]>
Commit | Line | Data |
---|---|---|
61f38a77 TT |
1 | <HTML> |
2 | <HEAD> | |
3 | <TITLE> Two-Level Tree Structure for Fast Pointer Lookup</TITLE> | |
ff6fe7a1 | 4 | <AUTHOR> Hans-J. Boehm, Silicon Graphics (now at HP)</author> |
61f38a77 TT |
5 | </HEAD> |
6 | <BODY> | |
7 | <H1>Two-Level Tree Structure for Fast Pointer Lookup</h1> | |
8 | <P> | |
9 | The conservative garbage collector described | |
ff6fe7a1 JS |
10 | <A HREF="http://www.hpl.hp.com/personal/Hans_Boehm/gc/">here</a> |
11 | uses a 2-level tree | |
61f38a77 TT |
12 | data structure to aid in fast pointer identification. |
13 | This data structure is described in a bit more detail here, since | |
14 | <OL> | |
15 | <LI> Variations of the data structure are more generally useful. | |
16 | <LI> It appears to be hard to understand by reading the code. | |
17 | <LI> Some other collectors appear to use inferior data structures to | |
18 | solve the same problem. | |
19 | <LI> It is central to fast collector operation. | |
20 | </ol> | |
21 | A candidate pointer is divided into three sections, the <I>high</i>, | |
22 | <I>middle</i>, and <I>low</i> bits. The exact division between these | |
23 | three groups of bits is dependent on the detailed collector configuration. | |
24 | <P> | |
25 | The high and middle bits are used to look up an entry in the table described | |
26 | here. The resulting table entry consists of either a block descriptor | |
27 | (<TT>struct hblkhdr *</tt> or <TT>hdr *</tt>) | |
28 | identifying the layout of objects in the block, or an indication that this | |
29 | address range corresponds to the middle of a large block, together with a | |
30 | hint for locating the actual block descriptor. Such a hint consist | |
31 | of a displacement that can be subtracted from the middle bits of the candidate | |
32 | pointer without leaving the object. | |
33 | <P> | |
34 | In either case, the block descriptor (<TT>struct hblkhdr</tt>) | |
35 | refers to a table of object starting addresses (the <TT>hb_map</tt> field). | |
36 | The starting address table is indexed by the low bits if the candidate pointer. | |
37 | The resulting entry contains a displacement to the beginning of the object, | |
38 | or an indication that this cannot be a valid object pointer. | |
39 | (If all interior pointer are recognized, pointers into large objects | |
40 | are handled specially, as appropriate.) | |
41 | ||
42 | <H2>The Tree</h2> | |
43 | <P> | |
44 | The rest of this discussion focuses on the two level data structure | |
45 | used to map the high and middle bits to the block descriptor. | |
46 | <P> | |
47 | The high bits are used as an index into the <TT>GC_top_index</tt> (really | |
48 | <TT>GC_arrays._top_index</tt>) array. Each entry points to a | |
49 | <TT>bottom_index</tt> data structure. This structure in turn consists | |
50 | mostly of an array <TT>index</tt> indexed by the middle bits of | |
51 | the candidate pointer. The <TT>index</tt> array contains the actual | |
52 | <TT>hdr</tt> pointers. | |
53 | <P> | |
54 | Thus a pointer lookup consists primarily of a handful of memory references, | |
55 | and can be quite fast: | |
56 | <OL> | |
57 | <LI> The appropriate <TT>bottom_index</tt> pointer is looked up in | |
58 | <TT>GC_top_index</tt>, based on the high bits of the candidate pointer. | |
59 | <LI> The appropriate <TT>hdr</tt> pointer is looked up in the | |
60 | <TT>bottom_index</tt> structure, based on the middle bits. | |
61 | <LI> The block layout map pointer is retrieved from the <TT>hdr</tt> | |
62 | structure. (This memory reference is necessary since we try to share | |
63 | block layout maps.) | |
64 | <LI> The displacement to the beginning of the object is retrieved from the | |
65 | above map. | |
66 | </ol> | |
67 | <P> | |
68 | In order to conserve space, not all <TT>GC_top_index</tt> entries in fact | |
69 | point to distinct <TT>bottom_index</tt> structures. If no address with | |
70 | the corresponding high bits is part of the heap, then the entry points | |
71 | to <TT>GC_all_nils</tt>, a single <TT>bottom_index</tt> structure consisting | |
72 | only of NULL <TT>hdr</tt> pointers. | |
73 | <P> | |
74 | <TT>Bottom_index</tt> structures contain slightly more information than | |
75 | just <TT>hdr</tt> pointers. The <TT>asc_link</tt> field is used to link | |
76 | all <TT>bottom_index</tt> structures in ascending order for fast traversal. | |
77 | This list is pointed to be <TT>GC_all_bottom_indices</tt>. | |
78 | It is maintained with the aid of <TT>key</tt> field that contains the | |
79 | high bits corresponding to the <TT>bottom_index</tt>. | |
80 | ||
81 | <H2>64 bit addresses</h2> | |
82 | <P> | |
83 | In the case of 64 bit addresses, this picture is complicated slightly | |
84 | by the fact that one of the index structures would have to be huge to | |
85 | cover the entire address space with a two level tree. We deal with this | |
86 | by turning <TT>GC_top_index</tt> into a chained hash table, instead of | |
87 | a simple array. This adds a <TT>hash_link</tt> field to the | |
88 | <TT>bottom_index</tt> structure. | |
89 | <P> | |
90 | The "hash function" consists of dropping the high bits. This is cheap to | |
91 | compute, and guarantees that there will be no collisions if the heap | |
92 | is contiguous and not excessively large. | |
93 | ||
94 | <H2>A picture</h2> | |
95 | <P> | |
96 | The following is an ASCII diagram of the data structure. | |
97 | This was contributed by Dave Barrett several years ago. | |
98 | <PRE> | |
99 | ||
100 | Data Structure used by GC_base in gc3.7: | |
101 | 21-Apr-94 | |
102 | ||
103 | ||
104 | ||
105 | ||
106 | 63 LOG_TOP_SZ[11] LOG_BOTTOM_SZ[10] LOG_HBLKSIZE[13] | |
107 | +------------------+----------------+------------------+------------------+ | |
108 | p:| | TL_HASH(hi) | | HBLKDISPL(p) | | |
109 | +------------------+----------------+------------------+------------------+ | |
110 | \-----------------------HBLKPTR(p)-------------------/ | |
111 | \------------hi-------------------/ | |
112 | \______ ________/ \________ _______/ \________ _______/ | |
113 | V V V | |
114 | | | | | |
115 | GC_top_index[] | | | | |
116 | --- +--------------+ | | | | |
117 | ^ | | | | | | |
118 | | | | | | | | |
119 | TOP +--------------+<--+ | | | |
120 | _SZ +-<| [] | * | | | |
121 | (items)| +--------------+ if 0 < bi< HBLKSIZE | | | |
122 | | | | | then large object | | | |
123 | | | | | starts at the bi'th | | | |
124 | v | | | HBLK before p. | i | | |
125 | --- | +--------------+ | (word- | | |
126 | v | aligned) | | |
127 | bi= |GET_BI(p){->hash_link}->key==hi | | | |
128 | v | | | |
129 | | (bottom_index) \ scratch_alloc'd | | | |
130 | | ( struct bi ) / by get_index() | | | |
131 | --- +->+--------------+ | | | |
132 | ^ | | | | | |
133 | ^ | | | | | |
134 | BOTTOM | | ha=GET_HDR_ADDR(p) | | | |
135 | _SZ(items)+--------------+<----------------------+ +-------+ | |
136 | | +--<| index[] | | | |
137 | | | +--------------+ GC_obj_map: v | |
138 | | | | | from / +-+-+-----+-+-+-+-+ --- | |
139 | v | | | GC_add < 0| | | | | | | | ^ | |
140 | --- | +--------------+ _map_entry \ +-+-+-----+-+-+-+-+ | | |
141 | | | asc_link | +-+-+-----+-+-+-+-+ MAXOBJSZ | |
142 | | +--------------+ +-->| | | j | | | | | +1 | |
143 | | | key | | +-+-+-----+-+-+-+-+ | | |
144 | | +--------------+ | +-+-+-----+-+-+-+-+ | | |
145 | | | hash_link | | | | | | | | | | v | |
146 | | +--------------+ | +-+-+-----+-+-+-+-+ --- | |
147 | | | |<--MAX_OFFSET--->| | |
148 | | | (bytes) | |
149 | HDR(p)| GC_find_header(p) | |<--MAP_ENTRIES-->| | |
150 | | \ from | =HBLKSIZE/WORDSZ | |
151 | | (hdr) (struct hblkhdr) / alloc_hdr() | (1024 on Alpha) | |
152 | +-->+----------------------+ | (8/16 bits each) | |
153 | GET_HDR(p)| word hb_sz (words) | | | |
154 | +----------------------+ | | |
155 | | struct hblk *hb_next | | | |
156 | +----------------------+ | | |
157 | |mark_proc hb_mark_proc| | | |
158 | +----------------------+ | | |
159 | | char * hb_map |>-------------+ | |
160 | +----------------------+ | |
161 | | ushort hb_obj_kind | | |
162 | +----------------------+ | |
163 | | hb_last_reclaimed | | |
164 | --- +----------------------+ | |
165 | ^ | | | |
166 | MARK_BITS| hb_marks[] | *if hdr is free, hb_sz + DISCARD_WORDS | |
167 | _SZ(words)| | is the size of a heap chunk (struct hblk) | |
168 | v | | of at least MININCR*HBLKSIZE bytes (below), | |
169 | --- +----------------------+ otherwise, size of each object in chunk. | |
170 | ||
171 | Dynamic data structures above are interleaved throughout the heap in blocks of | |
172 | size MININCR * HBLKSIZE bytes as done by gc_scratch_alloc which cannot be | |
173 | freed; free lists are used (e.g. alloc_hdr). HBLK's below are collected. | |
174 | ||
175 | (struct hblk) | |
176 | --- +----------------------+ < HBLKSIZE --- --- DISCARD_ | |
177 | ^ |garbage[DISCARD_WORDS]| aligned ^ ^ HDR_BYTES WORDS | |
178 | | | | | v (bytes) (words) | |
179 | | +-----hb_body----------+ < WORDSZ | --- --- | |
180 | | | | aligned | ^ ^ | |
181 | | | Object 0 | | hb_sz | | |
182 | | | | i |(word- (words)| | |
183 | | | | (bytes)|aligned) v | | |
184 | | + - - - - - - - - - - -+ --- | --- | | |
185 | | | | ^ | ^ | | |
186 | n * | | j (words) | hb_sz BODY_SZ | |
187 | HBLKSIZE | Object 1 | v v | (words) | |
188 | (bytes) | |--------------- v MAX_OFFSET | |
189 | | + - - - - - - - - - - -+ --- (bytes) | |
190 | | | | !All_INTERIOR_PTRS ^ | | |
191 | | | | sets j only for hb_sz | | |
192 | | | Object N | valid object offsets. | | | |
193 | v | | All objects WORDSZ v v | |
194 | --- +----------------------+ aligned. --- --- | |
195 | ||
196 | DISCARD_WORDS is normally zero. Indeed the collector has not been tested | |
197 | with another value in ages. | |
198 | </pre> | |
199 | </body> |