# uniform.rs - source
Source of the Rust file `/home/key/.cargo/registry/src/github.com-1ecc6299db9ec823/rand-0.8.5/src/distributions/uniform.rs`.
Keywords: rust, rustlang, rust-lang

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    // Copyright 2018-2020 Developers of the Rand project.
    // Copyright 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.

    //! A distribution uniformly sampling numbers within a given range.
    //!
    //! [`Uniform`] is the standard distribution to sample uniformly from a range;
    //! e.g. `Uniform::new_inclusive(1, 6)` can sample integers from 1 to 6, like a
    //! standard die. [`Rng::gen_range`] supports any type supported by
    //! [`Uniform`].
    //!
    //! This distribution is provided with support for several primitive types
    //! (all integer and floating-point types) as well as [`std::time::Duration`],
    //! and supports extension to user-defined types via a type-specific *back-end*
    //! implementation.
    //!
    //! The types [`UniformInt`], [`UniformFloat`] and [`UniformDuration`] are the
    //! back-ends supporting sampling from primitive integer and floating-point
    //! ranges as well as from [`std::time::Duration`]; these types do not normally
    //! need to be used directly (unless implementing a derived back-end).
    //!
    //! # Example usage
    //!
    //! ```
    //! use rand::{Rng, thread_rng};
    //! use rand::distributions::Uniform;
    //!
    //! let mut rng = thread_rng();
    //! let side = Uniform::new(-10.0, 10.0);
    //!
    //! // sample between 1 and 10 points
    //! for _ in 0..rng.gen_range(1..=10) {
    //!     // sample a point from the square with sides -10 - 10 in two dimensions
    //!     let (x, y) = (rng.sample(side), rng.sample(side));
    //!     println!("Point: {}, {}", x, y);
    //! }
    //! ```
    //!
    //! # Extending `Uniform` to support a custom type
    //!
    //! To extend [`Uniform`] to support your own types, write a back-end which
    //! implements the [`UniformSampler`] trait, then implement the [`SampleUniform`]
    //! helper trait to "register" your back-end. See the `MyF32` example below.
    //!
    //! At a minimum, the back-end needs to store any parameters needed for sampling
    //! (e.g. the target range) and implement `new`, `new_inclusive` and `sample`.
    //! Those methods should include an assert to check the range is valid (i.e.
    //! `low < high`). The example below merely wraps another back-end.
    //!
    //! The `new`, `new_inclusive` and `sample_single` functions use arguments of
    //! type SampleBorrow<X> in order to support passing in values by reference or
    //! by value. In the implementation of these functions, you can choose to
    //! simply use the reference returned by [`SampleBorrow::borrow`], or you can choose
    //! to copy or clone the value, whatever is appropriate for your type.
    //!
    //! ```
    //! use rand::prelude::*;
    //! use rand::distributions::uniform::{Uniform, SampleUniform,
    //!         UniformSampler, UniformFloat, SampleBorrow};
    //!
    //! struct MyF32(f32);
    //!
    //! #[derive(Clone, Copy, Debug)]
    //! struct UniformMyF32(UniformFloat<f32>);
    //!
    //! impl UniformSampler for UniformMyF32 {
    //!     type X = MyF32;
    //!     fn new<B1, B2>(low: B1, high: B2) -> Self
    //!         where B1: SampleBorrow<Self::X> + Sized,
    //!               B2: SampleBorrow<Self::X> + Sized
    //!     {
    //!         UniformMyF32(UniformFloat::<f32>::new(low.borrow().0, high.borrow().0))
    //!     }
    //!     fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
    //!         where B1: SampleBorrow<Self::X> + Sized,
    //!               B2: SampleBorrow<Self::X> + Sized
    //!     {
    //!         UniformMyF32(UniformFloat::<f32>::new_inclusive(
    //!             low.borrow().0,
    //!             high.borrow().0,
    //!         ))
    //!     }
    //!     fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
    //!         MyF32(self.0.sample(rng))
    //!     }
    //! }
    //!
    //! impl SampleUniform for MyF32 {
    //!     type Sampler = UniformMyF32;
    //! }
    //!
    //! let (low, high) = (MyF32(17.0f32), MyF32(22.0f32));
    //! let uniform = Uniform::new(low, high);
    //! let x = uniform.sample(&mut thread_rng());
    //! ```
    //!
    //! [`SampleUniform`]: crate::distributions::uniform::SampleUniform
    //! [`UniformSampler`]: crate::distributions::uniform::UniformSampler
    //! [`UniformInt`]: crate::distributions::uniform::UniformInt
    //! [`UniformFloat`]: crate::distributions::uniform::UniformFloat
    //! [`UniformDuration`]: crate::distributions::uniform::UniformDuration
    //! [`SampleBorrow::borrow`]: crate::distributions::uniform::SampleBorrow::borrow

    use core::time::Duration;
    use core::ops::{Range, RangeInclusive};

    use crate::distributions::float::IntoFloat;
    use crate::distributions::utils::{BoolAsSIMD, FloatAsSIMD, FloatSIMDUtils, WideningMultiply};
    use crate::distributions::Distribution;
    use crate::{Rng, RngCore};

    #[cfg(not(feature = "std"))]
    #[allow(unused_imports)] // rustc doesn't detect that this is actually used
    use crate::distributions::utils::Float;

    #[cfg(feature = "simd_support")] use packed_simd::*;

    #[cfg(feature = "serde1")]
    use serde::{Serialize, Deserialize};

    /// Sample values uniformly between two bounds.
    ///
    /// [`Uniform::new`] and [`Uniform::new_inclusive`] construct a uniform
    /// distribution sampling from the given range; these functions may do extra
    /// work up front to make sampling of multiple values faster. If only one sample
    /// from the range is required, [`Rng::gen_range`] can be more efficient.
    ///
    /// When sampling from a constant range, many calculations can happen at
    /// compile-time and all methods should be fast; for floating-point ranges and
    /// the full range of integer types this should have comparable performance to
    /// the `Standard` distribution.
    ///
    /// Steps are taken to avoid bias which might be present in naive
    /// implementations; for example `rng.gen::<u8>() % 170` samples from the range
    /// `[0, 169]` but is twice as likely to select numbers less than 85 than other
    /// values. Further, the implementations here give more weight to the high-bits
    /// generated by the RNG than the low bits, since with some RNGs the low-bits
    /// are of lower quality than the high bits.
    ///
    /// Implementations must sample in `[low, high)` range for
    /// `Uniform::new(low, high)`, i.e., excluding `high`. In particular, care must
    /// be taken to ensure that rounding never results values `< low` or `>= high`.
    ///
    /// # Example
    ///
    /// ```
    /// use rand::distributions::{Distribution, Uniform};
    ///
    /// let between = Uniform::from(10..10000);
    /// let mut rng = rand::thread_rng();
    /// let mut sum = 0;
    /// for _ in 0..1000 {
    ///     sum += between.sample(&mut rng);
    /// }
    /// println!("{}", sum);
    /// ```
    ///
    /// For a single sample, [`Rng::gen_range`] may be preferred:
    ///
    /// ```
    /// use rand::Rng;
    ///
    /// let mut rng = rand::thread_rng();
    /// println!("{}", rng.gen_range(0..10));
    /// ```
    ///
    /// [`new`]: Uniform::new
    /// [`new_inclusive`]: Uniform::new_inclusive
    /// [`Rng::gen_range`]: Rng::gen_range
    #[derive(Clone, Copy, Debug, PartialEq)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    #[cfg_attr(feature = "serde1", serde(bound(serialize = "X::Sampler: Serialize")))]
    #[cfg_attr(feature = "serde1", serde(bound(deserialize = "X::Sampler: Deserialize<'de>")))]
    pub struct Uniform<X: SampleUniform>(X::Sampler);

    impl<X: SampleUniform> Uniform<X> {
        /// Create a new `Uniform` instance which samples uniformly from the half
        /// open range `[low, high)` (excluding `high`). Panics if `low >= high`.
        pub fn new<B1, B2>(low: B1, high: B2) -> Uniform<X>
        where
            B1: SampleBorrow<X> + Sized,
            B2: SampleBorrow<X> + Sized,
        {
            Uniform(X::Sampler::new(low, high))
        }

        /// Create a new `Uniform` instance which samples uniformly from the closed
        /// range `[low, high]` (inclusive). Panics if `low > high`.
        pub fn new_inclusive<B1, B2>(low: B1, high: B2) -> Uniform<X>
        where
            B1: SampleBorrow<X> + Sized,
            B2: SampleBorrow<X> + Sized,
        {
            Uniform(X::Sampler::new_inclusive(low, high))
        }
    }

    impl<X: SampleUniform> Distribution<X> for Uniform<X> {
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> X {
            self.0.sample(rng)
        }
    }

    /// Helper trait for creating objects using the correct implementation of
    /// [`UniformSampler`] for the sampling type.
    ///
    /// See the [module documentation] on how to implement [`Uniform`] range
    /// sampling for a custom type.
    ///
    /// [module documentation]: crate::distributions::uniform
    pub trait SampleUniform: Sized {
        /// The `UniformSampler` implementation supporting type `X`.
        type Sampler: UniformSampler<X = Self>;
    }

    /// Helper trait handling actual uniform sampling.
    ///
    /// See the [module documentation] on how to implement [`Uniform`] range
    /// sampling for a custom type.
    ///
    /// Implementation of [`sample_single`] is optional, and is only useful when
    /// the implementation can be faster than `Self::new(low, high).sample(rng)`.
    ///
    /// [module documentation]: crate::distributions::uniform
    /// [`sample_single`]: UniformSampler::sample_single
    pub trait UniformSampler: Sized {
        /// The type sampled by this implementation.
        type X;

        /// Construct self, with inclusive lower bound and exclusive upper bound
        /// `[low, high)`.
        ///
        /// Usually users should not call this directly but instead use
        /// `Uniform::new`, which asserts that `low < high` before calling this.
        fn new<B1, B2>(low: B1, high: B2) -> Self
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized;

        /// Construct self, with inclusive bounds `[low, high]`.
        ///
        /// Usually users should not call this directly but instead use
        /// `Uniform::new_inclusive`, which asserts that `low <= high` before
        /// calling this.
        fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized;

        /// Sample a value.
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X;

        /// Sample a single value uniformly from a range with inclusive lower bound
        /// and exclusive upper bound `[low, high)`.
        ///
        /// By default this is implemented using
        /// `UniformSampler::new(low, high).sample(rng)`. However, for some types
        /// more optimal implementations for single usage may be provided via this
        /// method (which is the case for integers and floats).
        /// Results may not be identical.
        ///
        /// Note that to use this method in a generic context, the type needs to be
        /// retrieved via `SampleUniform::Sampler` as follows:
        /// ```
        /// use rand::{thread_rng, distributions::uniform::{SampleUniform, UniformSampler}};
        /// # #[allow(unused)]
        /// fn sample_from_range<T: SampleUniform>(lb: T, ub: T) -> T {
        ///     let mut rng = thread_rng();
        ///     <T as SampleUniform>::Sampler::sample_single(lb, ub, &mut rng)
        /// }
        /// ```
        fn sample_single<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R) -> Self::X
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized,
        {
            let uniform: Self = UniformSampler::new(low, high);
            uniform.sample(rng)
        }

        /// Sample a single value uniformly from a range with inclusive lower bound
        /// and inclusive upper bound `[low, high]`.
        ///
        /// By default this is implemented using
        /// `UniformSampler::new_inclusive(low, high).sample(rng)`. However, for
        /// some types more optimal implementations for single usage may be provided
        /// via this method.
        /// Results may not be identical.
        fn sample_single_inclusive<R: Rng + ?Sized, B1, B2>(low: B1, high: B2, rng: &mut R)
            -> Self::X
            where B1: SampleBorrow<Self::X> + Sized,
                  B2: SampleBorrow<Self::X> + Sized
        {
            let uniform: Self = UniformSampler::new_inclusive(low, high);
            uniform.sample(rng)
        }
    }

    impl<X: SampleUniform> From<Range<X>> for Uniform<X> {
        fn from(r: ::core::ops::Range<X>) -> Uniform<X> {
            Uniform::new(r.start, r.end)
        }
    }

    impl<X: SampleUniform> From<RangeInclusive<X>> for Uniform<X> {
        fn from(r: ::core::ops::RangeInclusive<X>) -> Uniform<X> {
            Uniform::new_inclusive(r.start(), r.end())
        }
    }

    /// Helper trait similar to [`Borrow`] but implemented
    /// only for SampleUniform and references to SampleUniform in
    /// order to resolve ambiguity issues.
    ///
    /// [`Borrow`]: std::borrow::Borrow
    pub trait SampleBorrow<Borrowed> {
        /// Immutably borrows from an owned value. See [`Borrow::borrow`]
        ///
        /// [`Borrow::borrow`]: std::borrow::Borrow::borrow
        fn borrow(&self) -> &Borrowed;
    }
    impl<Borrowed> SampleBorrow<Borrowed> for Borrowed
    where Borrowed: SampleUniform
    {
        #[inline(always)]
        fn borrow(&self) -> &Borrowed {
            self
        }
    }
    impl<'a, Borrowed> SampleBorrow<Borrowed> for &'a Borrowed
    where Borrowed: SampleUniform
    {
        #[inline(always)]
        fn borrow(&self) -> &Borrowed {
            *self
        }
    }

    /// Range that supports generating a single sample efficiently.
    ///
    /// Any type implementing this trait can be used to specify the sampled range
    /// for `Rng::gen_range`.
    pub trait SampleRange<T> {
        /// Generate a sample from the given range.
        fn sample_single<R: RngCore + ?Sized>(self, rng: &mut R) -> T;

        /// Check whether the range is empty.
        fn is_empty(&self) -> bool;
    }

    impl<T: SampleUniform + PartialOrd> SampleRange<T> for Range<T> {
        #[inline]
        fn sample_single<R: RngCore + ?Sized>(self, rng: &mut R) -> T {
            T::Sampler::sample_single(self.start, self.end, rng)
        }

        #[inline]
        fn is_empty(&self) -> bool {
            !(self.start < self.end)
        }
    }

    impl<T: SampleUniform + PartialOrd> SampleRange<T> for RangeInclusive<T> {
        #[inline]
        fn sample_single<R: RngCore + ?Sized>(self, rng: &mut R) -> T {
            T::Sampler::sample_single_inclusive(self.start(), self.end(), rng)
        }

        #[inline]
        fn is_empty(&self) -> bool {
            !(self.start() <= self.end())
        }
    }

    ////////////////////////////////////////////////////////////////////////////////

    // What follows are all back-ends.

    /// The back-end implementing [`UniformSampler`] for integer types.
    ///
    /// Unless you are implementing [`UniformSampler`] for your own type, this type
    /// should not be used directly, use [`Uniform`] instead.
    ///
    /// # Implementation notes
    ///
    /// For simplicity, we use the same generic struct `UniformInt<X>` for all
    /// integer types `X`. This gives us only one field type, `X`; to store unsigned
    /// values of this size, we take use the fact that these conversions are no-ops.
    ///
    /// For a closed range, the number of possible numbers we should generate is
    /// `range = (high - low + 1)`. To avoid bias, we must ensure that the size of
    /// our sample space, `zone`, is a multiple of `range`; other values must be
    /// rejected (by replacing with a new random sample).
    ///
    /// As a special case, we use `range = 0` to represent the full range of the
    /// result type (i.e. for `new_inclusive($ty::MIN, $ty::MAX)`).
    ///
    /// The optimum `zone` is the largest product of `range` which fits in our
    /// (unsigned) target type. We calculate this by calculating how many numbers we
    /// must reject: `reject = (MAX + 1) % range = (MAX - range + 1) % range`. Any (large)
    /// product of `range` will suffice, thus in `sample_single` we multiply by a
    /// power of 2 via bit-shifting (faster but may cause more rejections).
    ///
    /// The smallest integer PRNGs generate is `u32`. For 8- and 16-bit outputs we
    /// use `u32` for our `zone` and samples (because it's not slower and because
    /// it reduces the chance of having to reject a sample). In this case we cannot
    /// store `zone` in the target type since it is too large, however we know
    /// `ints_to_reject < range <= $unsigned::MAX`.
    ///
    /// An alternative to using a modulus is widening multiply: After a widening
    /// multiply by `range`, the result is in the high word. Then comparing the low
    /// word against `zone` makes sure our distribution is uniform.
    #[derive(Clone, Copy, Debug, PartialEq)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    pub struct UniformInt<X> {
        low: X,
        range: X,
        z: X, // either ints_to_reject or zone depending on implementation
    }

    macro_rules! uniform_int_impl {
        ($ty:ty, $unsigned:ident, $u_large:ident) => {
            impl SampleUniform for $ty {
                type Sampler = UniformInt<$ty>;
            }

            impl UniformSampler for UniformInt<$ty> {
                // We play free and fast with unsigned vs signed here
                // (when $ty is signed), but that's fine, since the
                // contract of this macro is for $ty and $unsigned to be
                // "bit-equal", so casting between them is a no-op.

                type X = $ty;

                #[inline] // if the range is constant, this helps LLVM to do the
                          // calculations at compile-time.
                fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    assert!(low < high, "Uniform::new called with `low >= high`");
                    UniformSampler::new_inclusive(low, high - 1)
                }

                #[inline] // if the range is constant, this helps LLVM to do the
                          // calculations at compile-time.
                fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    assert!(
                        low <= high,
                        "Uniform::new_inclusive called with `low > high`"
                    );
                    let unsigned_max = ::core::$u_large::MAX;

                    let range = high.wrapping_sub(low).wrapping_add(1) as $unsigned;
                    let ints_to_reject = if range > 0 {
                        let range = $u_large::from(range);
                        (unsigned_max - range + 1) % range
                    } else {
                        0
                    };

                    UniformInt {
                        low,
                        // These are really $unsigned values, but store as $ty:
                        range: range as $ty,
                        z: ints_to_reject as $unsigned as $ty,
                    }
                }

                #[inline]
                fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
                    let range = self.range as $unsigned as $u_large;
                    if range > 0 {
                        let unsigned_max = ::core::$u_large::MAX;
                        let zone = unsigned_max - (self.z as $unsigned as $u_large);
                        loop {
                            let v: $u_large = rng.gen();
                            let (hi, lo) = v.wmul(range);
                            if lo <= zone {
                                return self.low.wrapping_add(hi as $ty);
                            }
                        }
                    } else {
                        // Sample from the entire integer range.
                        rng.gen()
                    }
                }

                #[inline]
                fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Self::X
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    assert!(low < high, "UniformSampler::sample_single: low >= high");
                    Self::sample_single_inclusive(low, high - 1, rng)
                }

                #[inline]
                fn sample_single_inclusive<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Self::X
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    assert!(low <= high, "UniformSampler::sample_single_inclusive: low > high");
                    let range = high.wrapping_sub(low).wrapping_add(1) as $unsigned as $u_large;
                    // If the above resulted in wrap-around to 0, the range is $ty::MIN..=$ty::MAX,
                    // and any integer will do.
                    if range == 0 {
                        return rng.gen();
                    }

                    let zone = if ::core::$unsigned::MAX <= ::core::u16::MAX as $unsigned {
                        // Using a modulus is faster than the approximation for
                        // i8 and i16. I suppose we trade the cost of one
                        // modulus for near-perfect branch prediction.
                        let unsigned_max: $u_large = ::core::$u_large::MAX;
                        let ints_to_reject = (unsigned_max - range + 1) % range;
                        unsigned_max - ints_to_reject
                    } else {
                        // conservative but fast approximation. `- 1` is necessary to allow the
                        // same comparison without bias.
                        (range << range.leading_zeros()).wrapping_sub(1)
                    };

                    loop {
                        let v: $u_large = rng.gen();
                        let (hi, lo) = v.wmul(range);
                        if lo <= zone {
                            return low.wrapping_add(hi as $ty);
                        }
                    }
                }
            }
        };
    }

    uniform_int_impl! { i8, u8, u32 }
    uniform_int_impl! { i16, u16, u32 }
    uniform_int_impl! { i32, u32, u32 }
    uniform_int_impl! { i64, u64, u64 }
    uniform_int_impl! { i128, u128, u128 }
    uniform_int_impl! { isize, usize, usize }
    uniform_int_impl! { u8, u8, u32 }
    uniform_int_impl! { u16, u16, u32 }
    uniform_int_impl! { u32, u32, u32 }
    uniform_int_impl! { u64, u64, u64 }
    uniform_int_impl! { usize, usize, usize }
    uniform_int_impl! { u128, u128, u128 }

    #[cfg(feature = "simd_support")]
    macro_rules! uniform_simd_int_impl {
        ($ty:ident, $unsigned:ident, $u_scalar:ident) => {
            // The "pick the largest zone that can fit in an `u32`" optimization
            // is less useful here. Multiple lanes complicate things, we don't
            // know the PRNG's minimal output size, and casting to a larger vector
            // is generally a bad idea for SIMD performance. The user can still
            // implement it manually.

            // TODO: look into `Uniform::<u32x4>::new(0u32, 100)` functionality
            //       perhaps `impl SampleUniform for $u_scalar`?
            impl SampleUniform for $ty {
                type Sampler = UniformInt<$ty>;
            }

            impl UniformSampler for UniformInt<$ty> {
                type X = $ty;

                #[inline] // if the range is constant, this helps LLVM to do the
                          // calculations at compile-time.
                fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
                    where B1: SampleBorrow<Self::X> + Sized,
                          B2: SampleBorrow<Self::X> + Sized
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    assert!(low.lt(high).all(), "Uniform::new called with `low >= high`");
                    UniformSampler::new_inclusive(low, high - 1)
                }

                #[inline] // if the range is constant, this helps LLVM to do the
                          // calculations at compile-time.
                fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
                    where B1: SampleBorrow<Self::X> + Sized,
                          B2: SampleBorrow<Self::X> + Sized
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    assert!(low.le(high).all(),
                            "Uniform::new_inclusive called with `low > high`");
                    let unsigned_max = ::core::$u_scalar::MAX;

                    // NOTE: these may need to be replaced with explicitly
                    // wrapping operations if `packed_simd` changes
                    let range: $unsigned = ((high - low) + 1).cast();
                    // `% 0` will panic at runtime.
                    let not_full_range = range.gt($unsigned::splat(0));
                    // replacing 0 with `unsigned_max` allows a faster `select`
                    // with bitwise OR
                    let modulo = not_full_range.select(range, $unsigned::splat(unsigned_max));
                    // wrapping addition
                    let ints_to_reject = (unsigned_max - range + 1) % modulo;
                    // When `range` is 0, `lo` of `v.wmul(range)` will always be
                    // zero which means only one sample is needed.
                    let zone = unsigned_max - ints_to_reject;

                    UniformInt {
                        low,
                        // These are really $unsigned values, but store as $ty:
                        range: range.cast(),
                        z: zone.cast(),
                    }
                }

                fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
                    let range: $unsigned = self.range.cast();
                    let zone: $unsigned = self.z.cast();

                    // This might seem very slow, generating a whole new
                    // SIMD vector for every sample rejection. For most uses
                    // though, the chance of rejection is small and provides good
                    // general performance. With multiple lanes, that chance is
                    // multiplied. To mitigate this, we replace only the lanes of
                    // the vector which fail, iteratively reducing the chance of
                    // rejection. The replacement method does however add a little
                    // overhead. Benchmarking or calculating probabilities might
                    // reveal contexts where this replacement method is slower.
                    let mut v: $unsigned = rng.gen();
                    loop {
                        let (hi, lo) = v.wmul(range);
                        let mask = lo.le(zone);
                        if mask.all() {
                            let hi: $ty = hi.cast();
                            // wrapping addition
                            let result = self.low + hi;
                            // `select` here compiles to a blend operation
                            // When `range.eq(0).none()` the compare and blend
                            // operations are avoided.
                            let v: $ty = v.cast();
                            return range.gt($unsigned::splat(0)).select(result, v);
                        }
                        // Replace only the failing lanes
                        v = mask.select(v, rng.gen());
                    }
                }
            }
        };

        // bulk implementation
        ($(($unsigned:ident, $signed:ident),)+ $u_scalar:ident) => {
            $(
                uniform_simd_int_impl!($unsigned, $unsigned, $u_scalar);
                uniform_simd_int_impl!($signed, $unsigned, $u_scalar);
            )+
        };
    }

    #[cfg(feature = "simd_support")]
    uniform_simd_int_impl! {
        (u64x2, i64x2),
        (u64x4, i64x4),
        (u64x8, i64x8),
        u64
    }

    #[cfg(feature = "simd_support")]
    uniform_simd_int_impl! {
        (u32x2, i32x2),
        (u32x4, i32x4),
        (u32x8, i32x8),
        (u32x16, i32x16),
        u32
    }

    #[cfg(feature = "simd_support")]
    uniform_simd_int_impl! {
        (u16x2, i16x2),
        (u16x4, i16x4),
        (u16x8, i16x8),
        (u16x16, i16x16),
        (u16x32, i16x32),
        u16
    }

    #[cfg(feature = "simd_support")]
    uniform_simd_int_impl! {
        (u8x2, i8x2),
        (u8x4, i8x4),
        (u8x8, i8x8),
        (u8x16, i8x16),
        (u8x32, i8x32),
        (u8x64, i8x64),
        u8
    }

    impl SampleUniform for char {
        type Sampler = UniformChar;
    }

    /// The back-end implementing [`UniformSampler`] for `char`.
    ///
    /// Unless you are implementing [`UniformSampler`] for your own type, this type
    /// should not be used directly, use [`Uniform`] instead.
    ///
    /// This differs from integer range sampling since the range `0xD800..=0xDFFF`
    /// are used for surrogate pairs in UCS and UTF-16, and consequently are not
    /// valid Unicode code points. We must therefore avoid sampling values in this
    /// range.
    #[derive(Clone, Copy, Debug)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    pub struct UniformChar {
        sampler: UniformInt<u32>,
    }

    /// UTF-16 surrogate range start
    const CHAR_SURROGATE_START: u32 = 0xD800;
    /// UTF-16 surrogate range size
    const CHAR_SURROGATE_LEN: u32 = 0xE000 - CHAR_SURROGATE_START;

    /// Convert `char` to compressed `u32`
    fn char_to_comp_u32(c: char) -> u32 {
        match c as u32 {
            c if c >= CHAR_SURROGATE_START => c - CHAR_SURROGATE_LEN,
            c => c,
        }
    }

    impl UniformSampler for UniformChar {
        type X = char;

        #[inline] // if the range is constant, this helps LLVM to do the
                  // calculations at compile-time.
        fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized,
        {
            let low = char_to_comp_u32(*low_b.borrow());
            let high = char_to_comp_u32(*high_b.borrow());
            let sampler = UniformInt::<u32>::new(low, high);
            UniformChar { sampler }
        }

        #[inline] // if the range is constant, this helps LLVM to do the
                  // calculations at compile-time.
        fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized,
        {
            let low = char_to_comp_u32(*low_b.borrow());
            let high = char_to_comp_u32(*high_b.borrow());
            let sampler = UniformInt::<u32>::new_inclusive(low, high);
            UniformChar { sampler }
        }

        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
            let mut x = self.sampler.sample(rng);
            if x >= CHAR_SURROGATE_START {
                x += CHAR_SURROGATE_LEN;
            }
            // SAFETY: x must not be in surrogate range or greater than char::MAX.
            // This relies on range constructors which accept char arguments.
            // Validity of input char values is assumed.
            unsafe { core::char::from_u32_unchecked(x) }
        }
    }

    /// The back-end implementing [`UniformSampler`] for floating-point types.
    ///
    /// Unless you are implementing [`UniformSampler`] for your own type, this type
    /// should not be used directly, use [`Uniform`] instead.
    ///
    /// # Implementation notes
    ///
    /// Instead of generating a float in the `[0, 1)` range using [`Standard`], the
    /// `UniformFloat` implementation converts the output of an PRNG itself. This
    /// way one or two steps can be optimized out.
    ///
    /// The floats are first converted to a value in the `[1, 2)` interval using a
    /// transmute-based method, and then mapped to the expected range with a
    /// multiply and addition. Values produced this way have what equals 23 bits of
    /// random digits for an `f32`, and 52 for an `f64`.
    ///
    /// [`new`]: UniformSampler::new
    /// [`new_inclusive`]: UniformSampler::new_inclusive
    /// [`Standard`]: crate::distributions::Standard
    #[derive(Clone, Copy, Debug, PartialEq)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    pub struct UniformFloat<X> {
        low: X,
        scale: X,
    }

    macro_rules! uniform_float_impl {
        ($ty:ty, $uty:ident, $f_scalar:ident, $u_scalar:ident, $bits_to_discard:expr) => {
            impl SampleUniform for $ty {
                type Sampler = UniformFloat<$ty>;
            }

            impl UniformSampler for UniformFloat<$ty> {
                type X = $ty;

                fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    debug_assert!(
                        low.all_finite(),
                        "Uniform::new called with `low` non-finite."
                    );
                    debug_assert!(
                        high.all_finite(),
                        "Uniform::new called with `high` non-finite."
                    );
                    assert!(low.all_lt(high), "Uniform::new called with `low >= high`");
                    let max_rand = <$ty>::splat(
                        (::core::$u_scalar::MAX >> $bits_to_discard).into_float_with_exponent(0) - 1.0,
                    );

                    let mut scale = high - low;
                    assert!(scale.all_finite(), "Uniform::new: range overflow");

                    loop {
                        let mask = (scale * max_rand + low).ge_mask(high);
                        if mask.none() {
                            break;
                        }
                        scale = scale.decrease_masked(mask);
                    }

                    debug_assert!(<$ty>::splat(0.0).all_le(scale));

                    UniformFloat { low, scale }
                }

                fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    debug_assert!(
                        low.all_finite(),
                        "Uniform::new_inclusive called with `low` non-finite."
                    );
                    debug_assert!(
                        high.all_finite(),
                        "Uniform::new_inclusive called with `high` non-finite."
                    );
                    assert!(
                        low.all_le(high),
                        "Uniform::new_inclusive called with `low > high`"
                    );
                    let max_rand = <$ty>::splat(
                        (::core::$u_scalar::MAX >> $bits_to_discard).into_float_with_exponent(0) - 1.0,
                    );

                    let mut scale = (high - low) / max_rand;
                    assert!(scale.all_finite(), "Uniform::new_inclusive: range overflow");

                    loop {
                        let mask = (scale * max_rand + low).gt_mask(high);
                        if mask.none() {
                            break;
                        }
                        scale = scale.decrease_masked(mask);
                    }

                    debug_assert!(<$ty>::splat(0.0).all_le(scale));

                    UniformFloat { low, scale }
                }

                fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
                    // Generate a value in the range [1, 2)
                    let value1_2 = (rng.gen::<$uty>() >> $bits_to_discard).into_float_with_exponent(0);

                    // Get a value in the range [0, 1) in order to avoid
                    // overflowing into infinity when multiplying with scale
                    let value0_1 = value1_2 - 1.0;

                    // We don't use `f64::mul_add`, because it is not available with
                    // `no_std`. Furthermore, it is slower for some targets (but
                    // faster for others). However, the order of multiplication and
                    // addition is important, because on some platforms (e.g. ARM)
                    // it will be optimized to a single (non-FMA) instruction.
                    value0_1 * self.scale + self.low
                }

                #[inline]
                fn sample_single<R: Rng + ?Sized, B1, B2>(low_b: B1, high_b: B2, rng: &mut R) -> Self::X
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    let low = *low_b.borrow();
                    let high = *high_b.borrow();
                    debug_assert!(
                        low.all_finite(),
                        "UniformSampler::sample_single called with `low` non-finite."
                    );
                    debug_assert!(
                        high.all_finite(),
                        "UniformSampler::sample_single called with `high` non-finite."
                    );
                    assert!(
                        low.all_lt(high),
                        "UniformSampler::sample_single: low >= high"
                    );
                    let mut scale = high - low;
                    assert!(scale.all_finite(), "UniformSampler::sample_single: range overflow");

                    loop {
                        // Generate a value in the range [1, 2)
                        let value1_2 =
                            (rng.gen::<$uty>() >> $bits_to_discard).into_float_with_exponent(0);

                        // Get a value in the range [0, 1) in order to avoid
                        // overflowing into infinity when multiplying with scale
                        let value0_1 = value1_2 - 1.0;

                        // Doing multiply before addition allows some architectures
                        // to use a single instruction.
                        let res = value0_1 * scale + low;

                        debug_assert!(low.all_le(res) || !scale.all_finite());
                        if res.all_lt(high) {
                            return res;
                        }

                        // This handles a number of edge cases.
                        // * `low` or `high` is NaN. In this case `scale` and
                        //   `res` are going to end up as NaN.
                        // * `low` is negative infinity and `high` is finite.
                        //   `scale` is going to be infinite and `res` will be
                        //   NaN.
                        // * `high` is positive infinity and `low` is finite.
                        //   `scale` is going to be infinite and `res` will
                        //   be infinite or NaN (if value0_1 is 0).
                        // * `low` is negative infinity and `high` is positive
                        //   infinity. `scale` will be infinite and `res` will
                        //   be NaN.
                        // * `low` and `high` are finite, but `high - low`
                        //   overflows to infinite. `scale` will be infinite
                        //   and `res` will be infinite or NaN (if value0_1 is 0).
                        // So if `high` or `low` are non-finite, we are guaranteed
                        // to fail the `res < high` check above and end up here.
                        //
                        // While we technically should check for non-finite `low`
                        // and `high` before entering the loop, by doing the checks
                        // here instead, we allow the common case to avoid these
                        // checks. But we are still guaranteed that if `low` or
                        // `high` are non-finite we'll end up here and can do the
                        // appropriate checks.
                        //
                        // Likewise `high - low` overflowing to infinity is also
                        // rare, so handle it here after the common case.
                        let mask = !scale.finite_mask();
                        if mask.any() {
                            assert!(
                                low.all_finite() && high.all_finite(),
                                "Uniform::sample_single: low and high must be finite"
                            );
                            scale = scale.decrease_masked(mask);
                        }
                    }
                }
            }
        };
    }

    uniform_float_impl! { f32, u32, f32, u32, 32 - 23 }
    uniform_float_impl! { f64, u64, f64, u64, 64 - 52 }

    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f32x2, u32x2, f32, u32, 32 - 23 }
    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f32x4, u32x4, f32, u32, 32 - 23 }
    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f32x8, u32x8, f32, u32, 32 - 23 }
    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f32x16, u32x16, f32, u32, 32 - 23 }

    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f64x2, u64x2, f64, u64, 64 - 52 }
    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f64x4, u64x4, f64, u64, 64 - 52 }
    #[cfg(feature = "simd_support")]
    uniform_float_impl! { f64x8, u64x8, f64, u64, 64 - 52 }

    /// The back-end implementing [`UniformSampler`] for `Duration`.
    ///
    /// Unless you are implementing [`UniformSampler`] for your own types, this type
    /// should not be used directly, use [`Uniform`] instead.
    #[derive(Clone, Copy, Debug)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    pub struct UniformDuration {
        mode: UniformDurationMode,
        offset: u32,
    }

    #[derive(Debug, Copy, Clone)]
    #[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
    enum UniformDurationMode {
        Small {
            secs: u64,
            nanos: Uniform<u32>,
        },
        Medium {
            nanos: Uniform<u64>,
        },
        Large {
            max_secs: u64,
            max_nanos: u32,
            secs: Uniform<u64>,
        },
    }

    impl SampleUniform for Duration {
        type Sampler = UniformDuration;
    }

    impl UniformSampler for UniformDuration {
        type X = Duration;

        #[inline]
        fn new<B1, B2>(low_b: B1, high_b: B2) -> Self
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized,
        {
            let low = *low_b.borrow();
            let high = *high_b.borrow();
            assert!(low < high, "Uniform::new called with `low >= high`");
            UniformDuration::new_inclusive(low, high - Duration::new(0, 1))
        }

        #[inline]
        fn new_inclusive<B1, B2>(low_b: B1, high_b: B2) -> Self
        where
            B1: SampleBorrow<Self::X> + Sized,
            B2: SampleBorrow<Self::X> + Sized,
        {
            let low = *low_b.borrow();
            let high = *high_b.borrow();
            assert!(
                low <= high,
                "Uniform::new_inclusive called with `low > high`"
            );

            let low_s = low.as_secs();
            let low_n = low.subsec_nanos();
            let mut high_s = high.as_secs();
            let mut high_n = high.subsec_nanos();

            if high_n < low_n {
                high_s -= 1;
                high_n += 1_000_000_000;
            }

            let mode = if low_s == high_s {
                UniformDurationMode::Small {
                    secs: low_s,
                    nanos: Uniform::new_inclusive(low_n, high_n),
                }
            } else {
                let max = high_s
                    .checked_mul(1_000_000_000)
                    .and_then(|n| n.checked_add(u64::from(high_n)));

                if let Some(higher_bound) = max {
                    let lower_bound = low_s * 1_000_000_000 + u64::from(low_n);
                    UniformDurationMode::Medium {
                        nanos: Uniform::new_inclusive(lower_bound, higher_bound),
                    }
                } else {
                    // An offset is applied to simplify generation of nanoseconds
                    let max_nanos = high_n - low_n;
                    UniformDurationMode::Large {
                        max_secs: high_s,
                        max_nanos,
                        secs: Uniform::new_inclusive(low_s, high_s),
                    }
                }
            };
            UniformDuration {
                mode,
                offset: low_n,
            }
        }

        #[inline]
        fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Duration {
            match self.mode {
                UniformDurationMode::Small { secs, nanos } => {
                    let n = nanos.sample(rng);
                    Duration::new(secs, n)
                }
                UniformDurationMode::Medium { nanos } => {
                    let nanos = nanos.sample(rng);
                    Duration::new(nanos / 1_000_000_000, (nanos % 1_000_000_000) as u32)
                }
                UniformDurationMode::Large {
                    max_secs,
                    max_nanos,
                    secs,
                } => {
                    // constant folding means this is at least as fast as `Rng::sample(Range)`
                    let nano_range = Uniform::new(0, 1_000_000_000);
                    loop {
                        let s = secs.sample(rng);
                        let n = nano_range.sample(rng);
                        if !(s == max_secs && n > max_nanos) {
                            let sum = n + self.offset;
                            break Duration::new(s, sum);
                        }
                    }
                }
            }
        }
    }

    #[cfg(test)]
    mod tests {
        use super::*;
        use crate::rngs::mock::StepRng;

        #[test]
        #[cfg(feature = "serde1")]
        fn test_serialization_uniform_duration() {
            let distr = UniformDuration::new(Duration::from_secs(10), Duration::from_secs(60));
            let de_distr: UniformDuration = bincode::deserialize(&bincode::serialize(&distr).unwrap()).unwrap();
            assert_eq!(
                distr.offset, de_distr.offset
            );
            match (distr.mode, de_distr.mode) {
                (UniformDurationMode::Small {secs: a_secs, nanos: a_nanos}, UniformDurationMode::Small {secs, nanos}) => {
                    assert_eq!(a_secs, secs);

                    assert_eq!(a_nanos.0.low, nanos.0.low);
                    assert_eq!(a_nanos.0.range, nanos.0.range);
                    assert_eq!(a_nanos.0.z, nanos.0.z);
                }
                (UniformDurationMode::Medium {nanos: a_nanos} , UniformDurationMode::Medium {nanos}) => {
                    assert_eq!(a_nanos.0.low, nanos.0.low);
                    assert_eq!(a_nanos.0.range, nanos.0.range);
                    assert_eq!(a_nanos.0.z, nanos.0.z);
                }
                (UniformDurationMode::Large {max_secs:a_max_secs, max_nanos:a_max_nanos, secs:a_secs}, UniformDurationMode::Large {max_secs, max_nanos, secs} ) => {
                    assert_eq!(a_max_secs, max_secs);
                    assert_eq!(a_max_nanos, max_nanos);

                    assert_eq!(a_secs.0.low, secs.0.low);
                    assert_eq!(a_secs.0.range, secs.0.range);
                    assert_eq!(a_secs.0.z, secs.0.z);
                }
                _ => panic!("`UniformDurationMode` was not serialized/deserialized correctly")
            }
        }

        #[test]
        #[cfg(feature = "serde1")]
        fn test_uniform_serialization() {
            let unit_box: Uniform<i32>  = Uniform::new(-1, 1);
            let de_unit_box: Uniform<i32> = bincode::deserialize(&bincode::serialize(&unit_box).unwrap()).unwrap();

            assert_eq!(unit_box.0.low, de_unit_box.0.low);
            assert_eq!(unit_box.0.range, de_unit_box.0.range);
            assert_eq!(unit_box.0.z, de_unit_box.0.z);

            let unit_box: Uniform<f32> = Uniform::new(-1., 1.);
            let de_unit_box: Uniform<f32> = bincode::deserialize(&bincode::serialize(&unit_box).unwrap()).unwrap();

            assert_eq!(unit_box.0.low, de_unit_box.0.low);
            assert_eq!(unit_box.0.scale, de_unit_box.0.scale);
        }

        #[should_panic]
        #[test]
        fn test_uniform_bad_limits_equal_int() {
            Uniform::new(10, 10);
        }

        #[test]
        fn test_uniform_good_limits_equal_int() {
            let mut rng = crate::test::rng(804);
            let dist = Uniform::new_inclusive(10, 10);
            for _ in 0..20 {
                assert_eq!(rng.sample(dist), 10);
            }
        }

        #[should_panic]
        #[test]
        fn test_uniform_bad_limits_flipped_int() {
            Uniform::new(10, 5);
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_integers() {
            use core::{i128, u128};
            use core::{i16, i32, i64, i8, isize};
            use core::{u16, u32, u64, u8, usize};

            let mut rng = crate::test::rng(251);
            macro_rules! t {
                ($ty:ident, $v:expr, $le:expr, $lt:expr) => {{
                    for &(low, high) in $v.iter() {
                        let my_uniform = Uniform::new(low, high);
                        for _ in 0..1000 {
                            let v: $ty = rng.sample(my_uniform);
                            assert!($le(low, v) && $lt(v, high));
                        }

                        let my_uniform = Uniform::new_inclusive(low, high);
                        for _ in 0..1000 {
                            let v: $ty = rng.sample(my_uniform);
                            assert!($le(low, v) && $le(v, high));
                        }

                        let my_uniform = Uniform::new(&low, high);
                        for _ in 0..1000 {
                            let v: $ty = rng.sample(my_uniform);
                            assert!($le(low, v) && $lt(v, high));
                        }

                        let my_uniform = Uniform::new_inclusive(&low, &high);
                        for _ in 0..1000 {
                            let v: $ty = rng.sample(my_uniform);
                            assert!($le(low, v) && $le(v, high));
                        }

                        for _ in 0..1000 {
                            let v = <$ty as SampleUniform>::Sampler::sample_single(low, high, &mut rng);
                            assert!($le(low, v) && $lt(v, high));
                        }

                        for _ in 0..1000 {
                            let v = <$ty as SampleUniform>::Sampler::sample_single_inclusive(low, high, &mut rng);
                            assert!($le(low, v) && $le(v, high));
                        }
                    }
                }};

                // scalar bulk
                ($($ty:ident),*) => {{
                    $(t!(
                        $ty,
                        [(0, 10), (10, 127), ($ty::MIN, $ty::MAX)],
                        |x, y| x <= y,
                        |x, y| x < y
                    );)*
                }};

                // simd bulk
                ($($ty:ident),* => $scalar:ident) => {{
                    $(t!(
                        $ty,
                        [
                            ($ty::splat(0), $ty::splat(10)),
                            ($ty::splat(10), $ty::splat(127)),
                            ($ty::splat($scalar::MIN), $ty::splat($scalar::MAX)),
                        ],
                        |x: $ty, y| x.le(y).all(),
                        |x: $ty, y| x.lt(y).all()
                    );)*
                }};
            }
            t!(i8, i16, i32, i64, isize, u8, u16, u32, u64, usize, i128, u128);

            #[cfg(feature = "simd_support")]
            {
                t!(u8x2, u8x4, u8x8, u8x16, u8x32, u8x64 => u8);
                t!(i8x2, i8x4, i8x8, i8x16, i8x32, i8x64 => i8);
                t!(u16x2, u16x4, u16x8, u16x16, u16x32 => u16);
                t!(i16x2, i16x4, i16x8, i16x16, i16x32 => i16);
                t!(u32x2, u32x4, u32x8, u32x16 => u32);
                t!(i32x2, i32x4, i32x8, i32x16 => i32);
                t!(u64x2, u64x4, u64x8 => u64);
                t!(i64x2, i64x4, i64x8 => i64);
            }
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_char() {
            let mut rng = crate::test::rng(891);
            let mut max = core::char::from_u32(0).unwrap();
            for _ in 0..100 {
                let c = rng.gen_range('A'..='Z');
                assert!(('A'..='Z').contains(&c));
                max = max.max(c);
            }
            assert_eq!(max, 'Z');
            let d = Uniform::new(
                core::char::from_u32(0xD7F0).unwrap(),
                core::char::from_u32(0xE010).unwrap(),
            );
            for _ in 0..100 {
                let c = d.sample(&mut rng);
                assert!((c as u32) < 0xD800 || (c as u32) > 0xDFFF);
            }
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_floats() {
            let mut rng = crate::test::rng(252);
            let mut zero_rng = StepRng::new(0, 0);
            let mut max_rng = StepRng::new(0xffff_ffff_ffff_ffff, 0);
            macro_rules! t {
                ($ty:ty, $f_scalar:ident, $bits_shifted:expr) => {{
                    let v: &[($f_scalar, $f_scalar)] = &[
                        (0.0, 100.0),
                        (-1e35, -1e25),
                        (1e-35, 1e-25),
                        (-1e35, 1e35),
                        (<$f_scalar>::from_bits(0), <$f_scalar>::from_bits(3)),
                        (-<$f_scalar>::from_bits(10), -<$f_scalar>::from_bits(1)),
                        (-<$f_scalar>::from_bits(5), 0.0),
                        (-<$f_scalar>::from_bits(7), -0.0),
                        (0.1 * ::core::$f_scalar::MAX, ::core::$f_scalar::MAX),
                        (-::core::$f_scalar::MAX * 0.2, ::core::$f_scalar::MAX * 0.7),
                    ];
                    for &(low_scalar, high_scalar) in v.iter() {
                        for lane in 0..<$ty>::lanes() {
                            let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
                            let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
                            let my_uniform = Uniform::new(low, high);
                            let my_incl_uniform = Uniform::new_inclusive(low, high);
                            for _ in 0..100 {
                                let v = rng.sample(my_uniform).extract(lane);
                                assert!(low_scalar <= v && v < high_scalar);
                                let v = rng.sample(my_incl_uniform).extract(lane);
                                assert!(low_scalar <= v && v <= high_scalar);
                                let v = <$ty as SampleUniform>::Sampler
                                    ::sample_single(low, high, &mut rng).extract(lane);
                                assert!(low_scalar <= v && v < high_scalar);
                            }

                            assert_eq!(
                                rng.sample(Uniform::new_inclusive(low, low)).extract(lane),
                                low_scalar
                            );

                            assert_eq!(zero_rng.sample(my_uniform).extract(lane), low_scalar);
                            assert_eq!(zero_rng.sample(my_incl_uniform).extract(lane), low_scalar);
                            assert_eq!(<$ty as SampleUniform>::Sampler
                                ::sample_single(low, high, &mut zero_rng)
                                .extract(lane), low_scalar);
                            assert!(max_rng.sample(my_uniform).extract(lane) < high_scalar);
                            assert!(max_rng.sample(my_incl_uniform).extract(lane) <= high_scalar);

                            // Don't run this test for really tiny differences between high and low
                            // since for those rounding might result in selecting high for a very
                            // long time.
                            if (high_scalar - low_scalar) > 0.0001 {
                                let mut lowering_max_rng = StepRng::new(
                                    0xffff_ffff_ffff_ffff,
                                    (-1i64 << $bits_shifted) as u64,
                                );
                                assert!(
                                    <$ty as SampleUniform>::Sampler
                                        ::sample_single(low, high, &mut lowering_max_rng)
                                        .extract(lane) < high_scalar
                                );
                            }
                        }
                    }

                    assert_eq!(
                        rng.sample(Uniform::new_inclusive(
                            ::core::$f_scalar::MAX,
                            ::core::$f_scalar::MAX
                        )),
                        ::core::$f_scalar::MAX
                    );
                    assert_eq!(
                        rng.sample(Uniform::new_inclusive(
                            -::core::$f_scalar::MAX,
                            -::core::$f_scalar::MAX
                        )),
                        -::core::$f_scalar::MAX
                    );
                }};
            }

            t!(f32, f32, 32 - 23);
            t!(f64, f64, 64 - 52);
            #[cfg(feature = "simd_support")]
            {
                t!(f32x2, f32, 32 - 23);
                t!(f32x4, f32, 32 - 23);
                t!(f32x8, f32, 32 - 23);
                t!(f32x16, f32, 32 - 23);
                t!(f64x2, f64, 64 - 52);
                t!(f64x4, f64, 64 - 52);
                t!(f64x8, f64, 64 - 52);
            }
        }

        #[test]
        #[should_panic]
        fn test_float_overflow() {
            let _ = Uniform::from(::core::f64::MIN..::core::f64::MAX);
        }

        #[test]
        #[should_panic]
        fn test_float_overflow_single() {
            let mut rng = crate::test::rng(252);
            rng.gen_range(::core::f64::MIN..::core::f64::MAX);
        }

        #[test]
        #[cfg(all(
            feature = "std",
            not(target_arch = "wasm32"),
            not(target_arch = "asmjs")
        ))]
        fn test_float_assertions() {
            use super::SampleUniform;
            use std::panic::catch_unwind;
            fn range<T: SampleUniform>(low: T, high: T) {
                let mut rng = crate::test::rng(253);
                T::Sampler::sample_single(low, high, &mut rng);
            }

            macro_rules! t {
                ($ty:ident, $f_scalar:ident) => {{
                    let v: &[($f_scalar, $f_scalar)] = &[
                        (::std::$f_scalar::NAN, 0.0),
                        (1.0, ::std::$f_scalar::NAN),
                        (::std::$f_scalar::NAN, ::std::$f_scalar::NAN),
                        (1.0, 0.5),
                        (::std::$f_scalar::MAX, -::std::$f_scalar::MAX),
                        (::std::$f_scalar::INFINITY, ::std::$f_scalar::INFINITY),
                        (
                            ::std::$f_scalar::NEG_INFINITY,
                            ::std::$f_scalar::NEG_INFINITY,
                        ),
                        (::std::$f_scalar::NEG_INFINITY, 5.0),
                        (5.0, ::std::$f_scalar::INFINITY),
                        (::std::$f_scalar::NAN, ::std::$f_scalar::INFINITY),
                        (::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::NAN),
                        (::std::$f_scalar::NEG_INFINITY, ::std::$f_scalar::INFINITY),
                    ];
                    for &(low_scalar, high_scalar) in v.iter() {
                        for lane in 0..<$ty>::lanes() {
                            let low = <$ty>::splat(0.0 as $f_scalar).replace(lane, low_scalar);
                            let high = <$ty>::splat(1.0 as $f_scalar).replace(lane, high_scalar);
                            assert!(catch_unwind(|| range(low, high)).is_err());
                            assert!(catch_unwind(|| Uniform::new(low, high)).is_err());
                            assert!(catch_unwind(|| Uniform::new_inclusive(low, high)).is_err());
                            assert!(catch_unwind(|| range(low, low)).is_err());
                            assert!(catch_unwind(|| Uniform::new(low, low)).is_err());
                        }
                    }
                }};
            }

            t!(f32, f32);
            t!(f64, f64);
            #[cfg(feature = "simd_support")]
            {
                t!(f32x2, f32);
                t!(f32x4, f32);
                t!(f32x8, f32);
                t!(f32x16, f32);
                t!(f64x2, f64);
                t!(f64x4, f64);
                t!(f64x8, f64);
            }
        }

        #[test]
        #[cfg_attr(miri, ignore)] // Miri is too slow
        fn test_durations() {
            let mut rng = crate::test::rng(253);

            let v = &[
                (Duration::new(10, 50000), Duration::new(100, 1234)),
                (Duration::new(0, 100), Duration::new(1, 50)),
                (
                    Duration::new(0, 0),
                    Duration::new(u64::max_value(), 999_999_999),
                ),
            ];
            for &(low, high) in v.iter() {
                let my_uniform = Uniform::new(low, high);
                for _ in 0..1000 {
                    let v = rng.sample(my_uniform);
                    assert!(low <= v && v < high);
                }
            }
        }

        #[test]
        fn test_custom_uniform() {
            use crate::distributions::uniform::{
                SampleBorrow, SampleUniform, UniformFloat, UniformSampler,
            };
            #[derive(Clone, Copy, PartialEq, PartialOrd)]
            struct MyF32 {
                x: f32,
            }
            #[derive(Clone, Copy, Debug)]
            struct UniformMyF32(UniformFloat<f32>);
            impl UniformSampler for UniformMyF32 {
                type X = MyF32;

                fn new<B1, B2>(low: B1, high: B2) -> Self
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    UniformMyF32(UniformFloat::<f32>::new(low.borrow().x, high.borrow().x))
                }

                fn new_inclusive<B1, B2>(low: B1, high: B2) -> Self
                where
                    B1: SampleBorrow<Self::X> + Sized,
                    B2: SampleBorrow<Self::X> + Sized,
                {
                    UniformSampler::new(low, high)
                }

                fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
                    MyF32 {
                        x: self.0.sample(rng),
                    }
                }
            }
            impl SampleUniform for MyF32 {
                type Sampler = UniformMyF32;
            }

            let (low, high) = (MyF32 { x: 17.0f32 }, MyF32 { x: 22.0f32 });
            let uniform = Uniform::new(low, high);
            let mut rng = crate::test::rng(804);
            for _ in 0..100 {
                let x: MyF32 = rng.sample(uniform);
                assert!(low <= x && x < high);
            }
        }

        #[test]
        fn test_uniform_from_std_range() {
            let r = Uniform::from(2u32..7);
            assert_eq!(r.0.low, 2);
            assert_eq!(r.0.range, 5);
            let r = Uniform::from(2.0f64..7.0);
            assert_eq!(r.0.low, 2.0);
            assert_eq!(r.0.scale, 5.0);
        }

        #[test]
        fn test_uniform_from_std_range_inclusive() {
            let r = Uniform::from(2u32..=6);
            assert_eq!(r.0.low, 2);
            assert_eq!(r.0.range, 5);
            let r = Uniform::from(2.0f64..=7.0);
            assert_eq!(r.0.low, 2.0);
            assert!(r.0.scale > 5.0);
            assert!(r.0.scale < 5.0 + 1e-14);
        }

        #[test]
        fn value_stability() {
            fn test_samples<T: SampleUniform + Copy + core::fmt::Debug + PartialEq>(
                lb: T, ub: T, expected_single: &[T], expected_multiple: &[T],
            ) where Uniform<T>: Distribution<T> {
                let mut rng = crate::test::rng(897);
                let mut buf = [lb; 3];

                for x in &mut buf {
                    *x = T::Sampler::sample_single(lb, ub, &mut rng);
                }
                assert_eq!(&buf, expected_single);

                let distr = Uniform::new(lb, ub);
                for x in &mut buf {
                    *x = rng.sample(&distr);
                }
                assert_eq!(&buf, expected_multiple);
            }

            // We test on a sub-set of types; possibly we should do more.
            // TODO: SIMD types

            test_samples(11u8, 219, &[17, 66, 214], &[181, 93, 165]);
            test_samples(11u32, 219, &[17, 66, 214], &[181, 93, 165]);

            test_samples(0f32, 1e-2f32, &[0.0003070104, 0.0026630748, 0.00979833], &[
                0.008194133,
                0.00398172,
                0.007428536,
            ]);
            test_samples(
                -1e10f64,
                1e10f64,
                &[-4673848682.871551, 6388267422.932352, 4857075081.198343],
                &[1173375212.1808167, 1917642852.109581, 2365076174.3153973],
            );

            test_samples(
                Duration::new(2, 0),
                Duration::new(4, 0),
                &[
                    Duration::new(2, 532615131),
                    Duration::new(3, 638826742),
                    Duration::new(3, 485707508),
                ],
                &[
                    Duration::new(3, 117337521),
                    Duration::new(3, 191764285),
                    Duration::new(3, 236507617),
                ],
            );
        }

        #[test]
        fn uniform_distributions_can_be_compared() {
            assert_eq!(Uniform::new(1.0, 2.0), Uniform::new(1.0, 2.0));

            // To cover UniformInt
            assert_eq!(Uniform::new(1 as u32, 2 as u32), Uniform::new(1 as u32, 2 as u32));
        }
    }