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+

// Copyright 2018 Developers of the Rand project.
+// Copyright 2013-2017 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.
+
+//! [`Rng`] trait
+
+use rand_core::{Error, RngCore};
+use crate::distributions::uniform::{SampleRange, SampleUniform};
+use crate::distributions::{self, Distribution, Standard};
+use core::num::Wrapping;
+use core::{mem, slice};
+
+/// An automatically-implemented extension trait on [`RngCore`] providing high-level
+/// generic methods for sampling values and other convenience methods.
+///
+/// This is the primary trait to use when generating random values.
+///
+/// # Generic usage
+///
+/// The basic pattern is `fn foo<R: Rng + ?Sized>(rng: &mut R)`. Some
+/// things are worth noting here:
+///
+/// - Since `Rng: RngCore` and every `RngCore` implements `Rng`, it makes no
+///   difference whether we use `R: Rng` or `R: RngCore`.
+/// - The `+ ?Sized` un-bounding allows functions to be called directly on
+///   type-erased references; i.e. `foo(r)` where `r: &mut dyn RngCore`. Without
+///   this it would be necessary to write `foo(&mut r)`.
+///
+/// An alternative pattern is possible: `fn foo<R: Rng>(rng: R)`. This has some
+/// trade-offs. It allows the argument to be consumed directly without a `&mut`
+/// (which is how `from_rng(thread_rng())` works); also it still works directly
+/// on references (including type-erased references). Unfortunately within the
+/// function `foo` it is not known whether `rng` is a reference type or not,
+/// hence many uses of `rng` require an extra reference, either explicitly
+/// (`distr.sample(&mut rng)`) or implicitly (`rng.gen()`); one may hope the
+/// optimiser can remove redundant references later.
+///
+/// Example:
+///
+/// ```
+/// # use rand::thread_rng;
+/// use rand::Rng;
+///
+/// fn foo<R: Rng + ?Sized>(rng: &mut R) -> f32 {
+///     rng.gen()
+/// }
+///
+/// # let v = foo(&mut thread_rng());
+/// ```
+pub trait Rng: RngCore {
+    /// Return a random value supporting the [`Standard`] distribution.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// let mut rng = thread_rng();
+    /// let x: u32 = rng.gen();
+    /// println!("{}", x);
+    /// println!("{:?}", rng.gen::<(f64, bool)>());
+    /// ```
+    ///
+    /// # Arrays and tuples
+    ///
+    /// The `rng.gen()` method is able to generate arrays (up to 32 elements)
+    /// and tuples (up to 12 elements), so long as all element types can be
+    /// generated.
+    /// When using `rustc` ≥ 1.51, enable the `min_const_gen` feature to support
+    /// arrays larger than 32 elements.
+    ///
+    /// For arrays of integers, especially for those with small element types
+    /// (< 64 bit), it will likely be faster to instead use [`Rng::fill`].
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// let mut rng = thread_rng();
+    /// let tuple: (u8, i32, char) = rng.gen(); // arbitrary tuple support
+    ///
+    /// let arr1: [f32; 32] = rng.gen();        // array construction
+    /// let mut arr2 = [0u8; 128];
+    /// rng.fill(&mut arr2);                    // array fill
+    /// ```
+    ///
+    /// [`Standard`]: distributions::Standard
+    #[inline]
+    fn gen<T>(&mut self) -> T
+    where Standard: Distribution<T> {
+        Standard.sample(self)
+    }
+
+    /// Generate a random value in the given range.
+    ///
+    /// This function is optimised for the case that only a single sample is
+    /// made from the given range. See also the [`Uniform`] distribution
+    /// type which may be faster if sampling from the same range repeatedly.
+    ///
+    /// Only `gen_range(low..high)` and `gen_range(low..=high)` are supported.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the range is empty.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// let mut rng = thread_rng();
+    ///
+    /// // Exclusive range
+    /// let n: u32 = rng.gen_range(0..10);
+    /// println!("{}", n);
+    /// let m: f64 = rng.gen_range(-40.0..1.3e5);
+    /// println!("{}", m);
+    ///
+    /// // Inclusive range
+    /// let n: u32 = rng.gen_range(0..=10);
+    /// println!("{}", n);
+    /// ```
+    ///
+    /// [`Uniform`]: distributions::uniform::Uniform
+    fn gen_range<T, R>(&mut self, range: R) -> T
+    where
+        T: SampleUniform,
+        R: SampleRange<T>
+    {
+        assert!(!range.is_empty(), "cannot sample empty range");
+        range.sample_single(self)
+    }
+
+    /// Sample a new value, using the given distribution.
+    ///
+    /// ### Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    /// use rand::distributions::Uniform;
+    ///
+    /// let mut rng = thread_rng();
+    /// let x = rng.sample(Uniform::new(10u32, 15));
+    /// // Type annotation requires two types, the type and distribution; the
+    /// // distribution can be inferred.
+    /// let y = rng.sample::<u16, _>(Uniform::new(10, 15));
+    /// ```
+    fn sample<T, D: Distribution<T>>(&mut self, distr: D) -> T {
+        distr.sample(self)
+    }
+
+    /// Create an iterator that generates values using the given distribution.
+    ///
+    /// Note that this function takes its arguments by value. This works since
+    /// `(&mut R): Rng where R: Rng` and
+    /// `(&D): Distribution where D: Distribution`,
+    /// however borrowing is not automatic hence `rng.sample_iter(...)` may
+    /// need to be replaced with `(&mut rng).sample_iter(...)`.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    /// use rand::distributions::{Alphanumeric, Uniform, Standard};
+    ///
+    /// let mut rng = thread_rng();
+    ///
+    /// // Vec of 16 x f32:
+    /// let v: Vec<f32> = (&mut rng).sample_iter(Standard).take(16).collect();
+    ///
+    /// // String:
+    /// let s: String = (&mut rng).sample_iter(Alphanumeric)
+    ///     .take(7)
+    ///     .map(char::from)
+    ///     .collect();
+    ///
+    /// // Combined values
+    /// println!("{:?}", (&mut rng).sample_iter(Standard).take(5)
+    ///                              .collect::<Vec<(f64, bool)>>());
+    ///
+    /// // Dice-rolling:
+    /// let die_range = Uniform::new_inclusive(1, 6);
+    /// let mut roll_die = (&mut rng).sample_iter(die_range);
+    /// while roll_die.next().unwrap() != 6 {
+    ///     println!("Not a 6; rolling again!");
+    /// }
+    /// ```
+    fn sample_iter<T, D>(self, distr: D) -> distributions::DistIter<D, Self, T>
+    where
+        D: Distribution<T>,
+        Self: Sized,
+    {
+        distr.sample_iter(self)
+    }
+
+    /// Fill any type implementing [`Fill`] with random data
+    ///
+    /// The distribution is expected to be uniform with portable results, but
+    /// this cannot be guaranteed for third-party implementations.
+    ///
+    /// This is identical to [`try_fill`] except that it panics on error.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// let mut arr = [0i8; 20];
+    /// thread_rng().fill(&mut arr[..]);
+    /// ```
+    ///
+    /// [`fill_bytes`]: RngCore::fill_bytes
+    /// [`try_fill`]: Rng::try_fill
+    fn fill<T: Fill + ?Sized>(&mut self, dest: &mut T) {
+        dest.try_fill(self).unwrap_or_else(|_| panic!("Rng::fill failed"))
+    }
+
+    /// Fill any type implementing [`Fill`] with random data
+    ///
+    /// The distribution is expected to be uniform with portable results, but
+    /// this cannot be guaranteed for third-party implementations.
+    ///
+    /// This is identical to [`fill`] except that it forwards errors.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # use rand::Error;
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// # fn try_inner() -> Result<(), Error> {
+    /// let mut arr = [0u64; 4];
+    /// thread_rng().try_fill(&mut arr[..])?;
+    /// # Ok(())
+    /// # }
+    ///
+    /// # try_inner().unwrap()
+    /// ```
+    ///
+    /// [`try_fill_bytes`]: RngCore::try_fill_bytes
+    /// [`fill`]: Rng::fill
+    fn try_fill<T: Fill + ?Sized>(&mut self, dest: &mut T) -> Result<(), Error> {
+        dest.try_fill(self)
+    }
+
+    /// Return a bool with a probability `p` of being true.
+    ///
+    /// See also the [`Bernoulli`] distribution, which may be faster if
+    /// sampling from the same probability repeatedly.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// let mut rng = thread_rng();
+    /// println!("{}", rng.gen_bool(1.0 / 3.0));
+    /// ```
+    ///
+    /// # Panics
+    ///
+    /// If `p < 0` or `p > 1`.
+    ///
+    /// [`Bernoulli`]: distributions::Bernoulli
+    #[inline]
+    fn gen_bool(&mut self, p: f64) -> bool {
+        let d = distributions::Bernoulli::new(p).unwrap();
+        self.sample(d)
+    }
+
+    /// Return a bool with a probability of `numerator/denominator` of being
+    /// true. I.e. `gen_ratio(2, 3)` has chance of 2 in 3, or about 67%, of
+    /// returning true. If `numerator == denominator`, then the returned value
+    /// is guaranteed to be `true`. If `numerator == 0`, then the returned
+    /// value is guaranteed to be `false`.
+    ///
+    /// See also the [`Bernoulli`] distribution, which may be faster if
+    /// sampling from the same `numerator` and `denominator` repeatedly.
+    ///
+    /// # Panics
+    ///
+    /// If `denominator == 0` or `numerator > denominator`.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::{thread_rng, Rng};
+    ///
+    /// let mut rng = thread_rng();
+    /// println!("{}", rng.gen_ratio(2, 3));
+    /// ```
+    ///
+    /// [`Bernoulli`]: distributions::Bernoulli
+    #[inline]
+    fn gen_ratio(&mut self, numerator: u32, denominator: u32) -> bool {
+        let d = distributions::Bernoulli::from_ratio(numerator, denominator).unwrap();
+        self.sample(d)
+    }
+}
+
+impl<R: RngCore + ?Sized> Rng for R {}
+
+/// Types which may be filled with random data
+///
+/// This trait allows arrays to be efficiently filled with random data.
+///
+/// Implementations are expected to be portable across machines unless
+/// clearly documented otherwise (see the
+/// [Chapter on Portability](https://rust-random.github.io/book/portability.html)).
+pub trait Fill {
+    /// Fill self with random data
+    fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error>;
+}
+
+macro_rules! impl_fill_each {
+    () => {};
+    ($t:ty) => {
+        impl Fill for [$t] {
+            fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
+                for elt in self.iter_mut() {
+                    *elt = rng.gen();
+                }
+                Ok(())
+            }
+        }
+    };
+    ($t:ty, $($tt:ty,)*) => {
+        impl_fill_each!($t);
+        impl_fill_each!($($tt,)*);
+    };
+}
+
+impl_fill_each!(bool, char, f32, f64,);
+
+impl Fill for [u8] {
+    fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
+        rng.try_fill_bytes(self)
+    }
+}
+
+macro_rules! impl_fill {
+    () => {};
+    ($t:ty) => {
+        impl Fill for [$t] {
+            #[inline(never)] // in micro benchmarks, this improves performance
+            fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
+                if self.len() > 0 {
+                    rng.try_fill_bytes(unsafe {
+                        slice::from_raw_parts_mut(self.as_mut_ptr()
+                            as *mut u8,
+                            self.len() * mem::size_of::<$t>()
+                        )
+                    })?;
+                    for x in self {
+                        *x = x.to_le();
+                    }
+                }
+                Ok(())
+            }
+        }
+
+        impl Fill for [Wrapping<$t>] {
+            #[inline(never)]
+            fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
+                if self.len() > 0 {
+                    rng.try_fill_bytes(unsafe {
+                        slice::from_raw_parts_mut(self.as_mut_ptr()
+                            as *mut u8,
+                            self.len() * mem::size_of::<$t>()
+                        )
+                    })?;
+                    for x in self {
+                    *x = Wrapping(x.0.to_le());
+                    }
+                }
+                Ok(())
+            }
+        }
+    };
+    ($t:ty, $($tt:ty,)*) => {
+        impl_fill!($t);
+        // TODO: this could replace above impl once Rust #32463 is fixed
+        // impl_fill!(Wrapping<$t>);
+        impl_fill!($($tt,)*);
+    }
+}
+
+impl_fill!(u16, u32, u64, usize, u128,);
+impl_fill!(i8, i16, i32, i64, isize, i128,);
+
+#[cfg_attr(doc_cfg, doc(cfg(feature = "min_const_gen")))]
+#[cfg(feature = "min_const_gen")]
+impl<T, const N: usize> Fill for [T; N]
+where [T]: Fill
+{
+    fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
+        self[..].try_fill(rng)
+    }
+}
+
+#[cfg(not(feature = "min_const_gen"))]
+macro_rules! impl_fill_arrays {
+    ($n:expr,) => {};
+    ($n:expr, $N:ident) => {
+        impl<T> Fill for [T; $n] where [T]: Fill {
+            fn try_fill<R: Rng + ?Sized>(&mut self, rng: &mut R) -> Result<(), Error> {
+                self[..].try_fill(rng)
+            }
+        }
+    };
+    ($n:expr, $N:ident, $($NN:ident,)*) => {
+        impl_fill_arrays!($n, $N);
+        impl_fill_arrays!($n - 1, $($NN,)*);
+    };
+    (!div $n:expr,) => {};
+    (!div $n:expr, $N:ident, $($NN:ident,)*) => {
+        impl_fill_arrays!($n, $N);
+        impl_fill_arrays!(!div $n / 2, $($NN,)*);
+    };
+}
+#[cfg(not(feature = "min_const_gen"))]
+#[rustfmt::skip]
+impl_fill_arrays!(32, N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,N,);
+#[cfg(not(feature = "min_const_gen"))]
+impl_fill_arrays!(!div 4096, N,N,N,N,N,N,N,);
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use crate::test::rng;
+    use crate::rngs::mock::StepRng;
+    #[cfg(feature = "alloc")] use alloc::boxed::Box;
+
+    #[test]
+    fn test_fill_bytes_default() {
+        let mut r = StepRng::new(0x11_22_33_44_55_66_77_88, 0);
+
+        // check every remainder mod 8, both in small and big vectors.
+        let lengths = [0, 1, 2, 3, 4, 5, 6, 7, 80, 81, 82, 83, 84, 85, 86, 87];
+        for &n in lengths.iter() {
+            let mut buffer = [0u8; 87];
+            let v = &mut buffer[0..n];
+            r.fill_bytes(v);
+
+            // use this to get nicer error messages.
+            for (i, &byte) in v.iter().enumerate() {
+                if byte == 0 {
+                    panic!("byte {} of {} is zero", i, n)
+                }
+            }
+        }
+    }
+
+    #[test]
+    fn test_fill() {
+        let x = 9041086907909331047; // a random u64
+        let mut rng = StepRng::new(x, 0);
+
+        // Convert to byte sequence and back to u64; byte-swap twice if BE.
+        let mut array = [0u64; 2];
+        rng.fill(&mut array[..]);
+        assert_eq!(array, [x, x]);
+        assert_eq!(rng.next_u64(), x);
+
+        // Convert to bytes then u32 in LE order
+        let mut array = [0u32; 2];
+        rng.fill(&mut array[..]);
+        assert_eq!(array, [x as u32, (x >> 32) as u32]);
+        assert_eq!(rng.next_u32(), x as u32);
+
+        // Check equivalence using wrapped arrays
+        let mut warray = [Wrapping(0u32); 2];
+        rng.fill(&mut warray[..]);
+        assert_eq!(array[0], warray[0].0);
+        assert_eq!(array[1], warray[1].0);
+
+        // Check equivalence for generated floats
+        let mut array = [0f32; 2];
+        rng.fill(&mut array);
+        let gen: [f32; 2] = rng.gen();
+        assert_eq!(array, gen);
+    }
+
+    #[test]
+    fn test_fill_empty() {
+        let mut array = [0u32; 0];
+        let mut rng = StepRng::new(0, 1);
+        rng.fill(&mut array);
+        rng.fill(&mut array[..]);
+    }
+
+    #[test]
+    fn test_gen_range_int() {
+        let mut r = rng(101);
+        for _ in 0..1000 {
+            let a = r.gen_range(-4711..17);
+            assert!((-4711..17).contains(&a));
+            let a: i8 = r.gen_range(-3..42);
+            assert!((-3..42).contains(&a));
+            let a: u16 = r.gen_range(10..99);
+            assert!((10..99).contains(&a));
+            let a: i32 = r.gen_range(-100..2000);
+            assert!((-100..2000).contains(&a));
+            let a: u32 = r.gen_range(12..=24);
+            assert!((12..=24).contains(&a));
+
+            assert_eq!(r.gen_range(0u32..1), 0u32);
+            assert_eq!(r.gen_range(-12i64..-11), -12i64);
+            assert_eq!(r.gen_range(3_000_000..3_000_001), 3_000_000);
+        }
+    }
+
+    #[test]
+    fn test_gen_range_float() {
+        let mut r = rng(101);
+        for _ in 0..1000 {
+            let a = r.gen_range(-4.5..1.7);
+            assert!((-4.5..1.7).contains(&a));
+            let a = r.gen_range(-1.1..=-0.3);
+            assert!((-1.1..=-0.3).contains(&a));
+
+            assert_eq!(r.gen_range(0.0f32..=0.0), 0.);
+            assert_eq!(r.gen_range(-11.0..=-11.0), -11.);
+            assert_eq!(r.gen_range(3_000_000.0..=3_000_000.0), 3_000_000.);
+        }
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_gen_range_panic_int() {
+        #![allow(clippy::reversed_empty_ranges)]
+        let mut r = rng(102);
+        r.gen_range(5..-2);
+    }
+
+    #[test]
+    #[should_panic]
+    fn test_gen_range_panic_usize() {
+        #![allow(clippy::reversed_empty_ranges)]
+        let mut r = rng(103);
+        r.gen_range(5..2);
+    }
+
+    #[test]
+    fn test_gen_bool() {
+        #![allow(clippy::bool_assert_comparison)]
+
+        let mut r = rng(105);
+        for _ in 0..5 {
+            assert_eq!(r.gen_bool(0.0), false);
+            assert_eq!(r.gen_bool(1.0), true);
+        }
+    }
+
+    #[test]
+    fn test_rng_trait_object() {
+        use crate::distributions::{Distribution, Standard};
+        let mut rng = rng(109);
+        let mut r = &mut rng as &mut dyn RngCore;
+        r.next_u32();
+        r.gen::<i32>();
+        assert_eq!(r.gen_range(0..1), 0);
+        let _c: u8 = Standard.sample(&mut r);
+    }
+
+    #[test]
+    #[cfg(feature = "alloc")]
+    fn test_rng_boxed_trait() {
+        use crate::distributions::{Distribution, Standard};
+        let rng = rng(110);
+        let mut r = Box::new(rng) as Box<dyn RngCore>;
+        r.next_u32();
+        r.gen::<i32>();
+        assert_eq!(r.gen_range(0..1), 0);
+        let _c: u8 = Standard.sample(&mut r);
+    }
+
+    #[test]
+    #[cfg_attr(miri, ignore)] // Miri is too slow
+    fn test_gen_ratio_average() {
+        const NUM: u32 = 3;
+        const DENOM: u32 = 10;
+        const N: u32 = 100_000;
+
+        let mut sum: u32 = 0;
+        let mut rng = rng(111);
+        for _ in 0..N {
+            if rng.gen_ratio(NUM, DENOM) {
+                sum += 1;
+            }
+        }
+        // Have Binomial(N, NUM/DENOM) distribution
+        let expected = (NUM * N) / DENOM; // exact integer
+        assert!(((sum - expected) as i32).abs() < 500);
+    }
+}
+

+