diff --git a/CHANGELOG.md b/CHANGELOG.md
index 95b4022ec9d..57bb3614ff8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,10 @@ A [separate changelog is kept for rand_core](rand_core/CHANGELOG.md).
 You may also find the [Upgrade Guide](https://rust-random.github.io/book/update.html) useful.
 
 ## Unreleased
+### Fixes
+- The `Bernoulli` distribution constructors now reports an error on NaN and on
+  `denominator == 0`. (#925)
+
 ### Additions
 - Implement `std::error::Error` for `BernoulliError` (#919)
 
diff --git a/rand_core/src/lib.rs b/rand_core/src/lib.rs
index 6e91c3c576f..f0a9f9431e3 100644
--- a/rand_core/src/lib.rs
+++ b/rand_core/src/lib.rs
@@ -141,24 +141,22 @@ pub trait RngCore {
     ///
     /// 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`](impls::next_u32_via_fill).
+    /// using `self.next_u64() as u32` or via [`impls::next_u32_via_fill`].
     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`](impls::next_u64_via_u32) or via
-    /// [`fill_bytes`](impls::next_u64_via_fill).
+    /// via [`impls::next_u64_via_u32`] or via [`impls::next_u64_via_fill`].
     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*`](impls::fill_bytes_via_next) or
-    /// via [`try_fill_bytes`](RngCore::try_fill_bytes); if this generator can
+    /// via [`impls::fill_bytes_via_next`] or
+    /// via [`RngCore::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).
@@ -176,12 +174,10 @@ pub trait RngCore {
     /// 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`];
+    /// Other than error handling, this method is identical to [`RngCore::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`]: RngCore::fill_bytes
     fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error>;
 }
 
diff --git a/src/distributions/bernoulli.rs b/src/distributions/bernoulli.rs
index e8099606e65..024233a53b2 100644
--- a/src/distributions/bernoulli.rs
+++ b/src/distributions/bernoulli.rs
@@ -93,7 +93,7 @@ impl Bernoulli {
     /// 2<sup>-64</sup> in `[0, 1]` can be represented as a `f64`.)
     #[inline]
     pub fn new(p: f64) -> Result<Bernoulli, BernoulliError> {
-        if p < 0.0 || p >= 1.0 {
+        if !(p >= 0.0 && p < 1.0) {
             if p == 1.0 { return Ok(Bernoulli { p_int: ALWAYS_TRUE }) }
             return Err(BernoulliError::InvalidProbability);
         }
@@ -104,11 +104,13 @@ impl Bernoulli {
     /// `numerator`-in-`denominator`. I.e. `new_ratio(2, 3)` will return
     /// a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.
     ///
-    /// If `numerator == denominator` then the returned `Bernoulli` will always
     /// return `true`. If `numerator == 0` it will always return `false`.
+    /// For `numerator > denominator` and `denominator == 0`, this returns an
+    /// error. Otherwise, for `numerator == denominator`, samples are always
+    /// true; for `numerator == 0` samples are always false.
     #[inline]
     pub fn from_ratio(numerator: u32, denominator: u32) -> Result<Bernoulli, BernoulliError> {
-        if numerator > denominator {
+        if numerator > denominator || denominator == 0 {
             return Err(BernoulliError::InvalidProbability);
         }
         if numerator == denominator {
diff --git a/src/distributions/mod.rs b/src/distributions/mod.rs
index 5091d3ba8ab..7a1e7629aa0 100644
--- a/src/distributions/mod.rs
+++ b/src/distributions/mod.rs
@@ -31,14 +31,14 @@
 //! # The `Standard` distribution
 //!
 //! The [`Standard`] distribution is important to mention. This is the
-//! distribution used by [`Rng::gen()`] and represents the "default" way to
+//! distribution used by [`Rng::gen`] and represents the "default" way to
 //! produce a random value for many different types, including most primitive
 //! types, tuples, arrays, and a few derived types. See the documentation of
 //! [`Standard`] for more details.
 //!
 //! Implementing `Distribution<T>` for [`Standard`] for user types `T` makes it
-//! possible to generate type `T` with [`Rng::gen()`], and by extension also
-//! with the [`random()`] function.
+//! possible to generate type `T` with [`Rng::gen`], and by extension also
+//! with the [`random`] function.
 //!
 //! ## Random characters
 //! 
@@ -89,15 +89,7 @@
 //! [`rand_distr`]: https://crates.io/crates/rand_distr
 //! [`statrs`]: https://crates.io/crates/statrs
 
-//! [`Alphanumeric`]: distributions::Alphanumeric
-//! [`Bernoulli`]: distributions::Bernoulli
-//! [`Open01`]: distributions::Open01
-//! [`OpenClosed01`]: distributions::OpenClosed01
-//! [`Standard`]: distributions::Standard
-//! [`Uniform`]: distributions::Uniform
-//! [`Uniform::new`]: distributions::Uniform::new
-//! [`Uniform::new_inclusive`]: distributions::Uniform::new_inclusive
-//! [`weighted`]: distributions::weighted
+//! [`random`]: crate::random
 //! [`rand_distr`]: https://crates.io/crates/rand_distr
 //! [`statrs`]: https://crates.io/crates/statrs
 
diff --git a/src/rngs/mod.rs b/src/rngs/mod.rs
index abf3243c10f..1d9f5185d6e 100644
--- a/src/rngs/mod.rs
+++ b/src/rngs/mod.rs
@@ -84,13 +84,11 @@
 //! Some suggestions are: [`rand_chacha`], [`rand_pcg`], [`rand_xoshiro`].
 //! A full list can be found by searching for crates with the [`rng` tag].
 //!
-//! [`SmallRng`]: rngs::SmallRng
-//! [`StdRng`]: rngs::StdRng
-//! [`OsRng`]: rngs::OsRng
-//! [`ThreadRng`]: rngs::ThreadRng
-//! [`mock::StepRng`]: rngs::mock::StepRng
-//! [`adapter::ReadRng`]: rngs::adapter::ReadRng
-//! [`adapter::ReseedingRng`]: rngs::adapter::ReseedingRng
+//! [`Rng`]: crate::Rng
+//! [`RngCore`]: crate::RngCore
+//! [`CryptoRng`]: crate::CryptoRng
+//! [`SeedableRng`]: crate::SeedableRng
+//! [`thread_rng`]: crate::thread_rng
 //! [`rdrand`]: https://crates.io/crates/rdrand
 //! [`rand_jitter`]: https://crates.io/crates/rand_jitter
 //! [`rand_chacha`]: https://crates.io/crates/rand_chacha
diff --git a/src/rngs/std.rs b/src/rngs/std.rs
index 8ebe6b8ec1f..6d02c2d3891 100644
--- a/src/rngs/std.rs
+++ b/src/rngs/std.rs
@@ -22,8 +22,7 @@ pub(crate) use rand_chacha::ChaCha20Core as Core;
 /// on the current platform, to be statistically strong and unpredictable
 /// (meaning a cryptographically secure PRNG).
 ///
-/// The current algorithm used is the ChaCha block cipher with either 20 or 12
-/// rounds (see the `stdrng_*` feature flags, documented in the README).
+/// The current algorithm used is the ChaCha block cipher with 20 rounds.
 /// This may change as new evidence of cipher security and performance
 /// becomes available.
 ///
diff --git a/src/seq/mod.rs b/src/seq/mod.rs
index ea28ce33511..91f6c2808f1 100644
--- a/src/seq/mod.rs
+++ b/src/seq/mod.rs
@@ -10,15 +10,15 @@
 //! 
 //! This module provides:
 //! 
-//! *   [`seq::SliceRandom`] slice sampling and mutation
-//! *   [`seq::IteratorRandom`] iterator sampling
-//! *   [`seq::index::sample`] low-level API to choose multiple indices from
+//! *   [`SliceRandom`] slice sampling and mutation
+//! *   [`IteratorRandom`] iterator sampling
+//! *   [`index::sample`] low-level API to choose multiple indices from
 //!     `0..length`
 //! 
 //! Also see:
 //! 
-//! *   [`distributions::weighted`] module which provides implementations of
-//!     weighted index sampling.
+//! *   [`crate::distributions::weighted`] module which provides
+//!     implementations of weighted index sampling.
 //! 
 //! In order to make results reproducible across 32-64 bit architectures, all
 //! `usize` indices are sampled as a `u32` where possible (also providing a