Compute X * Y without arithmetical operators

sample.rs

fn main() {
    println!("123 * 345 = {}", multiply(123, 345));
}

fn multiply(mut a: u32, mut b: u32) -> u32 {
    let mut sum = 0;
    while a != 0 {
        if a & 1 == 1 {
            sum = add(sum, b);
        }
        a >>= 1;
        b <<= 1;
    }
    sum
}

// fn add(x: u32, y: u32) -> u32 {
//     if x == 0 || y == 0 {
//         return x | y;
//     }

//     let sum = x ^ y;
//     let carry = (x & y) << 1;
//     add(sum, carry)
// }

fn add(mut sum: u32, mut carry: u32) -> u32 {
    while carry != 0 {
        let next_carry = (sum & carry) << 1;
        sum ^= carry;
        carry = next_carry;
    }
    sum
}

#[test]
fn test_add_without_overflow() {
    assert_eq!(add(0, 41), 41);
    assert_eq!(add(43, 0), 43);
    assert_eq!(add(131, 37), 131 + 37);
}

#[test]
fn test_multiply_without_overflow() {
    assert_eq!(multiply(0, 41), 0);
    assert_eq!(multiply(43, 0), 0);
    assert_eq!(multiply(131, 37), 131 * 37);
}