10 KiB
Two-Level Tree Structure for Fast Pointer Lookup
The Boehm-Demers-Weiser conservative Garbage Collector 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
- Variations of the data structure are more generally useful.
- It appears to be hard to understand by reading the code.
- Some other collectors appear to use inferior data structures to solve the same problem.
- It is central to fast collector operation. A candidate pointer is divided into three sections, the high, middle, and low bits. The exact division between these three groups of bits is dependent on the detailed collector configuration.
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
(struct hblkhdr * or hdr *) 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.
In either case, the block descriptor (struct hblkhdr) refers to a table
of object starting addresses (the hb_map 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.)
The Tree
The rest of this discussion focuses on the two level data structure used to map the high and middle bits to the block descriptor.
The high bits are used as an index into the GC_top_index (really
GC_arrays._top_index) array. Each entry points to a bottom_index data
structure. This structure in turn consists mostly of an array index indexed
by the middle bits of the candidate pointer. The index array contains the
actual hdr pointers.
Thus a pointer lookup consists primarily of a handful of memory references, and can be quite fast:
- The appropriate
bottom_indexpointer is looked up inGC_top_index, based on the high bits of the candidate pointer. - The appropriate
hdrpointer is looked up in thebottom_indexstructure, based on the middle bits. - The block layout map pointer is retrieved from the
hdrstructure. (This memory reference is necessary since we try to share block layout maps.) - The displacement to the beginning of the object is retrieved from the above map.
In order to conserve space, not all GC_top_index entries in fact point
to distinct bottom_index structures. If no address with the corresponding
high bits is part of the heap, then the entry points to GC_all_nils,
a single bottom_index structure consisting only of NULL hdr pointers.
Bottom_index structures contain slightly more information than just hdr
pointers. The asc_link field is used to link all bottom_index structures
in ascending order for fast traversal. This list is pointed to be
GC_all_bottom_indices. It is maintained with the aid of key field that
contains the high bits corresponding to the bottom_index.
64-bit addresses
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
GC_top_index into a chained hash table, instead of a simple array. This adds
a hash_link field to the bottom_index structure.
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.
A picture
The following is an ASCII diagram of the data structure used by GC_base (as of GC v3.7, Apr 21, 1994). This was contributed by Dave Barrett.
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 is the size of
_SZ(words)| | a heap chunk (struct hblk) of at least
v | | 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) HDR_BYTES
--- +----------------------+ < HBLKSIZE --- (bytes)
^ +-----hb_body----------+ (and WORDSZ) ^ --- ---
| | | aligned | ^ ^
| | | | hb_sz |
| | | | (words) |
| | Object 0 | | | |
| | | i |(word- v |
| + - - - - - - - - - - -+ --- (bytes)|aligned) --- |
| | | ^ | ^ |
| | | j (words) | | |
n * | Object 1 | v v hb_sz BODY_SZ
HBLKSIZE | |--------------- | (words)
(bytes) | | v MAX_OFFSET
| + - - - - - - - - - - -+ --- (bytes)
| | | !ALL_INTERIOR_POINTERS ^ |
| | | sets j only for hb_sz |
| | Object N | valid object offsets. | |
v | | All objects WORDSZ v v
--- +----------------------+ aligned. --- ---