vendor/sharded-slab/IMPLEMENTATION.md

   1 Notes on `sharded-slab`'s implementation and design.
   2
   3 # Design
   4
   5 The sharded slab's design is strongly inspired by the ideas presented by
   6 Leijen, Zorn, and de Moura in [Mimalloc: Free List Sharding in
   7 Action][mimalloc]. In this report, the authors present a novel design for a
   8 memory allocator based on a concept of _free list sharding_.
   9
  10 Memory allocators must keep track of what memory regions are not currently
  11 allocated ("free") in order to provide them to future allocation requests.
  12 The term [_free list_][freelist] refers to a technique for performing this
  13 bookkeeping, where each free block stores a pointer to the next free block,
  14 forming a linked list. The memory allocator keeps a pointer to the most
  15 recently freed block, the _head_ of the free list. To allocate more memory,
  16 the allocator pops from the free list by setting the head pointer to the
  17 next free block of the current head block, and returning the previous head.
  18 To deallocate a block, the block is pushed to the free list by setting its
  19 first word to the current head pointer, and the head pointer is set to point
  20 to the deallocated block. Most implementations of slab allocators backed by
  21 arrays or vectors use a similar technique, where pointers are replaced by
  22 indices into the backing array.
  23
  24 When allocations and deallocations can occur concurrently across threads,
  25 they must synchronize accesses to the free list; either by putting the
  26 entire allocator state inside of a lock, or by using atomic operations to
  27 treat the free list as a lock-free structure (such as a [Treiber stack]). In
  28 both cases, there is a significant performance cost — even when the free
  29 list is lock-free, it is likely that a noticeable amount of time will be
  30 spent in compare-and-swap loops. Ideally, the global synchronzation point
  31 created by the single global free list could be avoided as much as possible.
  32
  33 The approach presented by Leijen, Zorn, and de Moura is to introduce
  34 sharding and thus increase the granularity of synchronization significantly.
  35 In mimalloc, the heap is _sharded_ so that each thread has its own
  36 thread-local heap. Objects are always allocated from the local heap of the
  37 thread where the allocation is performed. Because allocations are always
  38 done from a thread's local heap, they need not be synchronized.
  39
  40 However, since objects can move between threads before being deallocated,
  41 _deallocations_ may still occur concurrently. Therefore, Leijen et al.
  42 introduce a concept of _local_ and _global_ free lists. When an object is
  43 deallocated on the same thread it was originally allocated on, it is placed
  44 on the local free list; if it is deallocated on another thread, it goes on
  45 the global free list for the heap of the thread from which it originated. To
  46 allocate, the local free list is used first; if it is empty, the entire
  47 global free list is popped onto the local free list. Since the local free
  48 list is only ever accessed by the thread it belongs to, it does not require
  49 synchronization at all, and because the global free list is popped from
  50 infrequently, the cost of synchronization has a reduced impact. A majority
  51 of allocations can occur without any synchronization at all; and
  52 deallocations only require synchronization when an object has left its
  53 parent thread (a relatively uncommon case).
  54
  55 [mimalloc]: https://www.microsoft.com/en-us/research/uploads/prod/2019/06/mimalloc-tr-v1.pdf
  56 [freelist]: https://en.wikipedia.org/wiki/Free_list
  57 [Treiber stack]: https://en.wikipedia.org/wiki/Treiber_stack
  58
  59 # Implementation
  60
  61 A slab is represented as an array of [`MAX_THREADS`] _shards_. A shard
  62 consists of a vector of one or more _pages_ plus associated metadata.
  63 Finally, a page consists of an array of _slots_, head indices for the local
  64 and remote free lists.
  65
  66 ```text
  67 ┌─────────────┐
  68 │ shard 1     │
  69 │             │    ┌─────────────┐        ┌────────┐
  70 │ pages───────┼───▶│ page 1      │        │        │
  71 ├─────────────┤    ├─────────────┤  ┌────▶│  next──┼─┐
  72 │ shard 2     │    │ page 2      │  │     ├────────┤ │
  73 ├─────────────┤    │             │  │     │XXXXXXXX│ │
  74 │ shard 3     │    │ local_head──┼──┘     ├────────┤ │
  75 └─────────────┘    │ remote_head─┼──┐     │        │◀┘
  76       ...          ├─────────────┤  │     │  next──┼─┐
  77 ┌─────────────┐    │ page 3      │  │     ├────────┤ │
  78 │ shard n     │    └─────────────┘  │     │XXXXXXXX│ │
  79 └─────────────┘          ...        │     ├────────┤ │
  80                    ┌─────────────┐  │     │XXXXXXXX│ │
  81                    │ page n      │  │     ├────────┤ │
  82                    └─────────────┘  │     │        │◀┘
  83                                     └────▶│  next──┼───▶  ...
  84                                           ├────────┤
  85                                           │XXXXXXXX│
  86                                           └────────┘
  87 ```
  88
  89
  90 The size of the first page in a shard is always a power of two, and every
  91 subsequent page added after the first is twice as large as the page that
  92 preceeds it.
  93
  94 ```text
  95
  96 pg.
  97 ┌───┐   ┌─┬─┐
  98 │ 0 │───▶ │ │
  99 ├───┤   ├─┼─┼─┬─┐
 100 │ 1 │───▶ │ │ │ │
 101 ├───┤   ├─┼─┼─┼─┼─┬─┬─┬─┐
 102 │ 2 │───▶ │ │ │ │ │ │ │ │
 103 ├───┤   ├─┼─┼─┼─┼─┼─┼─┼─┼─┬─┬─┬─┬─┬─┬─┬─┐
 104 │ 3 │───▶ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
 105 └───┘   └─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘
 106 ```
 107
 108 When searching for a free slot, the smallest page is searched first, and if
 109 it is full, the search proceeds to the next page until either a free slot is
 110 found or all available pages have been searched. If all available pages have
 111 been searched and the maximum number of pages has not yet been reached, a
 112 new page is then allocated.
 113
 114 Since every page is twice as large as the previous page, and all page sizes
 115 are powers of two, we can determine the page index that contains a given
 116 address by shifting the address down by the smallest page size and
 117 looking at how many twos places necessary to represent that number,
 118 telling us what power of two page size it fits inside of. We can
 119 determine the number of twos places by counting the number of leading
 120 zeros (unused twos places) in the number's binary representation, and
 121 subtracting that count from the total number of bits in a word.
 122
 123 The formula for determining the page number that contains an offset is thus:
 124
 125 ```rust,ignore
 126 WIDTH - ((offset + INITIAL_PAGE_SIZE) >> INDEX_SHIFT).leading_zeros()
 127 ```
 128
 129 where `WIDTH` is the number of bits in a `usize`, and `INDEX_SHIFT` is
 130
 131 ```rust,ignore
 132 INITIAL_PAGE_SIZE.trailing_zeros() + 1;
 133 ```
 134
 135 [`MAX_THREADS`]: https://docs.rs/sharded-slab/latest/sharded_slab/trait.Config.html#associatedconstant.MAX_THREADS