// 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) {
// 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) {
// 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.
// 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
// 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
impl<'a, 'b> ops::Add<&'a BigInt> for &'b BigInt {
type Output = BigInt;
fn add(self, rhs: &'a BigInt) -> Self::Output {
impl<'a, 'b> ops::Add<&'a BigInt> for &'b BigInt {
type Output = BigInt;
fn add(self, rhs: &'a BigInt) -> Self::Output {
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]);