffsetNumber;
    }
 
    /*
     * Compute new lower and upper pointers for page, see if it'll fit.
     *
     * Note: do arithmetic as signed ints, to avoid mistakes if, say,
     * alignedSize > pd_upper.
     */
    if (offsetNumber == limit || needshuffle)
        lower = phdr->pd_lower + sizeof(ItemIdData);
    else
        lower = phdr->pd_lower;
 
    alignedSize = MAXALIGN(size);
 
    upper = (int) phdr->pd_upper - (int) alignedSize;
 
    if (lower > upper)
        return InvalidOffsetNumber;
 
    /*
     * OK to insert the item.  First, shuffle the existing pointers if needed.
     */
    itemId = PageGetItemId(page, offsetNumber);
 
    if (needshuffle)
        memmove(itemId + 1, itemId,
                (limit - offsetNumber) * sizeof(ItemIdData));
 
    /* set the line pointer */
    ItemIdSetNormal(itemId, upper, size);
 
    /*
     * Items normally contain no uninitialized bytes.  Core bufpage consumers
     * conform, but this is not a necessary coding rule; a new index AM could
     * opt to depart from it.  However, data type input functions and other
     * C-language functions that synthesize datums should initialize all
     * bytes; datumIsEqual() relies on this.  Testing here, along with the
     * similar check in printtup(), helps to catch such mistakes.
     *
     * Values of the "name" type retrieved via index-only scans may contain
     * uninitialized bytes; see comment in btrescan().  Valgrind will report
     * this as an error, but it is safe to ignore.
     */
    VALGRIND_CHECK_MEM_IS_DEFINED(item, size);
 
    /* copy the item's data onto the page */
    memcpy((char *) page + upper, item, size);
 
    /* adjust page header */
    phdr->pd_lower = (LocationIndex) lower;
    phdr->pd_upper = (LocationIndex) upper;
 
    return offsetNumber;
}
 
 
/*
 * PageGetTempPage
 *      Get a temporary page in local memory for special processing.
 *      The returned page is not initialized at all; caller must do that.
 */
Page
PageGetTempPage(Page page)
{
    Size        pageSize;
    Page        temp;
 
    pageSize = PageGetPageSize(page);
    temp = (Page) palloc(pageSize);
 
    return temp;
}
 
/*
 * PageGetTempPageCopy
 *      Get a temporary page in local memory for special processing.
 *      The page is initialized by copying the contents of the given page.
 */
Page
PageGetTempPageCopy(Page page)
{
    Size        pageSize;
    Page        temp;
 
    pageSize = PageGetPageSize(page);
    temp = (Page) palloc(pageSize);
 
    memcpy(temp, page, pageSize);
 
    return temp;
}
 
/*
 * PageGetTempPageCopySpecial
 *      Get a temporary page in local memory for special processing.
 *      The page is PageInit'd with the same special-space size as the
 *      given page, and the special space is copied from the given page.
 */
Page
PageGetTempPageCopySpecial(Page page)
{
    Size        pageSize;
    Page        temp;
 
    pageSize = PageGetPageSize(page);
    temp = (Page) palloc(pageSize);
 
    PageInit(temp, pageSize, PageGetSpecialSize(page));
    memcpy(PageGetSpecialPointer(temp),
           PageGetSpecialPointer(page),
           PageGetSpecialSize(page));
 
    return temp;
}
 
/*
 * PageRestoreTempPage
 *      Copy temporary page back to permanent page after special processing
 *      and release the temporary page.
 */
void
PageRestoreTempPage(Page tempPage, Page oldPage)
{
    Size        pageSize;
 
    pageSize = PageGetPageSize(tempPage);
    memcpy((char *) oldPage, (char *) tempPage, pageSize);
 
    pfree(tempPage);
}
 
/*
 * Tuple defrag support for PageRepairFragmentation and PageIndexMultiDelete
 */
typedef struct itemIdCompactData
{
    uint16      offsetindex;    /* linp array index */
    int16       itemoff;        /* page offset of item data */
    uint16      alignedlen;     /* MAXALIGN(item data len) */
} itemIdCompactData;
typedef itemIdCompactData *itemIdCompact;
 
/*
 * After removing or marking some line pointers unused, move the tuples to
 * remove the gaps caused by the removed items and reorder them back into
 * reverse line pointer order in the page.
 *
 * This function can often be fairly hot, so it pays to take some measures to
 * make it as optimal as possible.
 *
 * Callers may pass 'presorted' as true if the 'itemidbase' array is sorted in
 * descending order of itemoff.  When this is true we can just memmove()
 * tuples towards the end of the page.  This is quite a common case as it's
 * the order that tuples are initially inserted into pages.  When we call this
 * function to defragment the tuples in the page then any new line pointers
 * added to the page will keep that presorted order, so hitting this case is
 * still very common for tables that are commonly updated.
 *
 * When the 'itemidbase' array is not presorted then we're unable to just
 * memmove() tuples around freely.  Doing so could cause us to overwrite the
 * memory belonging to a tuple we've not moved yet.  In this case, we copy all
 * the tuples that need to be moved into a temporary buffer.  We can then
 * simply memcpy() out of that temp buffer back into the page at the correct
 * location.  Tuples are copied back into the page in the same order as the
 * 'itemidbase' array, so we end up reordering the tuples back into reverse
 * line pointer order.  This will increase the chances of hitting the
 * presorted case the next time around.
 *
 * Callers must ensure that nitems is > 0
 */
static void
compactify_tuples(itemIdCompact itemidbase, int nitems, Page page, bool presorted)
{
    PageHeader  phdr = (PageHeader) page;
    Offset      upper;
    Offset      copy_tail;
    Offset      copy_head;
    itemIdCompact itemidptr;
    int         i;
 
    /* Code within will not work correctly if nitems == 0 */
    Assert(nitems > 0);
 
    if (presorted)
    {
 
#ifdef USE_ASSERT_CHECKING
        {
            /*
             * Verify we've not gotten any new callers that are incorrectly
             * passing a true presorted value.
             */
            Offset      lastoff = phdr->pd_special;
 
            for (i = 0; i < nitems; i++)
            {
                itemidptr = &itemidbase[i];
 
                Assert(lastoff > itemidptr->itemoff);
 
                lastoff = itemidptr->itemoff;
            }
        }
#endif                          /* USE_ASSERT_CHECKING */
 
        /*
         * 'itemidbase' is already in the optimal order, i.e, lower item
         * pointers have a higher offset.  This allows us to memmove() the
         * tuples up to the end of the page without having to worry about
         * overwriting other tuples that have not been moved yet.
         *
         * There's a good chance that there are tuples already right at the
         * end of the page that we can simply skip over because they're
         * already in the correct location within the page.  We'll do that
         * first...
         */
        upper = phdr->pd_special;
        i = 0;
        do
        {
            itemidptr = &itemidbase[i];
            if (upper != itemidptr->itemoff + itemidptr->alignedlen)
                break;
            upper -= itemidptr->alignedlen;
 
            i++;
        } while (i < nitems);
 
        /*
         * Now that we've found the first tuple that needs to be moved, we can
         * do the tuple compactification.  We try and make the least number of
         * memmove() calls and only call memmove() when there's a gap.  When
         * we see a gap we just move all tuples after the gap up until the
         * point of the last move operation.
         */
        copy_tail = copy_head = itemidptr->itemoff + itemidptr->alignedlen;
        for (; i < nitems; i++)
        {
            ItemId      lp;
 
            itemidptr = &itemidbase[i];
            lp = PageGetItemId(page, itemidptr->offsetindex + 1);
 
            if (copy_head != itemidptr->itemoff + itemidptr->alignedlen)
            {
                memmove((char *) page + upper,
                        page + copy_head,
                        copy_tail - copy_head);
 
                /*
                 * We've now moved all tuples already seen, but not the
                 * current tuple, so we set the copy_tail to the end of this
                 * tuple so it can be moved in another iteration of the loop.
                 */
                copy_tail = itemidptr->itemoff + itemidptr->alignedlen;
            }
            /* shift the target offset down by the length of this tuple */
            upper -= itemidptr->alignedlen;
            /* point the copy_head to the start of this tuple */
            copy_head = itemidptr->itemoff;
 
            /* update the line pointer to reference the new offset */
            lp->lp_off = upper;
        }
 
        /* move the remaining tuples. */
        memmove((char *) page + upper,
                page + copy_head,
                copy_tail - copy_head);
    }
    else
    {
        PGAlignedBlock scratch;
        char       *scratchptr = scratch.data;
 
        /*
         * Non-presorted case:  The tuples in the itemidbase array may be in
         * any order.  So, in order to move these to the end of the page we
         * must make a temp copy of each tuple that needs to be moved before
         * we copy them back into the page at the new offset.
         *
         * If a large percentage of tuples have been pruned (>75%) then we'll
         * copy these into the temp buffer tuple-by-tuple, otherwise, we'll
         * just do a single memcpy() for all tuples that need to be moved.
         * When so many tuples have been removed there's likely to be a lot of
         * gaps and it's unlikely that many non-movable tuples remain at the
         * end of the page.
         */
        if (nitems < PageGetMaxOffsetNumber(page) / 4)
        {
            i = 0;
            do
            {
                itemidptr = &itemidbase[i];
                memcpy(scratchptr + itemidptr->itemoff, page + itemidptr->itemoff,
                       itemidptr->alignedlen);
                i++;
            } while (i < nitems);
 
            /* Set things up for the compactification code below */
            i = 0;
            itemidptr = &itemidbase[0];
            upper = phdr->pd_special;
        }
        else
        {
            upper = phdr->pd_special;
 
            /*
             * Many tuples are likely to already be in the correct location.
             * There's no need to copy these into the temp buffer.  Instead
             * we'll just skip forward in the itemidbase array to the position
             * that we do need to move tuples from so that the code below just
             * leaves these ones alone.
             */
            i = 0;
            do
            {
                itemidptr = &itemidbase[i];
                if (upper != itemidptr->itemoff + itemidptr->alignedlen)
                    break;
                upper -= itemidptr->alignedlen;
 
                i++;
            } while (i < nitems);
 
            /* Copy all tuples that need to be moved into the temp buffer */
            memcpy(scratchptr + phdr->pd_upper,
                   page + phdr->pd_upper,
                   upper - phdr->pd_upper);
        }
 
        /*
         * Do the tuple compactification.  itemidptr is already pointing to
         * the first tuple that we're going to move.  Here we collapse the
         * memcpy calls for adjacent tuples into a single call.  This is done
         * by delaying the memcpy call until we find a gap that needs to be
         * closed.
         */
        copy_tail = copy_head = itemidptr->itemoff + itemidptr->alignedlen;
        for (; i < nitems; i++)
        {
            ItemId      lp;
 
            itemidptr = &itemidbase[i];
            lp = PageGetItemId(page, itemidptr->offsetindex + 1);
 
            /* copy pending tuples when we detect a gap */
            if (copy_head != itemidptr->itemoff + itemidptr->alignedlen)
            {
                memcpy((char *) page + upper,
                       scratchptr + copy_head,
                       copy_tail - copy_head);
 
                /*
                 * We've now copied all tuples already seen, but not the
                 * current tuple, so we set the copy_tail to the end of this
                 * tuple.
                 */
                copy_tail = itemidptr->itemoff + itemidptr->alignedlen;
            }
            /* shift the target offset down by the length of this tuple */
            upper -= itemidptr->alignedlen;
            /* point the copy_head to the start of this tuple */
            copy_head = itemidptr->itemoff;
 
            /* update the line pointer to reference the new offset */
            lp->lp_off = upper;
        }
 
        /* Copy the remaining chunk */
        memcpy((char *) page + upper,
               scratchptr + copy_head,
               copy_tail - copy_head);
    }
 
    phdr->pd_upper = upper;
}
 
/*
 * PageRepairFragmentation
 *
 * Frees fragmented space on a heap page following pruning.
 *
 * This routine is usable for heap pages only, but see PageIndexMultiDelete.
 *
 * This routine removes unused line pointers from the end of the line pointer
 * array.  This is possible when dead heap-only tuples get removed by pruning,
 * especially when there were HOT chains with several tuples each beforehand.
 *
 * Caller had better have a full cleanup lock on page's buffer.  As a side
 * effect the page's PD_HAS_FREE_LINES hint bit will be set or unset as
 * needed.  Caller might also need to account for a reduction in the length of
 * the line pointer array following array truncation.
 */
void
PageRepairFragmentation(Page page)
{
    Offset      pd_lower = ((PageHeader) page)->pd_lower;
    Offset      pd_upper = ((PageHeader) page)->pd_upper;
    Offset      pd_special = ((PageHeader) page)->pd_special;
    Offset      last_offset;
    itemIdCompactData itemidbase[MaxHeapTuplesPerPage];
    itemIdCompact itemidptr;
    ItemId      lp;
    int         nline,
                nstorage,
                nunused;
    OffsetNumber finalusedlp = InvalidOffsetNumber;
    int         i;
    Size        totallen;
    bool        presorted = true;   /* For now */
 
    /*
     * It's worth the trouble to be more paranoid here than in most places,
     * because we are about to reshuffle data in (what is usually) a shared
     * disk buffer.  If we aren't careful then corrupted pointers, lengths,
     * etc could cause us to clobber adjacent disk buffers, spreading the data
     * loss further.  So, check everything.
     */
    if (pd_lower < SizeOfPageHeaderData ||
        pd_lower > pd_upper ||
        pd_upper > pd_special ||
        pd_special > BLCKSZ ||
        pd_special != MAXALIGN(pd_special))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted page pointers: lower = %u, upper = %u, special = %u",
                        pd_lower, pd_upper, pd_special)));
 
    /*
     * Run through the line pointer array and collect data about live items.
     */
    nline = PageGetMaxOffsetNumber(page);
    itemidptr = itemidbase;
    nunused = totallen = 0;
    last_offset = pd_special;
    for (i = FirstOffsetNumber; i <= nline; i++)
    {
        lp = PageGetItemId(page, i);
        if (ItemIdIsUsed(lp))
        {
            if (ItemIdHasStorage(lp))
            {
                itemidptr->offsetindex = i - 1;
                itemidptr->itemoff = ItemIdGetOffset(lp);
 
                if (last_offset > itemidptr->itemoff)
                    last_offset = itemidptr->itemoff;
                else
                    presorted = false;
 
                if (unlikely(itemidptr->itemoff < (int) pd_upper ||
                             itemidptr->itemoff >= (int) pd_special))
                    ereport(ERROR,
                            (errcode(ERRCODE_DATA_CORRUPTED),
                             errmsg("corrupted line pointer: %u",
                                    itemidptr->itemoff)));
                itemidptr->alignedlen = MAXALIGN(ItemIdGetLength(lp));
                totallen += itemidptr->alignedlen;
                itemidptr++;
            }
 
            finalusedlp = i;    /* Could be the final non-LP_UNUSED item */
        }
        else
        {
            /* Unused entries should have lp_len = 0, but make sure */
            Assert(!ItemIdHasStorage(lp));
            ItemIdSetUnused(lp);
            nunused++;
        }
    }
 
    nstorage = itemidptr - itemidbase;
    if (nstorage == 0)
    {
        /* Page is completely empty, so just reset it quickly */
        ((PageHeader) page)->pd_upper = pd_special;
    }
    else
    {
        /* Need to compact the page the hard way */
        if (totallen > (Size) (pd_special - pd_lower))
            ereport(ERROR,
                    (errcode(ERRCODE_DATA_CORRUPTED),
                     errmsg("corrupted item lengths: total %u, available space %u",
                            (unsigned int) totallen, pd_special - pd_lower)));
 
        compactify_tuples(itemidbase, nstorage, page, presorted);
    }
 
    if (finalusedlp != nline)
    {
        /* The last line pointer is not the last used line pointer */
        int         nunusedend = nline - finalusedlp;
 
        Assert(nunused >= nunusedend && nunusedend > 0);
 
        /* remove trailing unused line pointers from the count */
        nunused -= nunusedend;
        /* truncate the line pointer array */
        ((PageHeader) page)->pd_lower -= (sizeof(ItemIdData) * nunusedend);
    }
 
    /* Set hint bit for PageAddItemExtended */
    if (nunused > 0)
        PageSetHasFreeLinePointers(page);
    else
        PageClearHasFreeLinePointers(page);
}
 
/*
 * PageTruncateLinePointerArray
 *
 * Removes unused line pointers at the end of the line pointer array.
 *
 * This routine is usable for heap pages only.  It is called by VACUUM during
 * its second pass over the heap.  We expect at least one LP_UNUSED line
 * pointer on the page (if VACUUM didn't have an LP_DEAD item on the page that
 * it just set to LP_UNUSED then it should not call here).
 *
 * We avoid truncating the line pointer array to 0 items, if necessary by
 * leaving behind a single remaining LP_UNUSED item.  This is a little
 * arbitrary, but it seems like a good idea to avoid leaving a PageIsEmpty()
 * page behind.
 *
 * Caller can have either an exclusive lock or a full cleanup lock on page's
 * buffer.  The page's PD_HAS_FREE_LINES hint bit will be set or unset based
 * on whether or not we leave behind any remaining LP_UNUSED items.
 */
void
PageTruncateLinePointerArray(Page page)
{
    PageHeader  phdr = (PageHeader) page;
    bool        countdone = false,
                sethint = false;
    int         nunusedend = 0;
 
    /* Scan line pointer array back-to-front */
    for (int i = PageGetMaxOffsetNumber(page); i >= FirstOffsetNumber; i--)
    {
        ItemId      lp = PageGetItemId(page, i);
 
        if (!countdone && i > FirstOffsetNumber)
        {
            /*
             * Still determining which line pointers from the end of the array
             * will be truncated away.  Either count another line pointer as
             * safe to truncate, or notice that it's not safe to truncate
             * additional line pointers (stop counting line pointers).
             */
            if (!ItemIdIsUsed(lp))
                nunusedend++;
            else
                countdone = true;
        }
        else
        {
            /*
             * Once we've stopped counting we still need to figure out if
             * there are any remaining LP_UNUSED line pointers somewhere more
             * towards the front of the array.
             */
            if (!ItemIdIsUsed(lp))
            {
                /*
                 * This is an unused line pointer that we won't be truncating
                 * away -- so there is at least one.  Set hint on page.
                 */
                sethint = true;
                break;
            }
        }
    }
 
    if (nunusedend > 0)
    {
        phdr->pd_lower -= sizeof(ItemIdData) * nunusedend;
 
#ifdef CLOBBER_FREED_MEMORY
        memset((char *) page + phdr->pd_lower, 0x7F,
               sizeof(ItemIdData) * nunusedend);
#endif
    }
    else
        Assert(sethint);
 
    /* Set hint bit for PageAddItemExtended */
    if (sethint)
        PageSetHasFreeLinePointers(page);
    else
        PageClearHasFreeLinePointers(page);
}
 
/*
 * PageGetFreeSpace
 *      Returns the size of the free (allocatable) space on a page,
 *      reduced by the space needed for a new line pointer.
 *
 * Note: this should usually only be used on index pages.  Use
 * PageGetHeapFreeSpace on heap pages.
 */
Size
PageGetFreeSpace(Page page)
{
    int         space;
 
    /*
     * Use signed arithmetic here so that we behave sensibly if pd_lower >
     * pd_upper.
     */
    space = (int) ((PageHeader) page)->pd_upper -
        (int) ((PageHeader) page)->pd_lower;
 
    if (space < (int) sizeof(ItemIdData))
        return 0;
    space -= sizeof(ItemIdData);
 
    return (Size) space;
}
 
/*
 * PageGetFreeSpaceForMultipleTuples
 *      Returns the size of the free (allocatable) space on a page,
 *      reduced by the space needed for multiple new line pointers.
 *
 * Note: this should usually only be used on index pages.  Use
 * PageGetHeapFreeSpace on heap pages.
 */
Size
PageGetFreeSpaceForMultipleTuples(Page page, int ntups)
{
    int         space;
 
    /*
     * Use signed arithmetic here so that we behave sensibly if pd_lower >
     * pd_upper.
     */
    space = (int) ((PageHeader) page)->pd_upper -
        (int) ((PageHeader) page)->pd_lower;
 
    if (space < (int) (ntups * sizeof(ItemIdData)))
        return 0;
    space -= ntups * sizeof(ItemIdData);
 
    return (Size) space;
}
 
/*
 * PageGetExactFreeSpace
 *      Returns the size of the free (allocatable) space on a page,
 *      without any consideration for adding/removing line pointers.
 */
Size
PageGetExactFreeSpace(Page page)
{
    int         space;
 
    /*
     * Use signed arithmetic here so that we behave sensibly if pd_lower >
     * pd_upper.
     */
    space = (int) ((PageHeader) page)->pd_upper -
        (int) ((PageHeader) page)->pd_lower;
 
    if (space < 0)
        return 0;
 
    return (Size) space;
}
 
 
/*
 * PageGetHeapFreeSpace
 *      Returns the size of the free (allocatable) space on a page,
 *      reduced by the space needed for a new line pointer.
 *
 * The difference between this and PageGetFreeSpace is that this will return
 * zero if there are already MaxHeapTuplesPerPage line pointers in the page
 * and none are free.  We use this to enforce that no more than
 * MaxHeapTuplesPerPage line pointers are created on a heap page.  (Although
 * no more tuples than that could fit anyway, in the presence of redirected
 * or dead line pointers it'd be possible to have too many line pointers.
 * To avoid breaking code that assumes MaxHeapTuplesPerPage is a hard limit
 * on the number of line pointers, we make this extra check.)
 */
Size
PageGetHeapFreeSpace(Page page)
{
    Size        space;
 
    space = PageGetFreeSpace(page);
    if (space > 0)
    {
        OffsetNumber offnum,
                    nline;
 
        /*
         * Are there already MaxHeapTuplesPerPage line pointers in the page?
         */
        nline = PageGetMaxOffsetNumber(page);
        if (nline >= MaxHeapTuplesPerPage)
        {
            if (PageHasFreeLinePointers(page))
            {
                /*
                 * Since this is just a hint, we must confirm that there is
                 * indeed a free line pointer
                 */
                for (offnum = FirstOffsetNumber; offnum <= nline; offnum = OffsetNumberNext(offnum))
                {
                    ItemId      lp = PageGetItemId(page, offnum);
 
                    if (!ItemIdIsUsed(lp))
                        break;
                }
 
                if (offnum > nline)
                {
                    /*
                     * The hint is wrong, but we can't clear it here since we
                     * don't have the ability to mark the page dirty.
                     */
                    space = 0;
                }
            }
            else
            {
                /*
                 * Although the hint might be wrong, PageAddItem will believe
                 * it anyway, so we must believe it too.
                 */
                space = 0;
            }
        }
    }
    return space;
}
 
 
/*
 * PageIndexTupleDelete
 *
 * This routine does the work of removing a tuple from an index page.
 *
 * Unlike heap pages, we compact out the line pointer for the removed tuple.
 */
void
PageIndexTupleDelete(Page page, OffsetNumber offnum)
{
    PageHeader  phdr = (PageHeader) page;
    char       *addr;
    ItemId      tup;
    Size        size;
    unsigned    offset;
    int         nbytes;
    int         offidx;
    int         nline;
 
    /*
     * As with PageRepairFragmentation, paranoia seems justified.
     */
    if (phdr->pd_lower < SizeOfPageHeaderData ||
        phdr->pd_lower > phdr->pd_upper ||
        phdr->pd_upper > phdr->pd_special ||
        phdr->pd_special > BLCKSZ ||
        phdr->pd_special != MAXALIGN(phdr->pd_special))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted page pointers: lower = %u, upper = %u, special = %u",
                        phdr->pd_lower, phdr->pd_upper, phdr->pd_special)));
 
    nline = PageGetMaxOffsetNumber(page);
    if ((int) offnum <= 0 || (int) offnum > nline)
        elog(ERROR, "invalid index offnum: %u", offnum);
 
    /* change offset number to offset index */
    offidx = offnum - 1;
 
    tup = PageGetItemId(page, offnum);
    Assert(ItemIdHasStorage(tup));
    size = ItemIdGetLength(tup);
    offset = ItemIdGetOffset(tup);
 
    if (offset < phdr->pd_upper || (offset + size) > phdr->pd_special ||
        offset != MAXALIGN(offset))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted line pointer: offset = %u, size = %u",
                        offset, (unsigned int) size)));
 
    /* Amount of space to actually be deleted */
    size = MAXALIGN(size);
 
    /*
     * First, we want to get rid of the pd_linp entry for the index tuple. We
     * copy all subsequent linp's back one slot in the array. We don't use
     * PageGetItemId, because we are manipulating the _array_, not individual
     * linp's.
     */
    nbytes = phdr->pd_lower -
        ((char *) &phdr->pd_linp[offidx + 1] - (char *) phdr);
 
    if (nbytes > 0)
        memmove((char *) &(phdr->pd_linp[offidx]),
                (char *) &(phdr->pd_linp[offidx + 1]),
                nbytes);
 
    /*
     * Now move everything between the old upper bound (beginning of tuple
     * space) and the beginning of the deleted tuple forward, so that space in
     * the middle of the page is left free.  If we've just deleted the tuple
     * at the beginning of tuple space, then there's no need to do the copy.
     */
 
    /* beginning of tuple space */
    addr = (char *) page + phdr->pd_upper;
 
    if (offset > phdr->pd_upper)
        memmove(addr + size, addr, offset - phdr->pd_upper);
 
    /* adjust free space boundary pointers */
    phdr->pd_upper += size;
    phdr->pd_lower -= sizeof(ItemIdData);
 
    /*
     * Finally, we need to adjust the linp entries that remain.
     *
     * Anything that used to be before the deleted tuple's data was moved
     * forward by the size of the deleted tuple.
     */
    if (!PageIsEmpty(page))
    {
        int         i;
 
        nline--;                /* there's one less than when we started */
        for (i = 1; i <= nline; i++)
        {
            ItemId      ii = PageGetItemId(page, i);
 
            Assert(ItemIdHasStorage(ii));
            if (ItemIdGetOffset(ii) <= offset)
                ii->lp_off += size;
        }
    }
}
 
 
/*
 * PageIndexMultiDelete
 *
 * This routine handles the case of deleting multiple tuples from an
 * index page at once.  It is considerably faster than a loop around
 * PageIndexTupleDelete ... however, the caller *must* supply the array
 * of item numbers to be deleted in item number order!
 */
void
PageIndexMultiDelete(Page page, OffsetNumber *itemnos, int nitems)
{
    PageHeader  phdr = (PageHeader) page;
    Offset      pd_lower = phdr->pd_lower;
    Offset      pd_upper = phdr->pd_upper;
    Offset      pd_special = phdr->pd_special;
    Offset      last_offset;
    itemIdCompactData itemidbase[MaxIndexTuplesPerPage];
    ItemIdData  newitemids[MaxIndexTuplesPerPage];
    itemIdCompact itemidptr;
    ItemId      lp;
    int         nline,
                nused;
    Size        totallen;
    Size        size;
    unsigned    offset;
    int         nextitm;
    OffsetNumber offnum;
    bool        presorted = true;   /* For now */
 
    Assert(nitems <= MaxIndexTuplesPerPage);
 
    /*
     * If there aren't very many items to delete, then retail
     * PageIndexTupleDelete is the best way.  Delete the items in reverse
     * order so we don't have to think about adjusting item numbers for
     * previous deletions.
     *
     * TODO: tune the magic number here
     */
    if (nitems <= 2)
    {
        while (--nitems >= 0)
            PageIndexTupleDelete(page, itemnos[nitems]);
        return;
    }
 
    /*
     * As with PageRepairFragmentation, paranoia seems justified.
     */
    if (pd_lower < SizeOfPageHeaderData ||
        pd_lower > pd_upper ||
        pd_upper > pd_special ||
        pd_special > BLCKSZ ||
        pd_special != MAXALIGN(pd_special))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted page pointers: lower = %u, upper = %u, special = %u",
                        pd_lower, pd_upper, pd_special)));
 
    /*
     * Scan the line pointer array and build a list of just the ones we are
     * going to keep.  Notice we do not modify the page yet, since we are
     * still validity-checking.
     */
    nline = PageGetMaxOffsetNumber(page);
    itemidptr = itemidbase;
    totallen = 0;
    nused = 0;
    nextitm = 0;
    last_offset = pd_special;
    for (offnum = FirstOffsetNumber; offnum <= nline; offnum = OffsetNumberNext(offnum))
    {
        lp = PageGetItemId(page, offnum);
        Assert(ItemIdHasStorage(lp));
        size = ItemIdGetLength(lp);
        offset = ItemIdGetOffset(lp);
        if (offset < pd_upper ||
            (offset + size) > pd_special ||
            offset != MAXALIGN(offset))
            ereport(ERROR,
                    (errcode(ERRCODE_DATA_CORRUPTED),
                     errmsg("corrupted line pointer: offset = %u, size = %u",
                            offset, (unsigned int) size)));
 
        if (nextitm < nitems && offnum == itemnos[nextitm])
        {
            /* skip item to be deleted */
            nextitm++;
        }
        else
        {
            itemidptr->offsetindex = nused; /* where it will go */
            itemidptr->itemoff = offset;
 
            if (last_offset > itemidptr->itemoff)
                last_offset = itemidptr->itemoff;
            else
                presorted = false;
 
            itemidptr->alignedlen = MAXALIGN(size);
            totallen += itemidptr->alignedlen;
            newitemids[nused] = *lp;
            itemidptr++;
            nused++;
        }
    }
 
    /* this will catch invalid or out-of-order itemnos[] */
    if (nextitm != nitems)
        elog(ERROR, "incorrect index offsets supplied");
 
    if (totallen > (Size) (pd_special - pd_lower))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted item lengths: total %u, available space %u",
                        (unsigned int) totallen, pd_special - pd_lower)));
 
    /*
     * Looks good. Overwrite the line pointers with the copy, from which we've
     * removed all the unused items.
     */
    memcpy(phdr->pd_linp, newitemids, nused * sizeof(ItemIdData));
    phdr->pd_lower = SizeOfPageHeaderData + nused * sizeof(ItemIdData);
 
    /* and compactify the tuple data */
    if (nused > 0)
        compactify_tuples(itemidbase, nused, page, presorted);
    else
        phdr->pd_upper = pd_special;
}
 
 
/*
 * PageIndexTupleDeleteNoCompact
 *
 * Remove the specified tuple from an index page, but set its line pointer
 * to "unused" instead of compacting it out, except that it can be removed
 * if it's the last line pointer on the page.
 *
 * This is used for index AMs that require that existing TIDs of live tuples
 * remain unchanged, and are willing to allow unused line pointers instead.
 */
void
PageIndexTupleDeleteNoCompact(Page page, OffsetNumber offnum)
{
    PageHeader  phdr = (PageHeader) page;
    char       *addr;
    ItemId      tup;
    Size        size;
    unsigned    offset;
    int         nline;
 
    /*
     * As with PageRepairFragmentation, paranoia seems justified.
     */
    if (phdr->pd_lower < SizeOfPageHeaderData ||
        phdr->pd_lower > phdr->pd_upper ||
        phdr->pd_upper > phdr->pd_special ||
        phdr->pd_special > BLCKSZ ||
        phdr->pd_special != MAXALIGN(phdr->pd_special))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted page pointers: lower = %u, upper = %u, special = %u",
                        phdr->pd_lower, phdr->pd_upper, phdr->pd_special)));
 
    nline = PageGetMaxOffsetNumber(page);
    if ((int) offnum <= 0 || (int) offnum > nline)
        elog(ERROR, "invalid index offnum: %u", offnum);
 
    tup = PageGetItemId(page, offnum);
    Assert(ItemIdHasStorage(tup));
    size = ItemIdGetLength(tup);
    offset = ItemIdGetOffset(tup);
 
    if (offset < phdr->pd_upper || (offset + size) > phdr->pd_special ||
        offset != MAXALIGN(offset))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted line pointer: offset = %u, size = %u",
                        offset, (unsigned int) size)));
 
    /* Amount of space to actually be deleted */
    size = MAXALIGN(size);
 
    /*
     * Either set the line pointer to "unused", or zap it if it's the last
     * one.  (Note: it's possible that the next-to-last one(s) are already
     * unused, but we do not trouble to try to compact them out if so.)
     */
    if ((int) offnum < nline)
        ItemIdSetUnused(tup);
    else
    {
        phdr->pd_lower -= sizeof(ItemIdData);
        nline--;                /* there's one less than when we started */
    }
 
    /*
     * Now move everything between the old upper bound (beginning of tuple
     * space) and the beginning of the deleted tuple forward, so that space in
     * the middle of the page is left free.  If we've just deleted the tuple
     * at the beginning of tuple space, then there's no need to do the copy.
     */
 
    /* beginning of tuple space */
    addr = (char *) page + phdr->pd_upper;
 
    if (offset > phdr->pd_upper)
        memmove(addr + size, addr, offset - phdr->pd_upper);
 
    /* adjust free space boundary pointer */
    phdr->pd_upper += size;
 
    /*
     * Finally, we need to adjust the linp entries that remain.
     *
     * Anything that used to be before the deleted tuple's data was moved
     * forward by the size of the deleted tuple.
     */
    if (!PageIsEmpty(page))
    {
        int         i;
 
        for (i = 1; i <= nline; i++)
        {
            ItemId      ii = PageGetItemId(page, i);
 
            if (ItemIdHasStorage(ii) && ItemIdGetOffset(ii) <= offset)
                ii->lp_off += size;
        }
    }
}
 
 
/*
 * PageIndexTupleOverwrite
 *
 * Replace a specified tuple on an index page.
 *
 * The new tuple is placed exactly where the old one had been, shifting
 * other tuples' data up or down as needed to keep the page compacted.
 * This is better than deleting and reinserting the tuple, because it
 * avoids any data shifting when the tuple size doesn't change; and
 * even when it does, we avoid moving the line pointers around.
 * This could be used by an index AM that doesn't want to unset the
 * LP_DEAD bit when it happens to be set.  It could conceivably also be
 * used by an index AM that cares about the physical order of tuples as
 * well as their logical/ItemId order.
 *
 * If there's insufficient space for the new tuple, return false.  Other
 * errors represent data-corruption problems, so we just elog.
 */
bool
PageIndexTupleOverwrite(Page page, OffsetNumber offnum,
                        Item newtup, Size newsize)
{
    PageHeader  phdr = (PageHeader) page;
    ItemId      tupid;
    int         oldsize;
    unsigned    offset;
    Size        alignednewsize;
    int         size_diff;
    int         itemcount;
 
    /*
     * As with PageRepairFragmentation, paranoia seems justified.
     */
    if (phdr->pd_lower < SizeOfPageHeaderData ||
        phdr->pd_lower > phdr->pd_upper ||
        phdr->pd_upper > phdr->pd_special ||
        phdr->pd_special > BLCKSZ ||
        phdr->pd_special != MAXALIGN(phdr->pd_special))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted page pointers: lower = %u, upper = %u, special = %u",
                        phdr->pd_lower, phdr->pd_upper, phdr->pd_special)));
 
    itemcount = PageGetMaxOffsetNumber(page);
    if ((int) offnum <= 0 || (int) offnum > itemcount)
        elog(ERROR, "invalid index offnum: %u", offnum);
 
    tupid = PageGetItemId(page, offnum);
    Assert(ItemIdHasStorage(tupid));
    oldsize = ItemIdGetLength(tupid);
    offset = ItemIdGetOffset(tupid);
 
    if (offset < phdr->pd_upper || (offset + oldsize) > phdr->pd_special ||
        offset != MAXALIGN(offset))
        ereport(ERROR,
                (errcode(ERRCODE_DATA_CORRUPTED),
                 errmsg("corrupted line pointer: offset = %u, size = %u",
                        offset, (unsigned int) oldsize)));
 
    /*
     * Determine actual change in space requirement, check for page overflow.
     */
    oldsize = MAXALIGN(oldsize);
    alignednewsize = MAXALIGN(newsize);
    if (alignednewsize > oldsize + (phdr->pd_upper - phdr->pd_lower))
        return false;
 
    /*
     * Relocate existing data and update line pointers, unless the new tuple
     * is the same size as the old (after alignment), in which case there's
     * nothing to do.  Notice that what we have to relocate is data before the
     * target tuple, not data after, so it's convenient to express size_diff
     * as the amount by which the tuple's size is decreasing, making it the
     * delta to add to pd_upper and affected line pointers.
     */
    size_diff = oldsize - (int) alignednewsize;
    if (size_diff != 0)
    {
        char       *addr = (char *) page + phdr->pd_upper;
        int         i;
 
        /* relocate all tuple data before the target tuple */
        memmove(addr + size_diff, addr, offset - phdr->pd_upper);
 
        /* adjust free space boundary pointer */
        phdr->pd_upper += size_diff;
 
        /* adjust affected line pointers too */
        for (i = FirstOffsetNumber; i <= itemcount; i++)
        {
            ItemId      ii = PageGetItemId(page, i);
 
            /* Allow items without storage; currently only BRIN needs that */
            if (ItemIdHasStorage(ii) && ItemIdGetOffset(ii) <= offset)
                ii->lp_off += size_diff;
        }
    }
 
    /* Update the item's tuple length without changing its lp_flags field */
    tupid->lp_off = offset + size_diff;
    tupid->lp_len = newsize;
 
    /* Copy new tuple data onto page */
    memcpy(PageGetItem(page, tupid), newtup, newsize);
 
    return true;
}
 
 
/*
 * Set checksum for a page in shared buffers.
 *
 * If checksums are disabled, or if the page is not initialized, just return
 * the input.  Otherwise, we must make a copy of the page before calculating
 * the checksum, to prevent concurrent modifications (e.g. setting hint bits)
 * from making the final checksum invalid.  It doesn't matter if we include or
 * exclude hints during the copy, as long as we write a valid page and
 * associated checksum.
 *
 * Returns a pointer to the block-sized data that needs to be written. Uses
 * statically-allocated memory, so the caller must immediately write the
 * returned page and not refer to it again.
 */
char *
PageSetChecksumCopy(Page page, BlockNumber blkno)
{
    static char *pageCopy = NULL;
 
    /* If we don't need a checksum, just return the passed-in data */
    if (PageIsNew(page) || !DataChecksumsEnabled())
        return (char *) page;
 
    /*
     * We allocate the copy space once and use it over on each subsequent
     * call.  The point of palloc'ing here, rather than having a static char
     * array, is first to ensure adequate alignment for the checksumming code
     * and second to avoid wasting space in processes that never call this.
     */
    if (pageCopy == NULL)
        pageCopy = MemoryContextAllocAligned(TopMemoryContext,
                                             BLCKSZ,
                                             PG_IO_ALIGN_SIZE,
                                             0);
 
    memcpy(pageCopy, (char *) page, BLCKSZ);
    ((PageHeader) pageCopy)->pd_checksum = pg_checksum_page(pageCopy, blkno);
    return pageCopy;
}
 
/*
 * Set checksum for a page in private memory.
 *
 * This must only be used when we know that no other process can be modifying
 * the page buffer.
 */
void
PageSetChecksumInplace(Page page, BlockNumber blkno)
{
    /* If we don't need a checksum, just return */
    if (PageIsNew(page) || !DataChecksumsEnabled())
        return;
 
    ((PageHeader) page)->pd_checksum = pg_checksum_page((char *) page, blkno);
}