nbtree.h

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/*-------------------------------------------------------------------------
 *
 * nbtree.h
 *    header file for postgres btree access method implementation.
 *
 *
 * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * src/include/access/nbtree.h
 *
 *-------------------------------------------------------------------------
 */
#ifndef NBTREE_H
#define NBTREE_H

#include "access/amapi.h"
#include "access/itup.h"
#include "access/sdir.h"
#include "access/xlogreader.h"
#include "catalog/pg_am_d.h"
#include "catalog/pg_index.h"
#include "lib/stringinfo.h"
#include "storage/bufmgr.h"
#include "storage/shm_toc.h"

/* There's room for a 16-bit vacuum cycle ID in BTPageOpaqueData */
typedef uint16 BTCycleId;

/*
 *  BTPageOpaqueData -- At the end of every page, we store a pointer
 *  to both siblings in the tree.  This is used to do forward/backward
 *  index scans.  The next-page link is also critical for recovery when
 *  a search has navigated to the wrong page due to concurrent page splits
 *  or deletions; see src/backend/access/nbtree/README for more info.
 *
 *  In addition, we store the page's btree level (counting upwards from
 *  zero at a leaf page) as well as some flag bits indicating the page type
 *  and status.  If the page is deleted, we replace the level with the
 *  next-transaction-ID value indicating when it is safe to reclaim the page.
 *
 *  We also store a "vacuum cycle ID".  When a page is split while VACUUM is
 *  processing the index, a nonzero value associated with the VACUUM run is
 *  stored into both halves of the split page.  (If VACUUM is not running,
 *  both pages receive zero cycleids.)  This allows VACUUM to detect whether
 *  a page was split since it started, with a small probability of false match
 *  if the page was last split some exact multiple of MAX_BT_CYCLE_ID VACUUMs
 *  ago.  Also, during a split, the BTP_SPLIT_END flag is cleared in the left
 *  (original) page, and set in the right page, but only if the next page
 *  to its right has a different cycleid.
 *
 *  NOTE: the BTP_LEAF flag bit is redundant since level==0 could be tested
 *  instead.
 */

typedef struct BTPageOpaqueData
{
    BlockNumber btpo_prev;      /* left sibling, or P_NONE if leftmost */
    BlockNumber btpo_next;      /* right sibling, or P_NONE if rightmost */
    union
    {
        uint32      level;      /* tree level --- zero for leaf pages */
        TransactionId xact;     /* next transaction ID, if deleted */
    }           btpo;
    uint16      btpo_flags;     /* flag bits, see below */
    BTCycleId   btpo_cycleid;   /* vacuum cycle ID of latest split */
} BTPageOpaqueData;

typedef BTPageOpaqueData *BTPageOpaque;

/* Bits defined in btpo_flags */
#define BTP_LEAF        (1 << 0)    /* leaf page, i.e. not internal page */
#define BTP_ROOT        (1 << 1)    /* root page (has no parent) */
#define BTP_DELETED     (1 << 2)    /* page has been deleted from tree */
#define BTP_META        (1 << 3)    /* meta-page */
#define BTP_HALF_DEAD   (1 << 4)    /* empty, but still in tree */
#define BTP_SPLIT_END   (1 << 5)    /* rightmost page of split group */
#define BTP_HAS_GARBAGE (1 << 6)    /* page has LP_DEAD tuples (deprecated) */
#define BTP_INCOMPLETE_SPLIT (1 << 7)   /* right sibling's downlink is missing */

/*
 * The max allowed value of a cycle ID is a bit less than 64K.  This is
 * for convenience of pg_filedump and similar utilities: we want to use
 * the last 2 bytes of special space as an index type indicator, and
 * restricting cycle ID lets btree use that space for vacuum cycle IDs
 * while still allowing index type to be identified.
 */
#define MAX_BT_CYCLE_ID     0xFF7F


/*
 * The Meta page is always the first page in the btree index.
 * Its primary purpose is to point to the location of the btree root page.
 * We also point to the "fast" root, which is the current effective root;
 * see README for discussion.
 */

typedef struct BTMetaPageData
{
    uint32      btm_magic;      /* should contain BTREE_MAGIC */
    uint32      btm_version;    /* nbtree version (always <= BTREE_VERSION) */
    BlockNumber btm_root;       /* current root location */
    uint32      btm_level;      /* tree level of the root page */
    BlockNumber btm_fastroot;   /* current "fast" root location */
    uint32      btm_fastlevel;  /* tree level of the "fast" root page */
    /* remaining fields only valid when btm_version >= BTREE_NOVAC_VERSION */
    TransactionId btm_oldest_btpo_xact; /* oldest btpo_xact among all deleted
                                         * pages */
    float8      btm_last_cleanup_num_heap_tuples;   /* number of heap tuples
                                                     * during last cleanup */
    bool        btm_allequalimage;  /* are all columns "equalimage"? */
} BTMetaPageData;

#define BTPageGetMeta(p) \
    ((BTMetaPageData *) PageGetContents(p))

/*
 * The current Btree version is 4.  That's what you'll get when you create
 * a new index.
 *
 * Btree version 3 was used in PostgreSQL v11.  It is mostly the same as
 * version 4, but heap TIDs were not part of the keyspace.  Index tuples
 * with duplicate keys could be stored in any order.  We continue to
 * support reading and writing Btree versions 2 and 3, so that they don't
 * need to be immediately re-indexed at pg_upgrade.  In order to get the
 * new heapkeyspace semantics, however, a REINDEX is needed.
 *
 * Deduplication is safe to use when the btm_allequalimage field is set to
 * true.  It's safe to read the btm_allequalimage field on version 3, but
 * only version 4 indexes make use of deduplication.  Even version 4
 * indexes created on PostgreSQL v12 will need a REINDEX to make use of
 * deduplication, though, since there is no other way to set
 * btm_allequalimage to true (pg_upgrade hasn't been taught to set the
 * metapage field).
 *
 * Btree version 2 is mostly the same as version 3.  There are two new
 * fields in the metapage that were introduced in version 3.  A version 2
 * metapage will be automatically upgraded to version 3 on the first
 * insert to it.  INCLUDE indexes cannot use version 2.
 */
#define BTREE_METAPAGE  0       /* first page is meta */
#define BTREE_MAGIC     0x053162    /* magic number in metapage */
#define BTREE_VERSION   4       /* current version number */
#define BTREE_MIN_VERSION   2   /* minimum supported version */
#define BTREE_NOVAC_VERSION 3   /* version with all meta fields set */

/*
 * Maximum size of a btree index entry, including its tuple header.
 *
 * We actually need to be able to fit three items on every page,
 * so restrict any one item to 1/3 the per-page available space.
 *
 * There are rare cases where _bt_truncate() will need to enlarge
 * a heap index tuple to make space for a tiebreaker heap TID
 * attribute, which we account for here.
 */
#define BTMaxItemSize(page) \
    MAXALIGN_DOWN((PageGetPageSize(page) - \
                   MAXALIGN(SizeOfPageHeaderData + \
                            3*sizeof(ItemIdData)  + \
                            3*sizeof(ItemPointerData)) - \
                   MAXALIGN(sizeof(BTPageOpaqueData))) / 3)
#define BTMaxItemSizeNoHeapTid(page) \
    MAXALIGN_DOWN((PageGetPageSize(page) - \
                   MAXALIGN(SizeOfPageHeaderData + 3*sizeof(ItemIdData)) - \
                   MAXALIGN(sizeof(BTPageOpaqueData))) / 3)

/*
 * MaxTIDsPerBTreePage is an upper bound on the number of heap TIDs tuples
 * that may be stored on a btree leaf page.  It is used to size the
 * per-page temporary buffers used by index scans.
 *
 * Note: we don't bother considering per-tuple overheads here to keep
 * things simple (value is based on how many elements a single array of
 * heap TIDs must have to fill the space between the page header and
 * special area).  The value is slightly higher (i.e. more conservative)
 * than necessary as a result, which is considered acceptable.
 */
#define MaxTIDsPerBTreePage \
    (int) ((BLCKSZ - SizeOfPageHeaderData - sizeof(BTPageOpaqueData)) / \
           sizeof(ItemPointerData))

/*
 * The leaf-page fillfactor defaults to 90% but is user-adjustable.
 * For pages above the leaf level, we use a fixed 70% fillfactor.
 * The fillfactor is applied during index build and when splitting
 * a rightmost page; when splitting non-rightmost pages we try to
 * divide the data equally.  When splitting a page that's entirely
 * filled with a single value (duplicates), the effective leaf-page
 * fillfactor is 96%, regardless of whether the page is a rightmost
 * page.
 */
#define BTREE_MIN_FILLFACTOR        10
#define BTREE_DEFAULT_FILLFACTOR    90
#define BTREE_NONLEAF_FILLFACTOR    70
#define BTREE_SINGLEVAL_FILLFACTOR  96

/*
 *  In general, the btree code tries to localize its knowledge about
 *  page layout to a couple of routines.  However, we need a special
 *  value to indicate "no page number" in those places where we expect
 *  page numbers.  We can use zero for this because we never need to
 *  make a pointer to the metadata page.
 */

#define P_NONE          0

/*
 * Macros to test whether a page is leftmost or rightmost on its tree level,
 * as well as other state info kept in the opaque data.
 */
#define P_LEFTMOST(opaque)      ((opaque)->btpo_prev == P_NONE)
#define P_RIGHTMOST(opaque)     ((opaque)->btpo_next == P_NONE)
#define P_ISLEAF(opaque)        (((opaque)->btpo_flags & BTP_LEAF) != 0)
#define P_ISROOT(opaque)        (((opaque)->btpo_flags & BTP_ROOT) != 0)
#define P_ISDELETED(opaque)     (((opaque)->btpo_flags & BTP_DELETED) != 0)
#define P_ISMETA(opaque)        (((opaque)->btpo_flags & BTP_META) != 0)
#define P_ISHALFDEAD(opaque)    (((opaque)->btpo_flags & BTP_HALF_DEAD) != 0)
#define P_IGNORE(opaque)        (((opaque)->btpo_flags & (BTP_DELETED|BTP_HALF_DEAD)) != 0)
#define P_HAS_GARBAGE(opaque)   (((opaque)->btpo_flags & BTP_HAS_GARBAGE) != 0)
#define P_INCOMPLETE_SPLIT(opaque)  (((opaque)->btpo_flags & BTP_INCOMPLETE_SPLIT) != 0)

/*
 *  Lehman and Yao's algorithm requires a ``high key'' on every non-rightmost
 *  page.  The high key is not a tuple that is used to visit the heap.  It is
 *  a pivot tuple (see "Notes on B-Tree tuple format" below for definition).
 *  The high key on a page is required to be greater than or equal to any
 *  other key that appears on the page.  If we find ourselves trying to
 *  insert a key that is strictly > high key, we know we need to move right
 *  (this should only happen if the page was split since we examined the
 *  parent page).
 *
 *  Our insertion algorithm guarantees that we can use the initial least key
 *  on our right sibling as the high key.  Once a page is created, its high
 *  key changes only if the page is split.
 *
 *  On a non-rightmost page, the high key lives in item 1 and data items
 *  start in item 2.  Rightmost pages have no high key, so we store data
 *  items beginning in item 1.
 */

#define P_HIKEY             ((OffsetNumber) 1)
#define P_FIRSTKEY          ((OffsetNumber) 2)
#define P_FIRSTDATAKEY(opaque)  (P_RIGHTMOST(opaque) ? P_HIKEY : P_FIRSTKEY)

/*
 * Notes on B-Tree tuple format, and key and non-key attributes:
 *
 * INCLUDE B-Tree indexes have non-key attributes.  These are extra
 * attributes that may be returned by index-only scans, but do not influence
 * the order of items in the index (formally, non-key attributes are not
 * considered to be part of the key space).  Non-key attributes are only
 * present in leaf index tuples whose item pointers actually point to heap
 * tuples (non-pivot tuples).  _bt_check_natts() enforces the rules
 * described here.
 *
 * Non-pivot tuple format (plain/non-posting variant):
 *
 *  t_tid | t_info | key values | INCLUDE columns, if any
 *
 * t_tid points to the heap TID, which is a tiebreaker key column as of
 * BTREE_VERSION 4.
 *
 * Non-pivot tuples complement pivot tuples, which only have key columns.
 * The sole purpose of pivot tuples is to represent how the key space is
 * separated.  In general, any B-Tree index that has more than one level
 * (i.e. any index that does not just consist of a metapage and a single
 * leaf root page) must have some number of pivot tuples, since pivot
 * tuples are used for traversing the tree.  Suffix truncation can omit
 * trailing key columns when a new pivot is formed, which makes minus
 * infinity their logical value.  Since BTREE_VERSION 4 indexes treat heap
 * TID as a trailing key column that ensures that all index tuples are
 * physically unique, it is necessary to represent heap TID as a trailing
 * key column in pivot tuples, though very often this can be truncated
 * away, just like any other key column. (Actually, the heap TID is
 * omitted rather than truncated, since its representation is different to
 * the non-pivot representation.)
 *
 * Pivot tuple format:
 *
 *  t_tid | t_info | key values | [heap TID]
 *
 * We store the number of columns present inside pivot tuples by abusing
 * their t_tid offset field, since pivot tuples never need to store a real
 * offset (pivot tuples generally store a downlink in t_tid, though).  The
 * offset field only stores the number of columns/attributes when the
 * INDEX_ALT_TID_MASK bit is set, which doesn't count the trailing heap
 * TID column sometimes stored in pivot tuples -- that's represented by
 * the presence of BT_PIVOT_HEAP_TID_ATTR.  The INDEX_ALT_TID_MASK bit in
 * t_info is always set on BTREE_VERSION 4 pivot tuples, since
 * BTreeTupleIsPivot() must work reliably on heapkeyspace versions.
 *
 * In version 2 or version 3 (!heapkeyspace) indexes, INDEX_ALT_TID_MASK
 * might not be set in pivot tuples.  BTreeTupleIsPivot() won't work
 * reliably as a result.  The number of columns stored is implicitly the
 * same as the number of columns in the index, just like any non-pivot
 * tuple. (The number of columns stored should not vary, since suffix
 * truncation of key columns is unsafe within any !heapkeyspace index.)
 *
 * The 12 least significant bits from t_tid's offset number are used to
 * represent the number of key columns within a pivot tuple.  This leaves 4
 * status bits (BT_STATUS_OFFSET_MASK bits), which are shared by all tuples
 * that have the INDEX_ALT_TID_MASK bit set (set in t_info) to store basic
 * tuple metadata.  BTreeTupleIsPivot() and BTreeTupleIsPosting() use the
 * BT_STATUS_OFFSET_MASK bits.
 *
 * Sometimes non-pivot tuples also use a representation that repurposes
 * t_tid to store metadata rather than a TID.  PostgreSQL v13 introduced a
 * new non-pivot tuple format to support deduplication: posting list
 * tuples.  Deduplication merges together multiple equal non-pivot tuples
 * into a logically equivalent, space efficient representation.  A posting
 * list is an array of ItemPointerData elements.  Non-pivot tuples are
 * merged together to form posting list tuples lazily, at the point where
 * we'd otherwise have to split a leaf page.
 *
 * Posting tuple format (alternative non-pivot tuple representation):
 *
 *  t_tid | t_info | key values | posting list (TID array)
 *
 * Posting list tuples are recognized as such by having the
 * INDEX_ALT_TID_MASK status bit set in t_info and the BT_IS_POSTING status
 * bit set in t_tid's offset number.  These flags redefine the content of
 * the posting tuple's t_tid to store the location of the posting list
 * (instead of a block number), as well as the total number of heap TIDs
 * present in the tuple (instead of a real offset number).
 *
 * The 12 least significant bits from t_tid's offset number are used to
 * represent the number of heap TIDs present in the tuple, leaving 4 status
 * bits (the BT_STATUS_OFFSET_MASK bits).  Like any non-pivot tuple, the
 * number of columns stored is always implicitly the total number in the
 * index (in practice there can never be non-key columns stored, since
 * deduplication is not supported with INCLUDE indexes).
 */
#define INDEX_ALT_TID_MASK          INDEX_AM_RESERVED_BIT

/* Item pointer offset bit masks */
#define BT_OFFSET_MASK              0x0FFF
#define BT_STATUS_OFFSET_MASK       0xF000
/* BT_STATUS_OFFSET_MASK status bits */
#define BT_PIVOT_HEAP_TID_ATTR      0x1000
#define BT_IS_POSTING               0x2000

/*
 * Note: BTreeTupleIsPivot() can have false negatives (but not false
 * positives) when used with !heapkeyspace indexes
 */
static inline bool
BTreeTupleIsPivot(IndexTuple itup)
{
    if ((itup->t_info & INDEX_ALT_TID_MASK) == 0)
        return false;
    /* absence of BT_IS_POSTING in offset number indicates pivot tuple */
    if ((ItemPointerGetOffsetNumberNoCheck(&itup->t_tid) & BT_IS_POSTING) != 0)
        return false;

    return true;
}

static inline bool
BTreeTupleIsPosting(IndexTuple itup)
{
    if ((itup->t_info & INDEX_ALT_TID_MASK) == 0)
        return false;
    /* presence of BT_IS_POSTING in offset number indicates posting tuple */
    if ((ItemPointerGetOffsetNumberNoCheck(&itup->t_tid) & BT_IS_POSTING) == 0)
        return false;

    return true;
}

static inline void
BTreeTupleSetPosting(IndexTuple itup, uint16 nhtids, int postingoffset)
{
    Assert(nhtids > 1);
    Assert((nhtids & BT_STATUS_OFFSET_MASK) == 0);
    Assert((size_t) postingoffset == MAXALIGN(postingoffset));
    Assert(postingoffset < INDEX_SIZE_MASK);
    Assert(!BTreeTupleIsPivot(itup));

    itup->t_info |= INDEX_ALT_TID_MASK;
    ItemPointerSetOffsetNumber(&itup->t_tid, (nhtids | BT_IS_POSTING));
    ItemPointerSetBlockNumber(&itup->t_tid, postingoffset);
}

static inline uint16
BTreeTupleGetNPosting(IndexTuple posting)
{
    OffsetNumber existing;

    Assert(BTreeTupleIsPosting(posting));

    existing = ItemPointerGetOffsetNumberNoCheck(&posting->t_tid);
    return (existing & BT_OFFSET_MASK);
}

static inline uint32
BTreeTupleGetPostingOffset(IndexTuple posting)
{
    Assert(BTreeTupleIsPosting(posting));

    return ItemPointerGetBlockNumberNoCheck(&posting->t_tid);
}

static inline ItemPointer
BTreeTupleGetPosting(IndexTuple posting)
{
    return (ItemPointer) ((char *) posting +
                          BTreeTupleGetPostingOffset(posting));
}

static inline ItemPointer
BTreeTupleGetPostingN(IndexTuple posting, int n)
{
    return BTreeTupleGetPosting(posting) + n;
}

/*
 * Get/set downlink block number in pivot tuple.
 *
 * Note: Cannot assert that tuple is a pivot tuple.  If we did so then
 * !heapkeyspace indexes would exhibit false positive assertion failures.
 */
static inline BlockNumber
BTreeTupleGetDownLink(IndexTuple pivot)
{
    return ItemPointerGetBlockNumberNoCheck(&pivot->t_tid);
}

static inline void
BTreeTupleSetDownLink(IndexTuple pivot, BlockNumber blkno)
{
    ItemPointerSetBlockNumber(&pivot->t_tid, blkno);
}

/*
 * Get number of attributes within tuple.
 *
 * Note that this does not include an implicit tiebreaker heap TID
 * attribute, if any.  Note also that the number of key attributes must be
 * explicitly represented in all heapkeyspace pivot tuples.
 *
 * Note: This is defined as a macro rather than an inline function to
 * avoid including rel.h.
 */
#define BTreeTupleGetNAtts(itup, rel)   \
    ( \
        (BTreeTupleIsPivot(itup)) ? \
        ( \
            ItemPointerGetOffsetNumberNoCheck(&(itup)->t_tid) & BT_OFFSET_MASK \
        ) \
        : \
        IndexRelationGetNumberOfAttributes(rel) \
    )

/*
 * Set number of key attributes in tuple.
 *
 * The heap TID tiebreaker attribute bit may also be set here, indicating that
 * a heap TID value will be stored at the end of the tuple (i.e. using the
 * special pivot tuple representation).
 */
static inline void
BTreeTupleSetNAtts(IndexTuple itup, uint16 nkeyatts, bool heaptid)
{
    Assert(nkeyatts <= INDEX_MAX_KEYS);
    Assert((nkeyatts & BT_STATUS_OFFSET_MASK) == 0);
    Assert(!heaptid || nkeyatts > 0);
    Assert(!BTreeTupleIsPivot(itup) || nkeyatts == 0);

    itup->t_info |= INDEX_ALT_TID_MASK;

    if (heaptid)
        nkeyatts |= BT_PIVOT_HEAP_TID_ATTR;

    /* BT_IS_POSTING bit is deliberately unset here */
    ItemPointerSetOffsetNumber(&itup->t_tid, nkeyatts);
    Assert(BTreeTupleIsPivot(itup));
}

/*
 * Get/set leaf page's "top parent" link from its high key.  Used during page
 * deletion.
 *
 * Note: Cannot assert that tuple is a pivot tuple.  If we did so then
 * !heapkeyspace indexes would exhibit false positive assertion failures.
 */
static inline BlockNumber
BTreeTupleGetTopParent(IndexTuple leafhikey)
{
    return ItemPointerGetBlockNumberNoCheck(&leafhikey->t_tid);
}

static inline void
BTreeTupleSetTopParent(IndexTuple leafhikey, BlockNumber blkno)
{
    ItemPointerSetBlockNumber(&leafhikey->t_tid, blkno);
    BTreeTupleSetNAtts(leafhikey, 0, false);
}

/*
 * Get tiebreaker heap TID attribute, if any.
 *
 * This returns the first/lowest heap TID in the case of a posting list tuple.
 */
static inline ItemPointer
BTreeTupleGetHeapTID(IndexTuple itup)
{
    if (BTreeTupleIsPivot(itup))
    {
        /* Pivot tuple heap TID representation? */
        if ((ItemPointerGetOffsetNumberNoCheck(&itup->t_tid) &
             BT_PIVOT_HEAP_TID_ATTR) != 0)
            return (ItemPointer) ((char *) itup + IndexTupleSize(itup) -
                                  sizeof(ItemPointerData));

        /* Heap TID attribute was truncated */
        return NULL;
    }
    else if (BTreeTupleIsPosting(itup))
        return BTreeTupleGetPosting(itup);

    return &itup->t_tid;
}

/*
 * Get maximum heap TID attribute, which could be the only TID in the case of
 * a non-pivot tuple that does not have a posting list tuple.
 *
 * Works with non-pivot tuples only.
 */
static inline ItemPointer
BTreeTupleGetMaxHeapTID(IndexTuple itup)
{
    Assert(!BTreeTupleIsPivot(itup));

    if (BTreeTupleIsPosting(itup))
    {
        uint16      nposting = BTreeTupleGetNPosting(itup);

        return BTreeTupleGetPostingN(itup, nposting - 1);
    }

    return &itup->t_tid;
}

/*
 *  Operator strategy numbers for B-tree have been moved to access/stratnum.h,
 *  because many places need to use them in ScanKeyInit() calls.
 *
 *  The strategy numbers are chosen so that we can commute them by
 *  subtraction, thus:
 */
#define BTCommuteStrategyNumber(strat)  (BTMaxStrategyNumber + 1 - (strat))

/*
 *  When a new operator class is declared, we require that the user
 *  supply us with an amproc procedure (BTORDER_PROC) for determining
 *  whether, for two keys a and b, a < b, a = b, or a > b.  This routine
 *  must return < 0, 0, > 0, respectively, in these three cases.
 *
 *  To facilitate accelerated sorting, an operator class may choose to
 *  offer a second procedure (BTSORTSUPPORT_PROC).  For full details, see
 *  src/include/utils/sortsupport.h.
 *
 *  To support window frames defined by "RANGE offset PRECEDING/FOLLOWING",
 *  an operator class may choose to offer a third amproc procedure
 *  (BTINRANGE_PROC), independently of whether it offers sortsupport.
 *  For full details, see doc/src/sgml/btree.sgml.
 *
 *  To facilitate B-Tree deduplication, an operator class may choose to
 *  offer a forth amproc procedure (BTEQUALIMAGE_PROC).  For full details,
 *  see doc/src/sgml/btree.sgml.
 */

#define BTORDER_PROC        1
#define BTSORTSUPPORT_PROC  2
#define BTINRANGE_PROC      3
#define BTEQUALIMAGE_PROC   4
#define BTOPTIONS_PROC      5
#define BTNProcs            5

/*
 *  We need to be able to tell the difference between read and write
 *  requests for pages, in order to do locking correctly.
 */

#define BT_READ         BUFFER_LOCK_SHARE
#define BT_WRITE        BUFFER_LOCK_EXCLUSIVE

/*
 * BTStackData -- As we descend a tree, we push the location of pivot
 * tuples whose downlink we are about to follow onto a private stack.  If
 * we split a leaf, we use this stack to walk back up the tree and insert
 * data into its parent page at the correct location.  We also have to
 * recursively insert into the grandparent page if and when the parent page
 * splits.  Our private stack can become stale due to concurrent page
 * splits and page deletions, but it should never give us an irredeemably
 * bad picture.
 */
typedef struct BTStackData
{
    BlockNumber bts_blkno;
    OffsetNumber bts_offset;
    struct BTStackData *bts_parent;
} BTStackData;

typedef BTStackData *BTStack;

/*
 * BTScanInsertData is the btree-private state needed to find an initial
 * position for an indexscan, or to insert new tuples -- an "insertion
 * scankey" (not to be confused with a search scankey).  It's used to descend
 * a B-Tree using _bt_search.
 *
 * heapkeyspace indicates if we expect all keys in the index to be physically
 * unique because heap TID is used as a tiebreaker attribute, and if index may
 * have truncated key attributes in pivot tuples.  This is actually a property
 * of the index relation itself (not an indexscan).  heapkeyspace indexes are
 * indexes whose version is >= version 4.  It's convenient to keep this close
 * by, rather than accessing the metapage repeatedly.
 *
 * allequalimage is set to indicate that deduplication is safe for the index.
 * This is also a property of the index relation rather than an indexscan.
 *
 * anynullkeys indicates if any of the keys had NULL value when scankey was
 * built from index tuple (note that already-truncated tuple key attributes
 * set NULL as a placeholder key value, which also affects value of
 * anynullkeys).  This is a convenience for unique index non-pivot tuple
 * insertion, which usually temporarily unsets scantid, but shouldn't iff
 * anynullkeys is true.  Value generally matches non-pivot tuple's HasNulls
 * bit, but may not when inserting into an INCLUDE index (tuple header value
 * is affected by the NULL-ness of both key and non-key attributes).
 *
 * When nextkey is false (the usual case), _bt_search and _bt_binsrch will
 * locate the first item >= scankey.  When nextkey is true, they will locate
 * the first item > scan key.
 *
 * pivotsearch is set to true by callers that want to re-find a leaf page
 * using a scankey built from a leaf page's high key.  Most callers set this
 * to false.
 *
 * scantid is the heap TID that is used as a final tiebreaker attribute.  It
 * is set to NULL when index scan doesn't need to find a position for a
 * specific physical tuple.  Must be set when inserting new tuples into
 * heapkeyspace indexes, since every tuple in the tree unambiguously belongs
 * in one exact position (it's never set with !heapkeyspace indexes, though).
 * Despite the representational difference, nbtree search code considers
 * scantid to be just another insertion scankey attribute.
 *
 * scankeys is an array of scan key entries for attributes that are compared
 * before scantid (user-visible attributes).  keysz is the size of the array.
 * During insertion, there must be a scan key for every attribute, but when
 * starting a regular index scan some can be omitted.  The array is used as a
 * flexible array member, though it's sized in a way that makes it possible to
 * use stack allocations.  See nbtree/README for full details.
 */
typedef struct BTScanInsertData
{
    bool        heapkeyspace;
    bool        allequalimage;
    bool        anynullkeys;
    bool        nextkey;
    bool        pivotsearch;
    ItemPointer scantid;        /* tiebreaker for scankeys */
    int         keysz;          /* Size of scankeys array */
    ScanKeyData scankeys[INDEX_MAX_KEYS];   /* Must appear last */
} BTScanInsertData;

typedef BTScanInsertData *BTScanInsert;

/*
 * BTInsertStateData is a working area used during insertion.
 *
 * This is filled in after descending the tree to the first leaf page the new
 * tuple might belong on.  Tracks the current position while performing
 * uniqueness check, before we have determined which exact page to insert
 * to.
 *
 * (This should be private to nbtinsert.c, but it's also used by
 * _bt_binsrch_insert)
 */
typedef struct BTInsertStateData
{
    IndexTuple  itup;           /* Item we're inserting */
    Size        itemsz;         /* Size of itup -- should be MAXALIGN()'d */
    BTScanInsert itup_key;      /* Insertion scankey */

    /* Buffer containing leaf page we're likely to insert itup on */
    Buffer      buf;

    /*
     * Cache of bounds within the current buffer.  Only used for insertions
     * where _bt_check_unique is called.  See _bt_binsrch_insert and
     * _bt_findinsertloc for details.
     */
    bool        bounds_valid;
    OffsetNumber low;
    OffsetNumber stricthigh;

    /*
     * if _bt_binsrch_insert found the location inside existing posting list,
     * save the position inside the list.  -1 sentinel value indicates overlap
     * with an existing posting list tuple that has its LP_DEAD bit set.
     */
    int         postingoff;
} BTInsertStateData;

typedef BTInsertStateData *BTInsertState;

/*
 * State used to representing an individual pending tuple during
 * deduplication.
 */
typedef struct BTDedupInterval
{
    OffsetNumber baseoff;
    uint16      nitems;
} BTDedupInterval;

/*
 * BTDedupStateData is a working area used during deduplication.
 *
 * The status info fields track the state of a whole-page deduplication pass.
 * State about the current pending posting list is also tracked.
 *
 * A pending posting list is comprised of a contiguous group of equal items
 * from the page, starting from page offset number 'baseoff'.  This is the
 * offset number of the "base" tuple for new posting list.  'nitems' is the
 * current total number of existing items from the page that will be merged to
 * make a new posting list tuple, including the base tuple item.  (Existing
 * items may themselves be posting list tuples, or regular non-pivot tuples.)
 *
 * The total size of the existing tuples to be freed when pending posting list
 * is processed gets tracked by 'phystupsize'.  This information allows
 * deduplication to calculate the space saving for each new posting list
 * tuple, and for the entire pass over the page as a whole.
 */
typedef struct BTDedupStateData
{
    /* Deduplication status info for entire pass over page */
    bool        deduplicate;    /* Still deduplicating page? */
    int         nmaxitems;      /* Number of max-sized tuples so far */
    Size        maxpostingsize; /* Limit on size of final tuple */

    /* Metadata about base tuple of current pending posting list */
    IndexTuple  base;           /* Use to form new posting list */
    OffsetNumber baseoff;       /* page offset of base */
    Size        basetupsize;    /* base size without original posting list */

    /* Other metadata about pending posting list */
    ItemPointer htids;          /* Heap TIDs in pending posting list */
    int         nhtids;         /* Number of heap TIDs in htids array */
    int         nitems;         /* Number of existing tuples/line pointers */
    Size        phystupsize;    /* Includes line pointer overhead */

    /*
     * Array of tuples to go on new version of the page.  Contains one entry
     * for each group of consecutive items.  Note that existing tuples that
     * will not become posting list tuples do not appear in the array (they
     * are implicitly unchanged by deduplication pass).
     */
    int         nintervals;     /* current number of intervals in array */
    BTDedupInterval intervals[MaxIndexTuplesPerPage];
} BTDedupStateData;

typedef BTDedupStateData *BTDedupState;

/*
 * BTVacuumPostingData is state that represents how to VACUUM a posting list
 * tuple when some (though not all) of its TIDs are to be deleted.
 *
 * Convention is that itup field is the original posting list tuple on input,
 * and palloc()'d final tuple used to overwrite existing tuple on output.
 */
typedef struct BTVacuumPostingData
{
    /* Tuple that will be/was updated */
    IndexTuple  itup;
    OffsetNumber updatedoffset;

    /* State needed to describe final itup in WAL */
    uint16      ndeletedtids;
    uint16      deletetids[FLEXIBLE_ARRAY_MEMBER];
} BTVacuumPostingData;

typedef BTVacuumPostingData *BTVacuumPosting;

/*
 * BTScanOpaqueData is the btree-private state needed for an indexscan.
 * This consists of preprocessed scan keys (see _bt_preprocess_keys() for
 * details of the preprocessing), information about the current location
 * of the scan, and information about the marked location, if any.  (We use
 * BTScanPosData to represent the data needed for each of current and marked
 * locations.)  In addition we can remember some known-killed index entries
 * that must be marked before we can move off the current page.
 *
 * Index scans work a page at a time: we pin and read-lock the page, identify
 * all the matching items on the page and save them in BTScanPosData, then
 * release the read-lock while returning the items to the caller for
 * processing.  This approach minimizes lock/unlock traffic.  Note that we
 * keep the pin on the index page until the caller is done with all the items
 * (this is needed for VACUUM synchronization, see nbtree/README).  When we
 * are ready to step to the next page, if the caller has told us any of the
 * items were killed, we re-lock the page to mark them killed, then unlock.
 * Finally we drop the pin and step to the next page in the appropriate
 * direction.
 *
 * If we are doing an index-only scan, we save the entire IndexTuple for each
 * matched item, otherwise only its heap TID and offset.  The IndexTuples go
 * into a separate workspace array; each BTScanPosItem stores its tuple's
 * offset within that array.  Posting list tuples store a "base" tuple once,
 * allowing the same key to be returned for each TID in the posting list
 * tuple.
 */

typedef struct BTScanPosItem    /* what we remember about each match */
{
    ItemPointerData heapTid;    /* TID of referenced heap item */
    OffsetNumber indexOffset;   /* index item's location within page */
    LocationIndex tupleOffset;  /* IndexTuple's offset in workspace, if any */
} BTScanPosItem;

typedef struct BTScanPosData
{
    Buffer      buf;            /* if valid, the buffer is pinned */

    XLogRecPtr  lsn;            /* pos in the WAL stream when page was read */
    BlockNumber currPage;       /* page referenced by items array */
    BlockNumber nextPage;       /* page's right link when we scanned it */

    /*
     * moreLeft and moreRight track whether we think there may be matching
     * index entries to the left and right of the current page, respectively.
     * We can clear the appropriate one of these flags when _bt_checkkeys()
     * returns continuescan = false.
     */
    bool        moreLeft;
    bool        moreRight;

    /*
     * If we are doing an index-only scan, nextTupleOffset is the first free
     * location in the associated tuple storage workspace.
     */
    int         nextTupleOffset;

    /*
     * The items array is always ordered in index order (ie, increasing
     * indexoffset).  When scanning backwards it is convenient to fill the
     * array back-to-front, so we start at the last slot and fill downwards.
     * Hence we need both a first-valid-entry and a last-valid-entry counter.
     * itemIndex is a cursor showing which entry was last returned to caller.
     */
    int         firstItem;      /* first valid index in items[] */
    int         lastItem;       /* last valid index in items[] */
    int         itemIndex;      /* current index in items[] */

    BTScanPosItem items[MaxTIDsPerBTreePage];   /* MUST BE LAST */
} BTScanPosData;

typedef BTScanPosData *BTScanPos;

#define BTScanPosIsPinned(scanpos) \
( \
    AssertMacro(BlockNumberIsValid((scanpos).currPage) || \
                !BufferIsValid((scanpos).buf)), \
    BufferIsValid((scanpos).buf) \
)
#define BTScanPosUnpin(scanpos) \
    do { \
        ReleaseBuffer((scanpos).buf); \
        (scanpos).buf = InvalidBuffer; \
    } while (0)
#define BTScanPosUnpinIfPinned(scanpos) \
    do { \
        if (BTScanPosIsPinned(scanpos)) \
            BTScanPosUnpin(scanpos); \
    } while (0)

#define BTScanPosIsValid(scanpos) \
( \
    AssertMacro(BlockNumberIsValid((scanpos).currPage) || \
                !BufferIsValid((scanpos).buf)), \
    BlockNumberIsValid((scanpos).currPage) \
)
#define BTScanPosInvalidate(scanpos) \
    do { \
        (scanpos).currPage = InvalidBlockNumber; \
        (scanpos).nextPage = InvalidBlockNumber; \
        (scanpos).buf = InvalidBuffer; \
        (scanpos).lsn = InvalidXLogRecPtr; \
        (scanpos).nextTupleOffset = 0; \
    } while (0)

/* We need one of these for each equality-type SK_SEARCHARRAY scan key */
typedef struct BTArrayKeyInfo
{
    int         scan_key;       /* index of associated key in arrayKeyData */
    int         cur_elem;       /* index of current element in elem_values */
    int         mark_elem;      /* index of marked element in elem_values */
    int         num_elems;      /* number of elems in current array value */
    Datum      *elem_values;    /* array of num_elems Datums */
} BTArrayKeyInfo;

typedef struct BTScanOpaqueData
{
    /* these fields are set by _bt_preprocess_keys(): */
    bool        qual_ok;        /* false if qual can never be satisfied */
    int         numberOfKeys;   /* number of preprocessed scan keys */
    ScanKey     keyData;        /* array of preprocessed scan keys */

    /* workspace for SK_SEARCHARRAY support */
    ScanKey     arrayKeyData;   /* modified copy of scan->keyData */
    int         numArrayKeys;   /* number of equality-type array keys (-1 if
                                 * there are any unsatisfiable array keys) */
    int         arrayKeyCount;  /* count indicating number of array scan keys
                                 * processed */
    BTArrayKeyInfo *arrayKeys;  /* info about each equality-type array key */
    MemoryContext arrayContext; /* scan-lifespan context for array data */

    /* info about killed items if any (killedItems is NULL if never used) */
    int        *killedItems;    /* currPos.items indexes of killed items */
    int         numKilled;      /* number of currently stored items */

    /*
     * If we are doing an index-only scan, these are the tuple storage
     * workspaces for the currPos and markPos respectively.  Each is of size
     * BLCKSZ, so it can hold as much as a full page's worth of tuples.
     */
    char       *currTuples;     /* tuple storage for currPos */
    char       *markTuples;     /* tuple storage for markPos */

    /*
     * If the marked position is on the same page as current position, we
     * don't use markPos, but just keep the marked itemIndex in markItemIndex
     * (all the rest of currPos is valid for the mark position). Hence, to
     * determine if there is a mark, first look at markItemIndex, then at
     * markPos.
     */
    int         markItemIndex;  /* itemIndex, or -1 if not valid */

    /* keep these last in struct for efficiency */
    BTScanPosData currPos;      /* current position data */
    BTScanPosData markPos;      /* marked position, if any */
} BTScanOpaqueData;

typedef BTScanOpaqueData *BTScanOpaque;

/*
 * We use some private sk_flags bits in preprocessed scan keys.  We're allowed
 * to use bits 16-31 (see skey.h).  The uppermost bits are copied from the
 * index's indoption[] array entry for the index attribute.
 */
#define SK_BT_REQFWD    0x00010000  /* required to continue forward scan */
#define SK_BT_REQBKWD   0x00020000  /* required to continue backward scan */
#define SK_BT_INDOPTION_SHIFT  24   /* must clear the above bits */
#define SK_BT_DESC          (INDOPTION_DESC << SK_BT_INDOPTION_SHIFT)
#define SK_BT_NULLS_FIRST   (INDOPTION_NULLS_FIRST << SK_BT_INDOPTION_SHIFT)

typedef struct BTOptions
{
    int32       varlena_header_;    /* varlena header (do not touch directly!) */
    int         fillfactor;     /* page fill factor in percent (0..100) */
    /* fraction of newly inserted tuples prior to trigger index cleanup */
    float8      vacuum_cleanup_index_scale_factor;
    bool        deduplicate_items;  /* Try to deduplicate items? */
} BTOptions;

#define BTGetFillFactor(relation) \
    (AssertMacro(relation->rd_rel->relkind == RELKIND_INDEX && \
                 relation->rd_rel->relam == BTREE_AM_OID), \
     (relation)->rd_options ? \
     ((BTOptions *) (relation)->rd_options)->fillfactor : \
     BTREE_DEFAULT_FILLFACTOR)
#define BTGetTargetPageFreeSpace(relation) \
    (BLCKSZ * (100 - BTGetFillFactor(relation)) / 100)
#define BTGetDeduplicateItems(relation) \
    (AssertMacro(relation->rd_rel->relkind == RELKIND_INDEX && \
                 relation->rd_rel->relam == BTREE_AM_OID), \
    ((relation)->rd_options ? \
     ((BTOptions *) (relation)->rd_options)->deduplicate_items : true))

/*
 * Constant definition for progress reporting.  Phase numbers must match
 * btbuildphasename.
 */
/* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 (see progress.h) */
#define PROGRESS_BTREE_PHASE_INDEXBUILD_TABLESCAN       2
#define PROGRESS_BTREE_PHASE_PERFORMSORT_1              3
#define PROGRESS_BTREE_PHASE_PERFORMSORT_2              4
#define PROGRESS_BTREE_PHASE_LEAF_LOAD                  5

/*
 * external entry points for btree, in nbtree.c
 */
extern void btbuildempty(Relation index);
extern bool btinsert(Relation rel, Datum *values, bool *isnull,
                     ItemPointer ht_ctid, Relation heapRel,
                     IndexUniqueCheck checkUnique,
                     struct IndexInfo *indexInfo);
extern IndexScanDesc btbeginscan(Relation rel, int nkeys, int norderbys);
extern Size btestimateparallelscan(void);
extern void btinitparallelscan(void *target);
extern bool btgettuple(IndexScanDesc scan, ScanDirection dir);
extern int64 btgetbitmap(IndexScanDesc scan, TIDBitmap *tbm);
extern void btrescan(IndexScanDesc scan, ScanKey scankey, int nscankeys,
                     ScanKey orderbys, int norderbys);
extern void btparallelrescan(IndexScanDesc scan);
extern void btendscan(IndexScanDesc scan);
extern void btmarkpos(IndexScanDesc scan);
extern void btrestrpos(IndexScanDesc scan);
extern IndexBulkDeleteResult *btbulkdelete(IndexVacuumInfo *info,
                                           IndexBulkDeleteResult *stats,
                                           IndexBulkDeleteCallback callback,
                                           void *callback_state);
extern IndexBulkDeleteResult *btvacuumcleanup(IndexVacuumInfo *info,
                                              IndexBulkDeleteResult *stats);
extern bool btcanreturn(Relation index, int attno);

/*
 * prototypes for internal functions in nbtree.c
 */
extern bool _bt_parallel_seize(IndexScanDesc scan, BlockNumber *pageno);
extern void _bt_parallel_release(IndexScanDesc scan, BlockNumber scan_page);
extern void _bt_parallel_done(IndexScanDesc scan);
extern void _bt_parallel_advance_array_keys(IndexScanDesc scan);

/*
 * prototypes for functions in nbtdedup.c
 */
extern void _bt_dedup_pass(Relation rel, Buffer buf, Relation heapRel,
                           IndexTuple newitem, Size newitemsz,
                           bool checkingunique);
extern void _bt_dedup_start_pending(BTDedupState state, IndexTuple base,
                                    OffsetNumber baseoff);
extern bool _bt_dedup_save_htid(BTDedupState state, IndexTuple itup);
extern Size _bt_dedup_finish_pending(Page newpage, BTDedupState state);
extern IndexTuple _bt_form_posting(IndexTuple base, ItemPointer htids,
                                   int nhtids);
extern void _bt_update_posting(BTVacuumPosting vacposting);
extern IndexTuple _bt_swap_posting(IndexTuple newitem, IndexTuple oposting,
                                   int postingoff);

/*
 * prototypes for functions in nbtinsert.c
 */
extern bool _bt_doinsert(Relation rel, IndexTuple itup,
                         IndexUniqueCheck checkUnique, Relation heapRel);
extern void _bt_finish_split(Relation rel, Buffer lbuf, BTStack stack);
extern Buffer _bt_getstackbuf(Relation rel, BTStack stack, BlockNumber child);

/*
 * prototypes for functions in nbtsplitloc.c
 */
extern OffsetNumber _bt_findsplitloc(Relation rel, Page origpage,
                                     OffsetNumber newitemoff, Size newitemsz, IndexTuple newitem,
                                     bool *newitemonleft);

/*
 * prototypes for functions in nbtpage.c
 */
extern void _bt_initmetapage(Page page, BlockNumber rootbknum, uint32 level,
                             bool allequalimage);
extern void _bt_update_meta_cleanup_info(Relation rel,
                                         TransactionId oldestBtpoXact, float8 numHeapTuples);
extern void _bt_upgrademetapage(Page page);
extern Buffer _bt_getroot(Relation rel, int access);
extern Buffer _bt_gettrueroot(Relation rel);
extern int  _bt_getrootheight(Relation rel);
extern void _bt_metaversion(Relation rel, bool *heapkeyspace,
                            bool *allequalimage);
extern void _bt_checkpage(Relation rel, Buffer buf);
extern Buffer _bt_getbuf(Relation rel, BlockNumber blkno, int access);
extern Buffer _bt_relandgetbuf(Relation rel, Buffer obuf,
                               BlockNumber blkno, int access);
extern void _bt_relbuf(Relation rel, Buffer buf);
extern void _bt_lockbuf(Relation rel, Buffer buf, int access);
extern void _bt_unlockbuf(Relation rel, Buffer buf);
extern bool _bt_conditionallockbuf(Relation rel, Buffer buf);
extern void _bt_upgradelockbufcleanup(Relation rel, Buffer buf);
extern void _bt_pageinit(Page page, Size size);
extern bool _bt_page_recyclable(Page page);
extern void _bt_delitems_vacuum(Relation rel, Buffer buf,
                                OffsetNumber *deletable, int ndeletable,
                                BTVacuumPosting *updatable, int nupdatable);
extern void _bt_delitems_delete(Relation rel, Buffer buf,
                                OffsetNumber *deletable, int ndeletable,
                                Relation heapRel);
extern uint32 _bt_pagedel(Relation rel, Buffer leafbuf,
                          TransactionId *oldestBtpoXact);

/*
 * prototypes for functions in nbtsearch.c
 */
extern BTStack _bt_search(Relation rel, BTScanInsert key, Buffer *bufP,
                          int access, Snapshot snapshot);
extern Buffer _bt_moveright(Relation rel, BTScanInsert key, Buffer buf,
                            bool forupdate, BTStack stack, int access, Snapshot snapshot);
extern OffsetNumber _bt_binsrch_insert(Relation rel, BTInsertState insertstate);
extern int32 _bt_compare(Relation rel, BTScanInsert key, Page page, OffsetNumber offnum);
extern bool _bt_first(IndexScanDesc scan, ScanDirection dir);
extern bool _bt_next(IndexScanDesc scan, ScanDirection dir);
extern Buffer _bt_get_endpoint(Relation rel, uint32 level, bool rightmost,
                               Snapshot snapshot);

/*
 * prototypes for functions in nbtutils.c
 */
extern BTScanInsert _bt_mkscankey(Relation rel, IndexTuple itup);
extern void _bt_freestack(BTStack stack);
extern void _bt_preprocess_array_keys(IndexScanDesc scan);
extern void _bt_start_array_keys(IndexScanDesc scan, ScanDirection dir);
extern bool _bt_advance_array_keys(IndexScanDesc scan, ScanDirection dir);
extern void _bt_mark_array_keys(IndexScanDesc scan);
extern void _bt_restore_array_keys(IndexScanDesc scan);
extern void _bt_preprocess_keys(IndexScanDesc scan);
extern bool _bt_checkkeys(IndexScanDesc scan, IndexTuple tuple,
                          int tupnatts, ScanDirection dir, bool *continuescan);
extern void _bt_killitems(IndexScanDesc scan);
extern BTCycleId _bt_vacuum_cycleid(Relation rel);
extern BTCycleId _bt_start_vacuum(Relation rel);
extern void _bt_end_vacuum(Relation rel);
extern void _bt_end_vacuum_callback(int code, Datum arg);
extern Size BTreeShmemSize(void);
extern void BTreeShmemInit(void);
extern bytea *btoptions(Datum reloptions, bool validate);
extern bool btproperty(Oid index_oid, int attno,
                       IndexAMProperty prop, const char *propname,
                       bool *res, bool *isnull);
extern char *btbuildphasename(int64 phasenum);
extern IndexTuple _bt_truncate(Relation rel, IndexTuple lastleft,
                               IndexTuple firstright, BTScanInsert itup_key);
extern int  _bt_keep_natts_fast(Relation rel, IndexTuple lastleft,
                                IndexTuple firstright);
extern bool _bt_check_natts(Relation rel, bool heapkeyspace, Page page,
                            OffsetNumber offnum);
extern void _bt_check_third_page(Relation rel, Relation heap,
                                 bool needheaptidspace, Page page, IndexTuple newtup);
extern bool _bt_allequalimage(Relation rel, bool debugmessage);

/*
 * prototypes for functions in nbtvalidate.c
 */
extern bool btvalidate(Oid opclassoid);
extern void btadjustmembers(Oid opfamilyoid,
                            Oid opclassoid,
                            List *operators,
                            List *functions);

/*
 * prototypes for functions in nbtsort.c
 */
extern IndexBuildResult *btbuild(Relation heap, Relation index,
                                 struct IndexInfo *indexInfo);
extern void _bt_parallel_build_main(dsm_segment *seg, shm_toc *toc);

#endif                          /* NBTREE_H */