rand_core/src/lib.rs - third_party/rust-mirrors/rand - Git at Google

 // Copyright 2018 Developers of the Rand project.
 // Copyright 2017-2018 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.

 //! Random number generation traits
 //!
 //! This crate is mainly of interest to crates publishing implementations of
 //! [`RngCore`]. Other users are encouraged to use the [rand] crate instead
 //! which re-exports the main traits and error types.
 //!
 //! [`RngCore`] is the core trait implemented by algorithmic pseudo-random number
 //! generators and external random-number sources.
 //!
 //! [`SeedableRng`] is an extension trait for construction from fixed seeds and
 //! other random number generators.
 //!
 //! [`Error`] is provided for error-handling. It is safe to use in `no_std`
 //! environments.
 //!
 //! The [`impls`] and [`le`] sub-modules include a few small functions to assist
 //! implementation of [`RngCore`].
 //!
 //! [rand]: https://crates.io/crates/rand
 //! [`RngCore`]: trait.RngCore.html
 //! [`SeedableRng`]: trait.SeedableRng.html
 //! [`Error`]: struct.Error.html
 //! [`impls`]: impls/index.html
 //! [`le`]: le/index.html

 #![doc(html_logo_url = "https://www.rust-lang.org/logos/rust-logo-128x128-blk.png",
        html_favicon_url = "https://www.rust-lang.org/favicon.ico",
        html_root_url = "https://docs.rs/rand_core/0.3.0")]

 #![deny(missing_docs)]
 #![deny(missing_debug_implementations)]
 #![doc(test(attr(allow(unused_variables), deny(warnings))))]

 #![cfg_attr(not(feature="std"), no_std)]
 #![cfg_attr(all(feature="alloc", not(feature="std")), feature(alloc))]

 #[cfg(feature="std")] extern crate core;
 #[cfg(all(feature = "alloc", not(feature="std")))] extern crate alloc;
 #[cfg(feature="serde1")] extern crate serde;
 #[cfg(feature="serde1")] #[macro_use] extern crate serde_derive;


 use core::default::Default;
 use core::convert::AsMut;
 use core::ptr::copy_nonoverlapping;

 #[cfg(all(feature="alloc", not(feature="std")))] use alloc::boxed::Box;

 pub use error::{ErrorKind, Error};


 mod error;
 pub mod block;
 pub mod impls;
 pub mod le;


 /// The core of a random number generator.
 ///
 /// This trait encapsulates the low-level functionality common to all
 /// generators, and is the "back end", to be implemented by generators.
 /// End users should normally use [`Rng`] from the [rand] crate, which is
 /// automatically implemented for every type implementing `RngCore`.
 ///
 /// Three different methods for generating random data are provided since the
 /// optimal implementation of each is dependent on the type of generator. There
 /// is no required relationship between the output of each; e.g. many
 /// implementations of [`fill_bytes`] consume a whole number of `u32` or `u64`
 /// values and drop any remaining unused bytes.
 ///
 /// The [`try_fill_bytes`] method is a variant of [`fill_bytes`] allowing error
 /// handling; it is not deemed sufficiently useful to add equivalents for
 /// [`next_u32`] or [`next_u64`] since the latter methods are almost always used
 /// with algorithmic generators (PRNGs), which are normally infallible.
 ///
 /// Algorithmic generators implementing [`SeedableRng`] should normally have
 /// *portable, reproducible* output, i.e. fix Endianness when converting values
 /// to avoid platform differences, and avoid making any changes which affect
 /// output (except by communicating that the release has breaking changes).
 ///
 /// Typically implementators will implement only one of the methods available
 /// in this trait directly, then use the helper functions from the
 /// [`rand_core::impls`] module to implement the other methods.
 ///
 /// It is recommended that implementations also implement:
 ///
 /// - `Debug` with a custom implementation which *does not* print any internal
 ///   state (at least, [`CryptoRng`]s should not risk leaking state through
 ///   `Debug`).
 /// - `Serialize` and `Deserialize` (from Serde), preferably making Serde
 ///   support optional at the crate level in PRNG libs.
 /// - `Clone`, if possible.
 /// - *never* implement `Copy` (accidental copies may cause repeated values).
 /// - *do not* implement `Default` for pseudorandom generators, but instead
 ///   implement [`SeedableRng`], to guide users towards proper seeding.
 ///   External / hardware RNGs can choose to implement `Default`.
 /// - `Eq` and `PartialEq` could be implemented, but are probably not useful.
 ///
 /// # Example
 ///
 /// A simple example, obviously not generating very *random* output:
 ///
 /// ```
 /// #![allow(dead_code)]
 /// use rand_core::{RngCore, Error, impls};
 ///
 /// struct CountingRng(u64);
 ///
 /// impl RngCore for CountingRng {
 ///     fn next_u32(&mut self) -> u32 {
 ///         self.next_u64() as u32
 ///     }
 ///
 ///     fn next_u64(&mut self) -> u64 {
 ///         self.0 += 1;
 ///         self.0
 ///     }
 ///
 ///     fn fill_bytes(&mut self, dest: &mut [u8]) {
 ///         impls::fill_bytes_via_next(self, dest)
 ///     }
 ///
 ///     fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
 ///         Ok(self.fill_bytes(dest))
 ///     }
 /// }
 /// ```
 ///
 /// [rand]: https://crates.io/crates/rand
 /// [`Rng`]: ../rand/trait.Rng.html
 /// [`SeedableRng`]: trait.SeedableRng.html
 /// [`rand_core::impls`]: ../rand_core/impls/index.html
 /// [`try_fill_bytes`]: trait.RngCore.html#tymethod.try_fill_bytes
 /// [`fill_bytes`]: trait.RngCore.html#tymethod.fill_bytes
 /// [`next_u32`]: trait.RngCore.html#tymethod.next_u32
 /// [`next_u64`]: trait.RngCore.html#tymethod.next_u64
 /// [`CryptoRng`]: trait.CryptoRng.html
 pub trait RngCore {
     /// Return the next random `u32`.
     ///
     /// RNGs must implement at least one method from this trait directly. In
     /// the case this method is not implemented directly, it can be implemented
     /// using `self.next_u64() as u32` or
     /// [via `fill_bytes`](../rand_core/impls/fn.next_u32_via_fill.html).
     fn next_u32(&mut self) -> u32;

     /// Return the next random `u64`.
     ///
     /// RNGs must implement at least one method from this trait directly. In
     /// the case this method is not implemented directly, it can be implemented
     /// [via `next_u32`](../rand_core/impls/fn.next_u64_via_u32.html) or
     /// [via `fill_bytes`](../rand_core/impls/fn.next_u64_via_fill.html).
     fn next_u64(&mut self) -> u64;

     /// Fill `dest` with random data.
     ///
     /// RNGs must implement at least one method from this trait directly. In
     /// the case this method is not implemented directly, it can be implemented
     /// [via `next_u*`](../rand_core/impls/fn.fill_bytes_via_next.html) or
     /// via `try_fill_bytes`; if this generator can fail the implementation
     /// must choose how best to handle errors here (e.g. panic with a
     /// descriptive message or log a warning and retry a few times).
     ///
     /// This method should guarantee that `dest` is entirely filled
     /// with new data, and may panic if this is impossible
     /// (e.g. reading past the end of a file that is being used as the
     /// source of randomness).
     fn fill_bytes(&mut self, dest: &mut [u8]);

     /// Fill `dest` entirely with random data.
     ///
     /// This is the only method which allows an RNG to report errors while
     /// generating random data thus making this the primary method implemented
     /// by external (true) RNGs (e.g. `OsRng`) which can fail. It may be used
     /// directly to generate keys and to seed (infallible) PRNGs.
     ///
     /// Other than error handling, this method is identical to [`fill_bytes`];
     /// thus this may be implemented using `Ok(self.fill_bytes(dest))` or
     /// `fill_bytes` may be implemented with
     /// `self.try_fill_bytes(dest).unwrap()` or more specific error handling.
     ///
     /// [`fill_bytes`]: trait.RngCore.html#method.fill_bytes
     fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error>;
 }

 /// A marker trait used to indicate that an [`RngCore`] or [`BlockRngCore`]
 /// implementation is supposed to be cryptographically secure.
 ///
 /// *Cryptographically secure generators*, also known as *CSPRNGs*, should
 /// satisfy an additional properties over other generators: given the first
 /// *k* bits of an algorithm's output
 /// sequence, it should not be possible using polynomial-time algorithms to
 /// predict the next bit with probability significantly greater than 50%.
 ///
 /// Some generators may satisfy an additional property, however this is not
 /// required by this trait: if the CSPRNG's state is revealed, it should not be
 /// computationally-feasible to reconstruct output prior to this. Some other
 /// generators allow backwards-computation and are consided *reversible*.
 ///
 /// Note that this trait is provided for guidance only and cannot guarantee
 /// suitability for cryptographic applications. In general it should only be
 /// implemented for well-reviewed code implementing well-regarded algorithms.
 ///
 /// Note also that use of a `CryptoRng` does not protect against other
 /// weaknesses such as seeding from a weak entropy source or leaking state.
 ///
 /// [`RngCore`]: trait.RngCore.html
 /// [`BlockRngCore`]: ../rand_core/block/trait.BlockRngCore.html
 pub trait CryptoRng {}

 /// A random number generator that can be explicitly seeded.
 ///
 /// This trait encapsulates the low-level functionality common to all
 /// pseudo-random number generators (PRNGs, or algorithmic generators).
 ///
 /// The [`rand::FromEntropy`] trait is automatically implemented for every type
 /// implementing `SeedableRng`, providing a convenient `from_entropy()`
 /// constructor.
 ///
 /// [`rand::FromEntropy`]: ../rand/trait.FromEntropy.html
 pub trait SeedableRng: Sized {
     /// Seed type, which is restricted to types mutably-dereferencable as `u8`
     /// arrays (we recommend `[u8; N]` for some `N`).
     ///
     /// It is recommended to seed PRNGs with a seed of at least circa 100 bits,
     /// which means an array of `[u8; 12]` or greater to avoid picking RNGs with
     /// partially overlapping periods.
     ///
     /// For cryptographic RNG's a seed of 256 bits is recommended, `[u8; 32]`.
     ///
     ///
     /// # Implementing `SeedableRng` for RNGs with large seeds
     ///
     /// Note that the required traits `core::default::Default` and
     /// `core::convert::AsMut<u8>` are not implemented for large arrays
     /// `[u8; N]` with `N` > 32. To be able to implement the traits required by
     /// `SeedableRng` for RNGs with such large seeds, the newtype pattern can be
     /// used:
     ///
     /// ```
     /// use rand_core::SeedableRng;
     ///
     /// const N: usize = 64;
     /// pub struct MyRngSeed(pub [u8; N]);
     /// pub struct MyRng(MyRngSeed);
     ///
     /// impl Default for MyRngSeed {
     ///     fn default() -> MyRngSeed {
     ///         MyRngSeed([0; N])
     ///     }
     /// }
     ///
     /// impl AsMut<[u8]> for MyRngSeed {
     ///     fn as_mut(&mut self) -> &mut [u8] {
     ///         &mut self.0
     ///     }
     /// }
     ///
     /// impl SeedableRng for MyRng {
     ///     type Seed = MyRngSeed;
     ///
     ///     fn from_seed(seed: MyRngSeed) -> MyRng {
     ///         MyRng(seed)
     ///     }
     /// }
     /// ```
     type Seed: Sized + Default + AsMut<[u8]>;

     /// Create a new PRNG using the given seed.
     ///
     /// PRNG implementations are allowed to assume that bits in the seed are
     /// well distributed. That means usually that the number of one and zero
     /// bits are about equal, and values like 0, 1 and (size - 1) are unlikely.
     ///
     /// PRNG implementations are recommended to be reproducible. A PRNG seeded
     /// using this function with a fixed seed should produce the same sequence
     /// of output in the future and on different architectures (with for example
     /// different endianness).
     ///
     /// It is however not required that this function yield the same state as a
     /// reference implementation of the PRNG given equivalent seed; if necessary
     /// another constructor replicating behaviour from a reference
     /// implementation can be added.
     ///
     /// PRNG implementations should make sure `from_seed` never panics. In the
     /// case that some special values (like an all zero seed) are not viable
     /// seeds it is preferable to map these to alternative constant value(s),
     /// for example `0xBAD5EEDu32` or `0x0DDB1A5E5BAD5EEDu64` ("odd biases? bad
     /// seed"). This is assuming only a small number of values must be rejected.
     fn from_seed(seed: Self::Seed) -> Self;

     /// Create a new PRNG using a `u64` seed.
     ///
     /// This is a convenience-wrapper around `from_seed` to allow construction
     /// of any `SeedableRng` from a simple `u64` value. It is designed such that
     /// low Hamming Weight numbers like 0 and 1 can be used and should still
     /// result in good, independent seeds to the PRNG which is returned.
     ///
     /// This **is not suitable for cryptography**, as should be clear given that
     /// the input size is only 64 bits.
     ///
     /// Implementations for PRNGs *may* provide their own implementations of
     /// this function, but the default implementation should be good enough for
     /// all purposes. *Changing* the implementation of this function should be
     /// considered a value-breaking change.
     fn seed_from_u64(mut state: u64) -> Self {
         // We use PCG32 to generate a u32 sequence, and copy to the seed
         const MUL: u64 = 6364136223846793005;
         const INC: u64 = 11634580027462260723;

         let mut seed = Self::Seed::default();
         for chunk in seed.as_mut().chunks_mut(4) {
             // We advance the state first (to get away from the input value,
             // in case it has low Hamming Weight).
             state = state.wrapping_mul(MUL).wrapping_add(INC);

             // Use PCG output function with to_le to generate x:
             let xorshifted = (((state >> 18) ^ state) >> 27) as u32;
             let rot = (state >> 59) as u32;
             let x = xorshifted.rotate_right(rot).to_le();

             unsafe {
                 let p = &x as *const u32 as *const u8;
                 copy_nonoverlapping(p, chunk.as_mut_ptr(), chunk.len());
             }
         }

         Self::from_seed(seed)
     }

     /// Create a new PRNG seeded from another `Rng`.
     ///
     /// This is the recommended way to initialize PRNGs with fresh entropy. The
     /// [`FromEntropy`] trait provides a convenient `from_entropy` method
     /// based on `from_rng`.
     ///
     /// Usage of this method is not recommended when reproducibility is required
     /// since implementing PRNGs are not required to fix Endianness and are
     /// allowed to modify implementations in new releases.
     ///
     /// It is important to use a good source of randomness to initialize the
     /// PRNG. Cryptographic PRNG may be rendered insecure when seeded from a
     /// non-cryptographic PRNG or with insufficient entropy.
     /// Many non-cryptographic PRNGs will show statistical bias in their first
     /// results if their seed numbers are small or if there is a simple pattern
     /// between them.
     ///
     /// Prefer to seed from a strong external entropy source like [`OsRng`] or
     /// from a cryptographic PRNG; if creating a new generator for cryptographic
     /// uses you *must* seed from a strong source.
     ///
     /// Seeding a small PRNG from another small PRNG is possible, but
     /// something to be careful with. An extreme example of how this can go
     /// wrong is seeding an Xorshift RNG from another Xorshift RNG, which
     /// will effectively clone the generator. In general seeding from a
     /// generator which is hard to predict is probably okay.
     ///
     /// PRNG implementations are allowed to assume that a good RNG is provided
     /// for seeding, and that it is cryptographically secure when appropriate.
     ///
     /// [`FromEntropy`]: ../rand/trait.FromEntropy.html
     /// [`OsRng`]: ../rand/rngs/struct.OsRng.html
     fn from_rng<R: RngCore>(mut rng: R) -> Result<Self, Error> {
         let mut seed = Self::Seed::default();
         rng.try_fill_bytes(seed.as_mut())?;
         Ok(Self::from_seed(seed))
     }
 }

 // Implement `RngCore` for references to an `RngCore`.
 // Force inlining all functions, so that it is up to the `RngCore`
 // implementation and the optimizer to decide on inlining.
 impl<'a, R: RngCore + ?Sized> RngCore for &'a mut R {
     #[inline(always)]
     fn next_u32(&mut self) -> u32 {
         (**self).next_u32()
     }

     #[inline(always)]
     fn next_u64(&mut self) -> u64 {
         (**self).next_u64()
     }

     #[inline(always)]
     fn fill_bytes(&mut self, dest: &mut [u8]) {
         (**self).fill_bytes(dest)
     }

     #[inline(always)]
     fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
         (**self).try_fill_bytes(dest)
     }
 }

 // Implement `RngCore` for boxed references to an `RngCore`.
 // Force inlining all functions, so that it is up to the `RngCore`
 // implementation and the optimizer to decide on inlining.
 #[cfg(feature="alloc")]
 impl<R: RngCore + ?Sized> RngCore for Box<R> {
     #[inline(always)]
     fn next_u32(&mut self) -> u32 {
         (**self).next_u32()
     }

     #[inline(always)]
     fn next_u64(&mut self) -> u64 {
         (**self).next_u64()
     }

     #[inline(always)]
     fn fill_bytes(&mut self, dest: &mut [u8]) {
         (**self).fill_bytes(dest)
     }

     #[inline(always)]
     fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
         (**self).try_fill_bytes(dest)
     }
 }

 #[cfg(feature="std")]
 impl std::io::Read for RngCore {
     fn read(&mut self, buf: &mut [u8]) -> Result<usize, std::io::Error> {
         self.try_fill_bytes(buf)?;
         Ok(buf.len())
     }
 }

 // Implement `CryptoRng` for references to an `CryptoRng`.
 impl<'a, R: CryptoRng + ?Sized> CryptoRng for &'a mut R {}

 // Implement `CryptoRng` for boxed references to an `CryptoRng`.
 #[cfg(feature="alloc")]
 impl<R: CryptoRng + ?Sized> CryptoRng for Box<R> {}

 #[cfg(test)]
 mod test {
     use super::*;

     #[test]
     fn test_seed_from_u64() {
         struct SeedableNum(u64);
         impl SeedableRng for SeedableNum {
             type Seed = [u8; 8];
             fn from_seed(seed: Self::Seed) -> Self {
                 let mut x = [0u64; 1];
                 le::read_u64_into(&seed, &mut x);
                 SeedableNum(x[0])
             }
         }

         const N: usize = 8;
         const SEEDS: [u64; N] = [0u64, 1, 2, 3, 4, 8, 16, -1i64 as u64];
         let mut results = [0u64; N];
         for (i, seed) in SEEDS.iter().enumerate() {
             let SeedableNum(x) = SeedableNum::seed_from_u64(*seed);
             results[i] = x;
         }

         for (i1, r1) in results.iter().enumerate() {
             let weight = r1.count_ones();
             // This is the binomial distribution B(64, 0.5), so chance of
             // weight < 20 is binocdf(19, 64, 0.5) = 7.8e-4, and same for
             // weight > 44.
             assert!(weight >= 20 && weight <= 44);

             for (i2, r2) in results.iter().enumerate() {
                 if i1 == i2 { continue; }
                 let diff_weight = (r1 ^ r2).count_ones();
                 assert!(diff_weight >= 20);
             }
         }

         // value-breakage test:
         assert_eq!(results[0], 5029875928683246316);
     }
 }
	// Copyright 2018 Developers of the Rand project.
	// Copyright 2017-2018 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.

	//! Random number generation traits
	//!
	//! This crate is mainly of interest to crates publishing implementations of
	//! [`RngCore`]. Other users are encouraged to use the [rand] crate instead
	//! which re-exports the main traits and error types.
	//!
	//! [`RngCore`] is the core trait implemented by algorithmic pseudo-random number
	//! generators and external random-number sources.
	//!
	//! [`SeedableRng`] is an extension trait for construction from fixed seeds and
	//! other random number generators.
	//!
	//! [`Error`] is provided for error-handling. It is safe to use in `no_std`
	//! environments.
	//!
	//! The [`impls`] and [`le`] sub-modules include a few small functions to assist
	//! implementation of [`RngCore`].
	//!
	//! [rand]: https://crates.io/crates/rand
	//! [`RngCore`]: trait.RngCore.html
	//! [`SeedableRng`]: trait.SeedableRng.html
	//! [`Error`]: struct.Error.html
	//! [`impls`]: impls/index.html
	//! [`le`]: le/index.html

	#![doc(html_logo_url = "https://www.rust-lang.org/logos/rust-logo-128x128-blk.png",
	html_favicon_url = "https://www.rust-lang.org/favicon.ico",
	html_root_url = "https://docs.rs/rand_core/0.3.0")]

	#![deny(missing_docs)]
	#![deny(missing_debug_implementations)]
	#![doc(test(attr(allow(unused_variables), deny(warnings))))]

	#![cfg_attr(not(feature="std"), no_std)]
	#![cfg_attr(all(feature="alloc", not(feature="std")), feature(alloc))]

	#[cfg(feature="std")] extern crate core;
	#[cfg(all(feature = "alloc", not(feature="std")))] extern crate alloc;
	#[cfg(feature="serde1")] extern crate serde;
	#[cfg(feature="serde1")] #[macro_use] extern crate serde_derive;


	use core::default::Default;
	use core::convert::AsMut;
	use core::ptr::copy_nonoverlapping;

	#[cfg(all(feature="alloc", not(feature="std")))] use alloc::boxed::Box;

	pub use error::{ErrorKind, Error};


	mod error;
	pub mod block;
	pub mod impls;
	pub mod le;


	/// The core of a random number generator.
	///
	/// This trait encapsulates the low-level functionality common to all
	/// generators, and is the "back end", to be implemented by generators.
	/// End users should normally use [`Rng`] from the [rand] crate, which is
	/// automatically implemented for every type implementing `RngCore`.
	///
	/// Three different methods for generating random data are provided since the
	/// optimal implementation of each is dependent on the type of generator. There
	/// is no required relationship between the output of each; e.g. many
	/// implementations of [`fill_bytes`] consume a whole number of `u32` or `u64`
	/// values and drop any remaining unused bytes.
	///
	/// The [`try_fill_bytes`] method is a variant of [`fill_bytes`] allowing error
	/// handling; it is not deemed sufficiently useful to add equivalents for
	/// [`next_u32`] or [`next_u64`] since the latter methods are almost always used
	/// with algorithmic generators (PRNGs), which are normally infallible.
	///
	/// Algorithmic generators implementing [`SeedableRng`] should normally have
	/// portable, reproducible output, i.e. fix Endianness when converting values
	/// to avoid platform differences, and avoid making any changes which affect
	/// output (except by communicating that the release has breaking changes).
	///
	/// Typically implementators will implement only one of the methods available
	/// in this trait directly, then use the helper functions from the
	/// [`rand_core::impls`] module to implement the other methods.
	///
	/// It is recommended that implementations also implement:
	///
	/// - `Debug` with a custom implementation which does not print any internal
	/// state (at least, [`CryptoRng`]s should not risk leaking state through
	/// `Debug`).
	/// - `Serialize` and `Deserialize` (from Serde), preferably making Serde
	/// support optional at the crate level in PRNG libs.
	/// - `Clone`, if possible.
	/// - never implement `Copy` (accidental copies may cause repeated values).
	/// - do not implement `Default` for pseudorandom generators, but instead
	/// implement [`SeedableRng`], to guide users towards proper seeding.
	/// External / hardware RNGs can choose to implement `Default`.
	/// - `Eq` and `PartialEq` could be implemented, but are probably not useful.
	///
	/// # Example
	///
	/// A simple example, obviously not generating very random output:
	///
	/// ```
	/// #![allow(dead_code)]
	/// use rand_core::{RngCore, Error, impls};
	///
	/// struct CountingRng(u64);
	///
	/// impl RngCore for CountingRng {
	/// fn next_u32(&mut self) -> u32 {
	/// self.next_u64() as u32
	/// }
	///
	/// fn next_u64(&mut self) -> u64 {
	/// self.0 += 1;
	/// self.0
	/// }
	///
	/// fn fill_bytes(&mut self, dest: &mut [u8]) {
	/// impls::fill_bytes_via_next(self, dest)
	/// }
	///
	/// fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
	/// Ok(self.fill_bytes(dest))
	/// }
	/// }
	/// ```
	///
	/// [rand]: https://crates.io/crates/rand
	/// [`Rng`]: ../rand/trait.Rng.html
	/// [`SeedableRng`]: trait.SeedableRng.html
	/// [`rand_core::impls`]: ../rand_core/impls/index.html
	/// [`try_fill_bytes`]: trait.RngCore.html#tymethod.try_fill_bytes
	/// [`fill_bytes`]: trait.RngCore.html#tymethod.fill_bytes
	/// [`next_u32`]: trait.RngCore.html#tymethod.next_u32
	/// [`next_u64`]: trait.RngCore.html#tymethod.next_u64
	/// [`CryptoRng`]: trait.CryptoRng.html
	pub trait RngCore {
	/// Return the next random `u32`.
	///
	/// RNGs must implement at least one method from this trait directly. In
	/// the case this method is not implemented directly, it can be implemented
	/// using `self.next_u64() as u32` or
	/// [via `fill_bytes`](../rand_core/impls/fn.next_u32_via_fill.html).
	fn next_u32(&mut self) -> u32;

	/// Return the next random `u64`.
	///
	/// RNGs must implement at least one method from this trait directly. In
	/// the case this method is not implemented directly, it can be implemented
	/// [via `next_u32`](../rand_core/impls/fn.next_u64_via_u32.html) or
	/// [via `fill_bytes`](../rand_core/impls/fn.next_u64_via_fill.html).
	fn next_u64(&mut self) -> u64;

	/// Fill `dest` with random data.
	///
	/// RNGs must implement at least one method from this trait directly. In
	/// the case this method is not implemented directly, it can be implemented
	/// [via `next_u*`](../rand_core/impls/fn.fill_bytes_via_next.html) or
	/// via `try_fill_bytes`; if this generator can fail the implementation
	/// must choose how best to handle errors here (e.g. panic with a
	/// descriptive message or log a warning and retry a few times).
	///
	/// This method should guarantee that `dest` is entirely filled
	/// with new data, and may panic if this is impossible
	/// (e.g. reading past the end of a file that is being used as the
	/// source of randomness).
	fn fill_bytes(&mut self, dest: &mut [u8]);

	/// Fill `dest` entirely with random data.
	///
	/// This is the only method which allows an RNG to report errors while
	/// generating random data thus making this the primary method implemented
	/// by external (true) RNGs (e.g. `OsRng`) which can fail. It may be used
	/// directly to generate keys and to seed (infallible) PRNGs.
	///
	/// Other than error handling, this method is identical to [`fill_bytes`];
	/// thus this may be implemented using `Ok(self.fill_bytes(dest))` or
	/// `fill_bytes` may be implemented with
	/// `self.try_fill_bytes(dest).unwrap()` or more specific error handling.
	///
	/// [`fill_bytes`]: trait.RngCore.html#method.fill_bytes
	fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error>;
	}

	/// A marker trait used to indicate that an [`RngCore`] or [`BlockRngCore`]
	/// implementation is supposed to be cryptographically secure.
	///
	/// Cryptographically secure generators, also known as CSPRNGs, should
	/// satisfy an additional properties over other generators: given the first
	/// k bits of an algorithm's output
	/// sequence, it should not be possible using polynomial-time algorithms to
	/// predict the next bit with probability significantly greater than 50%.
	///
	/// Some generators may satisfy an additional property, however this is not
	/// required by this trait: if the CSPRNG's state is revealed, it should not be
	/// computationally-feasible to reconstruct output prior to this. Some other
	/// generators allow backwards-computation and are consided reversible.
	///
	/// Note that this trait is provided for guidance only and cannot guarantee
	/// suitability for cryptographic applications. In general it should only be
	/// implemented for well-reviewed code implementing well-regarded algorithms.
	///
	/// Note also that use of a `CryptoRng` does not protect against other
	/// weaknesses such as seeding from a weak entropy source or leaking state.
	///
	/// [`RngCore`]: trait.RngCore.html
	/// [`BlockRngCore`]: ../rand_core/block/trait.BlockRngCore.html
	pub trait CryptoRng {}

	/// A random number generator that can be explicitly seeded.
	///
	/// This trait encapsulates the low-level functionality common to all
	/// pseudo-random number generators (PRNGs, or algorithmic generators).
	///
	/// The [`rand::FromEntropy`] trait is automatically implemented for every type
	/// implementing `SeedableRng`, providing a convenient `from_entropy()`
	/// constructor.
	///
	/// [`rand::FromEntropy`]: ../rand/trait.FromEntropy.html
	pub trait SeedableRng: Sized {
	/// Seed type, which is restricted to types mutably-dereferencable as `u8`
	/// arrays (we recommend `[u8; N]` for some `N`).
	///
	/// It is recommended to seed PRNGs with a seed of at least circa 100 bits,
	/// which means an array of `[u8; 12]` or greater to avoid picking RNGs with
	/// partially overlapping periods.
	///
	/// For cryptographic RNG's a seed of 256 bits is recommended, `[u8; 32]`.
	///
	///
	/// # Implementing `SeedableRng` for RNGs with large seeds
	///
	/// Note that the required traits `core::default::Default` and
	/// `core::convert::AsMut<u8>` are not implemented for large arrays
	/// `[u8; N]` with `N` > 32. To be able to implement the traits required by
	/// `SeedableRng` for RNGs with such large seeds, the newtype pattern can be
	/// used:
	///
	/// ```
	/// use rand_core::SeedableRng;
	///
	/// const N: usize = 64;
	/// pub struct MyRngSeed(pub [u8; N]);
	/// pub struct MyRng(MyRngSeed);
	///
	/// impl Default for MyRngSeed {
	/// fn default() -> MyRngSeed {
	/// MyRngSeed([0; N])
	/// }
	/// }
	///
	/// impl AsMut<[u8]> for MyRngSeed {
	/// fn as_mut(&mut self) -> &mut [u8] {
	/// &mut self.0
	/// }
	/// }
	///
	/// impl SeedableRng for MyRng {
	/// type Seed = MyRngSeed;
	///
	/// fn from_seed(seed: MyRngSeed) -> MyRng {
	/// MyRng(seed)
	/// }
	/// }
	/// ```
	type Seed: Sized + Default + AsMut<[u8]>;

	/// Create a new PRNG using the given seed.
	///
	/// PRNG implementations are allowed to assume that bits in the seed are
	/// well distributed. That means usually that the number of one and zero
	/// bits are about equal, and values like 0, 1 and (size - 1) are unlikely.
	///
	/// PRNG implementations are recommended to be reproducible. A PRNG seeded
	/// using this function with a fixed seed should produce the same sequence
	/// of output in the future and on different architectures (with for example
	/// different endianness).
	///
	/// It is however not required that this function yield the same state as a
	/// reference implementation of the PRNG given equivalent seed; if necessary
	/// another constructor replicating behaviour from a reference
	/// implementation can be added.
	///
	/// PRNG implementations should make sure `from_seed` never panics. In the
	/// case that some special values (like an all zero seed) are not viable
	/// seeds it is preferable to map these to alternative constant value(s),
	/// for example `0xBAD5EEDu32` or `0x0DDB1A5E5BAD5EEDu64` ("odd biases? bad
	/// seed"). This is assuming only a small number of values must be rejected.
	fn from_seed(seed: Self::Seed) -> Self;

	/// Create a new PRNG using a `u64` seed.
	///
	/// This is a convenience-wrapper around `from_seed` to allow construction
	/// of any `SeedableRng` from a simple `u64` value. It is designed such that
	/// low Hamming Weight numbers like 0 and 1 can be used and should still
	/// result in good, independent seeds to the PRNG which is returned.
	///
	/// This is not suitable for cryptography, as should be clear given that
	/// the input size is only 64 bits.
	///
	/// Implementations for PRNGs may provide their own implementations of
	/// this function, but the default implementation should be good enough for
	/// all purposes. Changing the implementation of this function should be
	/// considered a value-breaking change.
	fn seed_from_u64(mut state: u64) -> Self {
	// We use PCG32 to generate a u32 sequence, and copy to the seed
	const MUL: u64 = 6364136223846793005;
	const INC: u64 = 11634580027462260723;

	let mut seed = Self::Seed::default();
	for chunk in seed.as_mut().chunks_mut(4) {
	// We advance the state first (to get away from the input value,
	// in case it has low Hamming Weight).
	state = state.wrapping_mul(MUL).wrapping_add(INC);

	// Use PCG output function with to_le to generate x:
	let xorshifted = (((state >> 18) ^ state) >> 27) as u32;
	let rot = (state >> 59) as u32;
	let x = xorshifted.rotate_right(rot).to_le();

	unsafe {
	let p = &x as const u32 as const u8;
	copy_nonoverlapping(p, chunk.as_mut_ptr(), chunk.len());
	}
	}

	Self::from_seed(seed)
	}

	/// Create a new PRNG seeded from another `Rng`.
	///
	/// This is the recommended way to initialize PRNGs with fresh entropy. The
	/// [`FromEntropy`] trait provides a convenient `from_entropy` method
	/// based on `from_rng`.
	///
	/// Usage of this method is not recommended when reproducibility is required
	/// since implementing PRNGs are not required to fix Endianness and are
	/// allowed to modify implementations in new releases.
	///
	/// It is important to use a good source of randomness to initialize the
	/// PRNG. Cryptographic PRNG may be rendered insecure when seeded from a
	/// non-cryptographic PRNG or with insufficient entropy.
	/// Many non-cryptographic PRNGs will show statistical bias in their first
	/// results if their seed numbers are small or if there is a simple pattern
	/// between them.
	///
	/// Prefer to seed from a strong external entropy source like [`OsRng`] or
	/// from a cryptographic PRNG; if creating a new generator for cryptographic
	/// uses you must seed from a strong source.
	///
	/// Seeding a small PRNG from another small PRNG is possible, but
	/// something to be careful with. An extreme example of how this can go
	/// wrong is seeding an Xorshift RNG from another Xorshift RNG, which
	/// will effectively clone the generator. In general seeding from a
	/// generator which is hard to predict is probably okay.
	///
	/// PRNG implementations are allowed to assume that a good RNG is provided
	/// for seeding, and that it is cryptographically secure when appropriate.
	///
	/// [`FromEntropy`]: ../rand/trait.FromEntropy.html
	/// [`OsRng`]: ../rand/rngs/struct.OsRng.html
	fn from_rng<R: RngCore>(mut rng: R) -> Result<Self, Error> {
	let mut seed = Self::Seed::default();
	rng.try_fill_bytes(seed.as_mut())?;
	Ok(Self::from_seed(seed))
	}
	}

	// Implement `RngCore` for references to an `RngCore`.
	// Force inlining all functions, so that it is up to the `RngCore`
	// implementation and the optimizer to decide on inlining.
	impl<'a, R: RngCore + ?Sized> RngCore for &'a mut R {
	#[inline(always)]
	fn next_u32(&mut self) -> u32 {
	(**self).next_u32()
	}

	#[inline(always)]
	fn next_u64(&mut self) -> u64 {
	(**self).next_u64()
	}

	#[inline(always)]
	fn fill_bytes(&mut self, dest: &mut [u8]) {
	(**self).fill_bytes(dest)
	}

	#[inline(always)]
	fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
	(**self).try_fill_bytes(dest)
	}
	}

	// Implement `RngCore` for boxed references to an `RngCore`.
	// Force inlining all functions, so that it is up to the `RngCore`
	// implementation and the optimizer to decide on inlining.
	#[cfg(feature="alloc")]
	impl<R: RngCore + ?Sized> RngCore for Box<R> {
	#[inline(always)]
	fn next_u32(&mut self) -> u32 {
	(**self).next_u32()
	}

	#[inline(always)]
	fn next_u64(&mut self) -> u64 {
	(**self).next_u64()
	}

	#[inline(always)]
	fn fill_bytes(&mut self, dest: &mut [u8]) {
	(**self).fill_bytes(dest)
	}

	#[inline(always)]
	fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
	(**self).try_fill_bytes(dest)
	}
	}

	#[cfg(feature="std")]
	impl std::io::Read for RngCore {
	fn read(&mut self, buf: &mut [u8]) -> Result<usize, std::io::Error> {
	self.try_fill_bytes(buf)?;
	Ok(buf.len())
	}
	}

	// Implement `CryptoRng` for references to an `CryptoRng`.
	impl<'a, R: CryptoRng + ?Sized> CryptoRng for &'a mut R {}

	// Implement `CryptoRng` for boxed references to an `CryptoRng`.
	#[cfg(feature="alloc")]
	impl<R: CryptoRng + ?Sized> CryptoRng for Box<R> {}

	#[cfg(test)]
	mod test {
	use super::*;

	#[test]
	fn test_seed_from_u64() {
	struct SeedableNum(u64);
	impl SeedableRng for SeedableNum {
	type Seed = [u8; 8];
	fn from_seed(seed: Self::Seed) -> Self {
	let mut x = [0u64; 1];
	le::read_u64_into(&seed, &mut x);
	SeedableNum(x[0])
	}
	}

	const N: usize = 8;
	const SEEDS: [u64; N] = [0u64, 1, 2, 3, 4, 8, 16, -1i64 as u64];
	let mut results = [0u64; N];
	for (i, seed) in SEEDS.iter().enumerate() {
	let SeedableNum(x) = SeedableNum::seed_from_u64(*seed);
	results[i] = x;
	}

	for (i1, r1) in results.iter().enumerate() {
	let weight = r1.count_ones();
	// This is the binomial distribution B(64, 0.5), so chance of
	// weight < 20 is binocdf(19, 64, 0.5) = 7.8e-4, and same for
	// weight > 44.
	assert!(weight >= 20 && weight <= 44);

	for (i2, r2) in results.iter().enumerate() {
	if i1 == i2 { continue; }
	let diff_weight = (r1 ^ r2).count_ones();
	assert!(diff_weight >= 20);
	}
	}

	// value-breakage test:
	assert_eq!(results[0], 5029875928683246316);
	}
	}