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<HTML>
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<HEAD>
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<TITLE> Two-Level Tree Structure for Fast Pointer Lookup</TITLE>
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<AUTHOR> Hans-J. Boehm, Silicon Graphics (now at HP)</author>
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</HEAD>
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<BODY>
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<H1>Two-Level Tree Structure for Fast Pointer Lookup</h1>
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<P>
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The conservative garbage collector described
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<A HREF="http://www.hpl.hp.com/personal/Hans_Boehm/gc/">here</a>
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uses a 2-level tree
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data structure to aid in fast pointer identification.
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This data structure is described in a bit more detail here, since
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<OL>
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<LI> Variations of the data structure are more generally useful.
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<LI> It appears to be hard to understand by reading the code.
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<LI> Some other collectors appear to use inferior data structures to
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solve the same problem.
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<LI> It is central to fast collector operation.
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</ol>
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A candidate pointer is divided into three sections, the <I>high</i>,
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<I>middle</i>, and <I>low</i> bits. The exact division between these
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three groups of bits is dependent on the detailed collector configuration.
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<P>
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The high and middle bits are used to look up an entry in the table described
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here. The resulting table entry consists of either a block descriptor
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(<TT>struct hblkhdr *</tt> or <TT>hdr *</tt>)
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identifying the layout of objects in the block, or an indication that this
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address range corresponds to the middle of a large block, together with a
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hint for locating the actual block descriptor. Such a hint consist
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of a displacement that can be subtracted from the middle bits of the candidate
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pointer without leaving the object.
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<P>
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In either case, the block descriptor (<TT>struct hblkhdr</tt>)
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refers to a table of object starting addresses (the <TT>hb_map</tt> field).
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The starting address table is indexed by the low bits if the candidate pointer.
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The resulting entry contains a displacement to the beginning of the object,
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or an indication that this cannot be a valid object pointer.
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(If all interior pointer are recognized, pointers into large objects
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are handled specially, as appropriate.)
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<H2>The Tree</h2>
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<P>
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The rest of this discussion focuses on the two level data structure
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used to map the high and middle bits to the block descriptor.
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<P>
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The high bits are used as an index into the <TT>GC_top_index</tt> (really
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<TT>GC_arrays._top_index</tt>) array. Each entry points to a
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<TT>bottom_index</tt> data structure. This structure in turn consists
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mostly of an array <TT>index</tt> indexed by the middle bits of
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the candidate pointer. The <TT>index</tt> array contains the actual
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<TT>hdr</tt> pointers.
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<P>
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Thus a pointer lookup consists primarily of a handful of memory references,
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and can be quite fast:
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<OL>
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<LI> The appropriate <TT>bottom_index</tt> pointer is looked up in
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<TT>GC_top_index</tt>, based on the high bits of the candidate pointer.
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<LI> The appropriate <TT>hdr</tt> pointer is looked up in the
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<TT>bottom_index</tt> structure, based on the middle bits.
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<LI> The block layout map pointer is retrieved from the <TT>hdr</tt>
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structure. (This memory reference is necessary since we try to share
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block layout maps.)
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<LI> The displacement to the beginning of the object is retrieved from the
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above map.
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</ol>
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<P>
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In order to conserve space, not all <TT>GC_top_index</tt> entries in fact
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point to distinct <TT>bottom_index</tt> structures. If no address with
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the corresponding high bits is part of the heap, then the entry points
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to <TT>GC_all_nils</tt>, a single <TT>bottom_index</tt> structure consisting
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only of NULL <TT>hdr</tt> pointers.
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<P>
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<TT>Bottom_index</tt> structures contain slightly more information than
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just <TT>hdr</tt> pointers. The <TT>asc_link</tt> field is used to link
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all <TT>bottom_index</tt> structures in ascending order for fast traversal.
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This list is pointed to be <TT>GC_all_bottom_indices</tt>.
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It is maintained with the aid of <TT>key</tt> field that contains the
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high bits corresponding to the <TT>bottom_index</tt>.
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<H2>64 bit addresses</h2>
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<P>
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In the case of 64 bit addresses, this picture is complicated slightly
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by the fact that one of the index structures would have to be huge to
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cover the entire address space with a two level tree. We deal with this
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by turning <TT>GC_top_index</tt> into a chained hash table, instead of
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a simple array. This adds a <TT>hash_link</tt> field to the
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<TT>bottom_index</tt> structure.
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<P>
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The "hash function" consists of dropping the high bits. This is cheap to
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compute, and guarantees that there will be no collisions if the heap
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is contiguous and not excessively large.
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<H2>A picture</h2>
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<P>
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The following is an ASCII diagram of the data structure.
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This was contributed by Dave Barrett several years ago.
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<PRE>
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Data Structure used by GC_base in gc3.7:
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21-Apr-94
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63 LOG_TOP_SZ[11] LOG_BOTTOM_SZ[10] LOG_HBLKSIZE[13]
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+------------------+----------------+------------------+------------------+
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p:| | TL_HASH(hi) | | HBLKDISPL(p) |
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+------------------+----------------+------------------+------------------+
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\-----------------------HBLKPTR(p)-------------------/
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\------------hi-------------------/
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\______ ________/ \________ _______/ \________ _______/
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V V V
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| | |
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GC_top_index[] | | |
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--- +--------------+ | | |
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^ | | | | |
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| | | | | |
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TOP +--------------+<--+ | |
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_SZ +-<| [] | * | |
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(items)| +--------------+ if 0 < bi< HBLKSIZE | |
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| | | | then large object | |
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| | | | starts at the bi'th | |
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v | | | HBLK before p. | i |
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--- | +--------------+ | (word- |
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v | aligned) |
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bi= |GET_BI(p){->hash_link}->key==hi | |
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v | |
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| (bottom_index) \ scratch_alloc'd | |
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| ( struct bi ) / by get_index() | |
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--- +->+--------------+ | |
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^ | | | |
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^ | | | |
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BOTTOM | | ha=GET_HDR_ADDR(p) | |
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_SZ(items)+--------------+<----------------------+ +-------+
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| +--<| index[] | |
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| | +--------------+ GC_obj_map: v
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| | | | from / +-+-+-----+-+-+-+-+ ---
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v | | | GC_add < 0| | | | | | | | ^
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--- | +--------------+ _map_entry \ +-+-+-----+-+-+-+-+ |
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| | asc_link | +-+-+-----+-+-+-+-+ MAXOBJSZ
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| +--------------+ +-->| | | j | | | | | +1
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| | key | | +-+-+-----+-+-+-+-+ |
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| +--------------+ | +-+-+-----+-+-+-+-+ |
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| | hash_link | | | | | | | | | | v
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| +--------------+ | +-+-+-----+-+-+-+-+ ---
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| | |<--MAX_OFFSET--->|
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| | (bytes)
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HDR(p)| GC_find_header(p) | |<--MAP_ENTRIES-->|
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| \ from | =HBLKSIZE/WORDSZ
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| (hdr) (struct hblkhdr) / alloc_hdr() | (1024 on Alpha)
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+-->+----------------------+ | (8/16 bits each)
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GET_HDR(p)| word hb_sz (words) | |
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+----------------------+ |
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| struct hblk *hb_next | |
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+----------------------+ |
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|mark_proc hb_mark_proc| |
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+----------------------+ |
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| char * hb_map |>-------------+
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+----------------------+
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| ushort hb_obj_kind |
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+----------------------+
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| hb_last_reclaimed |
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--- +----------------------+
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^ | |
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MARK_BITS| hb_marks[] | *if hdr is free, hb_sz + DISCARD_WORDS
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_SZ(words)| | is the size of a heap chunk (struct hblk)
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v | | of at least MININCR*HBLKSIZE bytes (below),
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--- +----------------------+ otherwise, size of each object in chunk.
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Dynamic data structures above are interleaved throughout the heap in blocks of
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size MININCR * HBLKSIZE bytes as done by gc_scratch_alloc which cannot be
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freed; free lists are used (e.g. alloc_hdr). HBLK's below are collected.
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(struct hblk)
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--- +----------------------+ < HBLKSIZE --- --- DISCARD_
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^ |garbage[DISCARD_WORDS]| aligned ^ ^ HDR_BYTES WORDS
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| | | | v (bytes) (words)
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| +-----hb_body----------+ < WORDSZ | --- ---
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| | | aligned | ^ ^
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| | Object 0 | | hb_sz |
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| | | i |(word- (words)|
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| | | (bytes)|aligned) v |
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| + - - - - - - - - - - -+ --- | --- |
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| | | ^ | ^ |
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n * | | j (words) | hb_sz BODY_SZ
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HBLKSIZE | Object 1 | v v | (words)
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(bytes) | |--------------- v MAX_OFFSET
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| + - - - - - - - - - - -+ --- (bytes)
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| | | !All_INTERIOR_PTRS ^ |
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| | | sets j only for hb_sz |
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| | Object N | valid object offsets. | |
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v | | All objects WORDSZ v v
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--- +----------------------+ aligned. --- ---
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DISCARD_WORDS is normally zero. Indeed the collector has not been tested
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with another value in ages.
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</pre>
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</body>
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