-/*#[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 `PratialEq` special in that it is wired to the operator `==`:
+//@ That operator can not 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)
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