-use std::cmp;
-use std::ops;
-use std::fmt;
-use part05::BigInt;
+// Rust-101, Part 08: Associated Types, Modules
+// ============================================
-impl PartialEq for BigInt {
- fn eq(&self, other: &BigInt) -> bool {
- debug_assert!(self.test_invariant() && other.test_invariant());
- self.data == other.data
- }
-}
-
-fn call_eq() {
- let b1 = BigInt::new(13);
- let b2 = BigInt::new(37);
- println!("b1 == b1: {} ; b1 == b2: {}; b1 != b2: {}", b1 == b1, b1 == b2, b1 != b2);
-}
-
-
-impl fmt::Debug for BigInt {
- fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
- self.data.fmt(f)
- }
-}
-
-
-
-impl BigInt {
- pub fn inc(&mut self, mut by: u64) {
- panic!("Not yet implemented.");
- }
-}
-
-
-#[test]
-fn test_inc() {
- let mut b = BigInt::new(1337);
- b.inc(1337);
- assert!(b == BigInt::new(1337 + 1337));
-
- b = BigInt::new(0);
- assert_eq!(b, BigInt::from_vec(vec![0]));
- b.inc(1 << 63);
- assert_eq!(b, BigInt::from_vec(vec![1 << 63]));
- b.inc(1 << 63);
- assert_eq!(b, BigInt::from_vec(vec![0, 1]));
- b.inc(1 << 63);
- assert_eq!(b, BigInt::from_vec(vec![1 << 63, 1]));
- b.inc(1 << 63);
- assert_eq!(b, BigInt::from_vec(vec![0, 2]));
-}
+use std::{cmp,ops};
+use part05::BigInt;
+//@ As our next goal, let us implement addition for our `BigInt`. The main issue here will be dealing with the overflow.
+//@ First of all, we will have to detect when an overflow happens. This is stored in a so-called *carry* bit, and we have to carry this
+//@ information on to the next pair of digits we add. The core primitive of addition therefore is to add two digits *and* a
+//@ carry, and to return the sum digit and the next carry.
-// Add with carry, returning the sum and the carry
+// So, let us write a function to "add with carry", and give it the appropriate type. Notice Rust's native support for pairs.
fn overflowing_add(a: u64, b: u64, carry: bool) -> (u64, bool) {
- let sum = u64::wrapping_add(a, b);
+ //@ Rust's stanza on integer overflows may be a bit surprising: In general, when we write `a + b`, an overflow is
+ //@ considered an *error*. If you compile your program in debug mode, Rust will actually check for that error and panic
+ //@ the program in case of overflows. For performance reasons, no such checks are currently inserted for release builds.
+ //@ The reason for this is that many serious security vulnerabilities have been caused by integer overflows, so just assuming
+ //@ "per default" that they are intended is dangerous. <br/>
+ //@ If you explicitly *do* want an overflow to happen, you can call the `wrapping_add`
+ //@ function (see [the documentation](https://doc.rust-lang.org/stable/std/primitive.u64.html#method.wrapping_add),
+ //@ there are similar functions for other arithmetic operations). There are also similar functions
+ //@ `checked_add` etc. to enforce the overflow check.
+ let sum = a.wrapping_add(b);
+ // If an overflow happened, then the sum will be smaller than *both* summands. Without an overflow, of course, it will be
+ // at least as large as both of them. So, let's just pick one and check.
if sum >= a {
- panic!("First addition did not overflow. Not implemented.");
+ // The addition did not overflow. <br/>
+ // **Exercise 08.1**: Write the code to handle adding the carry in this case.
+ let sum_total = sum.wrapping_add(if carry { 1 } else { 0 });/*@@*/
+ let had_overflow = sum_total < sum; /*@@*/
+ (sum_total, had_overflow) /*@@*/
} else {
- panic!("First addition *did* overflow. Not implemented.");
+ // Otherwise, the addition *did* overflow. It is impossible for the addition of the carry
+ // to overflow again, as we are just adding 0 or 1.
+ (sum + if carry { 1 } else { 0 }, true) /*@*/
}
}
+// `overflow_add` is a sufficiently intricate function that a test case is justified.
+// This should also help you to check your solution of the exercise.
/*#[test]*/
fn test_overflowing_add() {
assert_eq!(overflowing_add(10, 100, false), (110, false));
assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
}
-impl ops::Add for BigInt {
+// ## Associated Types
+//@ Now we are equipped to write the addition function for `BigInt`. As you may have guessed, the `+` operator
+//@ is tied to a trait (`std::ops::Add`), which we are going to implement for `BigInt`.
+//@
+//@ In general, addition need not be homogeneous: You could add things of different types, like vectors and points. So when implementing
+//@ `Add` for a type, one has to specify the type of the other operand. In this case, it will also be `BigInt` (and we could have left it
+//@ away, since that's the default).
+impl ops::Add<BigInt> for BigInt {
+ //@ Besides static functions and methods, traits can contain *associated types*: This is a type chosen by every particular implementation
+ //@ of the trait. The methods of the trait can then refer to that type. In the case of addition, it is used to give the type of the result.
+ //@ (Also see the [documentation of `Add`](https://doc.rust-lang.org/stable/std/ops/trait.Add.html).)
+ //@
+ //@ In general, you can consider the two `BigInt` given above (in the `impl` line) *input* types of trait search: When
+ //@ `a + b` is invoked with `a` having type `T` and `b` having type `U`, Rust tries to find an implementation of `Add` for
+ //@ `T` where the right-hand type is `U`. The associated types, on the other hand, are *output* types: For every combination
+ //@ of input types, there's a particular result type chosen by the corresponding implementation of `Add`.
+
+ // Here, we choose the result type to be again `BigInt`.
type Output = BigInt;
+
+ // Now we can write the actual function performing the addition.
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.");
+ // We know that the result will be *at least* as long as the longer of the two operands,
+ // so we can create a vector with sufficient capacity to avoid expensive reallocations.
+ let max_len = cmp::max(self.data.len(), rhs.data.len());
+ let mut result_vec:Vec<u64> = Vec::with_capacity(max_len);
+ let mut carry = false; /* the current carry bit */
+ for i in 0..max_len {
+ let lhs_val = if i < self.data.len() { self.data[i] } else { 0 };
+ let rhs_val = if i < rhs.data.len() { rhs.data[i] } else { 0 };
+ // Compute next digit and carry. Then, store the digit for the result, and the carry for later.
+ //@ Notice how we can obtain names for the two components of the pair that `overflowing_add` returns.
+ let (sum, new_carry) = overflowing_add(lhs_val, rhs_val, carry); /*@*/
+ result_vec.push(sum); /*@*/
+ carry = new_carry; /*@*/
+ }
+ // **Exercise 08.2**: Handle the final `carry`, and return the sum.
+ if carry { /*@@*/
+ result_vec.push(1); /*@@*/
+ } /*@@*/
+ BigInt { data: result_vec } /*@@*/
}
}
+
+// ## Traits and reference types
+//@ If you inspect the addition function above closely, you will notice that it actually consumes ownership of both operands
+//@ to produce the result. This is, of course, in general not what we want. We'd rather like to be able to add two `&BigInt`.
+
+// Writing this out becomes a bit tedious, because trait implementations (unlike functions) require full explicit annotation
+// of lifetimes. Make sure you understand exactly what the following definition says. Notice that we can implement a trait for
+// a reference type!
+impl<'a, 'b> ops::Add<&'a BigInt> for &'b BigInt {
+ type Output = BigInt;
+ fn add(self, rhs: &'a BigInt) -> Self::Output {
+ // **Exercise 08.3**: Implement this function.
+ unimplemented!()
+ }
+}
+
+// **Exercise 08.4**: Implement the two missing combinations of arguments for `Add`. You should not have to duplicate the implementation.
+
+// ## Modules
+//@ As you learned, tests can be written right in the middle of your development in Rust. However, it is
+//@ considered good style to bundle all tests together. This is particularly useful in cases where
+//@ you wrote utility functions for the tests, that no other code should use.
+
+// Rust calls a bunch of definitions that are grouped together a *module*. You can put the tests in a submodule as follows.
+//@ The `cfg` attribute controls whether this module is even compiled: If we added some functions that are useful for testing,
+//@ Rust would not bother compiling them when you just build your program for normal use. Other than that, tests work as usually.
+#[cfg(test)]
+mod tests {
+ use part05::BigInt;
+
+ /*#[test]*/
+ fn test_add() {
+ let b1 = BigInt::new(1 << 32);
+ let b2 = BigInt::from_vec(vec![0, 1]);
+
+ assert_eq!(&b1 + &b2, BigInt::from_vec(vec![1 << 32, 1]));
+ // **Exercise 08.5**: Add some more cases to this test.
+ }
+}
+//@ As already mentioned, outside of the module, only those items declared public with `pub` may be used. Submodules can access
+//@ everything defined in their parents. Modules themselves are also hidden from the outside per default, and can be made public
+//@ with `pub`. When you use an identifier (or, more general, a *path* like `mod1::submod::name`), it is interpreted as being
+//@ relative to the current module. So, for example, to access `overflowing_add` from within `my_mod`, you would have to give a more
+//@ explicit path by writing `super::overflowing_add`, which tells Rust to look in the parent module.
+//@
+//@ You can make names from other modules available locally with `use`. Per default, `use` works globally, so e.g.
+//@ `use std;` imports the *global* name `std`. By adding `super::` or `self::` to the beginning of the path, you make it relative
+//@ to the parent or current module, respectively. (You can also explicitly construct an absolute path by starting it with `::`,
+//@ e.g., `::std::cmp::min`). You can say `pub use path;` to simultaneously *import* names and make them publicly available to others.
+//@ Finally, you can import all public items of a module at once with `use module::*;`.
+//@
+//@ Modules can be put into separate files with the syntax `mod name;`. To explain this, let me take a small detour through
+//@ the Rust compilation process. Cargo starts by invoking`rustc` on the file `src/lib.rs` or `src/main.rs`, depending on whether
+//@ you compile an application or a library. When `rustc` encounters a `mod name;`, it looks for the files `name.rs` and
+//@ `name/mod.rs` and goes on compiling there. (It is an error for both of them to exist.) You can think of the contents of the
+//@ file being embedded at this place. However, only the file where compilation started, and files `name/mod.rs` can load modules
+//@ from other files. This ensures that the directory structure mirrors the structure of the modules, with `mod.rs`, `lib.rs`
+//@ and `main.rs` representing a directory or crate itself (similar to, e.g., `__init__.py` in Python).
+
+// **Exercise 08.6**: Write a subtraction function, and testcases for it. Decide for yourself how you want to handle negative results.
+// For example, you may want to return an `Option`, to panic, or to return `0`.
+
+//@ [index](main.html) | [previous](part07.html) | [raw source](workspace/src/part08.rs) | [next](part09.html)
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