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    // Copyright 2018 Developers of the Rand project.
    // Copyright 2016-2017 The Rust Project Developers.
    //
    // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
    // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
    // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
    // option. This file may not be copied, modified, or distributed
    // except according to those terms.

    //! The Cauchy distribution.
    #![allow(deprecated)]

    use crate::Rng;
    use crate::distributions::Distribution;
    use std::f64::consts::PI;

    /// The Cauchy distribution `Cauchy(median, scale)`.
    ///
    /// This distribution has a density function:
    /// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
    #[deprecated(since="0.7.0", note="moved to rand_distr crate")]
    #[derive(Clone, Copy, Debug)]
    pub struct Cauchy {
        median: f64,
        scale: f64
    }

    impl Cauchy {
        /// Construct a new `Cauchy` with the given shape parameters
        /// `median` the peak location and `scale` the scale factor.
        /// Panics if `scale <= 0`.
        pub fn new(median: f64, scale: f64) -> Cauchy {
            assert!(scale > 0.0, "Cauchy::new called with scale factor <= 0");
            Cauchy {
                median,
                scale
            }
        }
    }

    impl Distribution<f64> for Cauchy {
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64 {
            // sample from [0, 1)
            let x = rng.gen::<f64>();
            // get standard cauchy random number
            // note that π/2 is not exactly representable, even if x=0.5 the result is finite
            let comp_dev = (PI * x).tan();
            // shift and scale according to parameters
            let result = self.median + self.scale * comp_dev;
            result
        }
    }

    #[cfg(test)]
    mod test {
        use crate::distributions::Distribution;
        use super::Cauchy;

        fn median(mut numbers: &mut [f64]) -> f64 {
            sort(&mut numbers);
            let mid = numbers.len() / 2;
            numbers[mid]
        }

        fn sort(numbers: &mut [f64]) {
            numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
        }

        #[test]
        #[cfg(not(miri))] // Miri doesn't support transcendental functions
        fn test_cauchy_averages() {
            // NOTE: given that the variance and mean are undefined,
            // this test does not have any rigorous statistical meaning.
            let cauchy = Cauchy::new(10.0, 5.0);
            let mut rng = crate::test::rng(123);
            let mut numbers: [f64; 1000] = [0.0; 1000];
            let mut sum = 0.0;
            for i in 0..1000 {
                numbers[i] = cauchy.sample(&mut rng);
                sum += numbers[i];
            }
            let median = median(&mut numbers);
            println!("Cauchy median: {}", median);
            assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
            let mean = sum / 1000.0;
            println!("Cauchy mean: {}", mean);
            // for a Cauchy distribution the mean should not converge
            assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
        }

        #[test]
        #[should_panic]
        fn test_cauchy_invalid_scale_zero() {
            Cauchy::new(0.0, 0.0);
        }

        #[test]
        #[should_panic]
        fn test_cauchy_invalid_scale_neg() {
            Cauchy::new(0.0, -10.0);
        }
    }

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