generic-array Design and Usage Notes

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generic-array Design and Usage Notes

Design and Usage Notes

Sections

NOTE: This document uses

sections, so look out for collapsible parts with an arrow on the left.

How it works

generic-array is a method of achieving fixed-length fixed-size stack-allocated generic arrays without needing const generics in stable Rust.

That is to say this:

struct Foo {
    data: [i32; N],
}

or anything similar is not currently supported.

However, Rust’s type system is sufficiently advanced, and a “hack” for solving this was created in the form of the typenum crate, which recursively defines integer values in binary as nested types, and operations which can be applied to those type-numbers, such as Add , Sub , etc.

e.g. 6 would be UInt<UInt<UInt, B1>, B0>

Over time, I’ve come to see typenum as less of a hack and more as an elegant solution.

The recursive binary nature of typenum is what makes generic-array possible, so:

struct Foo<N: ArrayLength> {
    data: GenericArray,
}

is supported.

I often see questions about why ArrayLength requires the element type T in it’s signature, even though it’s not used in the inner ArrayType .

This is because GenericArray itself does not define the actual array. Rather, it is defined as:

pub struct GenericArray<T, N: ArrayLength> {
    data: N::ArrayType,
}

The trait ArrayLength does all the real heavy lifting for defining the data, with implementations on UInt , UInt and UTerm , which correspond to even, odd and zero numeric values, respectively.

ArrayLength ‘s implementations use type-level recursion to peel away each least significant bit and form sort of an opaque binary tree of contiguous data the correct physical size to store N elements of T . The tree, or block of data, is then stored inside of GenericArray to be reinterpreted as the array.

For example, GenericArray more or less expands to (at compile time):

Expand for code
GenericArray {
    // UInt<UInt<UInt, B1>, B0>
    data: EvenData {
        // UInt<UInt, B1>
        left: OddData {
            // UInt
            left: OddData {
                left: (),  // UTerm
                right: (), // UTerm
                data: T,   // Element 0
            },
            // UInt
            right: OddData {
                left: (),  // UTerm
                right: (), // UTerm
                data: T,   // Element 1
            },
            data: T        // Element 2
        },
        // UInt<UInt, B1>
        right: OddData {
            // UInt
            left: OddData {
                left: (),  // UTerm
                right: (), // UTerm
                data: T,   // Element 3
            },
            // UInt
            right: OddData {
                left: (),  // UTerm
                right: (), // UTerm
                data: T,   // Element 4
            },
            data: T        // Element 5
        }
    }
}

This has the added benefit of only being log2(N) deep, which is important for things like Drop , which we’ll go into later.

Then, we take data and cast it to *const T or *mut T and use it as a slice like:

unsafe {
    slice::from_raw_parts(
        self as *const Self as *const T,
        N::to_usize()
    )
}

It is useful to note that because typenum is compile-time with nested generics, to_usize , even if it isn’t a const fn , does expand to effectively 1 + 2 + 4 + 8 + ... and so forth, which LLVM is smart enough to reduce to a single compile-time constant. This helps hint to the optimizers about things such as bounds checks.

So, to reiterate, we’re working with a raw block of contiguous memory the correct physical size to store N elements of T . It’s really no different from how normal arrays are stored.

Pointer Safety

Of course, casting pointers around and constructing blocks of data out of thin air is normal for C, but here in Rust we try to be a bit less prone to segfaults. Therefore, great care is taken to minimize casual unsafe usage and restrict unsafe to specific parts of the API, making heavy use those exposed safe APIs internally.

For example, the above slice::from_raw_parts is only used twice in the entire library, once for &[T] and slice::from_raw_parts_mut once for &mut [T] . Everything else goes through those slices.

Initialization

Constant

“Constant” initialization, that is to say – without dynamic values, can be done via the arr![] macro, which works almost exactly like vec![] , but with an additional type parameter.

Example:

let my_arr = arr![i32; 1, 2, 3, 4, 5, 6, 7, 8];

Dynamic

Although some users have opted to use their own initializers, as of version 0.9 and beyond generic-array includes safe methods for initializing elements in the array.

The GenericSequence trait defines a generate method which can be used like so:

use generic_array::{GenericArray, sequence::GenericSequence};

let squares: GenericArray =
             GenericArray::generate(|i: usize| i as i32 * 2);

and GenericArray additionally implements FromIterator , although from_iter will panic if the number of elements is not at least N . It will ignore extra items.

The safety of these operations is described later.

Functional Programming

In addition to GenericSequence , this crate provides a FunctionalSequence , which allows extremely efficient map , zip and fold operations on GenericArray s.

As described at the end of thesection, FunctionalSequence uses clever specialization tactics to provide optimized methods wherever possible, while remaining perfectly safe.

Some examples, taken from tests/generic.rs :

Expand for code

This is so extensive to show how you can build up to processing totally arbitrary sequences, but for the most part these can be used on GenericArray instances without much added complexity.

/// Super-simple fixed-length i32 `GenericArray`s
pub fn generic_array_plain_zip_sum(a: GenericArray, b: GenericArray) -> i32 {
    a.zip(b, |l, r| l + r)
     .map(|x| x + 1)
     .fold(0, |a, x| x + a)
}

pub fn generic_array_variable_length_zip_sum(a: GenericArray, b: GenericArray) -> i32
where
    N: ArrayLength,
{
    a.zip(b, |l, r| l + r)
     .map(|x| x + 1)
     .fold(0, |a, x| x + a)
}

pub fn generic_array_same_type_variable_length_zip_sum(a: GenericArray, b: GenericArray) -> i32
where
    N: ArrayLength + ArrayLength<<T as Add>::Output>,
    T: Add,
{
    a.zip(b, |l, r| l + r)
     .map(|x| x + 1)
     .fold(0, |a, x| x + a)
}

/// Complex example using fully generic `GenericArray`s with the same length.
///
/// It's mostly just the repeated `Add` traits, which would be present in other systems anyway.
pub fn generic_array_zip_sum<A, B, N: ArrayLength + ArrayLength>(a: GenericArray, b: GenericArray) -> i32
where
    A: Add,
    N: ArrayLength<<A as Add>::Output> +
        ArrayLength<<<A as Add>::Output as Add>::Output>,
    <A as Add>::Output: Add,
    <<A as Add>::Output as Add>::Output: Add,
{
    a.zip(b, |l, r| l + r)
     .map(|x| x + 1)
     .fold(0, |a, x| x + a)
}

and if you really want to go off the deep end and support any arbitrary GenericSequence :

/// Complex example function using generics to pass N-length sequences, zip them, and then map that result.
///
/// If used with `GenericArray` specifically this isn't necessary
pub fn generic_sequence_zip_sum(a: A, b: B) -> i32
where
    A: FunctionalSequence,                                                                 // `.zip`
    B: FunctionalSequence,                                             // `.zip`
    A: MappedGenericSequence,                                                         // `i32` -> `i32`
    B: MappedGenericSequence<i32, i32, Mapped = MappedSequence>,                   // `i32` -> `i32`, prove A and B can map to the same output
    A::Item: Add,                                                        // `l + r`
    MappedSequence: MappedGenericSequence + FunctionalSequence,     // `.map`
    SequenceItem<MappedSequence>: Add,                            // `x + 1`
    MappedSequence<MappedSequence, i32, i32>: Debug,                               // `println!`
    MappedSequence<MappedSequence, i32, i32>: FunctionalSequence,             // `.fold`
    SequenceItem<MappedSequence<MappedSequence, i32, i32>>: Add   // `x + a`, note the order
{
    let c = a.zip(b, |l, r| l + r).map(|x| x + 1);

    println!("{:?}", c);

    c.fold(0, |a, x| x + a)
}

of course, as I stated before, that’s almost never necessary, especially when you know the concrete types of all the components.

The numeric-array crate uses these to apply numeric operations across all elements in a GenericArray , making full use of all the optimizations described in the last section here.

Miscellaneous Utilities

Although not usually advertised, generic-array contains traits for lengthening, shortening, splitting and concatenating arrays.

For example, these snippets are taken from tests/mod.rs :

Expand for code

Appending and prepending elements:

use generic_array::sequence::Lengthen;

#[test]
fn test_append() {
    let a = arr![i32; 1, 2, 3];

    let b = a.append(4);

    assert_eq!(b, arr![i32; 1, 2, 3, 4]);
}

#[test]
fn test_prepend() {
    let a = arr![i32; 1, 2, 3];

    let b = a.prepend(4);

    assert_eq!(b, arr![i32; 4, 1, 2, 3]);
}

Popping elements from the front of back of the array:

use generic_array::sequence::Shorten;

let a = arr![i32; 1, 2, 3, 4];

let (init, last) = a.pop_back();

assert_eq!(init, arr![i32; 1, 2, 3]);
assert_eq!(last, 4);

let (head, tail) = a.pop_front();

assert_eq!(head, 1);
assert_eq!(tail, arr![i32; 2, 3, 4]);

and of course concatenating and splitting:

use generic_array::sequence::{Concat, Split};

let a = arr![i32; 1, 2];
let b = arr![i32; 3, 4];

let c = a.concat(b);

assert_eq!(c, arr![i32; 1, 2, 3, 4]);

let (d, e) = c.split();

assert_eq!(d, arr![i32; 1]);
assert_eq!(e, arr![i32; 2, 3, 4]);

Split and Concat in these examples use type-inference to determine the lengths of the resulting arrays.

Safety

As stated earlier, for raw reinterpretations such as this, safety is a must even while working with unsafe code. Great care is taken to reduce or eliminate undefined behavior.

For most of the above code examples, the biggest potential undefined behavior hasn’t even been applicable for one simple reason: they were all primitive values.

The simplest way to lead into this is to post these questions:

Drop
GenericArray::generate

For a fully initialized GenericArray , the expanded structure as described in thecan implement Drop naturally, recursively dropping elements. As it is only log2(N) deep, the recursion is very small overall.

In fact, I tested it while writing this, the size of the array itself overflows the stack before any recursive calls to drop can.

However, partially initialized arrays, such as described in the above hypothetical, pose an issue where drop could be called on uninitialized data, which is undefined behavior.

To solve this, GenericArray implements two components named ArrayBuilder and ArrayConsumer , which work very similarly.

ArrayBuilder creates a block of wholly uninitialized memory via mem::unintialized() , and stores that in a ManuallyDrop wrapper. ManuallyDrop does exactly what it says on the tin, and simply doesn’t drop the value unless manually requested to.

So, as we’re initializing our array, ArrayBuilder keeps track of the current position through it, and if something happens, ArrayBuilder itself will iteratively and manually drop all currently initialized elements, ignoring any uninitialized ones, because those are just raw memory and should be ignored.

ArrayConsumer does almost the same, “moving” values out of the array and into something else, like user code. It uses ptr::read to “move” the value out, and increments a counter saying that value is no longer valid in the array.

If a panic occurs in the user code with that element, it’s dropped naturally as it was moved into that scope. ArrayConsumer then proceeds to iteratively and manually drop all remaining elements.

Combined, these two systems provide a safe system for building and consuming GenericArray s. In fact, they are used extensively inside the library itself for FromIterator , GenericSequence and FunctionalSequence , among others.

Even GenericArray s implementation of Clone makes use of this via:

impl Clone for GenericArray
where
    N: ArrayLength,
{
    fn clone(&self) -> GenericArray {
        self.map(|x| x.clone())
    }
}

where .map is from the FunctionalSequence , and uses those builder and consumer structures to safely move and initialize values. Although, in this particular case, a consumer is not necessary as we’re using references. More on how that is automatically deduced is described in the next section.

Optimization

Rust and LLVM is smart. Crazy smart. However, it’s not magic.

In my experience, most of Rust’s “zero-cost” abstractions stem more from the type system, rather than explicit optimizations. Most Rust code is very easily optimizable and inlinable by design, so it can be simplified and compacted rather well, as opposed to the spaghetti code of some other languages.

Unfortunately, unless rustc or LLVM can “prove” things about code to simplify it, it must still be run, and can prevent further optimization.

A great example of this, and why I created the GenericSequence and FunctionalSequence traits, are iterators.

Custom iterators are slow. Not terribly slow, but slow enough to prevent some rather important optimizations.

Take GenericArrayIter for example:

Expand for code
pub struct GenericArrayIter<T, N: ArrayLength> {
    array: ManuallyDrop<GenericArray>,
    index: usize,
    index_back: usize,
}

impl Iterator for GenericArrayIter
where
    N: ArrayLength,
{
    type Item = T;

    #[inline]
    fn next(&mut self) -> Option {
        if self.index < self.index_back {
            let p = unsafe {
                Some(ptr::read(self.array.get_unchecked(self.index)))
            };

            self.index += 1;

            p
        } else {
            None
        }
    }

    //and more
}

Seems simple enough, right? Move an element out of the array with ptr::read and increment the index. If the iterator is dropped, the remaining elements are dropped exactly as they would with ArrayConsumer . index_back is provided for DoubleEndedIterator .

Unfortunately, that single if statement is terrible. In my mind, this is one of the biggest flaws of the iterator design. A conditional jump on a mutable variable unrelated to the data we are accessing on each call foils the optimizer and generates suboptimal code for the above iterator, even when we use get_unchecked .

The optimizer is unable to see that we are simply accessing memory sequentially. In fact, almost all iterators are like this. Granted, this is usually fine and, especially if they have to handle errors, it’s perfectly acceptable.

However, there is one iterator in the standard library that is optimized perfectly: the slice iterator. So perfectly in fact that it allows the optimizer to do something even more special: auto-vectorization ! We’ll get to that later.

It’s a bit frustrating as to why slice iterators can be so perfectly optimized, and it basically boils down to that the iterator itself does not own the data the slice refers to, so it uses raw pointers to the array/sequence/etc. rather than having to use an index on a stack allocated and always moving array. It can check for if the iterator is empty by comparing some front and back pointers for equality, and because those directly correspond to the position in memory of the next element, LLVM can see that and make optimizations.

So, the gist of that is: always use slice iterators where possible.

Here comes the most important part of all of this: ArrayBuilder and ArrayConsumer don’t iterate the arrays themselves. Instead, we use slice iterators (immutable and mutable), with zip or enumerate , to apply operations to the entire array, incrementing the position in both ArrayBuilder or ArrayConsumer to keep track.

For example, GenericSequence::generate for GenericArray is:

Expand for code
fn generate(mut f: F) -> GenericArray
where
    F: FnMut(usize) -> T,
{
    unsafe {
        let mut destination = ArrayBuilder::new();

        {
            let (destination_iter, position) = destination.iter_position();

            for (i, dst) in destination_iter.enumerate() {
                ptr::write(dst, f(i));

                *position += 1;
            }
        }

        destination.into_inner()
    }
}

where ArrayBuilder::iter_position is just an internal convenience function:

pub unsafe fn iter_position(&mut self) -> (slice::IterMut, &mut usize) {
    (self.array.iter_mut(), &mut self.position)
}

Of course, this may appear to be redundant, if we’re using an iterator that keeps track of the position itself, and the builder is also keeping track of the position. However, the two are decoupled.

If the generation function doesn’t have a chance at panicking, and/or the array element type doesn’t implement Drop , the optimizer deems the Drop implementation on ArrayBuilder (and ArrayConsumer ) dead code, and therefore position is never actually read from, so it becomes dead code as well, and is removed.

So for simple non- Drop /non-panicking elements and generation functions, generate becomes a very simple loop that uses a slice iterator to write values to the array.

Next, let’s take a look at a more complex example where this really shines: .zip

To cut down on excessively verbose code, .zip uses FromIterator for building the array, which has almost identical code to generate , so it will be omitted.

The first implementation of .zip is defined as:

Expand for code
fn inverted_zip(
    self,
    lhs: GenericArray,
    mut f: F,
) -> MappedSequence<GenericArray, B, U>
where
    GenericArray:
        GenericSequence + MappedGenericSequence,
    Self: MappedGenericSequence,
    Self::Length: ArrayLength + ArrayLength,
    F: FnMut(B, Self::Item) -> U,
{
    unsafe {
        let mut left = ArrayConsumer::new(lhs);
        let mut right = ArrayConsumer::new(self);

        let (left_array_iter, left_position) = left.iter_position();
        let (right_array_iter, right_position) = right.iter_position();

        FromIterator::from_iter(left_array_iter.zip(right_array_iter).map(|(l, r)| {
            let left_value = ptr::read(l);
            let right_value = ptr::read(r);

            *left_position += 1;
            *right_position += 1;

            f(left_value, right_value)
        }))
    }
}

The gist of this is that we have two GenericArray instances that need to be zipped together and mapped to a new sequence. This employs two ArrayConsumer s, and more or less use the same pattern as the previous example.

Again, the position values can be optimized out, and so can the slice iterator adapters.

We can go a step further with this, however.

Consider this:

let a = arr![i32; 1, 3, 5, 7];
let b = arr![i32; 2, 4, 6, 8];

let c = a.zip(b, |l, r| l + r);

assert_eq!(c, arr![i32; 3, 7, 11, 15]);

when compiled with:

cargo rustc --lib --profile test --release -- -C target-cpu=native -C opt-level=3 --emit asm

will produce assembly with the following relevant instructions taken from the entire program:

; Copy constant to register
vmovaps  [email protected](%rip), %xmm0

; Copy constant to register
vmovaps  [email protected]002(%rip), %xmm0

; Add the two values together
vpaddd   192(%rsp), %xmm0, %xmm1

; Copy constant to register
vmovaps  [email protected](%rip), %xmm0

; Compare result of the addition with the last constant
vpcmpeqb 128(%rsp), %xmm0, %xmm0

so, aside from a bunch of obvious hygiene instructions around those selected instructions, it seriously boils down that .zip call to a SINGLE SIMD instruction. In fact, it continues to do this for even larger arrays. Although it does fall back to individual additions for fewer than four elements, as it can’t fit those into an SSE register evenly.

Using this property of auto-vectorization without sacrificing safety, I created the numeric-array crate which makes use of this to wrap GenericArray and implement numeric traits so that almost all operations can be auto-vectorized, even complex ones like fused multiple-add.

It doesn’t end there, though. You may have noticed that the function name for zip above wasn’t zip , but inverted_zip .

This is because generic-array employs a clever specialization tactic to ensure .zip works corrects with:

a.zip(b, ...)
(&a).zip(b, ...)
(&a).zip(&b, ...)
a.zip(&b, ...)

wherein GenericSequence and FunctionalSequence have default implementations of zip variants, with concrete implementations for GenericArray . As GenericSequence is implemented for &GenericArray , where calling into_iter on produces a slice iterator, it can use “naive” iterator adapters to the same effect, while the specialized implementations use ArrayConsumer .

The result is that any combination of move or reference calls to .zip , .map and .fold produce code that can be optimized, none of them falling back to slow non-slice iterators. All perfectly safe with the ArrayBuilder and ArrayConsumer systems.

Honestly, GenericArray is better than standard arrays at this point.

The Future

If/when const generics land in stable Rust, my intention is to reorient this crate or create a new crate to provide traits and wrappers for standard arrays to provide the same safety and performance discussed above.

原文 : Github

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