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    // Copyright 2018 Developers of the Rand project.
    //
    // 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 Bernoulli distribution.

    use crate::Rng;
    use crate::distributions::Distribution;

    /// The Bernoulli distribution.
    ///
    /// This is a special case of the Binomial distribution where `n = 1`.
    ///
    /// # Example
    ///
    /// ```rust
    /// use rand::distributions::{Bernoulli, Distribution};
    ///
    /// let d = Bernoulli::new(0.3).unwrap();
    /// let v = d.sample(&mut rand::thread_rng());
    /// println!("{} is from a Bernoulli distribution", v);
    /// ```
    ///
    /// # Precision
    ///
    /// This `Bernoulli` distribution uses 64 bits from the RNG (a `u64`),
    /// so only probabilities that are multiples of 2<sup>-64</sup> can be
    /// represented.
    #[derive(Clone, Copy, Debug)]
    pub struct Bernoulli {
        /// Probability of success, relative to the maximal integer.
        p_int: u64,
    }

    // To sample from the Bernoulli distribution we use a method that compares a
    // random `u64` value `v < (p * 2^64)`.
    //
    // If `p == 1.0`, the integer `v` to compare against can not represented as a
    // `u64`. We manually set it to `u64::MAX` instead (2^64 - 1 instead of 2^64).
    // Note that  value of `p < 1.0` can never result in `u64::MAX`, because an
    // `f64` only has 53 bits of precision, and the next largest value of `p` will
    // result in `2^64 - 2048`.
    //
    // Also there is a 100% theoretical concern: if someone consistenly wants to
    // generate `true` using the Bernoulli distribution (i.e. by using a probability
    // of `1.0`), just using `u64::MAX` is not enough. On average it would return
    // false once every 2^64 iterations. Some people apparently care about this
    // case.
    //
    // That is why we special-case `u64::MAX` to always return `true`, without using
    // the RNG, and pay the performance price for all uses that *are* reasonable.
    // Luckily, if `new()` and `sample` are close, the compiler can optimize out the
    // extra check.
    const ALWAYS_TRUE: u64 = ::core::u64::MAX;

    // This is just `2.0.powi(64)`, but written this way because it is not available
    // in `no_std` mode.
    const SCALE: f64 = 2.0 * (1u64 << 63) as f64;

    /// Error type returned from `Bernoulli::new`.
    #[derive(Clone, Copy, Debug, PartialEq, Eq)]
    pub enum BernoulliError {
        /// `p < 0` or `p > 1`.
        InvalidProbability,
    }

    impl Bernoulli {
        /// Construct a new `Bernoulli` with the given probability of success `p`.
        ///
        /// # Precision
        ///
        /// For `p = 1.0`, the resulting distribution will always generate true.
        /// For `p = 0.0`, the resulting distribution will always generate false.
        ///
        /// This method is accurate for any input `p` in the range `[0, 1]` which is
        /// a multiple of 2<sup>-64</sup>. (Note that not all multiples of
        /// 2<sup>-64</sup> in `[0, 1]` can be represented as a `f64`.)
        #[inline]
        pub fn new(p: f64) -> Result<Bernoulli, BernoulliError> {
            if p < 0.0 || p >= 1.0 {
                if p == 1.0 { return Ok(Bernoulli { p_int: ALWAYS_TRUE }) }
                return Err(BernoulliError::InvalidProbability);
            }
            Ok(Bernoulli { p_int: (p * SCALE) as u64 })
        }

        /// Construct a new `Bernoulli` with the probability of success of
        /// `numerator`-in-`denominator`. I.e. `new_ratio(2, 3)` will return
        /// a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.
        ///
        /// If `numerator == denominator` then the returned `Bernoulli` will always
        /// return `true`. If `numerator == 0` it will always return `false`.
        #[inline]
        pub fn from_ratio(numerator: u32, denominator: u32) -> Result<Bernoulli, BernoulliError> {
            if !(numerator <= denominator) {
                return Err(BernoulliError::InvalidProbability);
            }
            if numerator == denominator {
                return Ok(Bernoulli { p_int: ALWAYS_TRUE })
            }
            let p_int = ((numerator as f64 / denominator as f64) * SCALE) as u64;
            Ok(Bernoulli { p_int })
        }
    }

    impl Distribution<bool> for Bernoulli {
        #[inline]
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> bool {
            // Make sure to always return true for p = 1.0.
            if self.p_int == ALWAYS_TRUE { return true; }
            let v: u64 = rng.gen();
            v < self.p_int
        }
    }

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

        #[test]
        fn test_trivial() {
            let mut r = crate::test::rng(1);
            let always_false = Bernoulli::new(0.0).unwrap();
            let always_true = Bernoulli::new(1.0).unwrap();
            for _ in 0..5 {
                assert_eq!(r.sample::<bool, _>(&always_false), false);
                assert_eq!(r.sample::<bool, _>(&always_true), true);
                assert_eq!(Distribution::<bool>::sample(&always_false, &mut r), false);
                assert_eq!(Distribution::<bool>::sample(&always_true, &mut r), true);
            }
        }

        #[test]
        #[cfg(not(miri))] // Miri is too slow
        fn test_average() {
            const P: f64 = 0.3;
            const NUM: u32 = 3;
            const DENOM: u32 = 10;
            let d1 = Bernoulli::new(P).unwrap();
            let d2 = Bernoulli::from_ratio(NUM, DENOM).unwrap();
            const N: u32 = 100_000;

            let mut sum1: u32 = 0;
            let mut sum2: u32 = 0;
            let mut rng = crate::test::rng(2);
            for _ in 0..N {
                if d1.sample(&mut rng) {
                    sum1 += 1;
                }
                if d2.sample(&mut rng) {
                    sum2 += 1;
                }
            }
            let avg1 = (sum1 as f64) / (N as f64);
            assert!((avg1 - P).abs() < 5e-3);

            let avg2 = (sum2 as f64) / (N as f64);
            assert!((avg2 - (NUM as f64)/(DENOM as f64)).abs() < 5e-3);
        }
    }

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