rusty-numbers/src/lib.rs

//! # Rusty Numbers
//!
//! Playin' with Numerics in Rust
#![forbid(unsafe_code)]

#[cfg_attr(tarpaulin, skip)]
pub mod bigint;
pub mod num;
pub mod rational;

/// Calculate a number in the fibonacci sequence,
/// using a lookup table for better worst-case performance.
///
/// Can calculate up to 186 using native unsigned 128 bit integers.
///
/// Example:
/// ```rust
/// use rusty_numbers::fibonacci;
///
/// let valid = fibonacci(45); // Some(1134903170)
/// # assert_eq!(1134903170, fibonacci(45).unwrap());
/// # assert!(valid.is_some());
///
/// let invalid = fibonacci(187); // None
/// # assert!(invalid.is_none());
/// ```
#[inline]
pub fn mem_fibonacci(n: usize) -> Option<u128> {
    let mut table = [0u128; 187];
    table[0] = 0;
    table[1] = 1;
    table[2] = 1;

    _mem_fibonacci(n, &mut table)
}

/// Actual calculating function for `fibonacci`
#[inline]
fn _mem_fibonacci(n: usize, table: &mut [u128]) -> Option<u128> {
    if n > 186 {
        return None;
    }

    match table[n] {
        // The lookup array starts out zeroed, so a zero
        // is a not yet calculated value
        0 => {
            let a = _mem_fibonacci(n - 1, table)?;
            let b = _mem_fibonacci(n - 2, table)?;

            table[n] = a + b;

            Some(table[n])
        },
        x => Some(x)
    }
}

/// Calculate a number in the fibonacci sequence,
/// using naive recursion
///
/// REALLY SLOW
///
/// Can calculate up to 186 using native unsigned 128 bit integers.
#[inline]
pub fn rec_fibonacci(n: usize) -> Option<u128> {
    match n {
        0 => Some(0),
        1 => Some(1),
        n => {
            let a = rec_fibonacci(n - 1)?;
            let b = rec_fibonacci(n - 2)?;

            a.checked_add(b)
        }
    }
}

/// Calculate a number in the fibonacci sequence,
/// using iteration
///
/// Can calculate up to 186
#[inline]
pub fn fibonacci(n: usize) -> Option<u128> {
    let mut a: u128 = 0;
    let mut b: u128 = 1;

    match n {
        0 => Some(a),
        1 => Some(b),
        _ => {
            for _ in 0..n - 1 {
                let c: u128 = a.checked_add(b)?;

                a = b;
                b = c;
            }

            Some(b)
        }
    }
}

/// Calculate the value of a factorial,
/// using a lookup table for better worst-case performance.
///
/// Can calculate up to 34! using native unsigned 128 bit integers.
///
/// Example:
/// ```rust
/// use rusty_numbers::factorial;
///
/// let valid = factorial(3); // Some(6)
/// # assert_eq!(6, valid.unwrap());
///
/// let invalid = factorial(35); // None
/// # assert!(invalid.is_none());
/// ```
#[inline]
pub fn mem_factorial(n: usize) -> Option<u128> {
    let mut table = [0u128; 35];
    table[0] = 1;
    table[1] = 1;
    table[2] = 2;


    _mem_factorial(n, &mut table)
}

/// Actual Calculation function for factoral
#[inline]
fn _mem_factorial(n: usize, table: &mut [u128]) -> Option<u128> {
    if n > 34 {
        return None
    }

    match table[n] {
        // Empty spaces in the lookup array are zero-filled
        0 => {
            // The ? suffix passes along the Option value
            // to be handled later
            // See: https://doc.rust-lang.org/reference/expressions/operator-expr.html#the-question-mark-operator
            let prev = _mem_factorial(n - 1, table)?;

            table[n] = (n as u128) * prev;

            Some(table[n])
        },
        x => Some(x),
    }
}

/// Calculate the value of a factorial,
///
/// Can calculate up to 34! using native unsigned 128 bit integers.
///
/// Example:
/// ```rust
/// use rusty_numbers::factorial;
///
/// let valid = factorial(3); // Some(6)
/// # assert_eq!(6, valid.unwrap());
///
/// let invalid = factorial(35); // None
/// # assert!(invalid.is_none());
/// ```
#[inline]
pub fn factorial(n: usize) -> Option<u128> {
    match n {
        0 => Some(1u128),
        1 => Some(1u128),
        _ => {
            let prev = factorial(n - 1)?;

            (n as u128).checked_mul(prev)
        }
    }
}

#[cfg(test)]
#[cfg_attr(tarpaulin, skip)]
mod tests {
    use super::*;

    #[test]
    fn test_factorial() {
        assert_eq!(1, factorial(0).unwrap());
        assert_eq!(1, factorial(1).unwrap());
        assert_eq!(6, factorial(3).unwrap());

        let res = factorial(34);
        let res2 = mem_factorial(34);
        assert!(res.is_some());
        assert_eq!(res.unwrap(), res2.unwrap());

        let res = factorial(35);
        assert!(res.is_none());
    }

    #[test]
    fn test_fibonacci() {
        assert_eq!(0, fibonacci(0).unwrap());
        assert_eq!(1, fibonacci(1).unwrap());
        assert_eq!(1, fibonacci(2).unwrap());

        let res = fibonacci(20);
        let res2 = rec_fibonacci(20);
        assert_eq!(res, res2);

        let res = fibonacci(186);
        let res2 = mem_fibonacci(186);
        assert!(res.is_some());
        assert!(res2.is_some());
        assert_eq!(res.unwrap(), res2.unwrap());

        let res = fibonacci(187);
        assert!(res.is_none());
    }
}