boehm-gc/doc/tree.html

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