-// Rust-101, Part 06: Abstract Datastructure, Testing
-// ==================================================
+// Rust-101, Part 06: Copy, Lifetimes
+// ==================================
-use std::cmp;
-use std::ops;
-
-pub struct BigInt {
- data: Vec<u64>, // least significant digits first. The last block will *not* be 0.
-}
+// We continue to work on our `BigInt`, so we start by importing what we already established.
+use part05::BigInt;
+// With `BigInt` being about numbers, we should be able to write a version of `vec_min`
+// that computes the minimum of a list of `BigInt`. First, we have to write `min` for `BigInt`.
impl BigInt {
- pub fn new(x: u64) -> Self {
- if x == 0 {
- BigInt { data: vec![] }
+ fn min_try1(self, other: Self) -> Self {
+ //@ Just to be sure, we first check that both operands actually satisfy our invariant.
+ //@ `debug_assert!` is a macro that checks that its argument (must be of type `bool`) is
+ //@ `true`, and panics otherwise. It gets removed in release builds, which you do with
+ //@ `cargo build --release`.
+ debug_assert!(self.test_invariant() && other.test_invariant());
+ // Now our assumption of having no trailing zeros comes in handy:
+ // If the lengths of the two numbers differ, we already know which is larger.
+ if self.data.len() < other.data.len() {
+ self
+ } else if self.data.len() > other.data.len() {
+ other
} else {
- BigInt { data: vec![x] }
+ // **Exercise 06.1**: Fill in this code.
+ unimplemented!()
}
}
}
-/// Add with carry, returning the sum and the carry
-fn overflowing_add(a: u64, b: u64, carry: bool) -> (u64, bool) {
- match u64::checked_add(a, b) {
- Some(sum) if !carry => (sum, false),
- Some(sum) => { // we have to increment the sum by 1, where it may overflow again
- match u64::checked_add(sum, 1) {
- Some(total_sum) => (total_sum, false),
- None => (0, true) // we overflowed incrementing by 1, so we are just "at the edge"
- }
- },
- None => {
- // Get the remainder, i.e., the wrapping sum. This cannot overflow again by adding just 1, so it is safe
- // to add the carry here.
- let rem = u64::wrapping_add(a, b) + if carry { 1 } else { 0 };
- (rem, true)
- }
+// Now we can write `vec_min`.
+fn vec_min(v: &Vec<BigInt>) -> Option<BigInt> {
+ let mut min: Option<BigInt> = None;
+ // If `v` is a shared reference to a vector, then the default for iterating over it is to call
+ // `iter`, the iterator that borrows the elements.
+ for e in v {
+ let e = e.clone();
+ min = Some(match min { /*@*/
+ None => e, /*@*/
+ Some(n) => e.min_try1(n) /*@*/
+ }); /*@*/
}
+ min
}
+//@ Now, what's happening here? Why do we have to to make a full (deep) copy of `e`, and why did we
+//@ not have to do that in our previous version?
+//@
+//@ The answer is already hidden in the type of `vec_min`: `v` is just borrowed, but
+//@ the Option<BigInt> that it returns is *owned*. We can't just return one of the elements of `v`,
+//@ as that would mean that it is no longer in the vector! In our code, this comes up when we update
+//@ the intermediate variable `min`, which also has type `Option<BigInt>`. If you get rid of the
+//@ `e.clone()`, Rust will complain "Cannot move out of borrowed content". That's because
+//@ `e` is a `&BigInt`. Assigning `min = Some(*e)` works just like a function call: Ownership of the
+//@ underlying data is transferred from `e` to `min`. But that's not allowed, since
+//@ we just borrowed `e`, so we cannot empty it! We can, however, call `clone` on it. Then we own
+//@ the copy that was created, and hence we can store it in `min`. <br/>
+//@ Of course, making such a full copy is expensive, so we'd like to avoid it. We'll come to that
+//@ in the next part.
-#[test]
-fn test_overflowing_add() {
- assert_eq!(overflowing_add(10, 100, false), (110, false));
- assert_eq!(overflowing_add(10, 100, true), (111, false));
- assert_eq!(overflowing_add(1 << 63, 1 << 63, false), (0, true));
- assert_eq!(overflowing_add(1 << 63, 1 << 63, true), (1, true));
- assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
-}
+// ## `Copy` types
-impl ops::Add<BigInt> for BigInt {
- type Output = BigInt;
- fn add(self, rhs: BigInt) -> Self::Output {
- let mut result_vec:Vec<u64> = Vec::with_capacity(cmp::max(self.data.len(), rhs.data.len()));
- let mut carry:bool = false; // the carry bit
- for (i, val) in self.data.into_iter().enumerate() {
- // compute next digit and carry
- let rhs_val = if i < rhs.data.len() { rhs.data[i] } else { 0 };
- let (sum, new_carry) = overflowing_add(val, rhs_val, carry);
- // store them
- result_vec.push(sum);
- carry = new_carry;
- }
- BigInt { data: result_vec }
+//@ But before we go there, I should answer the second question I brought up above: Why did our old
+//@ `vec_min` work? We stored the minimal `i32` locally without cloning, and Rust did not complain.
+//@ That's because there isn't really much of an "ownership" when it comes to types like `i32` or
+//@ `bool`: If you move the value from one place to another, then both instances are "complete". We
+//@ also say the value has been *duplicated*. This is in stark contrast to types like `Vec<i32>`,
+//@ where moving the value results in both the old and the new vector to point to the same
+//@ underlying buffer. We don't have two vectors, there's no proper duplication.
+//@
+//@ Rust calls types that can be easily duplicated `Copy` types. `Copy` is another trait, and it is
+//@ implemented for types like `i32` and `bool`. Remember how we defined the trait `Minimum` by
+//@ writing `trait Minimum : Copy { ...`? This tells Rust that every type that implements `Minimum`
+//@ must also implement `Copy`, and that's why the compiler accepted our generic `vec_min` in part
+//@ 02. `Copy` is the first *marker trait* that we encounter: It does not provide any methods, but
+//@ makes a promise about the behavior of the type - in this case, being duplicable.
+//@ If you try to implement `Copy` for `BigInt`, you will notice that Rust does not let you do
+//@ that. A type can only be `Copy` if all its elements are `Copy`, and that's not the case for
+//@ `BigInt`. However, we can make `SomethingOrNothing<T>` copy if `T` is `Copy`.
+use part02::{SomethingOrNothing,Something,Nothing};
+impl<T: Copy> Copy for SomethingOrNothing<T> {}
+//@ Again, Rust can generate implementations of `Copy` automatically. If
+//@ you add `#[derive(Copy,Clone)]` right before the definition of `SomethingOrNothing`,
+//@ both `Copy` and `Clone` will automatically be implemented.
+
+//@ ## An operational perspective
+//@ Instead of looking at what happens "at the surface" (i.e., visible in Rust), one can also explain
+//@ ownership passing and how `Copy` and `Clone` fit in by looking at what happens on the machine.
+//@ <br/>
+//@ When Rust code is executed, passing a value (like `i32` or `Vec<i32>`) to a function will always
+//@ result in a shallow copy being performed: Rust just copies the bytes representing that value, and
+//@ considers itself done. That's just like the default copy constructor in C++. Rust, however, will
+//@ consider this a destructive operation: After copying the bytes elsewhere, the original value must
+//@ no longer be used. After all, the two could now share a pointer! If, however, you mark a type
+//@ `Copy`, then Rust will *not* consider a move destructive, and just like in C++, the old and new
+//@ value can happily coexist. Now, Rust does not allow you to overload the copy constructor. This
+//@ means that passing a value around will always be a fast operation, no allocation or any other
+//@ kind of heap access will happen. In the situations where you would write a copy constructor in
+//@ C++ (and hence incur a hidden cost on every copy of this type), you'd have the type *not*
+//@ implement `Copy`, but only `Clone`. This makes the cost explicit.
+
+// ## Lifetimes
+//@ To fix the performance problems of `vec_min`, we need to avoid using `clone`. We'd like the
+//@ return value to not be owned (remember that this was the source of our need for cloning), but
+//@ *borrowed*. In other words, we want to return a shared reference to the minimal element.
+//@ The function `head` demonstrates how that could work: It returns a reference to the first
+//@ element of a vector if it is non-empty. The type of the function says that it will either
+//@ return nothing, or it will return a borrowed `T`. We can then obtain a reference to the first
+//@ element of `v` and use it to construct the return value.
+fn head<T>(v: &Vec<T>) -> Option<&T> {
+ if v.len() > 0 {
+ Some(&v[0]) /*@*/
+ } else {
+ None
}
}
+// Technically, we are returning a pointer to the first element. But doesn't that mean that callers
+// have to be careful? Imagine `head` would be a C++ function, and we would write the following
+// code.
+/*
+ int foo(std::vector<int> v) {
+ int *first = head(v);
+ v.push_back(42);
+ return *first;
+ }
+*/
+//@ This is very much like our very first motivating example for ownership, at the beginning of
+//@ part 04: `push_back` could reallocate the buffer, making `first` an invalid pointer. Again, we
+//@ have aliasing (of `first` and `v`) and mutation. But this time, the bug is hidden behind the
+//@ call to `head`. How does Rust solve this? If we translate the code above to Rust, it doesn't
+//@ compile, so clearly we are good - but how and why?
+//@ (Notice that have to explicitly assert using //@ `unwrap` that `first` is not `None`, whereas
+//@ the C++ code above would silently dereference a //@ `NULL`-pointer. But that's another point.)
+fn rust_foo(mut v: Vec<i32>) -> i32 {
+ let first: Option<&i32> = head(&v);
+ /* v.push(42); */
+ *first.unwrap()
+}
+//@ To give the answer to this question, we have to talk about the *lifetime* of a reference. The
+//@ point is, saying that you borrowed your friend a `Vec<i32>`, or a book, is not good enough,
+//@ unless you also agree on *how long* your friend can borrow it. After all, you need to know when
+//@ you can rely on owning your data (or book) again.
+//@
+//@ Every reference in Rust has an associated lifetime, written `&'a T` for a reference with
+//@ lifetime `'a` to something of type `T`. The full type of `head` reads as follows: `fn<'a,
+//@ T>(&'a Vec<T>) -> Option<&'a T>`. Here, `'a` is a *lifetime variable*, which represents for how
+//@ long the vector has been borrowed. The function type expresses that argument and return value
+//@ have *the same lifetime*.
+//@
+//@ When analyzing the code of `rust_foo`, Rust has to assign a lifetime to `first`. It will choose
+//@ the scope where `first` is valid, which is the entire rest of the function. Because `head` ties
+//@ the lifetime of its argument and return value together, this means that `&v` also has to borrow
+//@ `v` for the entire duration of the function `rust_foo`. So when we try to create a unique
+//@ reference to `v` for `push`, Rust complains that the two references (the one for `head`, and
+//@ the one for `push`) overlap, so neither of them can be unique. Lucky us! Rust caught our
+//@ mistake and made sure we don't crash the program.
+//@
+//@ So, to sum this up: Lifetimes enable Rust to reason about *how long* a reference is valid, how
+//@ long ownership has been borrowed. We can thus safely write functions like `head`, that return
+//@ references into data they got as argument, and make sure they are used correctly, *while
+//@ looking only at the function type*. At no point in our analysis of `rust_foo` did we have to
+//@ look *into* `head`. That's, of course, crucial if we want to separate library code from
+//@ application code.
+//@ Most of the time, we don't have to explicitly add lifetimes to function types. This is thanks
+//@ to *lifetime elision*, where Rust will automatically insert lifetimes we did not specify,
+//@ following some simple, well-documented
+//@ [rules](https://doc.rust- lang.org/stable/book/lifetimes.html#lifetime-elision).
-
+//@ [index](main.html) | [previous](part05.html) | [raw source](workspace/src/part06.rs) |
+//@ [next](part07.html)
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