hmath 0.1.17

Big Integers and Rational Numbers
Documentation 
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use crate::{Ratio, BigInt, gcd_bi};

mod exp;
mod ln;
mod pow;
mod root;
mod trigo;

pub use exp::exp_iter;
pub use ln::{ln_iter, log_iter};
pub use pow::pow_iter;
pub use root::{sqrt_iter, cbrt_iter};
pub use trigo::{sin_iter, cos_iter, tan_iter};

/// a = v1 / v3, b = v2 / v3 where the return value is `(v1, v2, v3)`
#[must_use = "method returns a new number and does not mutate the original value"]
pub fn common_denom(a: &Ratio, b: &Ratio) -> (BigInt, BigInt, BigInt) {
    // v1 = a.numer * b.denom / gcd(a.denom, b.denom)
    // v2 = b.numer * a.denom / gcd(a.denom, b.denom)
    // v3 = a.denom * b.denom / gcd(a.denom, b.denom)

    let gcd = gcd_bi(&a.denom, &b.denom);
    let a_den_gcd = a.denom.div_bi(&gcd);
    let b_den_gcd = b.denom.div_bi(&gcd);

    (
        a.numer.mul_bi(&b_den_gcd),
        b.numer.mul_bi(&a_den_gcd),
        a.denom.mul_bi(&b_den_gcd),
    )
}

impl Ratio {

    #[must_use = "method returns a new number and does not mutate the original value"]
    pub fn neg(&self) -> Self {
        // Safety: if a and b are coprime, a and -b are also coprime. property 2 and 3 are satisfied because it doesn't change the sign of denom
        Ratio::from_denom_and_numer_raw(self.denom.clone(), self.numer.neg())
    }

    pub fn neg_mut(&mut self) {
        self.numer.neg_mut();
    }

    #[must_use = "method returns a new number and does not mutate the original value"]
    pub fn abs(&self) -> Self {
        // Safety: if a and b are coprime, a and -b are also coprime. property 2 and 3 are satisfied because it doesn't change the sign of denom
        Ratio::from_denom_and_numer_raw(self.denom.clone(), self.numer.abs())
    }

    pub fn abs_mut(&mut self) {
        self.numer.abs_mut();
    }

    /// 1 / self
    #[must_use = "method returns a new number and does not mutate the original value"]
    pub fn reci(&self) -> Self {
        // Safety: `self.denom` and `self.numer` is already coprime
        let mut result = Ratio::from_denom_and_numer_raw(
            self.numer.clone(),
            self.denom.clone()
        );

        if result.denom.is_zero() {
            panic!("Attempt to divide by zero: 1 / {self:?}");
        }

        if result.denom.is_neg() {
            result.denom.neg_mut();
            result.numer.neg_mut();
        }

        #[cfg(test)] assert!(result.is_valid());

        result
    }

    /// self = 1 / self
    pub fn reci_mut(&mut self) {
        *self = self.reci();
    }

    #[must_use = "method returns a new number and does not mutate the original value"]
    pub fn truncate(&self) -> Self {
        Ratio::from_bi(self.truncate_bi())
    }

    pub fn truncate_mut(&mut self) {
        self.numer.div_bi_mut(&self.denom);
        self.denom = BigInt::one();

        #[cfg(test)] assert!(self.is_valid());
    }

    #[must_use = "method returns a new number and does not mutate the original value"]
    pub fn truncate_bi(&self) -> BigInt {
        let result = self.numer.div_bi(&self.denom);

        #[cfg(test)] assert!(result.is_valid());

        result
    }

    #[must_use = "method returns a new number and does not mutate the original value"]
    /// self - truncate(self)
    pub fn frac(&self) -> Self {
        // Safety: (a % b) and b are coprime
        let result = Ratio::from_denom_and_numer_raw(self.denom.clone(), self.numer.rem_bi(&self.denom));

        #[cfg(test)] {
            assert!(result.is_valid());
            assert_eq!(&result.add_rat(&self.truncate()), self);

            let mut self_clone = self.clone();
            self_clone.frac_mut();

            assert_eq!(self_clone, result);
        }

        result
    }

    /// self -= truncate(self)
    pub fn frac_mut(&mut self) {
        self.numer.rem_bi_mut(&self.denom);
    }

    /// If you need both `self.truncate_bi` and `self.frac`, use this method. It's way cheaper.
    pub fn truncate_and_frac(&self) -> (BigInt, Self) {
        let trun = self.truncate_bi();

        // Safety: (a % b) and b are coprime
        let frac = Ratio::from_denom_and_numer_raw(self.denom.clone(), self.numer.sub_bi(&self.denom.mul_bi(&trun)));

        #[cfg(test)] assert_eq!(frac, self.frac());

        (trun, frac)
    }

    /// It returns the largest integer less than or equal to `self`.
    pub fn floor(&self) -> Ratio {
        Ratio::from_bi(self.floor_bi())
    }

    /// It returns the largest integer less than or equal to `self`.
    pub fn floor_bi(&self) -> BigInt {

        if self.is_neg() {

            if self.is_integer() {
                self.numer.clone()
            }

            else {
                self.truncate_bi().sub_i32(1)
            }

        }

        else {
            self.truncate_bi()
        }

    }

    /// If this method and [this method] behave differently, that's an error.
    ///
    /// [this method]: https://doc.rust-lang.org/stable/std/primitive.f64.html#method.round
    pub fn round(&self) -> Self {
        Ratio::from_bi(self.round_bi())
    }

    pub fn round_bi(&self) -> BigInt {
        let (trun, frac) = self.truncate_and_frac();

        let numer_double_abs = frac.numer.mul_i32(2).abs();
        use std::cmp::Ordering;

        match numer_double_abs.comp_bi(&frac.denom) {
            // less than 0.5
            Ordering::Less => trun,

            // half way between the two -> round away from 0.0
            // greater than 0.5 -> round away from 0.0
            _ => if self.is_neg() {
                trun.sub_i32(1)
            } else {
                trun.add_i32(1)
            }
        }

    }

    /// It returns a number between 0 and 1 (both exclusive).
    #[cfg(feature = "rand")]
    pub fn random() -> Self {
        let mut result = Ratio::from_raw(
            vec![0, 0, 0, 0, 1],
            false,
            (0..4).map(|_| rand::random::<u32>().max(1)).collect(),
            false
        );
        result.fit();

        #[cfg(test)] {
            assert!(result.is_valid());
            assert!(result.lt_one());
            assert!(!result.is_zero());
        }

        result
    }
}

#[cfg(test)]
mod tests {
    use crate::{Ratio, common_denom};

    #[test]
    fn round_test() {
        let mut curr = -8.0f64;

        while curr < 8.0 {
            let rounded = curr.round();
            let rounded_rat = Ratio::try_from(curr).unwrap().round();
            assert_eq!(<f64 as TryInto<Ratio>>::try_into(rounded).unwrap(), rounded_rat);
            curr += 0.125;
        }

    }

    #[test]
    fn frac_trunc_floor_test() {
        let samples = vec![
            ("3.7", "3.0", "3.0"),
            ("-3.7", "-3.0", "-4.0"),
            ("4.0", "4.0", "4.0"),
            ("-4.0", "-4.0", "-4.0"),
            ("0.0", "0.0", "0.0"),
            ("-0.0", "-0.0", "-0.0"),
        ];

        for (before, trun, floor) in samples.into_iter() {
            assert_eq!(
                Ratio::from_string(before).unwrap().truncate(),
                Ratio::from_string(trun).unwrap()
            );
            assert_eq!(
                Ratio::from_string(before).unwrap().floor(),
                Ratio::from_string(floor).unwrap()
            );

            // test code is inside the `.frac()` method
            let _ = Ratio::from_string(before).unwrap().frac();
            let _ = Ratio::from_string(trun).unwrap().frac();
        }

    }

    #[test]
    fn common_denom_test() {

        for denom1 in 1..11 {
            for denom1 in [denom1, -denom1] {
                for numer1 in -10..11 {
                    for denom2 in 1..11 {
                        for denom2 in [denom2, -denom2] {
                            for numer2 in -10..11 {
                                let n1 = Ratio::from_denom_and_numer_i32(denom1, numer1);
                                let n2 = Ratio::from_denom_and_numer_i32(denom2, numer2);

                                let (numer_res1, numer_res2, denom_res) = common_denom(&n1, &n2);

                                let n1_res = Ratio::from_denom_and_numer(denom_res.clone(), numer_res1);
                                let n2_res = Ratio::from_denom_and_numer(denom_res, numer_res2);

                                assert_eq!(n1, n1_res);
                                assert_eq!(n2, n2_res);
                            }
                        }
                    }
                }
            }
        }
    }

}