diff --git a/blog/content/second-edition/posts/11-allocator-designs/index.md b/blog/content/second-edition/posts/11-allocator-designs/index.md index 8e7ec0fde..c7db5b939 100644 --- a/blog/content/second-edition/posts/11-allocator-designs/index.md +++ b/blog/content/second-edition/posts/11-allocator-designs/index.md @@ -296,7 +296,7 @@ The `dealloc` function ignores the given pointer and `Layout` arguments. Instead #### Address Alignment -The `align_up` function is general enough that we can put it into the parent `allocator` module. It basic implementation looks like this: +The `align_up` function is general enough that we can put it into the parent `allocator` module. A basic implementation looks like this: ```rust // in src/allocator.rs @@ -316,34 +316,31 @@ The function first computes the [remainder] of the division of `addr` by `align` [remainder]: https://en.wikipedia.org/wiki/Euclidean_division -Note that this isn't the most efficient way to implement this function. A slightly faster implementation looks like this: +Note that this isn't the most efficient way to implement this function. A much faster implementation looks like this: ```rust +/// Align the given address `addr` upwards to alignment `align`. +/// +/// Requires that `align` is a power of two. fn align_up(addr: usize, align: usize) -> usize { - (addr + align - 1) / align * align; + (addr + align - 1) & !(align - 1) } ``` -Here we utilize the fact that dividing and then multiplying by `align` clears the lower bits to zero. To align the address upwards instead of downwards, we add `align - 1` before the division. This approach has the advantage that an already aligned address is not changed so that we don't need an `if` statement that slightly decreases performance. When the compiler is able to prove that `align` is always a power of two, it could even translate the division and multiplication operations to fast [bit shift operations]. - -[bit shift operations]: https://en.wikipedia.org/wiki/Logical_shift - -Given that address alignment is a very general problem, the Rust `core` library also provides an implementation for it through the [`align_offset`] method on raw pointers. With it, we can also implement `align_up`: - -[`align_offset`]: https://doc.rust-lang.org/std/primitive.pointer.html#method.align_offset +This method utilizes that the `GlobalAlloc` trait guarantees that `align` is always a power of two. This makes it possible to create a [bitmask] to align the address in a very efficient way. To understand how it works, let's go through it step by step starting on the right side: -```rust -fn align_up(addr: usize, align: usize) -> usize { - let offset = (addr as *const u8).align_offset(align); - addr + offset -} -``` +[bitmask]: https://en.wikipedia.org/wiki/Mask_(computing) -Here we convert the address to a `*const u8` pointer and then call [`align_offset`] to get the number of bytes that we need to add to align the address. It turns out that the implementation of `align_offset` is [hightly optimized][align-offset-impl], so this `align_up` variant has the best performance compared to the other variants. +- Since `align` is a power of two, its [binary representation] has only a single bit set (e.g. `0b000100000`). This means that `align - 1` has all the lower bits set (e.g. `0b00011111`). +- By creating the [bitwise `NOT`] through the `!` operator, we get a number that has all the bits set except for the bits lower than `align` (e.g. `0b…111111111100000`). +- By performing a [bitwise `AND`] on an address and `!(align - 1)`, we align the address _downwards_. This works by clearing all the bits that are lower than `align`. +- Since we want to align upwards instead of downwards, we increase the `addr` by `align - 1` before performing the bitwise `AND`. This way, already aligned addresses remain the same while non-aligned addresses are rounded to the next alignment boundary. -[align-offset-impl]: https://github.com/rust-lang/rust/blob/2f688ac602d50129388bb2a5519942049096cbff/src/libcore/ptr/mod.rs#L1031-L1143 +[binary representation]: https://en.wikipedia.org/wiki/Binary_number#Representation +[bitwise `NOT`]: https://en.wikipedia.org/wiki/Bitwise_operation#NOT +[bitwise `AND`]: https://en.wikipedia.org/wiki/Bitwise_operation#AND -Which variant you choose it up to you. They all compute the same result, only using different methods. +Which variant you choose it up to you. Both compute the same result, only using different methods. ### Using It