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<TITLE> Two-Level Tree Structure for Fast Pointer Lookup</TITLE> | |
<AUTHOR> Hans-J. Boehm, Silicon Graphics (now at HP)</author> | |
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<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> | |
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