Add exercise 10.2 (#24)

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

diff --git a/src/part08.rs b/src/part08.rs
index 90c35f65a526d0b5f702a84ccf7e43f2fe017ff2..17beefa0625b30230fe7720af35139ce720ee045 100644 (file)
--- a/src/part08.rs
+++ b/src/part08.rs
@@ -1,21 +1,49 @@
-// Rust-101, Part 08: Associated Types, Modules (WIP)
-// ==================================================
+// Rust-101, Part 08: Associated Types, Modules
+// ============================================

 
 

-use std::cmp;
-use std::ops;
-use std::fmt;
+use std::{cmp,ops};

 use part05::BigInt;
 
 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) {
 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));
 /*#[test]*/
 fn test_overflowing_add() {
     assert_eq!(overflowing_add(10, 100, false), (110, false));


@@ -25,12 +53,130 @@ fn test_overflowing_add() {
     assert_eq!(overflowing_add(1 << 63, (1 << 63) -1 , true), (0, true));
 }
 
     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;
     type Output = BigInt;

+
+    // Now we can write the actual function performing the addition.

     fn add(self, rhs: BigInt) -> Self::Output {
     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!()
     }
 }
 
         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)