Update CVS HEAD for 2007 copyright. Back branches are typically not

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

/*-------------------------------------------------------------------------
 *
 * nbtsearch.c
 *        Search code for postgres btrees.
 *
 *
 * Portions Copyright (c) 1996-2007, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *        $PostgreSQL: pgsql/src/backend/access/nbtree/nbtsearch.c,v 1.110 2007/01/05 22:19:23 momjian Exp $
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"

#include "access/genam.h"
#include "access/nbtree.h"
#include "pgstat.h"
#include "utils/lsyscache.h"


static bool _bt_readpage(IndexScanDesc scan, ScanDirection dir,
                         OffsetNumber offnum);
static bool _bt_steppage(IndexScanDesc scan, ScanDirection dir);
static Buffer _bt_walk_left(Relation rel, Buffer buf);
static bool _bt_endpoint(IndexScanDesc scan, ScanDirection dir);


/*
 *      _bt_search() -- Search the tree for a particular scankey,
 *              or more precisely for the first leaf page it could be on.
 *
 * The passed scankey must be an insertion-type scankey (see nbtree/README),
 * but it can omit the rightmost column(s) of the index.
 *
 * When nextkey is false (the usual case), we are looking for the first
 * item >= scankey.  When nextkey is true, we are looking for the first
 * item strictly greater than scankey.
 *
 * Return value is a stack of parent-page pointers.  *bufP is set to the
 * address of the leaf-page buffer, which is read-locked and pinned.
 * No locks are held on the parent pages, however!
 *
 * NOTE that the returned buffer is read-locked regardless of the access
 * parameter.  However, access = BT_WRITE will allow an empty root page
 * to be created and returned.  When access = BT_READ, an empty index
 * will result in *bufP being set to InvalidBuffer.
 */
BTStack
_bt_search(Relation rel, int keysz, ScanKey scankey, bool nextkey,
                   Buffer *bufP, int access)
{
        BTStack         stack_in = NULL;

        /* Get the root page to start with */
        *bufP = _bt_getroot(rel, access);

        /* If index is empty and access = BT_READ, no root page is created. */
        if (!BufferIsValid(*bufP))
                return (BTStack) NULL;

        /* Loop iterates once per level descended in the tree */
        for (;;)
        {
                Page            page;
                BTPageOpaque opaque;
                OffsetNumber offnum;
                ItemId          itemid;
                IndexTuple      itup;
                BlockNumber blkno;
                BlockNumber par_blkno;
                BTStack         new_stack;

                /*
                 * Race -- the page we just grabbed may have split since we read its
                 * pointer in the parent (or metapage).  If it has, we may need to
                 * move right to its new sibling.  Do that.
                 */
                *bufP = _bt_moveright(rel, *bufP, keysz, scankey, nextkey, BT_READ);

                /* if this is a leaf page, we're done */
                page = BufferGetPage(*bufP);
                opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                if (P_ISLEAF(opaque))
                        break;

                /*
                 * Find the appropriate item on the internal page, and get the child
                 * page that it points to.
                 */
                offnum = _bt_binsrch(rel, *bufP, keysz, scankey, nextkey);
                itemid = PageGetItemId(page, offnum);
                itup = (IndexTuple) PageGetItem(page, itemid);
                blkno = ItemPointerGetBlockNumber(&(itup->t_tid));
                par_blkno = BufferGetBlockNumber(*bufP);

                /*
                 * We need to save the location of the index entry we chose in the
                 * parent page on a stack. In case we split the tree, we'll use the
                 * stack to work back up to the parent page.  We also save the actual
                 * downlink (TID) to uniquely identify the index entry, in case it
                 * moves right while we're working lower in the tree.  See the paper
                 * by Lehman and Yao for how this is detected and handled. (We use the
                 * child link to disambiguate duplicate keys in the index -- Lehman
                 * and Yao disallow duplicate keys.)
                 */
                new_stack = (BTStack) palloc(sizeof(BTStackData));
                new_stack->bts_blkno = par_blkno;
                new_stack->bts_offset = offnum;
                memcpy(&new_stack->bts_btentry, itup, sizeof(IndexTupleData));
                new_stack->bts_parent = stack_in;

                /* drop the read lock on the parent page, acquire one on the child */
                *bufP = _bt_relandgetbuf(rel, *bufP, blkno, BT_READ);

                /* okay, all set to move down a level */
                stack_in = new_stack;
        }

        return stack_in;
}

/*
 *      _bt_moveright() -- move right in the btree if necessary.
 *
 * When we follow a pointer to reach a page, it is possible that
 * the page has changed in the meanwhile.  If this happens, we're
 * guaranteed that the page has "split right" -- that is, that any
 * data that appeared on the page originally is either on the page
 * or strictly to the right of it.
 *
 * This routine decides whether or not we need to move right in the
 * tree by examining the high key entry on the page.  If that entry
 * is strictly less than the scankey, or <= the scankey in the nextkey=true
 * case, then we followed the wrong link and we need to move right.
 *
 * The passed scankey must be an insertion-type scankey (see nbtree/README),
 * but it can omit the rightmost column(s) of the index.
 *
 * When nextkey is false (the usual case), we are looking for the first
 * item >= scankey.  When nextkey is true, we are looking for the first
 * item strictly greater than scankey.
 *
 * On entry, we have the buffer pinned and a lock of the type specified by
 * 'access'.  If we move right, we release the buffer and lock and acquire
 * the same on the right sibling.  Return value is the buffer we stop at.
 */
Buffer
_bt_moveright(Relation rel,
                          Buffer buf,
                          int keysz,
                          ScanKey scankey,
                          bool nextkey,
                          int access)
{
        Page            page;
        BTPageOpaque opaque;
        int32           cmpval;

        page = BufferGetPage(buf);
        opaque = (BTPageOpaque) PageGetSpecialPointer(page);

        /*
         * When nextkey = false (normal case): if the scan key that brought us to
         * this page is > the high key stored on the page, then the page has split
         * and we need to move right.  (If the scan key is equal to the high key,
         * we might or might not need to move right; have to scan the page first
         * anyway.)
         *
         * When nextkey = true: move right if the scan key is >= page's high key.
         *
         * The page could even have split more than once, so scan as far as
         * needed.
         *
         * We also have to move right if we followed a link that brought us to a
         * dead page.
         */
        cmpval = nextkey ? 0 : 1;

        while (!P_RIGHTMOST(opaque) &&
                   (P_IGNORE(opaque) ||
                        _bt_compare(rel, keysz, scankey, page, P_HIKEY) >= cmpval))
        {
                /* step right one page */
                BlockNumber rblkno = opaque->btpo_next;

                buf = _bt_relandgetbuf(rel, buf, rblkno, access);
                page = BufferGetPage(buf);
                opaque = (BTPageOpaque) PageGetSpecialPointer(page);
        }

        if (P_IGNORE(opaque))
                elog(ERROR, "fell off the end of \"%s\"",
                         RelationGetRelationName(rel));

        return buf;
}

/*
 *      _bt_binsrch() -- Do a binary search for a key on a particular page.
 *
 * The passed scankey must be an insertion-type scankey (see nbtree/README),
 * but it can omit the rightmost column(s) of the index.
 *
 * When nextkey is false (the usual case), we are looking for the first
 * item >= scankey.  When nextkey is true, we are looking for the first
 * item strictly greater than scankey.
 *
 * On a leaf page, _bt_binsrch() returns the OffsetNumber of the first
 * key >= given scankey, or > scankey if nextkey is true.  (NOTE: in
 * particular, this means it is possible to return a value 1 greater than the
 * number of keys on the page, if the scankey is > all keys on the page.)
 *
 * On an internal (non-leaf) page, _bt_binsrch() returns the OffsetNumber
 * of the last key < given scankey, or last key <= given scankey if nextkey
 * is true.  (Since _bt_compare treats the first data key of such a page as
 * minus infinity, there will be at least one key < scankey, so the result
 * always points at one of the keys on the page.)  This key indicates the
 * right place to descend to be sure we find all leaf keys >= given scankey
 * (or leaf keys > given scankey when nextkey is true).
 *
 * This procedure is not responsible for walking right, it just examines
 * the given page.      _bt_binsrch() has no lock or refcount side effects
 * on the buffer.
 */
OffsetNumber
_bt_binsrch(Relation rel,
                        Buffer buf,
                        int keysz,
                        ScanKey scankey,
                        bool nextkey)
{
        Page            page;
        BTPageOpaque opaque;
        OffsetNumber low,
                                high;
        int32           result,
                                cmpval;

        page = BufferGetPage(buf);
        opaque = (BTPageOpaque) PageGetSpecialPointer(page);

        low = P_FIRSTDATAKEY(opaque);
        high = PageGetMaxOffsetNumber(page);

        /*
         * If there are no keys on the page, return the first available slot. Note
         * this covers two cases: the page is really empty (no keys), or it
         * contains only a high key.  The latter case is possible after vacuuming.
         * This can never happen on an internal page, however, since they are
         * never empty (an internal page must have children).
         */
        if (high < low)
                return low;

        /*
         * Binary search to find the first key on the page >= scan key, or first
         * key > scankey when nextkey is true.
         *
         * For nextkey=false (cmpval=1), the loop invariant is: all slots before
         * 'low' are < scan key, all slots at or after 'high' are >= scan key.
         *
         * For nextkey=true (cmpval=0), the loop invariant is: all slots before
         * 'low' are <= scan key, all slots at or after 'high' are > scan key.
         *
         * We can fall out when high == low.
         */
        high++;                                         /* establish the loop invariant for high */

        cmpval = nextkey ? 0 : 1;       /* select comparison value */

        while (high > low)
        {
                OffsetNumber mid = low + ((high - low) / 2);

                /* We have low <= mid < high, so mid points at a real slot */

                result = _bt_compare(rel, keysz, scankey, page, mid);

                if (result >= cmpval)
                        low = mid + 1;
                else
                        high = mid;
        }

        /*
         * At this point we have high == low, but be careful: they could point
         * past the last slot on the page.
         *
         * On a leaf page, we always return the first key >= scan key (resp. >
         * scan key), which could be the last slot + 1.
         */
        if (P_ISLEAF(opaque))
                return low;

        /*
         * On a non-leaf page, return the last key < scan key (resp. <= scan key).
         * There must be one if _bt_compare() is playing by the rules.
         */
        Assert(low > P_FIRSTDATAKEY(opaque));

        return OffsetNumberPrev(low);
}

/*----------
 *      _bt_compare() -- Compare scankey to a particular tuple on the page.
 *
 * The passed scankey must be an insertion-type scankey (see nbtree/README),
 * but it can omit the rightmost column(s) of the index.
 *
 *      keysz: number of key conditions to be checked (might be less than the
 *              number of index columns!)
 *      page/offnum: location of btree item to be compared to.
 *
 *              This routine returns:
 *                      <0 if scankey < tuple at offnum;
 *                       0 if scankey == tuple at offnum;
 *                      >0 if scankey > tuple at offnum.
 *              NULLs in the keys are treated as sortable values.  Therefore
 *              "equality" does not necessarily mean that the item should be
 *              returned to the caller as a matching key!
 *
 * CRUCIAL NOTE: on a non-leaf page, the first data key is assumed to be
 * "minus infinity": this routine will always claim it is less than the
 * scankey.  The actual key value stored (if any, which there probably isn't)
 * does not matter.  This convention allows us to implement the Lehman and
 * Yao convention that the first down-link pointer is before the first key.
 * See backend/access/nbtree/README for details.
 *----------
 */
int32
_bt_compare(Relation rel,
                        int keysz,
                        ScanKey scankey,
                        Page page,
                        OffsetNumber offnum)
{
        TupleDesc       itupdesc = RelationGetDescr(rel);
        BTPageOpaque opaque = (BTPageOpaque) PageGetSpecialPointer(page);
        IndexTuple      itup;
        int                     i;

        /*
         * Force result ">" if target item is first data item on an internal page
         * --- see NOTE above.
         */
        if (!P_ISLEAF(opaque) && offnum == P_FIRSTDATAKEY(opaque))
                return 1;

        itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));

        /*
         * The scan key is set up with the attribute number associated with each
         * term in the key.  It is important that, if the index is multi-key, the
         * scan contain the first k key attributes, and that they be in order.  If
         * you think about how multi-key ordering works, you'll understand why
         * this is.
         *
         * We don't test for violation of this condition here, however.  The
         * initial setup for the index scan had better have gotten it right (see
         * _bt_first).
         */

        for (i = 1; i <= keysz; i++)
        {
                Datum           datum;
                bool            isNull;
                int32           result;

                datum = index_getattr(itup, scankey->sk_attno, itupdesc, &isNull);

                /* see comments about NULLs handling in btbuild */
                if (scankey->sk_flags & SK_ISNULL)              /* key is NULL */
                {
                        if (isNull)
                                result = 0;             /* NULL "=" NULL */
                        else
                                result = 1;             /* NULL ">" NOT_NULL */
                }
                else if (isNull)                /* key is NOT_NULL and item is NULL */
                {
                        result = -1;            /* NOT_NULL "<" NULL */
                }
                else
                {
                        /*
                         * The sk_func needs to be passed the index value as left arg and
                         * the sk_argument as right arg (they might be of different
                         * types).      Since it is convenient for callers to think of
                         * _bt_compare as comparing the scankey to the index item, we have
                         * to flip the sign of the comparison result.
                         *
                         * Note: curious-looking coding is to avoid overflow if comparison
                         * function returns INT_MIN.  There is no risk of overflow for
                         * positive results.
                         */
                        result = DatumGetInt32(FunctionCall2(&scankey->sk_func,
                                                                                                 datum,
                                                                                                 scankey->sk_argument));
                        result = (result < 0) ? 1 : -result;
                }

                /* if the keys are unequal, return the difference */
                if (result != 0)
                        return result;

                scankey++;
        }

        /* if we get here, the keys are equal */
        return 0;
}

/*
 *      _bt_first() -- Find the first item in a scan.
 *
 *              We need to be clever about the direction of scan, the search
 *              conditions, and the tree ordering.      We find the first item (or,
 *              if backwards scan, the last item) in the tree that satisfies the
 *              qualifications in the scan key.  On success exit, the page containing
 *              the current index tuple is pinned but not locked, and data about
 *              the matching tuple(s) on the page has been loaded into so->currPos,
 *              and scan->xs_ctup.t_self is set to the heap TID of the current tuple.
 *
 * If there are no matching items in the index, we return FALSE, with no
 * pins or locks held.
 *
 * Note that scan->keyData[], and the so->keyData[] scankey built from it,
 * are both search-type scankeys (see nbtree/README for more about this).
 * Within this routine, we build a temporary insertion-type scankey to use
 * in locating the scan start position.
 */
bool
_bt_first(IndexScanDesc scan, ScanDirection dir)
{
        Relation        rel = scan->indexRelation;
        BTScanOpaque so = (BTScanOpaque) scan->opaque;
        Buffer          buf;
        BTStack         stack;
        OffsetNumber offnum;
        StrategyNumber strat;
        bool            nextkey;
        bool            goback;
        ScanKey         startKeys[INDEX_MAX_KEYS];
        ScanKeyData scankeys[INDEX_MAX_KEYS];
        int                     keysCount = 0;
        int                     i;
        StrategyNumber strat_total;

        pgstat_count_index_scan(&scan->xs_pgstat_info);

        /*
         * Examine the scan keys and eliminate any redundant keys; also mark the
         * keys that must be matched to continue the scan.
         */
        _bt_preprocess_keys(scan);

        /*
         * Quit now if _bt_preprocess_keys() discovered that the scan keys can
         * never be satisfied (eg, x == 1 AND x > 2).
         */
        if (!so->qual_ok)
                return false;

        /*----------
         * Examine the scan keys to discover where we need to start the scan.
         *
         * We want to identify the keys that can be used as starting boundaries;
         * these are =, >, or >= keys for a forward scan or =, <, <= keys for
         * a backwards scan.  We can use keys for multiple attributes so long as
         * the prior attributes had only =, >= (resp. =, <=) keys.      Once we accept
         * a > or < boundary or find an attribute with no boundary (which can be
         * thought of as the same as "> -infinity"), we can't use keys for any
         * attributes to its right, because it would break our simplistic notion
         * of what initial positioning strategy to use.
         *
         * When the scan keys include cross-type operators, _bt_preprocess_keys
         * may not be able to eliminate redundant keys; in such cases we will
         * arbitrarily pick a usable one for each attribute.  This is correct
         * but possibly not optimal behavior.  (For example, with keys like
         * "x >= 4 AND x >= 5" we would elect to scan starting at x=4 when
         * x=5 would be more efficient.)  Since the situation only arises given
         * a poorly-worded query plus an incomplete opfamily, live with it.
         *
         * When both equality and inequality keys appear for a single attribute
         * (again, only possible when cross-type operators appear), we *must*
         * select one of the equality keys for the starting point, because
         * _bt_checkkeys() will stop the scan as soon as an equality qual fails.
         * For example, if we have keys like "x >= 4 AND x = 10" and we elect to
         * start at x=4, we will fail and stop before reaching x=10.  If multiple
         * equality quals survive preprocessing, however, it doesn't matter which
         * one we use --- by definition, they are either redundant or
         * contradictory.
         *
         * In this loop, row-comparison keys are treated the same as keys on their
         * first (leftmost) columns.  We'll add on lower-order columns of the row
         * comparison below, if possible.
         *
         * The selected scan keys (at most one per index column) are remembered by
         * storing their addresses into the local startKeys[] array.
         *----------
         */
        strat_total = BTEqualStrategyNumber;
        if (so->numberOfKeys > 0)
        {
                AttrNumber      curattr;
                ScanKey         chosen;
                ScanKey         cur;

                /*
                 * chosen is the so-far-chosen key for the current attribute, if any.
                 * We don't cast the decision in stone until we reach keys for the
                 * next attribute.
                 */
                curattr = 1;
                chosen = NULL;

                /*
                 * Loop iterates from 0 to numberOfKeys inclusive; we use the last
                 * pass to handle after-last-key processing.  Actual exit from the
                 * loop is at one of the "break" statements below.
                 */
                for (cur = so->keyData, i = 0;; cur++, i++)
                {
                        if (i >= so->numberOfKeys || cur->sk_attno != curattr)
                        {
                                /*
                                 * Done looking at keys for curattr.  If we didn't find a
                                 * usable boundary key, quit; else save the boundary key
                                 * pointer in startKeys.
                                 */
                                if (chosen == NULL)
                                        break;
                                startKeys[keysCount++] = chosen;

                                /*
                                 * Adjust strat_total, and quit if we have stored a > or <
                                 * key.
                                 */
                                strat = chosen->sk_strategy;
                                if (strat != BTEqualStrategyNumber)
                                {
                                        strat_total = strat;
                                        if (strat == BTGreaterStrategyNumber ||
                                                strat == BTLessStrategyNumber)
                                                break;
                                }

                                /*
                                 * Done if that was the last attribute, or if next key is not
                                 * in sequence (implying no boundary key is available for the
                                 * next attribute).
                                 */
                                if (i >= so->numberOfKeys ||
                                        cur->sk_attno != curattr + 1)
                                        break;

                                /*
                                 * Reset for next attr.
                                 */
                                curattr = cur->sk_attno;
                                chosen = NULL;
                        }

                        /* Can we use this key as a starting boundary for this attr? */
                        switch (cur->sk_strategy)
                        {
                                case BTLessStrategyNumber:
                                case BTLessEqualStrategyNumber:
                                        if (chosen == NULL && ScanDirectionIsBackward(dir))
                                                chosen = cur;
                                        break;
                                case BTEqualStrategyNumber:
                                        /* override any non-equality choice */
                                        chosen = cur;
                                        break;
                                case BTGreaterEqualStrategyNumber:
                                case BTGreaterStrategyNumber:
                                        if (chosen == NULL && ScanDirectionIsForward(dir))
                                                chosen = cur;
                                        break;
                        }
                }
        }

        /*
         * If we found no usable boundary keys, we have to start from one end of
         * the tree.  Walk down that edge to the first or last key, and scan from
         * there.
         */
        if (keysCount == 0)
                return _bt_endpoint(scan, dir);

        /*
         * We want to start the scan somewhere within the index.  Set up an
         * insertion scankey we can use to search for the boundary point we
         * identified above.  The insertion scankey is built in the local
         * scankeys[] array, using the keys identified by startKeys[].
         */
        Assert(keysCount <= INDEX_MAX_KEYS);
        for (i = 0; i < keysCount; i++)
        {
                ScanKey         cur = startKeys[i];

                Assert(cur->sk_attno == i + 1);

                if (cur->sk_flags & SK_ROW_HEADER)
                {
                        /*
                         * Row comparison header: look to the first row member instead.
                         *
                         * The member scankeys are already in insertion format (ie, they
                         * have sk_func = 3-way-comparison function), but we have to watch
                         * out for nulls, which _bt_preprocess_keys didn't check. A null
                         * in the first row member makes the condition unmatchable, just
                         * like qual_ok = false.
                         */
                        cur = (ScanKey) DatumGetPointer(cur->sk_argument);
                        Assert(cur->sk_flags & SK_ROW_MEMBER);
                        if (cur->sk_flags & SK_ISNULL)
                                return false;
                        memcpy(scankeys + i, cur, sizeof(ScanKeyData));

                        /*
                         * If the row comparison is the last positioning key we accepted,
                         * try to add additional keys from the lower-order row members.
                         * (If we accepted independent conditions on additional index
                         * columns, we use those instead --- doesn't seem worth trying to
                         * determine which is more restrictive.)  Note that this is OK
                         * even if the row comparison is of ">" or "<" type, because the
                         * condition applied to all but the last row member is effectively
                         * ">=" or "<=", and so the extra keys don't break the positioning
                         * scheme.
                         */
                        if (i == keysCount - 1)
                        {
                                while (!(cur->sk_flags & SK_ROW_END))
                                {
                                        cur++;
                                        Assert(cur->sk_flags & SK_ROW_MEMBER);
                                        if (cur->sk_attno != keysCount + 1)
                                                break;  /* out-of-sequence, can't use it */
                                        if (cur->sk_flags & SK_ISNULL)
                                                break;  /* can't use null keys */
                                        Assert(keysCount < INDEX_MAX_KEYS);
                                        memcpy(scankeys + keysCount, cur, sizeof(ScanKeyData));
                                        keysCount++;
                                }
                                break;                  /* done with outer loop */
                        }
                }
                else
                {
                        /*
                         * Ordinary comparison key.  Transform the search-style scan key
                         * to an insertion scan key by replacing the sk_func with the
                         * appropriate btree comparison function.
                         *
                         * If scankey operator is not a cross-type comparison, we can use
                         * the cached comparison function; otherwise gotta look it up in
                         * the catalogs.  (That can't lead to infinite recursion, since no
                         * indexscan initiated by syscache lookup will use cross-data-type
                         * operators.)
                         *
                         * We support the convention that sk_subtype == InvalidOid means
                         * the opclass input type; this is a hack to simplify life for
                         * ScanKeyInit().
                         */
                        if (cur->sk_subtype == rel->rd_opcintype[i] ||
                                cur->sk_subtype == InvalidOid)
                        {
                                FmgrInfo   *procinfo;

                                procinfo = index_getprocinfo(rel, cur->sk_attno, BTORDER_PROC);
                                ScanKeyEntryInitializeWithInfo(scankeys + i,
                                                                                           cur->sk_flags,
                                                                                           cur->sk_attno,
                                                                                           InvalidStrategy,
                                                                                           cur->sk_subtype,
                                                                                           procinfo,
                                                                                           cur->sk_argument);
                        }
                        else
                        {
                                RegProcedure cmp_proc;

                                cmp_proc = get_opfamily_proc(rel->rd_opfamily[i],
                                                                                         rel->rd_opcintype[i],
                                                                                         cur->sk_subtype,
                                                                                         BTORDER_PROC);
                                if (!RegProcedureIsValid(cmp_proc))
                                        elog(ERROR, "missing support function %d(%u,%u) for attribute %d of index \"%s\"",
                                                 BTORDER_PROC, rel->rd_opcintype[i], cur->sk_subtype,
                                                 cur->sk_attno, RelationGetRelationName(rel));
                                ScanKeyEntryInitialize(scankeys + i,
                                                                           cur->sk_flags,
                                                                           cur->sk_attno,
                                                                           InvalidStrategy,
                                                                           cur->sk_subtype,
                                                                           cmp_proc,
                                                                           cur->sk_argument);
                        }
                }
        }

        /*----------
         * Examine the selected initial-positioning strategy to determine exactly
         * where we need to start the scan, and set flag variables to control the
         * code below.
         *
         * If nextkey = false, _bt_search and _bt_binsrch will locate the first
         * item >= scan key.  If nextkey = true, they will locate the first
         * item > scan key.
         *
         * If goback = true, we will then step back one item, while if
         * goback = false, we will start the scan on the located item.
         *
         * it's yet other place to add some code later for is(not)null ...
         *----------
         */
        switch (strat_total)
        {
                case BTLessStrategyNumber:

                        /*
                         * Find first item >= scankey, then back up one to arrive at last
                         * item < scankey.      (Note: this positioning strategy is only used
                         * for a backward scan, so that is always the correct starting
                         * position.)
                         */
                        nextkey = false;
                        goback = true;
                        break;

                case BTLessEqualStrategyNumber:

                        /*
                         * Find first item > scankey, then back up one to arrive at last
                         * item <= scankey.  (Note: this positioning strategy is only used
                         * for a backward scan, so that is always the correct starting
                         * position.)
                         */
                        nextkey = true;
                        goback = true;
                        break;

                case BTEqualStrategyNumber:

                        /*
                         * If a backward scan was specified, need to start with last equal
                         * item not first one.
                         */
                        if (ScanDirectionIsBackward(dir))
                        {
                                /*
                                 * This is the same as the <= strategy.  We will check at the
                                 * end whether the found item is actually =.
                                 */
                                nextkey = true;
                                goback = true;
                        }
                        else
                        {
                                /*
                                 * This is the same as the >= strategy.  We will check at the
                                 * end whether the found item is actually =.
                                 */
                                nextkey = false;
                                goback = false;
                        }
                        break;

                case BTGreaterEqualStrategyNumber:

                        /*
                         * Find first item >= scankey.  (This is only used for forward
                         * scans.)
                         */
                        nextkey = false;
                        goback = false;
                        break;

                case BTGreaterStrategyNumber:

                        /*
                         * Find first item > scankey.  (This is only used for forward
                         * scans.)
                         */
                        nextkey = true;
                        goback = false;
                        break;

                default:
                        /* can't get here, but keep compiler quiet */
                        elog(ERROR, "unrecognized strat_total: %d", (int) strat_total);
                        return false;
        }

        /*
         * Use the manufactured insertion scan key to descend the tree and
         * position ourselves on the target leaf page.
         */
        stack = _bt_search(rel, keysCount, scankeys, nextkey, &buf, BT_READ);

        /* don't need to keep the stack around... */
        _bt_freestack(stack);

        /* remember which buffer we have pinned, if any */
        so->currPos.buf = buf;

        if (!BufferIsValid(buf))
        {
                /* Only get here if index is completely empty */
                return false;
        }

        /* initialize moreLeft/moreRight appropriately for scan direction */
        if (ScanDirectionIsForward(dir))
        {
                so->currPos.moreLeft = false;
                so->currPos.moreRight = true;
        }
        else
        {
                so->currPos.moreLeft = true;
                so->currPos.moreRight = false;
        }
        so->numKilled = 0;                      /* just paranoia */
        so->markItemIndex = -1;         /* ditto */

        /* position to the precise item on the page */
        offnum = _bt_binsrch(rel, buf, keysCount, scankeys, nextkey);

        /*
         * If nextkey = false, we are positioned at the first item >= scan key, or
         * possibly at the end of a page on which all the existing items are less
         * than the scan key and we know that everything on later pages is greater
         * than or equal to scan key.
         *
         * If nextkey = true, we are positioned at the first item > scan key, or
         * possibly at the end of a page on which all the existing items are less
         * than or equal to the scan key and we know that everything on later
         * pages is greater than scan key.
         *
         * The actually desired starting point is either this item or the prior
         * one, or in the end-of-page case it's the first item on the next page or
         * the last item on this page.  Adjust the starting offset if needed. (If
         * this results in an offset before the first item or after the last one,
         * _bt_readpage will report no items found, and then we'll step to the
         * next page as needed.)
         */
        if (goback)
                offnum = OffsetNumberPrev(offnum);

        /*
         * Now load data from the first page of the scan.
         */
        if (!_bt_readpage(scan, dir, offnum))
        {
                /*
                 * There's no actually-matching data on this page.  Try to advance to
                 * the next page.  Return false if there's no matching data at all.
                 */
                if (!_bt_steppage(scan, dir))
                        return false;
        }

        /* Drop the lock, but not pin, on the current page */
        LockBuffer(so->currPos.buf, BUFFER_LOCK_UNLOCK);

        /* OK, itemIndex says what to return */
        scan->xs_ctup.t_self = so->currPos.items[so->currPos.itemIndex].heapTid;

        return true;
}

/*
 *      _bt_next() -- Get the next item in a scan.
 *
 *              On entry, so->currPos describes the current page, which is pinned
 *              but not locked, and so->currPos.itemIndex identifies which item was
 *              previously returned.
 *
 *              On successful exit, scan->xs_ctup.t_self is set to the TID of the
 *              next heap tuple, and so->currPos is updated as needed.
 *
 *              On failure exit (no more tuples), we release pin and set
 *              so->currPos.buf to InvalidBuffer.
 */
bool
_bt_next(IndexScanDesc scan, ScanDirection dir)
{
        BTScanOpaque so = (BTScanOpaque) scan->opaque;

        /*
         * Advance to next tuple on current page; or if there's no more, try to
         * step to the next page with data.
         */
        if (ScanDirectionIsForward(dir))
        {
                if (++so->currPos.itemIndex > so->currPos.lastItem)
                {
                        /* We must acquire lock before applying _bt_steppage */
                        Assert(BufferIsValid(so->currPos.buf));
                        LockBuffer(so->currPos.buf, BT_READ);
                        if (!_bt_steppage(scan, dir))
                                return false;
                        /* Drop the lock, but not pin, on the new page */
                        LockBuffer(so->currPos.buf, BUFFER_LOCK_UNLOCK);
                }
        }
        else
        {
                if (--so->currPos.itemIndex < so->currPos.firstItem)
                {
                        /* We must acquire lock before applying _bt_steppage */
                        Assert(BufferIsValid(so->currPos.buf));
                        LockBuffer(so->currPos.buf, BT_READ);
                        if (!_bt_steppage(scan, dir))
                                return false;
                        /* Drop the lock, but not pin, on the new page */
                        LockBuffer(so->currPos.buf, BUFFER_LOCK_UNLOCK);
                }
        }

        /* OK, itemIndex says what to return */
        scan->xs_ctup.t_self = so->currPos.items[so->currPos.itemIndex].heapTid;

        return true;
}

/*
 *      _bt_readpage() -- Load data from current index page into so->currPos
 *
 * Caller must have pinned and read-locked so->currPos.buf; the buffer's state
 * is not changed here.  Also, currPos.moreLeft and moreRight must be valid;
 * they are updated as appropriate.  All other fields of so->currPos are
 * initialized from scratch here.
 *
 * We scan the current page starting at offnum and moving in the indicated
 * direction.  All items matching the scan keys are loaded into currPos.items.
 * moreLeft or moreRight (as appropriate) is cleared if _bt_checkkeys reports
 * that there can be no more matching tuples in the current scan direction.
 *
 * Returns true if any matching items found on the page, false if none.
 */
static bool
_bt_readpage(IndexScanDesc scan, ScanDirection dir, OffsetNumber offnum)
{
        BTScanOpaque so = (BTScanOpaque) scan->opaque;
        Page            page;
        BTPageOpaque opaque;
        OffsetNumber minoff;
        OffsetNumber maxoff;
        int                     itemIndex;
        bool            continuescan;

        /* we must have the buffer pinned and locked */
        Assert(BufferIsValid(so->currPos.buf));

        page = BufferGetPage(so->currPos.buf);
        opaque = (BTPageOpaque) PageGetSpecialPointer(page);
        minoff = P_FIRSTDATAKEY(opaque);
        maxoff = PageGetMaxOffsetNumber(page);

        /*
         * we must save the page's right-link while scanning it; this tells us
         * where to step right to after we're done with these items.  There is no
         * corresponding need for the left-link, since splits always go right.
         */
        so->currPos.nextPage = opaque->btpo_next;

        if (ScanDirectionIsForward(dir))
        {
                /* load items[] in ascending order */
                itemIndex = 0;

                offnum = Max(offnum, minoff);

                while (offnum <= maxoff)
                {
                        if (_bt_checkkeys(scan, page, offnum, dir, &continuescan))
                        {
                                /* tuple passes all scan key conditions, so remember it */
                                /* _bt_checkkeys put the heap ptr into scan->xs_ctup.t_self */
                                so->currPos.items[itemIndex].heapTid = scan->xs_ctup.t_self;
                                so->currPos.items[itemIndex].indexOffset = offnum;
                                itemIndex++;
                        }
                        if (!continuescan)
                        {
                                /* there can't be any more matches, so stop */
                                so->currPos.moreRight = false;
                                break;
                        }

                        offnum = OffsetNumberNext(offnum);
                }

                Assert(itemIndex <= MaxIndexTuplesPerPage);
                so->currPos.firstItem = 0;
                so->currPos.lastItem = itemIndex - 1;
                so->currPos.itemIndex = 0;
        }
        else
        {
                /* load items[] in descending order */
                itemIndex = MaxIndexTuplesPerPage;

                offnum = Min(offnum, maxoff);

                while (offnum >= minoff)
                {
                        if (_bt_checkkeys(scan, page, offnum, dir, &continuescan))
                        {
                                /* tuple passes all scan key conditions, so remember it */
                                /* _bt_checkkeys put the heap ptr into scan->xs_ctup.t_self */
                                itemIndex--;
                                so->currPos.items[itemIndex].heapTid = scan->xs_ctup.t_self;
                                so->currPos.items[itemIndex].indexOffset = offnum;
                        }
                        if (!continuescan)
                        {
                                /* there can't be any more matches, so stop */
                                so->currPos.moreLeft = false;
                                break;
                        }

                        offnum = OffsetNumberPrev(offnum);
                }

                Assert(itemIndex >= 0);
                so->currPos.firstItem = itemIndex;
                so->currPos.lastItem = MaxIndexTuplesPerPage - 1;
                so->currPos.itemIndex = MaxIndexTuplesPerPage - 1;
        }

        return (so->currPos.firstItem <= so->currPos.lastItem);
}

/*
 *      _bt_steppage() -- Step to next page containing valid data for scan
 *
 * On entry, so->currPos.buf must be pinned and read-locked.  We'll drop
 * the lock and pin before moving to next page.
 *
 * On success exit, we hold pin and read-lock on the next interesting page,
 * and so->currPos is updated to contain data from that page.
 *
 * If there are no more matching records in the given direction, we drop all
 * locks and pins, set so->currPos.buf to InvalidBuffer, and return FALSE.
 */
static bool
_bt_steppage(IndexScanDesc scan, ScanDirection dir)
{
        BTScanOpaque so = (BTScanOpaque) scan->opaque;
        Relation        rel;
        Page            page;
        BTPageOpaque opaque;

        /* we must have the buffer pinned and locked */
        Assert(BufferIsValid(so->currPos.buf));

        /* Before leaving current page, deal with any killed items */
        if (so->numKilled > 0)
                _bt_killitems(scan, true);

        /*
         * Before we modify currPos, make a copy of the page data if there was a
         * mark position that needs it.
         */
        if (so->markItemIndex >= 0)
        {
                /* bump pin on current buffer for assignment to mark buffer */
                IncrBufferRefCount(so->currPos.buf);
                memcpy(&so->markPos, &so->currPos,
                           offsetof(BTScanPosData, items[1]) +
                           so->currPos.lastItem * sizeof(BTScanPosItem));
                so->markPos.itemIndex = so->markItemIndex;
                so->markItemIndex = -1;
        }

        rel = scan->indexRelation;

        if (ScanDirectionIsForward(dir))
        {
                /* Walk right to the next page with data */
                /* We must rely on the previously saved nextPage link! */
                BlockNumber blkno = so->currPos.nextPage;

                /* Remember we left a page with data */
                so->currPos.moreLeft = true;

                for (;;)
                {
                        /* if we're at end of scan, release the buffer and return */
                        if (blkno == P_NONE || !so->currPos.moreRight)
                        {
                                _bt_relbuf(rel, so->currPos.buf);
                                so->currPos.buf = InvalidBuffer;
                                return false;
                        }
                        /* step right one page */
                        so->currPos.buf = _bt_relandgetbuf(rel, so->currPos.buf,
                                                                                           blkno, BT_READ);
                        /* check for deleted page */
                        page = BufferGetPage(so->currPos.buf);
                        opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                        if (!P_IGNORE(opaque))
                        {
                                /* see if there are any matches on this page */
                                /* note that this will clear moreRight if we can stop */
                                if (_bt_readpage(scan, dir, P_FIRSTDATAKEY(opaque)))
                                        break;
                        }
                        /* nope, keep going */
                        blkno = opaque->btpo_next;
                }
        }
        else
        {
                /* Remember we left a page with data */
                so->currPos.moreRight = true;

                /*
                 * Walk left to the next page with data.  This is much more complex
                 * than the walk-right case because of the possibility that the page
                 * to our left splits while we are in flight to it, plus the
                 * possibility that the page we were on gets deleted after we leave
                 * it.  See nbtree/README for details.
                 */
                for (;;)
                {
                        /* Done if we know there are no matching keys to the left */
                        if (!so->currPos.moreLeft)
                        {
                                _bt_relbuf(rel, so->currPos.buf);
                                so->currPos.buf = InvalidBuffer;
                                return false;
                        }

                        /* Step to next physical page */
                        so->currPos.buf = _bt_walk_left(rel, so->currPos.buf);

                        /* if we're physically at end of index, return failure */
                        if (so->currPos.buf == InvalidBuffer)
                                return false;

                        /*
                         * Okay, we managed to move left to a non-deleted page. Done if
                         * it's not half-dead and contains matching tuples. Else loop back
                         * and do it all again.
                         */
                        page = BufferGetPage(so->currPos.buf);
                        opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                        if (!P_IGNORE(opaque))
                        {
                                /* see if there are any matches on this page */
                                /* note that this will clear moreLeft if we can stop */
                                if (_bt_readpage(scan, dir, PageGetMaxOffsetNumber(page)))
                                        break;
                        }
                }
        }

        return true;
}

/*
 * _bt_walk_left() -- step left one page, if possible
 *
 * The given buffer must be pinned and read-locked.  This will be dropped
 * before stepping left.  On return, we have pin and read lock on the
 * returned page, instead.
 *
 * Returns InvalidBuffer if there is no page to the left (no lock is held
 * in that case).
 *
 * When working on a non-leaf level, it is possible for the returned page
 * to be half-dead; the caller should check that condition and step left
 * again if it's important.
 */
static Buffer
_bt_walk_left(Relation rel, Buffer buf)
{
        Page            page;
        BTPageOpaque opaque;

        page = BufferGetPage(buf);
        opaque = (BTPageOpaque) PageGetSpecialPointer(page);

        for (;;)
        {
                BlockNumber obknum;
                BlockNumber lblkno;
                BlockNumber blkno;
                int                     tries;

                /* if we're at end of tree, release buf and return failure */
                if (P_LEFTMOST(opaque))
                {
                        _bt_relbuf(rel, buf);
                        break;
                }
                /* remember original page we are stepping left from */
                obknum = BufferGetBlockNumber(buf);
                /* step left */
                blkno = lblkno = opaque->btpo_prev;
                buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
                page = BufferGetPage(buf);
                opaque = (BTPageOpaque) PageGetSpecialPointer(page);

                /*
                 * If this isn't the page we want, walk right till we find what we
                 * want --- but go no more than four hops (an arbitrary limit). If we
                 * don't find the correct page by then, the most likely bet is that
                 * the original page got deleted and isn't in the sibling chain at all
                 * anymore, not that its left sibling got split more than four times.
                 *
                 * Note that it is correct to test P_ISDELETED not P_IGNORE here,
                 * because half-dead pages are still in the sibling chain.      Caller
                 * must reject half-dead pages if wanted.
                 */
                tries = 0;
                for (;;)
                {
                        if (!P_ISDELETED(opaque) && opaque->btpo_next == obknum)
                        {
                                /* Found desired page, return it */
                                return buf;
                        }
                        if (P_RIGHTMOST(opaque) || ++tries > 4)
                                break;
                        blkno = opaque->btpo_next;
                        buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
                        page = BufferGetPage(buf);
                        opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                }

                /* Return to the original page to see what's up */
                buf = _bt_relandgetbuf(rel, buf, obknum, BT_READ);
                page = BufferGetPage(buf);
                opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                if (P_ISDELETED(opaque))
                {
                        /*
                         * It was deleted.      Move right to first nondeleted page (there
                         * must be one); that is the page that has acquired the deleted
                         * one's keyspace, so stepping left from it will take us where we
                         * want to be.
                         */
                        for (;;)
                        {
                                if (P_RIGHTMOST(opaque))
                                        elog(ERROR, "fell off the end of \"%s\"",
                                                 RelationGetRelationName(rel));
                                blkno = opaque->btpo_next;
                                buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
                                page = BufferGetPage(buf);
                                opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                                if (!P_ISDELETED(opaque))
                                        break;
                        }

                        /*
                         * Now return to top of loop, resetting obknum to point to this
                         * nondeleted page, and try again.
                         */
                }
                else
                {
                        /*
                         * It wasn't deleted; the explanation had better be that the page
                         * to the left got split or deleted. Without this check, we'd go
                         * into an infinite loop if there's anything wrong.
                         */
                        if (opaque->btpo_prev == lblkno)
                                elog(ERROR, "could not find left sibling in \"%s\"",
                                         RelationGetRelationName(rel));
                        /* Okay to try again with new lblkno value */
                }
        }

        return InvalidBuffer;
}

/*
 * _bt_get_endpoint() -- Find the first or last page on a given tree level
 *
 * If the index is empty, we will return InvalidBuffer; any other failure
 * condition causes ereport().  We will not return a dead page.
 *
 * The returned buffer is pinned and read-locked.
 */
Buffer
_bt_get_endpoint(Relation rel, uint32 level, bool rightmost)
{
        Buffer          buf;
        Page            page;
        BTPageOpaque opaque;
        OffsetNumber offnum;
        BlockNumber blkno;
        IndexTuple      itup;

        /*
         * If we are looking for a leaf page, okay to descend from fast root;
         * otherwise better descend from true root.  (There is no point in being
         * smarter about intermediate levels.)
         */
        if (level == 0)
                buf = _bt_getroot(rel, BT_READ);
        else
                buf = _bt_gettrueroot(rel);

        if (!BufferIsValid(buf))
        {
                /* empty index... */
                return InvalidBuffer;
        }

        page = BufferGetPage(buf);
        opaque = (BTPageOpaque) PageGetSpecialPointer(page);

        for (;;)
        {
                /*
                 * If we landed on a deleted page, step right to find a live page
                 * (there must be one).  Also, if we want the rightmost page, step
                 * right if needed to get to it (this could happen if the page split
                 * since we obtained a pointer to it).
                 */
                while (P_IGNORE(opaque) ||
                           (rightmost && !P_RIGHTMOST(opaque)))
                {
                        blkno = opaque->btpo_next;
                        if (blkno == P_NONE)
                                elog(ERROR, "fell off the end of \"%s\"",
                                         RelationGetRelationName(rel));
                        buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
                        page = BufferGetPage(buf);
                        opaque = (BTPageOpaque) PageGetSpecialPointer(page);
                }

                /* Done? */
                if (opaque->btpo.level == level)
                        break;
                if (opaque->btpo.level < level)
                        elog(ERROR, "btree level %u not found", level);

                /* Descend to leftmost or rightmost child page */
                if (rightmost)
                        offnum = PageGetMaxOffsetNumber(page);
                else
                        offnum = P_FIRSTDATAKEY(opaque);

                itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offnum));
                blkno = ItemPointerGetBlockNumber(&(itup->t_tid));

                buf = _bt_relandgetbuf(rel, buf, blkno, BT_READ);
                page = BufferGetPage(buf);
                opaque = (BTPageOpaque) PageGetSpecialPointer(page);
        }

        return buf;
}

/*
 *      _bt_endpoint() -- Find the first or last page in the index, and scan
 * from there to the first key satisfying all the quals.
 *
 * This is used by _bt_first() to set up a scan when we've determined
 * that the scan must start at the beginning or end of the index (for
 * a forward or backward scan respectively).  Exit conditions are the
 * same as for _bt_first().
 */
static bool
_bt_endpoint(IndexScanDesc scan, ScanDirection dir)
{
        Relation        rel = scan->indexRelation;
        BTScanOpaque so = (BTScanOpaque) scan->opaque;
        Buffer          buf;
        Page            page;
        BTPageOpaque opaque;
        OffsetNumber start;

        /*
         * Scan down to the leftmost or rightmost leaf page.  This is a simplified
         * version of _bt_search().  We don't maintain a stack since we know we
         * won't need it.
         */
        buf = _bt_get_endpoint(rel, 0, ScanDirectionIsBackward(dir));

        if (!BufferIsValid(buf))
        {
                /* empty index... */
                so->currPos.buf = InvalidBuffer;
                return false;
        }

        page = BufferGetPage(buf);
        opaque = (BTPageOpaque) PageGetSpecialPointer(page);
        Assert(P_ISLEAF(opaque));

        if (ScanDirectionIsForward(dir))
        {
                /* There could be dead pages to the left, so not this: */
                /* Assert(P_LEFTMOST(opaque)); */

                start = P_FIRSTDATAKEY(opaque);
        }
        else if (ScanDirectionIsBackward(dir))
        {
                Assert(P_RIGHTMOST(opaque));

                start = PageGetMaxOffsetNumber(page);
        }
        else
        {
                elog(ERROR, "invalid scan direction: %d", (int) dir);
                start = 0;                              /* keep compiler quiet */
        }

        /* remember which buffer we have pinned */
        so->currPos.buf = buf;

        /* initialize moreLeft/moreRight appropriately for scan direction */
        if (ScanDirectionIsForward(dir))
        {
                so->currPos.moreLeft = false;
                so->currPos.moreRight = true;
        }
        else
        {
                so->currPos.moreLeft = true;
                so->currPos.moreRight = false;
        }
        so->numKilled = 0;                      /* just paranoia */
        so->markItemIndex = -1;         /* ditto */

        /*
         * Now load data from the first page of the scan.
         */
        if (!_bt_readpage(scan, dir, start))
        {
                /*
                 * There's no actually-matching data on this page.  Try to advance to
                 * the next page.  Return false if there's no matching data at all.
                 */
                if (!_bt_steppage(scan, dir))
                        return false;
        }

        /* Drop the lock, but not pin, on the current page */
        LockBuffer(so->currPos.buf, BUFFER_LOCK_UNLOCK);

        /* OK, itemIndex says what to return */
        scan->xs_ctup.t_self = so->currPos.items[so->currPos.itemIndex].heapTid;

        return true;
}