Reintroduce allocator designs post

The post was split off the Heap Allocations post because it became too large. To keep the tree clean, it was then temporarily removed. This commit restores the post by reverting the removal commit.

This reverts commit 029d77ef21.

blog/content/second-edition/posts/11-allocator-designs/index.md

@@ -0,0 +1,726 @@
++++
+title = "Allocator Designs"
+weight = 11
+path = "allocator-designs"
+date = 0000-01-01
++++
+
+TODO
+
+<!-- more -->
+
+This blog is openly developed on [GitHub]. If you have any problems or questions, please open an issue there. You can also leave comments [at the bottom]. The complete source code for this post can be found in the [`post-10`][post branch] branch.
+
+[GitHub]: https://github.com/phil-opp/blog_os
+[at the bottom]: #comments
+[post branch]: https://github.com/phil-opp/blog_os/tree/post-10
+
+<!-- toc -->
+
+TODO optional
+
+## Introduction
+
+TODO
+
+## Design Goals
+
+The responsibility of an allocator is to manage the available heap memory. It needs to return unused memory on `alloc` calls and keep track of memory freed by `dealloc` so that it can be reused again. Most importantly, it must never hand out memory that is already in use somewhere else because this would cause undefined behavior.
+
+Apart from correctness, there are many secondary design goals. For example, it should effectively utilize the available memory and keep [fragmentation] low. Furthermore, it should work well for concurrent applications and scale to any number of processors. For maximal performance, it could even optimize the memory layout with respect to the CPU caches to improve [cache locality] and avoid [false sharing].
+
+[cache locality]: http://docs.cray.com/books/S-2315-50/html-S-2315-50/qmeblljm.html
+[fragmentation]: https://en.wikipedia.org/wiki/Fragmentation_(computing)
+[false sharing]: http://mechanical-sympathy.blogspot.de/2011/07/false-sharing.html
+
+These requirements can make good allocators very complex. For example, [jemalloc] has over 30.000 lines of code. This complexity often undesired in kernel code where a single bug can lead to severe security vulnerabilities. Fortunately, the allocation patterns of kernel code are often much simpler compared to userspace code, so that relatively simple allocator design often suffice. In the following we explain three possible kernel allocator designs and explain their advantages and drawbacks.
+
+[jemalloc]: http://jemalloc.net/
+
+## Bump Allocator
+
+The most simple allocator design is a _bump allocator_. It allocates memory linearly and only keeps track of the number of allocated bytes and the number of allocations. It is only useful in very specific use cases because it has a severe limitation: it can only free all memory at once.
+
+The base type looks like this:
+
+```rust
+// in src/allocator.rs
+
+pub struct BumpAllocator {
+    heap_start: usize,
+    heap_end: usize,
+    next: usize,
+    allocations: usize,
+}
+
+impl BumpAllocator {
+    /// Creates a new bump allocator with the given heap bounds.
+    ///
+    /// This method is unsafe because the caller must ensure that the given
+    /// memory range is unused.
+    pub const unsafe fn new(heap_start: usize, heap_size: usize) -> Self {
+        BumpAllocator {
+            heap_start,
+            heap_end: heap_start + heap_size,
+            next: heap_start,
+            allocations: 0,
+        }
+    }
+}
+```
+
+Instead of using the `HEAP_START` and `HEAP_SIZE` constants directly, we use separate `heap_start` and `heap_end` fields. This makes the type more flexible, for example it also works when we only want to assign a part of the heap region. The purpose of the `next` field is to always point to the first unused byte of the heap, i.e. the start address of the next allocation. The `allocations` field is a simple counter for the active allocations with the goal of resetting the allocator after the last allocation was freed.
+
+We provide a simple constructor function that creates a new `BumpAllocator`. It initializes the `heap_start` and `heap_end` fields using the given start address and size. The `allocations` counter is initialized with 0. The `next` field is set to `heap_start` since the whole heap should be unused at this point. Since this is something that the caller must guarantee, the function needs to be unsafe. Given an invalid memory range, the planned implementation of the `GlobalAlloc` trait would cause undefined behavior when it is used as global allocator.
+
+### A `Locked` Wrapper
+
+Implementing the [`GlobalAlloc`] trait directly for the `BumpAllocator` struct is not possible. The problem is that the `alloc` and `dealloc` methods of the trait only take an immutable `&self` reference, but we need to update the `next` and `allocations` fields for every allocation, which is only possible with an exclusive `&mut self` reference. The reason that the `GlobalAlloc` trait is specified this way is that the global allocator needs to be stored in an immutable `static` that only allows `&self` references.
+
+To be able to implement the trait for our `BumpAllocator` struct, we need to add synchronized [interior mutability] to get mutable field access through the `&self` reference. A type that adds the required synchronization and allows interior mutabilty is the [`spin::Mutex`] spinlock that we already used multiple times for our kernel, for example [for our VGA buffer writer][vga-mutex]. To use it, we create a `Locked` wrapper type:
+
+[interior mutability]: https://doc.rust-lang.org/book/ch15-05-interior-mutability.html
+[`spin::Mutex`]: https://docs.rs/spin/0.5.0/spin/struct.Mutex.html
+[vga-mutex]: ./second-edition/posts/03-vga-text-buffer/index.md#spinlocks
+
+```rust
+// in src/allocator.rs
+
+pub struct Locked<A> {
+    inner: spin::Mutex<A>,
+}
+
+impl<A> Locked<A> {
+    pub const fn new(inner: A) -> Self {
+        Locked {
+            inner: spin::Mutex::new(inner),
+        }
+    }
+}
+```
+
+The type is a generic wrapper around a `spin::Mutex<A>`. It imposes no restrictions on the wrapped type `A`, so it can be used to wrap all kinds of types, not just allocators. It provides a simple `new` constructor function that wraps a given value.
+
+### Implementing `GlobalAlloc`
+
+With the help of the `Locked` wrapper type we now can implement the `GlobalAlloc` trait for our bump allocator. The trick is to implement the trait not for the `BumpAllocator` directly, but for the wrapped `Locked<BumpAllocator>` type. The implementation looks like this:
+
+```rust
+// in src/allocator.rs
+
+unsafe impl GlobalAlloc for Locked<BumpAllocator> {
+    unsafe fn alloc(&self, layout: Layout) -> *mut u8 {
+        let mut bump = self.inner.lock();
+
+        let alloc_start = align_up(bump.next, layout.align());
+        let alloc_end = alloc_start + layout.size();
+
+        if alloc_end > bump.heap_end {
+            null_mut() // out of memory
+        } else {
+            bump.next = alloc_end;
+            bump.allocations += 1;
+            alloc_start as *mut u8
+        }
+    }
+
+    unsafe fn dealloc(&self, _ptr: *mut u8, _layout: Layout) {
+        let mut bump = self.inner.lock();
+
+        bump.allocations -= 1;
+        if bump.allocations == 0 {
+            bump.next = bump.heap_start;
+        }
+    }
+}
+```
+
+The first step for both `alloc` and `dealloc` is to call the [`Mutex::lock`] method to get a mutable reference to the wrapped allocator type. The instance remains locked until the end of the method, so that no data race can occur in multithreaded contexts (we will add threading support soon).
+
+[`Mutex::lock`]: https://docs.rs/spin/0.5.0/spin/struct.Mutex.html#method.lock
+
+The `alloc` implementation first performs the required alignment on the `next` address, as specified by the given [`Layout`]. This yields the start address of the allocation. The code for the `align_up` function is shown below. Next, we add the requested allocation size to `alloc_start` to get the end address of the allocation. If it is larger than the end address of the heap, we return a null pointer since there is not enough memory available. Otherwise, we update the `next` address (the next allocation should start after the current allocation), increase the `allocations` counter by 1, and return the `alloc_start` address converted to a `*mut u8` pointer.
+
+The `dealloc` function ignores the given pointer and `Layout` arguments. Instead, it just decreases the `allocations` counter. If the counter reaches `0` again, it means that all allocations were freed again. In this case, it resets the `next` address to the `heap_start` address to make the complete heap memory available again.
+
+The last remaining part of the implementation is the `align_up` function, which looks like this:
+
+```rust
+// in src/allocator.rs
+
+fn align_up(addr: usize, align: usize) -> usize {
+    let remainder = addr % align;
+    if remainder == 0 {
+        addr // addr already aligned
+    } else {
+        addr - remainder + align
+    }
+}
+```
+
+The function first computes the [remainder] of the division of `addr` by `align`. If the remainder is `0`, the address is already aligned with the given alignment. Otherwise, we align the address by subtracting the remainder (so that the new remainder is 0) and then adding the alignment (so that the address does not become smaller than the original address).
+
+[remainder]: https://en.wikipedia.org/wiki/Euclidean_division
+
+### Using It
+
+To use the bump allocator instead of the dummy allocator, we need to update the `ALLOCATOR` static in `lib.rs`:
+
+```rust
+// in src/lib.rs
+
+use allocator::{Locked, BumpAllocator, HEAP_START, HEAP_SIZE};
+
+#[global_allocator]
+static ALLOCATOR: Locked<BumpAllocator> =
+    Locked::new(BumpAllocator::new(HEAP_START, HEAP_SIZE));
+```
+
+Here it becomes important that we declared both the `Locked::new` and the `BumpAllocator::new` as [`const` functions]. If they were normal functions, a compilation error would occur because the initialization expression of a `static` must evaluable at compile time.
+
+[`const` functions]: https://doc.rust-lang.org/reference/items/functions.html#const-functions
+
+Now we can use `Box` and `Vec` without runtime errors:
+
+```rust
+// in src/main.rs
+
+use alloc::{boxed::Box, vec::Vec, collections::BTreeMap};
+
+fn kernel_main(boot_info: &'static BootInfo) -> ! {
+    // […] initialize interrupts, mapper, frame_allocator, heap
+
+    // allocate a number on the heap
+    let heap_value = Box::new(41);
+    println!("heap_value at {:p}", heap_value);
+
+    // create a dynamically sized vector
+    let mut vec = Vec::new();
+    for i in 0..500 {
+        vec.push(i);
+    }
+    println!("vec at {:p}", vec.as_slice());
+
+    // try to create one million boxes
+    for _ in 0..1_000_000 {
+        let _ = Box::new(1);
+    }
+
+    // […] call `test_main` in test context
+    println!("It did not crash!");
+    blog_os::hlt_loop();
+}
+```
+
+This code example only uses the `Box` and `Vec` types, but there are many more allocation and collection types in the `alloc` crate that we can now all use in our kernel, including:
+
+- the reference counted pointers [`Rc`] and [`Arc`]
+- the owned string type [`String`] and the [`format!`] macro
+- [`LinkedList`]
+- the growable ring buffer [`VecDeque`]
+- [`BinaryHeap`]
+- [`BTreeMap`] and [`BTreeSet`]
+
+[`Rc`]: https://doc.rust-lang.org/alloc/rc/
+[`Arc`]: https://doc.rust-lang.org/alloc/arc/
+[`String`]: https://doc.rust-lang.org/collections/string/struct.String.html
+[`format!`]: https://doc.rust-lang.org/alloc/macro.format.html
+[`LinkedList`]: https://doc.rust-lang.org/collections/linked_list/struct.LinkedList.html
+[`VecDeque`]: https://doc.rust-lang.org/collections/vec_deque/struct.VecDeque.html
+[`BinaryHeap`]: https://doc.rust-lang.org/collections/binary_heap/struct.BinaryHeap.html
+[`BTreeMap`]: https://doc.rust-lang.org/collections/btree_map/struct.BTreeMap.html
+[`BTreeSet`]: https://doc.rust-lang.org/collections/btree_set/struct.BTreeSet.html
+
+When we run our project now, we see the following:
+
+![QEMU printing `
+heap_value at 0x444444440000
+vec at 0x4444444408000
+panicked at 'allocation error: Layout { size_: 4, align_: 4 }', src/lib.rs:91:5
+](qemu-bump-allocator.png)
+
+As expected, we see that the `Box` and `Vec` values live on the heap, as indicated by the pointer starting with `0x_4444_4444`. The reason that the vector starts at offset `0x800` is not that the boxed value is `0x800` bytes large, but the [reallocations] that occur when the vector needs to increase its capacity. For example, when the vector's capacity is 32 and we try to add the next element, the vector allocates a new backing array with capacity 64 behind the scenes and copies all elements over. Then it frees the old allocation, which in our case is equivalent to leaking it since our bump allocator doesn't reuse freed memory.
+
+[reallocations]: https://doc.rust-lang.org/alloc/vec/struct.Vec.html#capacity-and-reallocation
+
+While the basic `Box` and `Vec` examples work as expected, our loop that tries to create one million boxes causes a panic. The reason is that the bump allocator never reuses freed memory, so that for each created `Box` a few bytes are leaked. This makes the bump allocator unsuitable for many applications in practice, apart from some very specific use cases.
+
+### When to use a Bump Allocator
+
+The big advantage of bump allocation is that it's very fast. Compared to other allocator designs (see below) that need to actively look for a fitting memory block and perform various bookkeeping tasks on `alloc` and `dealloc`, a bump allocator can be optimized to just a few assembly instructions. This makes bump allocators useful for optimizing the allocation performance, for example when creating a [virtual DOM library].
+
+[virtual DOM library]: https://hacks.mozilla.org/2019/03/fast-bump-allocated-virtual-doms-with-rust-and-wasm/
+
+While a bump allocator is seldom used as the global allocator, the principle of bump allocation is often applied in form of [arena allocation], which basically batches individual allocations together to improve performance. An example for an arena allocator for Rust is the [`toolshed`] crate.
+
+[arena allocation]: https://mgravell.github.io/Pipelines.Sockets.Unofficial/docs/arenas.html
+[`toolshed`]: https://docs.rs/toolshed/0.8.1/toolshed/index.html
+
+### Reusing Freed Memory?
+
+The main limitation of a bump allocator is that it never reuses deallocated memory. The question is: Can we extend our bump allocator somehow to remove this limitation?
+
+As we learned at the beginning of this post, allocations can live arbitarily long and can be freed in an arbitrary order. This means that we need to keep track of a potentially unbounded number of non-continuous, unused memory regions, as illustrated by the following example:
+
+![](allocation-fragmentation.svg)
+
+The graphic shows the heap over the course of time. At the beginning, the complete heap is unused and the `next` address is equal to `heap_start` (line 1). Then the first allocation occurs (line 2). In line 3, a second memory block is allocated and the first allocation is freed. Many more allocations are added in line 4. Half of them are very short-lived and already get freed in line 5, where also another new allocation is added.
+
+Line 5 shows the fundamental problem: We have five unused memory regions with different sizes in total, but the `next` pointer can only point to the beginning of the last region. While we could store the start addresses and sizes of the other unused memory regions in an array of size 4 for this example, this isn't a general solution since we could easily create an example with 8, 16, or 1000 unused memory regions.
+
+Normally when we have a potentially unbounded number of items, we can just use a heap allocated collection. This isn't really possible in our case, since the heap allocator can't depend on itself (it would cause endless recursion or deadlocks). So we need to find a different solution.
+
+## LinkedList Allocator
+
+A common trick to keep track of an arbitrary number of free memory areas is to use these areas itself as backing storage. This utilizes the fact that the regions are still mapped to a virtual address and backed by a physical frame, but the stored information is not needed anymore. By storing the information about the freed region in the region itself, we can keep track of an unbounded number of freed regions without needing additional memory.
+
+The most common implementation approach is to construct a single linked list in the freed memory, with each node being a freed memory region:
+
+![](linked-list-allocation.svg)
+
+Each list node contains two fields: The size of the memory region and a pointer to the next unused memory region. With this approach, we only need a pointer to the first unused region (called `head`), independent of the number of memory regions.
+
+In the following, we will create a simple `LinkedListAllocator` type that uses the above approach for keeping track of freed memory regions. Since the implementation is a bit longer, we will start with a simple placeholder type before we start to implement the `alloc` and `dealloc` operations.
+
+### The Allocator Type
+
+We start by creating a private `ListNode` struct:
+
+```rust
+// in src/allocator.rs
+
+struct ListNode {
+    size: usize,
+    next: Option<&'static mut ListNode>,
+}
+
+impl ListNode {
+    const fn new(size: usize) -> Self {
+        ListNode {
+            size,
+            next: None,
+        }
+    }
+
+    fn start_addr(&self) -> usize {
+        self as *const Self as usize
+    }
+
+    fn end_addr(&self) -> usize {
+        self.start_addr() + self.size
+    }
+}
+```
+
+Like in the graphic, a list node has a `size` field and an optional pointer to the next node. The type has a simple constructor function and methods to calculate the start and end addresses of the represented region.
+
+With the `ListNode` struct as building block, we can now create the `LinkedListAllocator` struct:
+
+```rust
+// in src/allocator.rs
+
+pub struct LinkedListAllocator {
+    head: ListNode,
+}
+
+impl LinkedListAllocator {
+    pub const fn new() -> Self {
+        Self {
+            head: ListNode::new(0),
+        }
+    }
+
+    /// Initialize the allocator with the given heap bounds.
+    ///
+    /// This function is unsafe because the caller must guarantee that the given
+    /// heap bounds are valid and that the heap is unused. This method must be
+    /// called only once.
+    pub unsafe fn init(&mut self, heap_start: usize, heap_size: usize) {
+        self.add_free_region(heap_start, heap_size);
+    }
+
+    /// Adds the given memory region to the front of the list.
+    unsafe fn add_free_region(&mut self, addr: usize, size: usize) {
+        unimplemented!();
+    }
+}
+```
+
+The struct contains a `head` node that points to the first heap region. We are only interested in the value of the `next` pointer, so we set the `size` to 0 in the `new` function. Making `head` a `ListNode` instead of just a `&'static mut ListNode` has the advantage that the implementation of the `alloc` method will be simpler.
+
+In contrast to the bump allocator, the `new` function doesn't initialize the allocator with the heap bounds. The reason is that the initialization requires to write a node to the heap memory, which can only happen at runtime. The `new` function, however, needs to be a [`const` function] that can be evaluated at compile time, because it will be used for initializing the `ALLOCATOR` static. To work around this, we provide a separate `init` method that can be called at runtime.
+
+[`const` function]: https://doc.rust-lang.org/reference/items/functions.html#const-functions
+
+The `init` method uses a `add_free_region` method, whose implementation will be shown in a moment. For now, we use the [`unimplemented!`] macro to provide a placeholder implementation that always panics.
+
+[`unimplemented!`]: https://doc.rust-lang.org/core/macro.unimplemented.html
+
+Our first goal is to set a prototype of the `LinkedListAllocator` as the global allocator. In order to be able to do that, we need to provide a placeholder implementation of the `GlobalAlloc` trait:
+
+```rust
+// in src/allocator.rs
+
+unsafe impl GlobalAlloc for Locked<LinkedListAllocator> {
+    unsafe fn alloc(&self, layout: Layout) -> *mut u8 {
+        unimplemented!();
+    }
+
+    unsafe fn dealloc(&self, ptr: *mut u8, layout: Layout) {
+        unimplemented!();
+    }
+}
+```
+
+Like with the bump allocator, we don't implement the trait directly for the `LinkedListAllocator`, but only for a wrapped `Locked<LinkedListAllocator>`. The [`Locked` wrapper] adds interior mutability through a spinlock, which allows us to modify the allocator instance even though the `alloc` and `dealloc` methods only take `&self` references. Instead of providing an implementation, we use the [`unimplemented!`] macro again to get a minimal prototype.
+
+[`Locked` wrapper]: ./second-edition/posts/10-heap-allocation/index.md#a-locked-wrapper
+
+With this placeholder implementation, we can now change the global allocator to a `LinkedListAllocator`:
+
+```rust
+// in src/lib.rs
+
+use allocator::{Locked, LinkedListAllocator};
+
+#[global_allocator]
+static ALLOCATOR: Locked<LinkedListAllocator> =
+    Locked::new(LinkedListAllocator::new());
+```
+
+Since the `new` method creates an empty allocator, we also need to update our `allocator::init` function to call `LinkedListAllocator::init` with the heap bounds:
+
+```rust
+// in src/allocator.rs
+
+pub fn init_heap(
+    mapper: &mut impl Mapper<Size4KiB>,
+    frame_allocator: &mut impl FrameAllocator<Size4KiB>,
+) -> Result<(), MapToError> {
+    // […] map all heap pages
+
+    // new
+    unsafe {
+        super::ALLOCATOR.inner.lock().init(HEAP_START, HEAP_SIZE);
+    }
+
+    Ok(())
+}
+```
+
+It's important to call the `init` function after the mapping of the heap pages, because the function will already write to the heap (once we'll properly implement it). The `unsafe` block is safe here because we just mapped the heap region to unused frames, so that the passed heap region is valid.
+
+When we run our code now, it will of course panic since it runs into the `unimplemented!` in `add_free_region`. Let's fix that by providing a proper implementation for that method.
+
+### The `add_free_region` Method
+
+The `add_free_region` method provides the fundamental _push_ operation on the linked list. We currently only call this method from `init`, but it will also be the central method in our `dealloc` implementation. Remember, the `dealloc` method is called when an allocated memory region is freed again. To keep track of this freed memory region, we want to push it to the linked list.
+
+The implementation of the `add_free_region` method looks like this:
+
+```rust
+// in src/allocator.rs
+
+impl LinkedListAllocator {
+    /// Adds the given memory region to the front of the list.
+    unsafe fn add_free_region(&mut self, addr: usize, size: usize) {
+        // ensure that the freed region is capable of holding ListNode
+        assert!(align_up(addr, mem::align_of::<ListNode>()) == addr);
+        assert!(size >= mem::size_of::<ListNode>());
+
+        // create a new list node and append it at the start of the list
+        let mut node = ListNode::new(size);
+        node.next = self.head.next.take();
+        let node_ptr = addr as *mut ListNode;
+        node_ptr.write(node);
+        self.head.next = Some(&mut *node_ptr)
+    }
+}
+```
+
+The method takes a memory region represented by an address and size as argument and adds it to the front of the list. First, it ensures that the given region has the neccessary size and alignment for storing a `ListNode`. Then it creates the node and inserts it to the list through the following steps:
+
+![](linked-list-allocator-push.svg)
+
+Step 0 shows the state of the heap before `add_free_region` is called. In step 1, the method is called with the memory region marked as `freed` in the graphic. After the initial checks, the method creates a new `node` on its stack with the size of the freed region. It then uses the [`Option::take`] method to set the `next` pointer of the node to the current `head` pointer, thereby resetting the `head` pointer to `None`.
+
+[`Option::take`]: https://doc.rust-lang.org/core/option/enum.Option.html#method.take
+
+In step 2, the method writes the newly created `node` to the beginning of the freed memory region through the [`write`] method. It then points the `head` pointer to the new node. The resulting pointer structure looks a bit chaotic because the freed region is always inserted at the beginning of the list, but if we follow the pointers we see that each free region is still reachable from the `head` pointer.
+
+[`write`]: https://doc.rust-lang.org/std/primitive.pointer.html#method.write
+
+### The `find_region` Method
+
+The second fundamental operation on a linked list is finding an entry and removing it from the list. This is the central operation needed for implementing the `alloc` method. We implement the operation as a `find_region` method in the following way:
+
+```rust
+// in src/allocator.rs
+
+impl LinkedListAllocator {
+    /// Looks for a free region with the given size and alignment and removes
+    /// it from the list.
+    ///
+    /// Returns a tuple of the list node and the start address of the allocation.
+    fn find_region(&mut self, size: usize, align: usize)
+        -> Option<(&'static mut ListNode, usize)>
+    {
+        // reference to current list node, updated for each iteration
+        let mut current = &mut self.head;
+        // look for a large enough memory region in linked list
+        while let Some(ref mut region) = current.next {
+            if let Ok(alloc_start) = Self::alloc_from_region(&region, size, align) {
+                // region suitable for allocation -> remove node from list
+                let next = region.next.take();
+                let ret = Some((current.next.take().unwrap(), alloc_start));
+                current.next = next;
+                return ret;
+            } else {
+                // region not suitable -> continue with next region
+                current = current.next.as_mut().unwrap();
+            }
+        }
+
+        // no suitable region found
+        None
+    }
+}
+```
+
+The method uses a `current` variable and a [`while let` loop] to iterate over the list elements. At the beginning, `current` is set to the (dummy) `head` node. On each iteration, it is then updated to to the `next` field of the current node (in the `else` block). If the region is suitable for an allocation with the given size and alignment, the region is removed from the list and returned together with the `alloc_start` address.
+
+[`while let` loop]: https://doc.rust-lang.org/reference/expressions/loop-expr.html#predicate-pattern-loops
+
+When the `current.next` pointer becomes `None`, the loop exits. This means that we iterated over the whole list but found no region that is suitable for an allocation. In that case, we return `None`. The check whether a region is suitable is done by a `alloc_from_region` function, whose implementation will be shown in a moment.
+
+Let's take a more detailed look at how a suitable region is removed from the list:
+
+![](linked-list-allocator-remove-region.svg)
+
+Step 0 shows the situation before any pointer adjustments. The `region` and `current` regions and the `region.next` and `current.next` pointers are marked in the graphic. In step 1, both the `region.next` and `current.next` pointers are reset to `None` by using the [`Option::take`] method. The original pointers are stored in local variables called `next` and `ret`.
+
+In step 2, the `current.next` pointer is set to the local `next` pointer, which is the original `region.next` pointer. The effect is that `current` now directly points to the region after `region`, so that `region` is no longer element of the linked list. The function then returns the pointer to `region` stored in the local `ret` variable.
+
+### The `alloc_from_region` Function
+
+The `alloc_from_region` function returns whether a region is suitable for an allocation with given size and alignment. It is defined like this:
+
+```rust
+// in src/allocator.rs
+
+impl LinkedListAllocator {
+    /// Try to use the given region for an allocation with given size and alignment.
+    ///
+    /// Returns the allocation start address on success.
+    fn alloc_from_region(region: &ListNode, size: usize, align: usize)
+        -> Result<usize, ()>
+    {
+        let alloc_start = align_up(region.start_addr(), align);
+        let alloc_end = alloc_start + size;
+
+        if alloc_end > region.end_addr() {
+            // region too small
+            return Err(());
+        }
+
+        let excess_size = region.end_addr() - alloc_end;
+        if excess_size > 0 && excess_size < mem::size_of::<ListNode>() {
+            // rest of region too small to hold a ListNode (required because the
+            // allocation splits the region in a used and a free part)
+            return Err(());
+        }
+
+        // region suitable for allocation
+        Ok(alloc_start)
+    }
+}
+```
+
+First, the function calculates the start and end address of a potential allocation, using the `align_up` function we defined earlier. If the end address is behind the end address of the region, the allocation doesn't fit in the region and we return an error.
+
+The function performs a less obvious check after that. This check is neccessary because most of the time an allocation does not fit a suitable region perfectly, so that a part of the region remains usable after the allocation. This part of the region must store its own `ListNode` after the allocation, so it must be large enough to do so. The check verifies exactly that: either the allocation fits perfectly (`excess_size == 0`) or the excess size is large enough to store a `ListNode`.
+
+### Implementing `GlobalAlloc`
+
+With the fundamental operations provided by the `add_free_region` and `find_region` methods, we can now finally implement the `GlobalAlloc` trait:
+
+```rust
+// in src/allocator.rs
+
+unsafe impl GlobalAlloc for Locked<LinkedListAllocator> {
+    unsafe fn alloc(&self, layout: Layout) -> *mut u8 {
+        // perform layout adjustments
+        let (size, align) = LinkedListAllocator::size_align(layout);
+        let mut allocator = self.inner.lock();
+
+        if let Some((region, alloc_start)) = allocator.find_region(size, align) {
+            let alloc_end = alloc_start + size;
+            let excess_size = region.end_addr() - alloc_end;
+            if excess_size > 0 {
+                allocator.add_free_region(alloc_end, excess_size);
+            }
+            alloc_start as *mut u8
+        } else {
+            null_mut()
+        }
+    }
+
+    unsafe fn dealloc(&self, ptr: *mut u8, layout: Layout) {
+        // perform layout adjustments
+        let (size, _) = LinkedListAllocator::size_align(layout);
+
+        self.inner.lock().add_free_region(ptr as usize, size)
+    }
+}
+```
+
+Let's start with the `dealloc` method because it is simpler: First, it performs some layout adjustments, which we will explain in a moment, and retrieves a `&mut LinkedListAllocator` reference by calling the [`Mutex::lock`] function on the [`Locked` wrapper]. Then it calls the `add_free_region` function to add the deallocated region to the free list.
+
+The `alloc` method is a bit more complex. It starts with the same layout adjustments and also calls the [`Mutex::lock`] function to receive a mutable allocator reference. Then it uses the `find_region` method to find a suitable memory region for the allocation and remove it from the list. If this doesn't succeed and `None` is returned, it returns `null_mut` to signal an error as there is no suitable memory region.
+
+In the success case, the `find_region` method returns a tuple of the suitable region (no longer in the list) and the start address of the allocation. Using `alloc_start`, the allocation size, and the end address of the region, it calculates the end address of the allocation and the excess size again. If the excess size is not null, it calls `add_free_region` to add the excess size of the memory region back to the free list. Finally, it returns the `alloc_start` address casted as a `*mut u8` pointer.
+
+### Layout Adjustments
+
+```rust
+// in src/allocator.rs
+
+impl LinkedListAllocator {
+    /// Adjust the given layout so that the resulting allocated memory
+    /// region is also capable of storing a `ListNode`.
+    ///
+    /// Returns the adjusted size    and alignment as a (size, align) tuple.
+    fn size_align(layout: Layout) -> (usize, usize) {
+        let layout = layout.align_to(mem::align_of::<ListNode>())
+            .and_then(|l| l.pad_to_align())
+            .expect("adjusting alignment failed");
+        let size = layout.size().max(mem::size_of::<ListNode>());
+        (size, layout.align())
+    }
+}
+```
+
+
+
+
+
+
+
+
+
+
+##### Allocation
+In order to allocate a block of memory, we need to find a hole that satisfies the size and alignment requirements. If the found hole is larger than required, we split it into two smaller holes. For example, when we allocate a 24 byte block right after initialization, we split the single hole into a hole of size 24 and a hole with the remaining size:
+
+![split hole](split-hole.svg)
+
+Then we use the new 24 byte hole to perform the allocation:
+
+![24 bytes allocated](allocate.svg)
+
+To find a suitable hole, we can use several search strategies:
+
+- **best fit**: Search the whole list and choose the _smallest_ hole that satisfies the requirements.
+- **worst fit**: Search the whole list and choose the _largest_ hole that satisfies the requirements.
+- **first fit**: Search the list from the beginning and choose the _first_ hole that satisfies the requirements.
+
+Each strategy has its advantages and disadvantages. Best fit uses the smallest hole possible and leaves larger holes for large allocations. But splitting the smallest hole might create a tiny hole, which is too small for most allocations. In contrast, the worst fit strategy always chooses the largest hole. Thus, it does not create tiny holes, but it consumes the large block, which might be required for large allocations.
+
+For our use case, the best fit strategy is better than worst fit. The reason is that we have a minimal hole size of 16 bytes, since each hole needs to be able to store a size (8 bytes) and a pointer to the next hole (8 bytes). Thus, even the best fit strategy leads to holes of usable size. Furthermore, we will need to allocate very large blocks occasionally (e.g. for [DMA] buffers).
+
+[DMA]: https://en.wikipedia.org/wiki/Direct_memory_access
+
+However, both best fit and worst fit have a significant problem: They need to scan the whole list for each allocation in order to find the optimal block. This leads to long allocation times if the list is long. The first fit strategy does not have this problem, as it returns as soon as it finds a suitable hole. It is fairly fast for small allocations and might only need to scan the whole list for large allocations.
+
+### Deallocation
+To deallocate a block of memory, we can just insert its corresponding hole somewhere into the list. However, we need to merge adjacent holes. Otherwise, we are unable to reuse the freed memory for larger allocations. For example:
+
+![deallocate memory, which leads to adjacent holes](deallocate.svg)
+
+In order to use these adjacent holes for a large allocation, we need to merge them to a single large hole first:
+
+![merge adjacent holes and allocate large block](merge-holes-and-allocate.svg)
+
+The easiest way to ensure that adjacent holes are always merged, is to keep the hole list sorted by address. Thus, we only need to check the predecessor and the successor in the list when we free a memory block. If they are adjacent to the freed block, we merge the corresponding holes. Else, we insert the freed block as a new hole at the correct position.
+
+## Implementation
+The detailed implementation would go beyond the scope of this post, since it contains several hidden difficulties. For example:
+
+- Several merge cases: Merge with the previous hole, merge with the next hole, merge with both holes.
+- We need to satisfy the alignment requirements, which requires additional splitting logic.
+- The minimal hole size of 16 bytes: We must not create smaller holes when splitting a hole.
+
+I created the [linked_list_allocator] crate to handle all of these cases. It consists of a [Heap struct] that provides an `allocate_first_fit` and a `deallocate` method. It also contains a [LockedHeap] type that wraps `Heap` into spinlock so that it's usable as a static system allocator. If you are interested in the implementation details, check out the [source code][linked_list_allocator source].
+
+[linked_list_allocator]: https://docs.rs/crate/linked_list_allocator/0.4.1
+[Heap struct]: https://docs.rs/linked_list_allocator/0.4.1/linked_list_allocator/struct.Heap.html
+[LockedHeap]: https://docs.rs/linked_list_allocator/0.4.1/linked_list_allocator/struct.LockedHeap.html
+[linked_list_allocator source]: https://github.com/phil-opp/linked-list-allocator
+
+We need to add the extern crate to our `Cargo.toml` and our `lib.rs`:
+
+``` shell
+> cargo add linked_list_allocator
+```
+
+```rust
+// in src/lib.rs
+extern crate linked_list_allocator;
+```
+
+Now we can change our global allocator:
+
+```rust
+use linked_list_allocator::LockedHeap;
+
+#[global_allocator]
+static HEAP_ALLOCATOR: LockedHeap = LockedHeap::empty();
+```
+
+We can't initialize the linked list allocator statically, since it needs to initialize the first hole (like described [above](#initialization)). This can't be done at compile time, so the function can't be a `const` function. Therefore we can only create an empty heap and initialize it later at runtime. For that, we add the following lines to our `rust_main` function:
+
+```rust
+// in src/lib.rs
+
+#[no_mangle]
+pub extern "C" fn rust_main(multiboot_information_address: usize) {
+    […]
+
+    // set up guard page and map the heap pages
+    memory::init(boot_info);
+
+    // initialize the heap allocator
+    unsafe {
+        HEAP_ALLOCATOR.lock().init(HEAP_START, HEAP_START + HEAP_SIZE);
+    }
+    […]
+}
+```
+
+It is important that we initialize the heap _after_ mapping the heap pages, since the init function writes to the heap memory (the first hole).
+
+Our kernel uses the new allocator now, so we can deallocate memory without leaking it. The example from above should work now without causing an OOM situation:
+
+```rust
+// in rust_main in src/lib.rs
+
+for i in 0..10000 {
+    format!("Some String");
+}
+```
+
+## Performance
+The linked list based approach has some performance problems. Each allocation or deallocation might need to scan the complete list of holes in the worst case. However, I think it's good enough for now, since our heap will stay relatively small for the near future. When our allocator becomes a performance problem eventually, we can just replace it with a faster alternative.
+
+## Summary
+Now we're able to use heap storage in our kernel without leaking memory. This allows us to effectively process dynamic data such as user supplied strings in the future. We can also use `Rc` and `Arc` to create types with shared ownership. And we have access to various data structures such as `Vec` or `Linked List`, which will make our lives much easier. We even have some well tested and optimized [binary heap] and [B-tree] implementations!
+
+[binary heap]:https://en.wikipedia.org/wiki/Binary_heap
+[B-tree]: https://en.wikipedia.org/wiki/B-tree
+
+
+---
+
+TODO: update date
+
+---

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