spgist_private.h

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/*-------------------------------------------------------------------------
 *
 * spgist_private.h
 *    Private declarations for SP-GiST access method.
 *
 *
 * Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * src/include/access/spgist_private.h
 *
 *-------------------------------------------------------------------------
 */
#ifndef SPGIST_PRIVATE_H
#define SPGIST_PRIVATE_H
 
#include "access/itup.h"
#include "access/spgist.h"
#include "catalog/pg_am_d.h"
#include "nodes/tidbitmap.h"
#include "storage/buf.h"
#include "utils/geo_decls.h"
#include "utils/relcache.h"
 
 
typedef struct SpGistOptions
{
    int32       varlena_header_;    /* varlena header (do not touch directly!) */
    int         fillfactor;     /* page fill factor in percent (0..100) */
} SpGistOptions;
 
#define SpGistGetFillFactor(relation) \
    (AssertMacro(relation->rd_rel->relkind == RELKIND_INDEX && \
                 relation->rd_rel->relam == SPGIST_AM_OID), \
     (relation)->rd_options ? \
     ((SpGistOptions *) (relation)->rd_options)->fillfactor : \
     SPGIST_DEFAULT_FILLFACTOR)
#define SpGistGetTargetPageFreeSpace(relation) \
    (BLCKSZ * (100 - SpGistGetFillFactor(relation)) / 100)
 
 
/* SPGiST leaf tuples have one key column, optionally have included columns */
#define spgKeyColumn 0
#define spgFirstIncludeColumn 1
 
/* Page numbers of fixed-location pages */
#define SPGIST_METAPAGE_BLKNO    (0)    /* metapage */
#define SPGIST_ROOT_BLKNO        (1)    /* root for normal entries */
#define SPGIST_NULL_BLKNO        (2)    /* root for null-value entries */
#define SPGIST_LAST_FIXED_BLKNO  SPGIST_NULL_BLKNO
 
#define SpGistBlockIsRoot(blkno) \
    ((blkno) == SPGIST_ROOT_BLKNO || (blkno) == SPGIST_NULL_BLKNO)
#define SpGistBlockIsFixed(blkno) \
    ((BlockNumber) (blkno) <= (BlockNumber) SPGIST_LAST_FIXED_BLKNO)
 
/*
 * Contents of page special space on SPGiST index pages
 */
typedef struct SpGistPageOpaqueData
{
    uint16      flags;          /* see bit definitions below */
    uint16      nRedirection;   /* number of redirection tuples on page */
    uint16      nPlaceholder;   /* number of placeholder tuples on page */
    /* note there's no count of either LIVE or DEAD tuples ... */
    uint16      spgist_page_id; /* for identification of SP-GiST indexes */
} SpGistPageOpaqueData;
 
typedef SpGistPageOpaqueData *SpGistPageOpaque;
 
/* Flag bits in page special space */
#define SPGIST_META         (1<<0)
#define SPGIST_DELETED      (1<<1)  /* never set, but keep for backwards
                                     * compatibility */
#define SPGIST_LEAF         (1<<2)
#define SPGIST_NULLS        (1<<3)
 
#define SpGistPageGetOpaque(page) ((SpGistPageOpaque) PageGetSpecialPointer(page))
#define SpGistPageIsMeta(page) (SpGistPageGetOpaque(page)->flags & SPGIST_META)
#define SpGistPageIsDeleted(page) (SpGistPageGetOpaque(page)->flags & SPGIST_DELETED)
#define SpGistPageIsLeaf(page) (SpGistPageGetOpaque(page)->flags & SPGIST_LEAF)
#define SpGistPageStoresNulls(page) (SpGistPageGetOpaque(page)->flags & SPGIST_NULLS)
 
/*
 * The page ID is for the convenience of pg_filedump and similar utilities,
 * which otherwise would have a hard time telling pages of different index
 * types apart.  It should be the last 2 bytes on the page.  This is more or
 * less "free" due to alignment considerations.
 *
 * See comments above GinPageOpaqueData.
 */
#define SPGIST_PAGE_ID      0xFF82
 
/*
 * Each backend keeps a cache of last-used page info in its index->rd_amcache
 * area.  This is initialized from, and occasionally written back to,
 * shared storage in the index metapage.
 */
typedef struct SpGistLastUsedPage
{
    BlockNumber blkno;          /* block number, or InvalidBlockNumber */
    int         freeSpace;      /* page's free space (could be obsolete!) */
} SpGistLastUsedPage;
 
/* Note: indexes in cachedPage[] match flag assignments for SpGistGetBuffer */
#define SPGIST_CACHED_PAGES 8
 
typedef struct SpGistLUPCache
{
    SpGistLastUsedPage cachedPage[SPGIST_CACHED_PAGES];
} SpGistLUPCache;
 
/*
 * metapage
 */
typedef struct SpGistMetaPageData
{
    uint32      magicNumber;    /* for identity cross-check */
    SpGistLUPCache lastUsedPages;   /* shared storage of last-used info */
} SpGistMetaPageData;
 
#define SPGIST_MAGIC_NUMBER (0xBA0BABEE)
 
#define SpGistPageGetMeta(p) \
    ((SpGistMetaPageData *) PageGetContents(p))
 
/*
 * Private state of index AM.  SpGistState is common to both insert and
 * search code; SpGistScanOpaque is for searches only.
 */
 
typedef struct SpGistLeafTupleData *SpGistLeafTuple;    /* forward reference */
 
/* Per-datatype info needed in SpGistState */
typedef struct SpGistTypeDesc
{
    Oid         type;
    int16       attlen;
    bool        attbyval;
    char        attalign;
    char        attstorage;
} SpGistTypeDesc;
 
typedef struct SpGistState
{
    Relation    index;          /* index we're working with */
 
    spgConfigOut config;        /* filled in by opclass config method */
 
    SpGistTypeDesc attType;     /* type of values to be indexed/restored */
    SpGistTypeDesc attLeafType; /* type of leaf-tuple values */
    SpGistTypeDesc attPrefixType;   /* type of inner-tuple prefix values */
    SpGistTypeDesc attLabelType;    /* type of node label values */
 
    /* leafTupDesc typically points to index's tupdesc, but not always */
    TupleDesc   leafTupDesc;    /* descriptor for leaf-level tuples */
 
    char       *deadTupleStorage;   /* workspace for spgFormDeadTuple */
 
    TransactionId myXid;        /* XID to use when creating a redirect tuple */
    bool        isBuild;        /* true if doing index build */
} SpGistState;
 
/* Item to be re-examined later during a search */
typedef struct SpGistSearchItem
{
    pairingheap_node phNode;    /* pairing heap node */
    Datum       value;          /* value reconstructed from parent, or
                                 * leafValue if isLeaf */
    SpGistLeafTuple leafTuple;  /* whole leaf tuple, if needed */
    void       *traversalValue; /* opclass-specific traverse value */
    int         level;          /* level of items on this page */
    ItemPointerData heapPtr;    /* heap info, if heap tuple */
    bool        isNull;         /* SearchItem is NULL item */
    bool        isLeaf;         /* SearchItem is heap item */
    bool        recheck;        /* qual recheck is needed */
    bool        recheckDistances;   /* distance recheck is needed */
 
    /* array with numberOfOrderBys entries */
    double      distances[FLEXIBLE_ARRAY_MEMBER];
} SpGistSearchItem;
 
#define SizeOfSpGistSearchItem(n_distances) \
    (offsetof(SpGistSearchItem, distances) + sizeof(double) * (n_distances))
 
/*
 * Private state of an index scan
 */
typedef struct SpGistScanOpaqueData
{
    SpGistState state;          /* see above */
    pairingheap *scanQueue;     /* queue of to be visited items */
    MemoryContext tempCxt;      /* short-lived memory context */
    MemoryContext traversalCxt; /* single scan lifetime memory context */
 
    /* Control flags showing whether to search nulls and/or non-nulls */
    bool        searchNulls;    /* scan matches (all) null entries */
    bool        searchNonNulls; /* scan matches (some) non-null entries */
 
    /* Index quals to be passed to opclass (null-related quals removed) */
    int         numberOfKeys;   /* number of index qualifier conditions */
    ScanKey     keyData;        /* array of index qualifier descriptors */
    int         numberOfOrderBys;   /* number of ordering operators */
    int         numberOfNonNullOrderBys;    /* number of ordering operators
                                             * with non-NULL arguments */
    ScanKey     orderByData;    /* array of ordering op descriptors */
    Oid        *orderByTypes;   /* array of ordering op return types */
    int        *nonNullOrderByOffsets;  /* array of offset of non-NULL
                                         * ordering keys in the original array */
    Oid         indexCollation; /* collation of index column */
 
    /* Opclass defined functions: */
    FmgrInfo    innerConsistentFn;
    FmgrInfo    leafConsistentFn;
 
    /* Pre-allocated workspace arrays: */
    double     *zeroDistances;
    double     *infDistances;
 
    /* These fields are only used in amgetbitmap scans: */
    TIDBitmap  *tbm;            /* bitmap being filled */
    int64       ntids;          /* number of TIDs passed to bitmap */
 
    /* These fields are only used in amgettuple scans: */
    bool        want_itup;      /* are we reconstructing tuples? */
    TupleDesc   reconTupDesc;   /* if so, descriptor for reconstructed tuples */
    int         nPtrs;          /* number of TIDs found on current page */
    int         iPtr;           /* index for scanning through same */
    ItemPointerData heapPtrs[MaxIndexTuplesPerPage];    /* TIDs from cur page */
    bool        recheck[MaxIndexTuplesPerPage]; /* their recheck flags */
    bool        recheckDistances[MaxIndexTuplesPerPage];    /* distance recheck
                                                             * flags */
    HeapTuple   reconTups[MaxIndexTuplesPerPage];   /* reconstructed tuples */
 
    /* distances (for recheck) */
    IndexOrderByDistance *distances[MaxIndexTuplesPerPage];
 
    /*
     * Note: using MaxIndexTuplesPerPage above is a bit hokey since
     * SpGistLeafTuples aren't exactly IndexTuples; however, they are larger,
     * so this is safe.
     */
} SpGistScanOpaqueData;
 
typedef SpGistScanOpaqueData *SpGistScanOpaque;
 
/*
 * This struct is what we actually keep in index->rd_amcache.  It includes
 * static configuration information as well as the lastUsedPages cache.
 */
typedef struct SpGistCache
{
    spgConfigOut config;        /* filled in by opclass config method */
 
    SpGistTypeDesc attType;     /* type of values to be indexed/restored */
    SpGistTypeDesc attLeafType; /* type of leaf-tuple values */
    SpGistTypeDesc attPrefixType;   /* type of inner-tuple prefix values */
    SpGistTypeDesc attLabelType;    /* type of node label values */
 
    SpGistLUPCache lastUsedPages;   /* local storage of last-used info */
} SpGistCache;
 
 
/*
 * SPGiST tuple types.  Note: inner, leaf, and dead tuple structs
 * must have the same tupstate field in the same position!  Real inner and
 * leaf tuples always have tupstate = LIVE; if the state is something else,
 * use the SpGistDeadTuple struct to inspect the tuple.
 */
 
/* values of tupstate (see README for more info) */
#define SPGIST_LIVE         0   /* normal live tuple (either inner or leaf) */
#define SPGIST_REDIRECT     1   /* temporary redirection placeholder */
#define SPGIST_DEAD         2   /* dead, cannot be removed because of links */
#define SPGIST_PLACEHOLDER  3   /* placeholder, used to preserve offsets */
 
/*
 * SPGiST inner tuple: list of "nodes" that subdivide a set of tuples
 *
 * Inner tuple layout:
 * header/optional prefix/array of nodes, which are SpGistNodeTuples
 *
 * size and prefixSize must be multiples of MAXALIGN
 *
 * If the prefix datum is of a pass-by-value type, it is stored in its
 * Datum representation, that is its on-disk representation is of length
 * sizeof(Datum).  This is a fairly unfortunate choice, because in no other
 * place does Postgres use Datum as an on-disk representation; it creates
 * an unnecessary incompatibility between 32-bit and 64-bit builds.  But the
 * compatibility loss is mostly theoretical since MAXIMUM_ALIGNOF typically
 * differs between such builds, too.  Anyway we're stuck with it now.
 */
typedef struct SpGistInnerTupleData
{
    unsigned int tupstate:2,    /* LIVE/REDIRECT/DEAD/PLACEHOLDER */
                allTheSame:1,   /* all nodes in tuple are equivalent */
                nNodes:13,      /* number of nodes within inner tuple */
                prefixSize:16;  /* size of prefix, or 0 if none */
    uint16      size;           /* total size of inner tuple */
    /* On most machines there will be a couple of wasted bytes here */
    /* prefix datum follows, then nodes */
} SpGistInnerTupleData;
 
typedef SpGistInnerTupleData *SpGistInnerTuple;
 
/* these must match largest values that fit in bit fields declared above */
#define SGITMAXNNODES       0x1FFF
#define SGITMAXPREFIXSIZE   0xFFFF
#define SGITMAXSIZE         0xFFFF
 
#define SGITHDRSZ           MAXALIGN(sizeof(SpGistInnerTupleData))
#define _SGITDATA(x)        (((char *) (x)) + SGITHDRSZ)
#define SGITDATAPTR(x)      ((x)->prefixSize ? _SGITDATA(x) : NULL)
#define SGITDATUM(x, s)     ((x)->prefixSize ? \
                             ((s)->attPrefixType.attbyval ? \
                              *(Datum *) _SGITDATA(x) : \
                              PointerGetDatum(_SGITDATA(x))) \
                             : (Datum) 0)
#define SGITNODEPTR(x)      ((SpGistNodeTuple) (_SGITDATA(x) + (x)->prefixSize))
 
/* Macro for iterating through the nodes of an inner tuple */
#define SGITITERATE(x, i, nt)   \
    for ((i) = 0, (nt) = SGITNODEPTR(x); \
         (i) < (x)->nNodes; \
         (i)++, (nt) = (SpGistNodeTuple) (((char *) (nt)) + IndexTupleSize(nt)))
 
/*
 * SPGiST node tuple: one node within an inner tuple
 *
 * Node tuples use the same header as ordinary Postgres IndexTuples, but
 * we do not use a null bitmap, because we know there is only one column
 * so the INDEX_NULL_MASK bit suffices.  Also, pass-by-value datums are
 * stored in Datum form, the same convention as for inner tuple prefixes.
 */
 
typedef IndexTupleData SpGistNodeTupleData;
 
typedef SpGistNodeTupleData *SpGistNodeTuple;
 
#define SGNTHDRSZ           MAXALIGN(sizeof(SpGistNodeTupleData))
#define SGNTDATAPTR(x)      (((char *) (x)) + SGNTHDRSZ)
#define SGNTDATUM(x, s)     ((s)->attLabelType.attbyval ? \
                             *(Datum *) SGNTDATAPTR(x) : \
                             PointerGetDatum(SGNTDATAPTR(x)))
 
/*
 * SPGiST leaf tuple: carries a leaf datum and a heap tuple TID,
 * and optionally some "included" columns.
 *
 * In the simplest case, the leaf datum is the same as the indexed value;
 * but it could also be a suffix or some other sort of delta that permits
 * reconstruction given knowledge of the prefix path traversed to get here.
 * Any included columns are stored without modification.
 *
 * A nulls bitmap is present if there are included columns AND any of the
 * datums are NULL.  We do not need a nulls bitmap for the case of a null
 * leaf datum without included columns, as we can infer whether the leaf
 * datum is null from whether the tuple is stored on a nulls page.  (This
 * provision is mostly for backwards compatibility, but it does save space
 * on 32-bit machines.)  As with other PG index tuple designs, if the nulls
 * bitmap exists then it's of size INDEX_MAX_KEYS bits regardless of the
 * actual number of attributes.  For the usual choice of INDEX_MAX_KEYS,
 * this costs nothing because of alignment considerations.
 *
 * The size field is wider than could possibly be needed for an on-disk leaf
 * tuple, but this allows us to form leaf tuples even when the datum is too
 * wide to be stored immediately, and it costs nothing because of alignment
 * considerations.
 *
 * t_info holds the nextOffset field (14 bits wide, enough for supported
 * page sizes) plus the has-nulls-bitmap flag bit; another flag bit is free.
 *
 * Normally, nextOffset links to the next tuple belonging to the same parent
 * node (which must be on the same page), or it's 0 if there is no next tuple.
 * But when the root page is a leaf page, we don't chain its tuples,
 * so nextOffset is always 0 on the root.
 *
 * size must be a multiple of MAXALIGN; also, it must be at least SGDTSIZE
 * so that the tuple can be converted to REDIRECT status later.  (This
 * restriction only adds bytes for a NULL leaf datum stored on a 32-bit
 * machine; otherwise alignment restrictions force it anyway.)
 */
typedef struct SpGistLeafTupleData
{
    unsigned int tupstate:2,    /* LIVE/REDIRECT/DEAD/PLACEHOLDER */
                size:30;        /* large enough for any palloc'able value */
    uint16      t_info;         /* nextOffset, which links to the next tuple
                                 * in chain, plus two flag bits */
    ItemPointerData heapPtr;    /* TID of represented heap tuple */
    /* nulls bitmap follows if the flag bit for it is set */
    /* leaf datum, then any included datums, follows on a MAXALIGN boundary */
} SpGistLeafTupleData;
 
/* Macros to access nextOffset and bit fields inside t_info */
#define SGLT_GET_NEXTOFFSET(spgLeafTuple) \
    ((spgLeafTuple)->t_info & 0x3FFF)
#define SGLT_GET_HASNULLMASK(spgLeafTuple) \
    (((spgLeafTuple)->t_info & 0x8000) ? true : false)
#define SGLT_SET_NEXTOFFSET(spgLeafTuple, offsetNumber) \
    ((spgLeafTuple)->t_info = \
     ((spgLeafTuple)->t_info & 0xC000) | ((offsetNumber) & 0x3FFF))
#define SGLT_SET_HASNULLMASK(spgLeafTuple, hasnulls) \
    ((spgLeafTuple)->t_info = \
     ((spgLeafTuple)->t_info & 0x7FFF) | ((hasnulls) ? 0x8000 : 0))
 
#define SGLTHDRSZ(hasnulls) \
    ((hasnulls) ? MAXALIGN(sizeof(SpGistLeafTupleData) + \
                           sizeof(IndexAttributeBitMapData)) : \
     MAXALIGN(sizeof(SpGistLeafTupleData)))
#define SGLTDATAPTR(x)      (((char *) (x)) + SGLTHDRSZ(SGLT_GET_HASNULLMASK(x)))
#define SGLTDATUM(x, s)     fetch_att(SGLTDATAPTR(x), \
                                      (s)->attLeafType.attbyval, \
                                      (s)->attLeafType.attlen)
 
/*
 * SPGiST dead tuple: declaration for examining non-live tuples
 *
 * The tupstate field of this struct must match those of regular inner and
 * leaf tuples, and its size field must match a leaf tuple's.
 * Also, the pointer field must be in the same place as a leaf tuple's heapPtr
 * field, to satisfy some Asserts that we make when replacing a leaf tuple
 * with a dead tuple.
 * We don't use t_info, but it's needed to align the pointer field.
 * pointer and xid are only valid when tupstate = REDIRECT.
 */
typedef struct SpGistDeadTupleData
{
    unsigned int tupstate:2,    /* LIVE/REDIRECT/DEAD/PLACEHOLDER */
                size:30;
    uint16      t_info;         /* not used in dead tuples */
    ItemPointerData pointer;    /* redirection inside index */
    TransactionId xid;          /* ID of xact that inserted this tuple */
} SpGistDeadTupleData;
 
typedef SpGistDeadTupleData *SpGistDeadTuple;
 
#define SGDTSIZE        MAXALIGN(sizeof(SpGistDeadTupleData))
 
/*
 * Macros for doing free-space calculations.  Note that when adding up the
 * space needed for tuples, we always consider each tuple to need the tuple's
 * size plus sizeof(ItemIdData) (for the line pointer).  This works correctly
 * so long as tuple sizes are always maxaligned.
 */
 
/* Page capacity after allowing for fixed header and special space */
#define SPGIST_PAGE_CAPACITY  \
    MAXALIGN_DOWN(BLCKSZ - \
                  SizeOfPageHeaderData - \
                  MAXALIGN(sizeof(SpGistPageOpaqueData)))
 
/*
 * Compute free space on page, assuming that up to n placeholders can be
 * recycled if present (n should be the number of tuples to be inserted)
 */
#define SpGistPageGetFreeSpace(p, n) \
    (PageGetExactFreeSpace(p) + \
     Min(SpGistPageGetOpaque(p)->nPlaceholder, n) * \
     (SGDTSIZE + sizeof(ItemIdData)))
 
/*
 * XLOG stuff
 */
 
#define STORE_STATE(s, d)  \
    do { \
        (d).myXid = (s)->myXid; \
        (d).isBuild = (s)->isBuild; \
    } while(0)
 
/*
 * The "flags" argument for SpGistGetBuffer should be either GBUF_LEAF to
 * get a leaf page, or GBUF_INNER_PARITY(blockNumber) to get an inner
 * page in the same triple-parity group as the specified block number.
 * (Typically, this should be GBUF_INNER_PARITY(parentBlockNumber + 1)
 * to follow the rule described in spgist/README.)
 * In addition, GBUF_NULLS can be OR'd in to get a page for storage of
 * null-valued tuples.
 *
 * Note: these flag values are used as indexes into lastUsedPages.
 */
#define GBUF_LEAF               0x03
#define GBUF_INNER_PARITY(x)    ((x) % 3)
#define GBUF_NULLS              0x04
 
#define GBUF_PARITY_MASK        0x03
#define GBUF_REQ_LEAF(flags)    (((flags) & GBUF_PARITY_MASK) == GBUF_LEAF)
#define GBUF_REQ_NULLS(flags)   ((flags) & GBUF_NULLS)
 
/* spgutils.c */
 
/* reloption parameters */
#define SPGIST_MIN_FILLFACTOR           10
#define SPGIST_DEFAULT_FILLFACTOR       80
 
extern SpGistCache *spgGetCache(Relation index);
extern TupleDesc getSpGistTupleDesc(Relation index, SpGistTypeDesc *keyType);
extern void initSpGistState(SpGistState *state, Relation index);
extern Buffer SpGistNewBuffer(Relation index);
extern void SpGistUpdateMetaPage(Relation index);
extern Buffer SpGistGetBuffer(Relation index, int flags,
                              int needSpace, bool *isNew);
extern void SpGistSetLastUsedPage(Relation index, Buffer buffer);
extern void SpGistInitPage(Page page, uint16 f);
extern void SpGistInitBuffer(Buffer b, uint16 f);
extern void SpGistInitMetapage(Page page);
extern unsigned int SpGistGetInnerTypeSize(SpGistTypeDesc *att, Datum datum);
extern Size SpGistGetLeafTupleSize(TupleDesc tupleDescriptor,
                                   Datum *datums, bool *isnulls);
extern SpGistLeafTuple spgFormLeafTuple(SpGistState *state,
                                        ItemPointer heapPtr,
                                        Datum *datums, bool *isnulls);
extern SpGistNodeTuple spgFormNodeTuple(SpGistState *state,
                                        Datum label, bool isnull);
extern SpGistInnerTuple spgFormInnerTuple(SpGistState *state,
                                          bool hasPrefix, Datum prefix,
                                          int nNodes, SpGistNodeTuple *nodes);
extern SpGistDeadTuple spgFormDeadTuple(SpGistState *state, int tupstate,
                                        BlockNumber blkno, OffsetNumber offnum);
extern void spgDeformLeafTuple(SpGistLeafTuple tup, TupleDesc tupleDescriptor,
                               Datum *datums, bool *isnulls,
                               bool keyColumnIsNull);
extern Datum *spgExtractNodeLabels(SpGistState *state,
                                   SpGistInnerTuple innerTuple);
extern OffsetNumber SpGistPageAddNewItem(SpGistState *state, Page page,
                                         Item item, Size size,
                                         OffsetNumber *startOffset,
                                         bool errorOK);
extern bool spgproperty(Oid index_oid, int attno,
                        IndexAMProperty prop, const char *propname,
                        bool *res, bool *isnull);
 
/* spgdoinsert.c */
extern void spgUpdateNodeLink(SpGistInnerTuple tup, int nodeN,
                              BlockNumber blkno, OffsetNumber offset);
extern void spgPageIndexMultiDelete(SpGistState *state, Page page,
                                    OffsetNumber *itemnos, int nitems,
                                    int firststate, int reststate,
                                    BlockNumber blkno, OffsetNumber offnum);
extern bool spgdoinsert(Relation index, SpGistState *state,
                        ItemPointer heapPtr, Datum *datums, bool *isnulls);
 
/* spgproc.c */
extern double *spg_key_orderbys_distances(Datum key, bool isLeaf,
                                          ScanKey orderbys, int norderbys);
extern BOX *box_copy(BOX *orig);
 
#endif                          /* SPGIST_PRIVATE_H */