Update nitrokey crate to 0.4.0

This change finally updates the version of the nitrokey crate that we
consume to 0.4.0. Along with that we update rand_core, one of its
dependencies, to 0.5.1. Further more we add cfg-if in version 0.1.10 and
getrandom in version 0.1.13, both of which are now new (non-development)
dependencies.

Import subrepo nitrokey/:nitrokey at e81057037e9b4f370b64c0a030a725bc6bdfb870
Import subrepo cfg-if/:cfg-if at 4484a6faf816ff8058088ad857b0c6bb2f4b02b2
Import subrepo getrandom/:getrandom at d661aa7e1b8cc80b47dabe3d2135b3b47d2858af
Import subrepo rand/:rand at d877ed528248b52d947e0484364a4e1ae59ca502

1 files changed, 120 insertions, 0 deletions

diff --git a/rand/rand_distr/src/cauchy.rs b/rand/rand_distr/src/cauchy.rs
new file mode 100644
index 0000000..6b0e7c6
--- /dev/null
+++ b/rand/rand_distr/src/cauchy.rs
@@ -0,0 +1,120 @@
+// 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.
+
+use rand::Rng;
+use crate::{Distribution, Standard};
+use crate::utils::Float;
+
+/// The Cauchy distribution `Cauchy(median, scale)`.
+///
+/// This distribution has a density function:
+/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
+///
+/// # Example
+///
+/// ```
+/// use rand_distr::{Cauchy, Distribution};
+///
+/// let cau = Cauchy::new(2.0, 5.0).unwrap();
+/// let v = cau.sample(&mut rand::thread_rng());
+/// println!("{} is from a Cauchy(2, 5) distribution", v);
+/// ```
+#[derive(Clone, Copy, Debug)]
+pub struct Cauchy<N> {
+    median: N,
+    scale: N,
+}
+
+/// Error type returned from `Cauchy::new`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Error {
+    /// `scale <= 0` or `nan`.
+    ScaleTooSmall,
+}
+
+impl<N: Float> Cauchy<N>
+where Standard: Distribution<N>
+{
+    /// Construct a new `Cauchy` with the given shape parameters
+    /// `median` the peak location and `scale` the scale factor.
+    pub fn new(median: N, scale: N) -> Result<Cauchy<N>, Error> {
+        if !(scale > N::from(0.0)) {
+            return Err(Error::ScaleTooSmall);
+        }
+        Ok(Cauchy {
+            median,
+            scale
+        })
+    }
+}
+
+impl<N: Float> Distribution<N> for Cauchy<N>
+where Standard: Distribution<N>
+{
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
+        // sample from [0, 1)
+        let x = Standard.sample(rng);
+        // 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 = (N::pi() * x).tan();
+        // shift and scale according to parameters
+        self.median + self.scale * comp_dev
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use crate::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]
+    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).unwrap();
+        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).unwrap();
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_cauchy_invalid_scale_neg() {
+        Cauchy::new(0.0, -10.0).unwrap();
+    }
+}