// Rust-101, Part 08: Associated Types, Modules
// ============================================
-use std::cmp;
-use std::ops;
-use std::fmt;
+use std::{cmp,ops};
use part05::BigInt;
-// Add with carry, returning the sum and the carry
+//@ 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.
+
+// 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);
- if sum >= a { // first addition did not overflow
- unimplemented!()
- } else { // first addition *did* overflow
- unimplemented!()
+ //@ 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 {
+ // 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 {
+ // 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()));
+ // 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!()
}
}
-// [index](main.html) | [previous](part07.html) | [next](main.html)
+// **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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