// This module exists only to provide a separate page for the implementation
// documentation.

//! Notes on `sharded-slab`'s implementation and design.
//!
//! # Design
//!
//! The sharded slab's design is strongly inspired by the ideas presented by
//! Leijen, Zorn, and de Moura in [Mimalloc: Free List Sharding in
//! Action][mimalloc]. In this report, the authors present a novel design for a
//! memory allocator based on a concept of _free list sharding_.
//!
//! Memory allocators must keep track of what memory regions are not currently
//! allocated ("free") in order to provide them to future allocation requests.
//! The term [_free list_][freelist] refers to a technique for performing this
//! bookkeeping, where each free block stores a pointer to the next free block,
//! forming a linked list. The memory allocator keeps a pointer to the most
//! recently freed block, the _head_ of the free list. To allocate more memory,
//! the allocator pops from the free list by setting the head pointer to the
//! next free block of the current head block, and returning the previous head.
//! To deallocate a block, the block is pushed to the free list by setting its
//! first word to the current head pointer, and the head pointer is set to point
//! to the deallocated block. Most implementations of slab allocators backed by
//! arrays or vectors use a similar technique, where pointers are replaced by
//! indices into the backing array.
//!
//! When allocations and deallocations can occur concurrently across threads,
//! they must synchronize accesses to the free list; either by putting the
//! entire allocator state inside of a lock, or by using atomic operations to
//! treat the free list as a lock-free structure (such as a [Treiber stack]). In
//! both cases, there is a significant performance cost — even when the free
//! list is lock-free, it is likely that a noticeable amount of time will be
//! spent in compare-and-swap loops. Ideally, the global synchronzation point
//! created by the single global free list could be avoided as much as possible.
//!
//! The approach presented by Leijen, Zorn, and de Moura is to introduce
//! sharding and thus increase the granularity of synchronization significantly.
//! In mimalloc, the heap is _sharded_ so that each thread has its own
//! thread-local heap. Objects are always allocated from the local heap of the
//! thread where the allocation is performed. Because allocations are always
//! done from a thread's local heap, they need not be synchronized.
//!
//! However, since objects can move between threads before being deallocated,
//! _deallocations_ may still occur concurrently. Therefore, Leijen et al.
//! introduce a concept of _local_ and _global_ free lists. When an object is
//! deallocated on the same thread it was originally allocated on, it is placed
//! on the local free list; if it is deallocated on another thread, it goes on
//! the global free list for the heap of the thread from which it originated. To
//! allocate, the local free list is used first; if it is empty, the entire
//! global free list is popped onto the local free list. Since the local free
//! list is only ever accessed by the thread it belongs to, it does not require
//! synchronization at all, and because the global free list is popped from
//! infrequently, the cost of synchronization has a reduced impact. A majority
//! of allocations can occur without any synchronization at all; and
//! deallocations only require synchronization when an object has left its
//! parent thread (a relatively uncommon case).
//!
//! [mimalloc]: https://www.microsoft.com/en-us/research/uploads/prod/2019/06/mimalloc-tr-v1.pdf
//! [freelist]: https://en.wikipedia.org/wiki/Free_list
//! [Treiber stack]: https://en.wikipedia.org/wiki/Treiber_stack
//!
//! # Implementation
//!
//! A slab is represented as an array of [`MAX_THREADS`] _shards_. A shard
//! consists of a vector of one or more _pages_ plus associated metadata.
//! Finally, a page consists of an array of _slots_, head indices for the local
//! and remote free lists.
//!
//! ```text
//! ┌─────────────┐
//! │ shard 1     │
//! │             │    ┌─────────────┐        ┌────────┐
//! │ pages───────┼───▶│ page 1      │        │        │
//! ├─────────────┤    ├─────────────┤  ┌────▶│  next──┼─┐
//! │ shard 2     │    │ page 2      │  │     ├────────┤ │
//! ├─────────────┤    │             │  │     │XXXXXXXX│ │
//! │ shard 3     │    │ local_head──┼──┘     ├────────┤ │
//! └─────────────┘    │ remote_head─┼──┐     │        │◀┘
//!       ...          ├─────────────┤  │     │  next──┼─┐
//! ┌─────────────┐    │ page 3      │  │     ├────────┤ │
//! │ shard n     │    └─────────────┘  │     │XXXXXXXX│ │
//! └─────────────┘          ...        │     ├────────┤ │
//!                    ┌─────────────┐  │     │XXXXXXXX│ │
//!                    │ page n      │  │     ├────────┤ │
//!                    └─────────────┘  │     │        │◀┘
//!                                     └────▶│  next──┼───▶  ...
//!                                           ├────────┤
//!                                           │XXXXXXXX│
//!                                           └────────┘
//! ```
//!
//!
//! The size of the first page in a shard is always a power of two, and every
//! subsequent page added after the first is twice as large as the page that
//! preceeds it.
//!
//! ```text
//!
//! pg.
//! ┌───┐   ┌─┬─┐
//! │ 0 │───▶ │ │
//! ├───┤   ├─┼─┼─┬─┐
//! │ 1 │───▶ │ │ │ │
//! ├───┤   ├─┼─┼─┼─┼─┬─┬─┬─┐
//! │ 2 │───▶ │ │ │ │ │ │ │ │
//! ├───┤   ├─┼─┼─┼─┼─┼─┼─┼─┼─┬─┬─┬─┬─┬─┬─┬─┐
//! │ 3 │───▶ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
//! └───┘   └─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┴─┘
//! ```
//!
//! When searching for a free slot, the smallest page is searched first, and if
//! it is full, the search proceeds to the next page until either a free slot is
//! found or all available pages have been searched. If all available pages have
//! been searched and the maximum number of pages has not yet been reached, a
//! new page is then allocated.
//!
//! Since every page is twice as large as the previous page, and all page sizes
//! are powers of two, we can determine the page index that contains a given
//! address by shifting the address down by the smallest page size and
//! looking at how many twos places necessary to represent that number,
//! telling us what power of two page size it fits inside of. We can
//! determine the number of twos places by counting the number of leading
//! zeros (unused twos places) in the number's binary representation, and
//! subtracting that count from the total number of bits in a word.
//!
//! The formula for determining the page number that contains an offset is thus:
//!
//! ```rust,ignore
//! WIDTH - ((offset + INITIAL_PAGE_SIZE) >> INDEX_SHIFT).leading_zeros()
//! ```
//!
//! where `WIDTH` is the number of bits in a `usize`, and `INDEX_SHIFT` is
//!
//! ```rust,ignore
//! INITIAL_PAGE_SIZE.trailing_zeros() + 1;
//! ```
//!
//! [`MAX_THREADS`]: https://docs.rs/sharded-slab/latest/sharded_slab/trait.Config.html#associatedconstant.MAX_THREADS