//@ 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`
//@ 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`
//@ there are similar functions for other arithmetic operations). There are also similar functions
//@ `checked_add` etc. to enforce the overflow check.
//@ there are similar functions for other arithmetic operations). There are also similar functions
//@ `checked_add` etc. to enforce the overflow check.
// 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.
// 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.
} 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.
} 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.
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.
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.
//@
//@ 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
//@
//@ 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
fn test_add() {
let b1 = BigInt::new(1 << 32);
let b2 = BigInt::from_vec(vec![0, 1]);
fn test_add() {
let b1 = BigInt::new(1 << 32);
let b2 = BigInt::from_vec(vec![0, 1]);
// **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`.
// **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`.