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