orx-imp-vec

An ImpVec wraps a vector implementing PinnedVec, and hence, inherits the following feature:

• the data stays pinned in place; i.e., memory location of an item added to the vector will never change unless the vector is dropped or cleared.

Two main PinnedVec implementations which can be converted into an ImpVec are:

• SplitVec which allows for flexible strategies to explicitly define how the vector should grow, and
• FixedVec with a strict predetermined capacity while providing the speed of a standard vector.

Using the guarantees of PinnedVec, ImpVec provides additional abilities to push to or extend the vector with an immutable reference and provide a safe and convenient api to build vectors with self-referencing elements.

Therefore, it is called the ImpVec 👿 standing for 'immutable push vector'.

A. The goal

Four relevant types work together towards a common goal as follows:

• trait PinnedVec defines the safety guarantees for keeping the memory locations of already pushed elements;
  • struct FixedVec implements PinnedVec with a pre-determined fixed capacity while providing standard vector's complexity and performance;
  • struct SplitVec implements PinnedVec allowing for a dynamic capacity with an additional level of abstraction;
• struct ImpVec wraps any PinnedVec implementations and provides the safe api to allow for building vectors where elements may hold references to each other.

Therefore, the main goal is to make it convenient and safe to build tricky data structures, child structures of which holds references to each other. This is a common and a very useful pattern to represent structures such as trees, graphs or linked lists. The approach here can be summarized as follows:

• references rather than indices → to overcome the complexity of the memory model, we often tend to use usize indices to define a relation between children of a data structure; although this might be safe except for out-of-bounds errors, it is difficult to maintain and justify the correctness of relations through plain numbers.
• thin references rather than smart pointers → the relations among elements of the vector are defined by plain references which helps in keeping child structures smaller and in avoiding heap allocations.
• better cache locality → using a pinned vector as the underlying data structures, child elements will be close to each other.

B. Safety

B.1. Safety: immutable push

Pushing to a vector with an immutable reference sounds unsafe; however, ImpVec provides the safety guarantees.

Consider the following example using std::vec::Vec which does not compile:

```rust let mut vec = Vec::withcapacity(2); vec.extendfrom_slice(&[0, 1]);

let ref0 = &vec[0]; vec.push(2); // let value0 = *ref0; // does not compile! ```

Why does push invalidate the reference to the first element? * the vector has a capacity of 2; and hence, the push leads to an expansion of the vector's capacity; * it is possible that the underlying data will be copied to another place in memory; * in this case ref0 will be an invalid reference and dereferencing it would lead to an undefined behavior (UB).

However, ImpVec uses the PinnedVec as its underlying data which guarantees that the memory location of an item added to the vector will never change unless the vector is dropped or cleared.

Therefore, the following ImpVec version compiles and preserves the validity of the references.

```rust use orximpvec::prelude::*;

let vec: ImpVec<_> = SplitVec::withinitialcapacity(2).into(); vec.push(0); vec.push(1);

let ref0 = &vec[0]; let ref0_addr = ref0 as *const i32; // address before growth

vec.push(2); // capacity is increased here

let ref0addraftergrowth = &vec[0] as *const i32; // address after growth asserteq!(ref0addr, ref0addraftergrowth); // the pushed elements are pinned

// so it is safe to read from this memory location, // which will return the correct data let value0 = *ref0; assert_eq!(value0, 0); ```

B.2. Safety: reference breaking mutations

On the other hand, the following operations would change the memory locations of elements of the vector:

• inserting an element to an arbitrary location of the vector,
• popping or removeing from the vector,
• swapping elements, or
• truncate-ing the vector.

Therefore, similar to Vec, these operations require a mutable reference of ImpVec. Thanks to the ownership rules, all references are dropped before using these operations.

For instance, the following code safely will not compile.

```rust use orximpvec::prelude::*;

let mut vec: ImpVec<_, _> = SplitVec::withlineargrowth(4).into(); // mut required for the insert call

// push the first item and hold a reference to it let ref0 = vec.pushgetref(0);

// this is okay vec.push(1);

// this operation invalidates ref0 which is now the address of value 42. vec.insert(0, 42); assert_eq!(vec, &[42, 0, 1]);

// therefore, this line will lead to a compiler error!! // let value0 = *ref0; ```

B.3. Safety: reference breaking mutations for self referencing vectors

On the other hand, when the element type is not a NotSelfRefVecItem, the above-mentioned mutations become much more significant.

Consider the following example.

```rust use crate::prelude::*;

struct Person<'a> { name: String, helps: Option<&'a Person<'a>>, }

let people: ImpVec<_> = SplitVec::new().into();

let john = people.pushgetref(Person { name: String::from("john"), helps: None, }); people.push(Person { name: String::from("jane"), helps: Some(john), });

asserteq!(None, people[0].helps.map(|x| x.name.asstr())); asserteq!(Some("john"), people[1].helps.map(|x| x.name.asstr())); ```

Note that Person type is a self referencing vector item; and hence, is not a NotSelfRefVecItem.

In the built people vector, jane helps john; which is represented in memory as people[1] helps people[0].

Now assume that we call people.insert(0, mary). After this operation, the vector would be [mary, john, jane] breaking the relation between john and jane:

• people[1] helps people[0] would now correspond to john helps mary,which is incorrect. In addition, remove and pop operations could further lead to undefined behavior.

For this reason, these methods are not available when the element type is not NotSelfRefVecItem. Instead, there exist unsafe counterparts such as unsafe_insert.

For similar reasons, clone is only available when the element type is NotSelfRefVecItem.

C. Practicality

An ImpVec is particularly useful in representing and building data structures where the child structures are related to each other; rather than independent as in a standard vector. This is a very common pattern which is useful in defining trees, graphs, linked lists, etc.

Due to stronger emphasis on safety, defining is such relations is trickier in rust; and there appears to be two common approaches:

a. These relations can be defined by smart pointers such as Box or Rc. This approach is convenient and safe to correctly maintain the interdependencies among child structures. However, it comes with a performance cost. Each child element needs to be allocated on the heap. Furthermore, each these logically related elements will be in random locations in memory leading to inferior cache locality.

b. The second approach avoids the abovementioned drawbacks by holding elements in a array-like memory close to each other. In this case, it is challenging to define the relationships by references. Therefore, a common approach is to use indices, or positions in the storage, to define the relations. For instance, a tree node might have the field parent: Option<usize> which is Some of the position of the parent in the containing vector if the node is not the root. Although this approach manages to represent these tricky data structures, it requires lots of care to achieve correctness since index is only a plain number which mimics to represent the actual relation.

ImpVec's approach aims to combine the best of these two approaches:

• It defines relationships using references which can lead to index-free data structures. It is more expressive and safe to define a parent of a node as a reference to another node as in parent: Option<&'a Node<'a>>.
• Unlike the original pointer approach, imp-vec uses plain thin & references rather than wide smart pointers.
• It keeps its elements in a PinnedVec which may be a contagious memory when FixedVec is used, or a sequence of contagious memory chunks if SplitVec is used. In either way, the elements are not in arbitrary locations in memory.
• The safety checks are handled internally by ImpVec allowing to conveniently build wrapping data structures.

On top of everything, the last point is particularly important. It is not possible to completely avoid unsafe while defining such dependencies with thin references in rust. On the other hand, we lose lots of guarantees by using unsafe. ImpVec aims to carefully encapsulate the required unsafe calls allowing to define relational data structures from a higher level using the provided safe api.

C.1. Self referencing vectors (acyclic)

Being able to safely push to a collection with an immutable reference turns out to be a convenient tool for building relationships among children of a parent structure.

You may see below how ImpVec helps to easily represent some tricky data structures.

C.1.a. An alternative cons list

Recall the classical cons list example. Here is the code from the book which would not compile and used to discuss challenges and introduce smart pointers.

ignore enum List { Cons(i32, List), Nil, } fn main() { let list = Cons(1, Cons(2, Cons(3, Nil))); }

Below is a convenient cons list implementation using ImpVec as a storage:

• to which we can immutably push new lists,
• while simultaneously holding onto and using references to already created lists.

```rust use orximpvec::prelude::*;

[derive(Debug)]

enum List<'a, T> { Cons(T, &'a List<'a, T>), Nil, } impl<'a, T: PartialEq> PartialEq for List<'a, T> { // compare references fn eq(&self, other: &Self) -> bool { let ptreq = |l1, r1| std::ptr::eq(l1 as *const &'a List<'a, T>, r1 as *const &'a List<'a, T>); match (self, other) { (Self::Cons(l0, l1), Self::Cons(r0, r1)) => l0 == r0 && ptreq(l1, r1), _ => core::mem::discriminant(self) == core::mem::discriminant(other), } } } impl<'a, T> List<'a, T> { fn cons(&self) -> Option<&'a List<'a, T>> { match self { List::Nil => None, List::Cons(_, x) => Some(*x), } } }

let lists: ImpVec<_, _> = SplitVec::withexponentialgrowth(10, 1.5).into(); let nil = lists.pushgetref(List::Nil); // Nil let r3 = lists.pushgetref(List::Cons(3, nil)); // Cons(3) -> Nil let r2 = lists.pushgetref(List::Cons(42, r3)); // Cons(42) -> Cons(3) let r1 = lists.pushgetref(List::Cons(42, r2)); // Cons(42) -> Cons(42)

asserteq!(r1.cons(), Some(r2)); asserteq!(r2.cons(), Some(r3)); asserteq!(r3.cons(), Some(nil)); asserteq!(nil.cons(), None);

// use index in the outer collection assert_eq!(r1, &lists[3]);

// both are Cons variant with value 42; however, pointing to different list assert_ne!(r2, r3); ```

Alternatively, the ImpVec can be used only internally leading to a cons list implementation with a nice api to build the list. The storage will keep growing seamlessly while making sure that all references are thin and valid.

```rust use orximpvec::prelude::*; type ImpVecLin = ImpVec>;

enum List<'a, T> { Cons(T, &'a List<'a, T>), Nil(ImpVecLin>), } impl<'a, T> List<'a, T> { fn storage(&self) -> &ImpVecLin> { match self { List::Cons(, list) => list.storage(), List::Nil(storage) => storage, } } pub fn nil() -> Self { Self::Nil(ImpVecLin::default()) } pub fn connectfrom(&'a self, value: T) -> &Self { let newlist = Self::Cons(value, self); self.storage().pushgetref(newlist) } }

let nil = List::nil(); // sentinel holds the storage let r3 = nil.connectfrom(3); // Cons(3) -> Nil let r2 = r3.connectfrom(2); // Cons(2) -> Cons(3) let r1 = r2.connect_from(1); // Cons(2) -> Cons(1) ```

C.1.b. Directed Acyclic Graph

The cons list example reveals a pattern; ImpVec can safely store and allow references when the structure is built backwards starting from a sentinel node.

Direct acyclic graphs (DAG) or trees are examples for such cases. In the following, we define the Braess network as an example DAG, having edges:

• A -> B
• A -> C
• B -> D
• C -> D
• B -> C (the link causing the paradox!)

Such a graph could be constructed very conveniently with an ImpVec where the nodes are connected via regular references.

```rust use orximpvec::prelude::*; use std::fmt::Debug;

[derive(PartialEq, Eq)]

struct Node<'a, T> { id: T, targetnodes: Vec<&'a Node<'a, T>>, } impl<'a, T: Debug> Debug for Node<'a, T> { fn fmt(&self, f: &mut std::fmt::Formatter<'>) -> std::fmt::Result { write!( f, "node({:?})\t\tout-degree={}\t\tconnected-to={:?}", self.id, self.targetnodes.len(), self.targetnodes.iter().map(|n| &n.id).collect::>() ) } }

[derive(Default)]

struct Graph<'a, T>(ImpVec>);

impl<'a, T> Graph<'a, T> { fn addnode(&self, id: T, targetnodes: Vec<&'a Node<'a, T>>) -> &Node<'a, T> { let node = Node { id, targetnodes }; self.0.pushget_ref(node) } }

let graph = Graph::default(); let d = graph.addnode("D".tostring(), vec![]); let c = graph.addnode("C".tostring(), vec![d]); let b = graph.addnode("B".tostring(), vec![c, d]); let a = graph.addnode("A".tostring(), vec![b, c]);

for node in graph.0.into_iter() { println!("{:?}", node); }

asserteq!(2, a.targetnodes.len()); asserteq!(vec![b, c], a.targetnodes); asserteq!(vec![c, d], a.targetnodes[0].targetnodes); asserteq!(vec![d], a.targetnodes[0].targetnodes[0].targetnodes); assert!(a.targetnodes[0].targetnodes[0].targetnodes[0] .targetnodes .isempty()); ```

C.2. Self referencing vectors (any!)

As it has become apparent from the previous example, self referencing vectors can easily and conveniently be represented and built using an ImpVec provided that the references are acyclic. Although useful, this is limited.

ImpVec provides further abilities to build cyclic references as well which requires only slightly more care. orx-pinned-vec crate defines a general purpose SelfRefVecItem trait which is able to define all practical relations among elements of the vector. All methods have default do-nothing implementations; therefore, only the relevant methods need to be implemented. ImpVec provides corresponding methods for conveniently and safely managing the relations among elements.

As you may see in the following example, the methods which are required to be implemented are nothing but the relevant getters and setters.

C.2.a. Cyclic reference example

Consider for instance a circle of people holding hands. We can define the complete circle by defining the person to the right of each person. Say our circle starts with: a -> b -> c -> d -> a -> .... Note that we have a cyclic relation and we cannot build this only with the push_get_ref method. Further assume that people are switching places and we want to be able to update the relations. For the example, there will be a single such move where b and c will switch places leading to the new circle a -> c -> b -> d -> a -> ....

In this case, we only need to implement next (use next for right-to) and set_next methods of SelfRefVecItem trait; and this allows us to utilize set_next method of ImpVec to define and update relationships among people regardless of the relations being cyclic or acyclic.

```rust use orximpvec::prelude::*;

struct Person<'a> { name: String, persononright: Option<&'a Person<'a>>, } impl<'a> Person<'a> { fn persononrightname(&self) -> Option<&'a str> { self.persononright.map(|p| p.name.asstr()) } } impl<'a> SelfRefVecItem<'a> for Person<'a> { fn next(&self) -> Option<&'a Self> { self.persononright } fn setnext(&mut self, next: Option<&'a Self>) { self.personon_right = next; } }

let mut people: ImpVec<_> = SplitVec::withinitialcapacity(4).into();

// just push the people without the relationship let names = &["a", "b", "c", "d"]; for name in names { people.push(Person { name: name.tostring(), personon_right: None, }); }

// define the circle: a -> b -> c -> d -> a -> ... for i in 1..people.len() { people.setnext(i - 1, Some(i)); } people.setnext(people.len() - 1, Some(0));

asserteq!(Some("b"), people[0].persononrightname()); // a -> b asserteq!(Some("c"), people[1].persononrightname()); // b -> c asserteq!(Some("d"), people[2].persononrightname()); // c -> d asserteq!(Some("a"), people[3].persononrightname()); // d -> a

// now let b & c switch without any data copies people.setnext(0, Some(2)); // a -> c people.setnext(2, Some(1)); // c -> b people.set_next(1, Some(3)); // b -> d

asserteq!(Some("c"), people[0].persononrightname()); // a -> c asserteq!(Some("d"), people[1].persononrightname()); // b -> d asserteq!(Some("b"), people[2].persononrightname()); // c -> b asserteq!(Some("a"), people[3].persononrightname()); // d -> a

```

C.2.b. Crates utlizing ImpVec

orx-linked-list::LinkedList

See here for an alternative, convenient and efficient implementation of the doubly-LinkedList:

• All relations between elements are defined by thin & references avoiding wide smart pointers such as Box or Rc. This is useful in reducing the size of each linked list node. More importantly, it allows to avoid heap allocations for each element. Furthermore, the relations are defined without requiring to work with plain indices.
• All elements are stored in the underlying PinnedVec close to each other rather than in random memory locations; hence, improving cache locality.

Note that unsafe keyword appears twice in the orx-linked-list crate. On the other hand, at the point of writing, unsafe appears 63 times in the file defining the standard linked list. As mentioned in section C, it is not possible to completely avoid unsafe for defining the interdependencies among elements of a linked list; however, ImpVec almost completely encapsulates these calls.