use std::fmt;
use std::ops;

#[derive(Clone, Copy)]
pub struct Gaussian {
    pi: f64,
    tau: f64,
}

impl fmt::Debug for Gaussian {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "N(mu={:.03}, sigma={:.03}, pi={:.03}, tau={:.03})", self.mu(), self.sigma(), self.pi(), self.tau())
    }
}

impl Gaussian {
    pub fn from_pi_tau(pi: f64, tau: f64) -> Gaussian {
        Gaussian { pi, tau }
    }

    pub fn from_mu_sigma(mu: f64, sigma: f64) -> Gaussian {
        let pi = 1.0 / (sigma * sigma);

        Self::from_pi_tau(pi, pi * mu)
    }

    pub fn pi(&self) -> f64 {
        self.pi
    }

    pub fn tau(&self) -> f64 {
        self.tau
    }

    pub fn mu(&self) -> f64 {
        if self.pi == 0.0 {
            return 0.0;
        } else {
            self.tau / self.pi
        }
    }

    pub fn sigma(&self) -> f64 {
        (1.0 / self.pi).sqrt()
    }
}

impl ops::Mul<Gaussian> for Gaussian {
    type Output = Gaussian;

    fn mul(self, rhs: Gaussian) -> Gaussian {
        Gaussian::from_pi_tau(self.pi + rhs.pi, self.tau + rhs.tau)
    }
}

impl ops::Div<Gaussian> for Gaussian {
    type Output = Gaussian;

    fn div(self, rhs: Gaussian) -> Gaussian {
        Gaussian::from_pi_tau(self.pi - rhs.pi, self.tau - rhs.tau)
    }
}