Add exercise 10.2 (#24)

[rust-101.git] / src / part08.rs

// Rust-101, Part 08: Associated Types, Modules
// ============================================

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.

// 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) {
    //@ 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(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));
}

// ## 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 {
        // 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`.

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