-use std::cmp;
-use std::ops;
-use part05::BigInt;
-
-// Add with carry, returning the sum and the carry
-fn overflowing_add(a: u64, b: u64, carry: bool) -> (u64, bool) {
- let sum = u64::wrapping_add(a, b);
- if sum >= a {
- panic!("First addition did not overflow. Not implemented.");
- } else {
- panic!("First addition *did* overflow. Not implemented.");
+// Rust-101, Part 07: Operator Overloading, Tests, Formatting
+// ==========================================================
+
+pub use part05::BigInt;
+
+// With our new knowledge of lifetimes, we are now able to write down the desired type of `min`:
+//@ We want the function to take two references *with the same lifetime*, and then
+//@ return a reference with that lifetime. If the two input lifetimes would be different, we
+//@ would not know which lifetime to use for the result.
+pub trait Minimum {
+ fn min<'a>(&'a self, other: &'a Self) -> &'a Self;
+}
+
+//@ Now we can implement a generic function `vec_min` that works on above trait.
+//@ The code is pretty much straight-forward, and Rust checks that all the
+//@ lifetimes actually work out. Observe that we don't have to make any copies!
+pub fn vec_min<T: Minimum>(v: &Vec<T>) -> Option<&T> {
+ let mut min: Option<&T> = None;
+ for e in v {
+ min = Some(match min {
+ None => e,
+ Some(n) => n.min(e)
+ });
}
+ min
}
+//@ Notice that the return type `Option<&T>` is technically (leaving the borrowing story aside) a
+//@ pointer to a `T`, that could optionally be invalid. In other words, it's just like a pointer in
+//@ C(++) or Java that can be `NULL`! However, thanks to `Option` being an `enum`, we cannot forget
+//@ to check the pointer for validity, avoiding the safety issues of C(++). <br/>
+//@ Also, if you are worried about wasting space, notice that Rust knows that `&T` can never be
+//@ `NULL`, and hence optimizes `Option<&T>` to be no larger than `&T`. The `None` case is
+//@ represented as `NULL`. This is another great example of a zero-cost abstraction: `Option<&T>`
+//@ is exactly like a pointer in C(++), if you look at what happens during execution - but it's
+//@ much safer to use.
-/*#[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));
-}
-
-impl ops::Add 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()));
- panic!("Not yet implemented.");
+// **Exercise 07.1**: For our `vec_min` to be usable with `BigInt`, you will have to provide an
+// implementation of `Minimum`. You should be able to pretty much copy the code you wrote for
+// exercise 06.1. You should *not* make any copies of `BigInt`!
+impl Minimum for BigInt {
+ fn min<'a>(&'a self, other: &'a Self) -> &'a Self {
+ unimplemented!()
+ }
+}
+
+// ## Operator Overloading
+//@ How can we know that our `min` function actually does what we want it to do? One possibility
+//@ here is to do *testing*. Rust comes with nice built-in support for both unit tests and
+//@ integration tests. However, before we go there, we need to have a way of checking whether the
+//@ results of function calls are correct. In other words, we need to define how to test equality
+//@ of `BigInt`. Being able to test equality is a property of a type, that - you guessed it - Rust
+//@ expresses as a trait: `PartialEq`.
+
+//@ Doing this for `BigInt` is fairly easy, thanks to our requirement that there be no trailing
+//@ zeros. We simply re-use the equality test on vectors, which compares all the elements
+//@ individually.
+//@ The `inline` attribute tells Rust that we will typically want this function to be inlined.
+impl PartialEq for BigInt {
+ #[inline]
+ fn eq(&self, other: &BigInt) -> bool {
+ debug_assert!(self.test_invariant() && other.test_invariant());
+ self.data == other.data /*@*/
}
}
+
+//@ Since implementing `PartialEq` is a fairly mechanical business, you can let Rust automate this
+//@ by adding the attribute `derive(PartialEq)` to the type definition. In case you wonder about
+//@ the "partial", I suggest you check out the documentation of
+//@ [`PartialEq`](https://doc.rust-lang.org/std/cmp/trait.PartialEq.html) and
+//@ [`Eq`](https://doc.rust-lang.org/std/cmp/trait.Eq.html). `Eq` can be automatically derived as
+//@ well.
+
+// Now we can compare `BigInt`s. Rust treats `PartialEq` special in that it is wired to the operator
+// `==`:
+//@ That operator can now be used on our numbers! Speaking in C++ terms, we just overloaded the
+//@ `==` operator for `BigInt`. Rust does not have function overloading (i.e., it will not dispatch
+//@ to different functions depending on the type of the argument). Instead, one typically finds (or
+//@ defines) a trait that catches the core characteristic common to all the overloads, and writes a
+//@ single function that's generic in the trait. For example, instead of overloading a function for
+//@ all the ways a string can be represented, one writes a generic functions over
+//@ [ToString](https://doc.rust-lang.org/std/string/trait.ToString.html).
+//@ Usually, there is a trait like this that fits the purpose - and if there is, this has the great
+//@ advantage that any type *you* write, that can convert to a string, just has to implement
+//@ that trait to be immediately usable with all the functions out there that generalize over
+//@ `ToString`.
+//@ Compare that to C++ or Java, where the only chance to add a new overloading variant is to
+//@ edit the class of the receiver.
+//@
+//@ Why can we also use `!=`, even though we just overloaded `==`? The answer lies in what's called
+//@ a *default implementation*. If you check out the documentation of `PartialEq` I linked above,
+//@ you will see that the trait actually provides two methods: `eq` to test equality, and `ne` to
+//@ test inequality. As you may have guessed, `!=` is wired to `ne`. The trait *definition* also
+//@ provides a default implementation of `ne` to be the negation of `eq`. Hence you can just
+//@ provide `eq`, and `!=` will work fine. Or, if you have a more efficient way of deciding
+//@ inequality, you can provide `ne` for your type yourself.
+fn compare_big_ints() {
+ let b1 = BigInt::new(13);
+ let b2 = BigInt::new(37);
+ println!("b1 == b1: {} ; b1 == b2: {}; b1 != b2: {}", b1 == b1, b1 == b2, b1 != b2);
+}
+
+// ## Testing
+// With our equality test written, we are now ready to write our first testcase.
+//@ It doesn't get much simpler: You just write a function (with no arguments or return value),
+//@ and give it the `test` attribute. `assert!` is like `debug_assert!`, but does not get compiled
+//@ away in a release build.
+#[test]
+fn test_min() {
+ let b1 = BigInt::new(1);
+ let b2 = BigInt::new(42);
+ let b3 = BigInt::from_vec(vec![0, 1]);
+
+ assert!(*b1.min(&b2) == b1); /*@*/
+ assert!(*b3.min(&b2) == b2); /*@*/
+}
+// Now run `cargo test` to execute the test. If you implemented `min` correctly, it should all work!
+
+// ## Formatting
+//@ There is also a macro `assert_eq!` that's specialized to test for equality, and that prints the
+//@ two values (left and right) if they differ. To be able to do that, the macro needs to know how
+//@ to format the value for printing. This means that we - guess what? - have to implement an
+//@ appropriate trait. Rust knows about two ways of formatting a value: `Display` is for pretty-
+//@ printing something in a way that users can understand, while `Debug` is meant to show the
+//@ internal state of data and targeted at the programmer. The latter is what we want for
+//@ `assert_eq!`, so let's get started.
+
+// All formating is handled by [`std::fmt`](https://doc.rust-lang.org/std/fmt/index.html). I won't
+// explain all the details, and refer you to the documentation instead.
+use std::fmt;
+
+//@ In the case of `BigInt`, we'd like to just output our internal `data` array, so we
+//@ simply call the formating function of `Vec<u64>`.
+impl fmt::Debug for BigInt {
+ fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+ self.data.fmt(f)
+ }
+}
+//@ `Debug` implementations can be automatically generated using the `derive(Debug)` attribute.
+
+// Now we are ready to use `assert_eq!` to test `vec_min`.
+/*#[test]*/
+fn test_vec_min() {
+ let b1 = BigInt::new(1);
+ let b2 = BigInt::new(42);
+ let b3 = BigInt::from_vec(vec![0, 1]);
+
+ let v1 = vec![b2.clone(), b1.clone(), b3.clone()];
+ let v2 = vec![b2.clone(), b3.clone()];
+ assert_eq!(vec_min(&v1), Some(&b1)); /*@*/
+ assert_eq!(vec_min(&v2), Some(&b2)); /*@*/
+}
+
+// **Exercise 07.1**: Add some more testcases. In particular, make sure you test the behavior of
+// `vec_min` on an empty vector. Also add tests for `BigInt::from_vec` (in particular, removing
+// trailing zeros). Finally, break one of your functions in a subtle way and watch the test fail.
+
+// **Exercise 07.2**: Go back to your good ol' `SomethingOrNothing`, and implement `Display` for it.
+// (This will, of course, need a `Display` bound on `T`.) Then you should be able to use them with
+// `println!` just like you do with numbers, and get rid of the inherent functions to print
+// `SomethingOrNothing<i32>` and `SomethingOrNothing<f32>`.
+
+//@ [index](main.html) | [previous](part06.html) | [raw source](workspace/src/part07.rs) |
+//@ [next](part08.html)
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