// ========================
// ## Big Numbers
-// In the course of the next few parts, we are going to build a data-structure for computations with
-// *big* numbers. We would like to not have an upper bound to how large these numbers can get, with
-// the memory of the machine being the only limit.
-//
-// We start by deciding how to represent such big numbers. One possibility here is
-// to use a vector "digits" of the big number. This is like "1337" being a vector of four digits (1, 3, 3, 7),
-// except that we will use `u64` as type of our digits. Now we just have to decide
-// the order in which we store numbers. I decided that we will store the least significant
-// digit first. This means that "1337" would actually become (7, 3, 3, 1).<br/>
-// Finally, we declare that there must not be any trailing zeros (corresponding to
-// useless leading zeros in our usual way of writing numbers). This is to ensure that
-// the same number can only be stored in one way.
-// To write this down in Rust, we use a `struct`, which is a lot like structs in C:
-// Just a bunch of named fields. Every field can be private to the current module (which is the default),
-// or public (which is indicated by a `pub` in front of the name). For the sake of the tutorial, we make
-// `data` public - otherwise, the next parts of this course could not work on `BigInt`s. Of course, in a
-// real program, one would make the field private to ensure that the invariant (no trailing zeros) is maintained.
+//@ In the course of the next few parts, we are going to build a data-structure for computations
+//@ with *big* numbers. We would like to not have an upper bound to how large these numbers can
+//@ get, with the memory of the machine being the only limit.
+//@
+//@ We start by deciding how to represent such big numbers. One possibility here is to use a vector
+//@ "digits" of the number. This is like "1337" being a vector of four digits (1, 3, 3, 7), except
+//@ that we will use `u64` as type of our digits, meaning we have 2^64 individual digits. Now we
+//@ just have to decide the order in which we store numbers. I decided that we will store the least
+//@ significant digit first. This means that "1337" would actually become (7, 3, 3, 1). <br/>
+//@ Finally, we declare that there must not be any trailing zeros (corresponding to
+//@ useless leading zeros in our usual way of writing numbers). This is to ensure that
+//@ the same number can only be stored in one way.
+
+//@ To write this down in Rust, we use a `struct`, which is a lot like structs in C:
+//@ Just a bunch of named fields. Every field can be private to the current module (which is the
+//@ default), or public (which is indicated by a `pub` in front of the name). For the sake of the
+//@ tutorial, we make `data` public - otherwise, the next parts of this course could not work on
+//@ `BigInt`s. Of course, in a real program, one would make the field private to ensure that the
+//@ invariant (no trailing zeros) is maintained.
pub struct BigInt {
- pub data: Vec<u64>,
+ pub data: Vec<u64>, // least significant digit first, no trailing zeros
}
// Now that we fixed the data representation, we can start implementing methods on it.
impl BigInt {
- // Let's start with a constructor, creating a `BigInt` from an ordinary integer.
- // To create an instance of a struct, we write its name followed by a list of
- // fields and initial values assigned to them.
+ //@ Let's start with a constructor, creating a `BigInt` from an ordinary integer.
+ //@ To create an instance of a struct, we write its name followed by a list of
+ //@ fields and initial values assigned to them.
pub fn new(x: u64) -> Self {
if x == 0 {
- BigInt { data: vec![] }
+ BigInt { data: vec![] } /*@*/
} else {
- BigInt { data: vec![x] }
+ BigInt { data: vec![x] } /*@*/
}
}
- // It can often be useful to encode the invariant of a data-structure in code, so here
- // is a check that detects useless trailing zeros.
+ //@ It can often be useful to encode the invariant of a data-structure in code, so here
+ //@ is a check that detects useless trailing zeros.
pub fn test_invariant(&self) -> bool {
if self.data.len() == 0 {
true
} else {
- self.data[self.data.len() - 1] != 0
+ self.data[self.data.len() - 1] != 0 /*@*/
}
}
- // We can convert any vector of digits into a number, by removing trailing zeros. The `mut`
- // declaration for `v` here is just like the one in `let mut ...`, it says that we will locally
- // change the vector `v`. In this case, we need to make that annotation to be able to call `pop`
- // on `v`.
+ // We can convert any little-endian vector of digits (i.e., least-significant digit first) into
+ // a number, by removing trailing zeros. The `mut` declaration for `v` here is just like the
+ // one in `let mut ...`: We completely own `v`, but Rust still asks us to make our intention of
+ // modifying it explicit. This `mut` is *not* part of the type of `from_vec` - the caller has
+ // to give up ownership of `v` anyway, so they don't care anymore what you do to it.
+ //
+ // **Exercise 05.1**: Implement this function.
+ //
+ // *Hint*: You can use `pop` to remove the last element of a vector.
pub fn from_vec(mut v: Vec<u64>) -> Self {
- while v.len() > 0 && v[v.len()-1] == 0 {
- v.pop();
- }
- BigInt { data: v }
+ unimplemented!()
}
}
-// **Exercise 05.1**: Write a function on `BigInt` that returns the number of digits. Write another one
-// that increments the number by 1.
-//
-// *Hint*: To take `self` as a mutable borrow, write `fn inc1(&mut self)`.
-
// ## Cloning
-// If you have a close look at the type of `BigInt::from_vec`, you will notice that it
-// consumes the vector `v`. The caller hence loses access. There is however something
-// we can do if we don't want that to happen: We can explicitly `clone` the vector,
-// which means that a full (or *deep*) copy will be performed. Technically,
-// `clone` takes a borrowed vector, and returns a fully owned one.
+//@ If you take a close look at the type of `BigInt::from_vec`, you will notice that it consumes
+//@ the vector `v`. The caller hence loses access to its vector. However, there is something we can
+//@ do if we don't want that to happen: We can explicitly `clone` the vector, which means that a
+//@ full (or *deep*) copy will be performed. Technically, `clone` takes a borrowed vector in the
+//@ form of a shared reference, and returns a fully owned one.
fn clone_demo() {
let v = vec![0,1 << 16];
let b1 = BigInt::from_vec((&v).clone());
let b2 = BigInt::from_vec(v);
}
-// Rust has special treatment for methods that borrow its `self` argument (like `clone`, or
-// like `test_invariant` above): It is not necessary to explicitly borrow the receiver of the
-// method. Hence you could replace `(&v).clone()` by `v.clone()` above. Just try it!
+//@ Rust has special treatment for methods that borrow their `self` argument (like `clone`, or
+//@ like `test_invariant` above): It is not necessary to explicitly borrow the receiver of the
+//@ method. Hence you could replace `(&v).clone()` by `v.clone()` above. Just try it!
-// To be clonable is a property of a type, and as such, naturally expressed with a trait.
-// In fact, Rust already comes with a trait `Clone` for exactly this purpose. We can hence
-// make our `BigInt` clonable as well.
+//@ To be clonable is a property of a type, and as such, naturally expressed with a trait.
+//@ In fact, Rust already comes with a trait `Clone` for exactly this purpose. We can hence
+//@ make our `BigInt` clonable as well.
impl Clone for BigInt {
fn clone(&self) -> Self {
- BigInt { data: self.data.clone() }
+ BigInt { data: self.data.clone() } /*@*/
}
}
-// Making a type clonable is such a common exercise that Rust can even help you doing it:
-// If you add `#[derive(Clone)]` right in front of the definition of `BigInt`, Rust will
-// generate an implementation of `Clone` that simply clones all the fields. Try it!
-// These `#[...]` annotations at types (and functions, modules, crates) are called *attributes*.
-// We will see some more examples of attributes later.
+//@ Making a type clonable is such a common exercise that Rust can even help you doing it:
+//@ If you add `#[derive(Clone)]` right in front of the definition of `BigInt`, Rust will
+//@ generate an implementation of `Clone` that simply clones all the fields. Try it!
+//@ These `#[...]` annotations at types (and functions, modules, crates) are called *attributes*.
+//@ We will see some more examples of attributes later.
-// We can also make the type `SomethingOrNothing<T>` implement `Clone`. However, that
-// can only work if `T` is `Clone`! So we have to add this bound to `T` when we introduce
-// the type variable.
+// We can also make the type `SomethingOrNothing<T>` implement `Clone`.
+//@ However, that can only work if `T` is `Clone`! So we have to add this bound to `T` when we
+//@ introduce the type variable.
use part02::{SomethingOrNothing,Something,Nothing};
impl<T: Clone> Clone for SomethingOrNothing<T> {
fn clone(&self) -> Self {
- match *self {
- Nothing => Nothing,
- // In the second arm of the match, we need to talk about the value `v`
- // that's stored in `self`. However, if we would write the pattern as
- // `Something(v)`, that would indicate that we *own* `v` in the code
- // after the arrow. That can't work though, we have to leave `v` owned by
- // whoever called us - after all, we don't even own `self`, we just borrowed it.
- // By writing `Something(ref v)`, we borrow `v` for the duration of the match
- // arm. That's good enough for cloning it.
- Something(ref v) => Something(v.clone()),
- }
+ match *self { /*@*/
+ Nothing => Nothing, /*@*/
+ //@ In the second arm of the match, we need to talk about the value `v`
+ //@ that's stored in `self`. However, if we were to write the pattern as
+ //@ `Something(v)`, that would indicate that we *own* `v` in the code
+ //@ after the arrow. That can't work though, we have to leave `v` owned by
+ //@ whoever called us - after all, we don't even own `self`, we just borrowed it.
+ //@ By writing `Something(ref v)`, we borrow `v` for the duration of the match
+ //@ arm. That's good enough for cloning it.
+ Something(ref v) => Something(v.clone()), /*@*/
+ } /*@*/
}
}
-// Again, Rust will generate this implementation automatically if you add
-// `#[derive(Clone)]` right before the definition of `SomethingOrNothing`.
+//@ Again, Rust will generate this implementation automatically if you add
+//@ `#[derive(Clone)]` right before the definition of `SomethingOrNothing`.
+
+// **Exercise 05.2**: Write some more functions on `BigInt`. What about a function that returns the
+// number of digits? The number of non-zero digits? The smallest/largest digit? Of course, these
+// should all take `self` as a shared reference (i.e., in borrowed form).
// ## Mutation + aliasing considered harmful (part 2)
-// Now that we know how to borrow a part of an `enum` (like `v` above), there's another example for why we
-// have to rule out mutation in the presence of aliasing. First, we define an `enum` that can hold either
-// a number, or a string.
+//@ Now that we know how to create references to contents of an `enum` (like `v` above), there's
+//@ another example we can look at for why we have to rule out mutation in the presence of
+//@ aliasing. First, we define an `enum` that can hold either a number, or a string.
enum Variant {
Number(i32),
Text(String),
}
-// Now consider the following piece of code. Like above, `n` will be a borrow of a part of `var`,
-// and since we wrote `ref mut`, they will be mutable borrows. In other words, right after the match, `ptr`
-// points to the number that's stored in `var`, where `var` is a `Number`. Remember that `_` means
-// "we don't care".
+//@ Now consider the following piece of code. Like above, `n` will be a reference to a part of
+//@ `var`, and since we wrote `ref mut`, the reference will be unique and mutable. In other words,
+//@ right after the match, `ptr` points to the number that's stored in `var`, where `var` is a
+//@ `Number`. Remember that `_` means "we don't care".
fn work_on_variant(mut var: Variant, text: String) {
let mut ptr: &mut i32;
match var {
Variant::Number(ref mut n) => ptr = n,
Variant::Text(_) => return,
}
- /* var = Variant::Text(text); */
+ /* var = Variant::Text(text); */ /* BAD! */
*ptr = 1337;
}
-// Now, imagine what would happen if we were permitted to also mutate `var`. We could, for example,
-// make it a `Text`. However, `ptr` still points to the old location! Hence `ptr` now points somewhere
-// into the representation of a `String`. By changing `ptr`, we manipulate the string in completely
-// unpredictable ways, and anything could happen if we were to use it again! (Technically, the first field
-// of a `String` is a pointer to its character data, so by overwriting that pointer with an integer,
-// we make it a completely invalid address. When the destructor of `var` runs, it would try to deallocate
-// that address, and Rust would eat your laundry - or whatever.)
-//
-// I hope this example clarifies why Rust has to rule out mutation in the presence of aliasing *in general*,
-// not just for the specific case of a buffer being reallocated, and old pointers becoming hence invalid.
+//@ Now, imagine what would happen if we were permitted to also mutate `var`. We could, for
+//@ example, make it a `Text`. However, `ptr` still points to the old location! Hence `ptr` now
+//@ points somewhere into the representation of a `String`. By changing `ptr`, we manipulate the
+//@ string in completely unpredictable ways, and anything could happen if we were to use it again!
+//@ (Technically, the first field of a `String` is a pointer to its character data, so by
+//@ overwriting that pointer with an integer, we make it a completely invalid address. When the
+//@ destructor of `var` runs, it would try to deallocate that address, and Rust would eat your
+//@ laundry - or whatever.) I hope this example clarifies why Rust has to rule out mutation in the
+//@ presence of aliasing *in general*, not just for the specific case of a buffer being
+//@ reallocated, and old pointers becoming hence invalid.
-// [index](main.html) | [previous](part04.html) | [next](part06.html)
+//@ [index](main.html) | [previous](part04.html) | [raw source](workspace/src/part05.rs) |
+//@ [next](part06.html)
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