diff --git a/core/src/num/f32.rs b/core/src/num/f32.rs
index 29b36521f..6548ad2e5 100644
--- a/core/src/num/f32.rs
+++ b/core/src/num/f32.rs
@@ -393,6 +393,15 @@ impl f32 {
     pub const MAX_10_EXP: i32 = 38;
 
     /// Not a Number (NaN).
+    ///
+    /// Note that IEEE-745 doesn't define just a single NaN value;
+    /// a plethora of bit patterns are considered to be NaN.
+    /// Furthermore, the standard makes a difference
+    /// between a "signaling" and a "quiet" NaN,
+    /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
+    /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
+    /// and the stability of its representation over Rust versions
+    /// and target platforms isn't guaranteed.
     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
     pub const NAN: f32 = 0.0_f32 / 0.0_f32;
     /// Infinity (∞).
@@ -402,7 +411,7 @@ impl f32 {
     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
     pub const NEG_INFINITY: f32 = -1.0_f32 / 0.0_f32;
 
-    /// Returns `true` if this value is `NaN`.
+    /// Returns `true` if this value is NaN.
     ///
     /// ```
     /// let nan = f32::NAN;
@@ -455,7 +464,7 @@ impl f32 {
         (self == f32::INFINITY) | (self == f32::NEG_INFINITY)
     }
 
-    /// Returns `true` if this number is neither infinite nor `NaN`.
+    /// Returns `true` if this number is neither infinite nor NaN.
     ///
     /// ```
     /// let f = 7.0f32;
@@ -506,7 +515,7 @@ impl f32 {
     }
 
     /// Returns `true` if the number is neither zero, infinite,
-    /// [subnormal], or `NaN`.
+    /// [subnormal], or NaN.
     ///
     /// ```
     /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
@@ -622,8 +631,12 @@ impl f32 {
         }
     }
 
-    /// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
-    /// positive sign bit and positive infinity.
+    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
+    /// positive sign bit and positive infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_positive` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
     ///
     /// ```
     /// let f = 7.0_f32;
@@ -640,8 +653,12 @@ impl f32 {
         !self.is_sign_negative()
     }
 
-    /// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
-    /// negative sign bit and negative infinity.
+    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
+    /// negative sign bit and negative infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_negative` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
     ///
     /// ```
     /// let f = 7.0f32;
@@ -713,10 +730,12 @@ impl f32 {
         self * (value / 180.0f32)
     }
 
-    /// Returns the maximum of the two numbers.
+    /// Returns the maximum of the two numbers, ignoring NaN.
     ///
-    /// Follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs.
-    /// This matches the behavior of libm’s fmax.
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmax.
     ///
     /// ```
     /// let x = 1.0f32;
@@ -724,8 +743,6 @@ impl f32 {
     ///
     /// assert_eq!(x.max(y), y);
     /// ```
-    ///
-    /// If one of the arguments is NaN, then the other argument is returned.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
@@ -733,10 +750,12 @@ impl f32 {
         intrinsics::maxnumf32(self, other)
     }
 
-    /// Returns the minimum of the two numbers.
+    /// Returns the minimum of the two numbers, ignoring NaN.
     ///
-    /// Follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs.
-    /// This matches the behavior of libm’s fmin.
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmin.
     ///
     /// ```
     /// let x = 1.0f32;
@@ -744,8 +763,6 @@ impl f32 {
     ///
     /// assert_eq!(x.min(y), x);
     /// ```
-    ///
-    /// If one of the arguments is NaN, then the other argument is returned.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
@@ -753,7 +770,7 @@ impl f32 {
         intrinsics::minnumf32(self, other)
     }
 
-    /// Returns the maximum of the two numbers, propagating NaNs.
+    /// Returns the maximum of the two numbers, propagating NaN.
     ///
     /// This returns NaN when *either* argument is NaN, as opposed to
     /// [`f32::max`] which only returns NaN when *both* arguments are NaN.
@@ -770,6 +787,9 @@ impl f32 {
     /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
     /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
     /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[unstable(feature = "float_minimum_maximum", issue = "91079")]
     #[inline]
@@ -785,7 +805,7 @@ impl f32 {
         }
     }
 
-    /// Returns the minimum of the two numbers, propagating NaNs.
+    /// Returns the minimum of the two numbers, propagating NaN.
     ///
     /// This returns NaN when *either* argument is NaN, as opposed to
     /// [`f32::min`] which only returns NaN when *both* arguments are NaN.
@@ -802,6 +822,9 @@ impl f32 {
     /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
     /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
     /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[unstable(feature = "float_minimum_maximum", issue = "91079")]
     #[inline]
@@ -1009,6 +1032,9 @@ impl f32 {
     /// Return the memory representation of this floating point number as a byte array in
     /// big-endian (network) byte order.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1027,6 +1053,9 @@ impl f32 {
     /// Return the memory representation of this floating point number as a byte array in
     /// little-endian byte order.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1051,6 +1080,9 @@ impl f32 {
     /// [`to_be_bytes`]: f32::to_be_bytes
     /// [`to_le_bytes`]: f32::to_le_bytes
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1075,6 +1107,9 @@ impl f32 {
 
     /// Create a floating point value from its representation as a byte array in big endian.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1091,6 +1126,9 @@ impl f32 {
 
     /// Create a floating point value from its representation as a byte array in little endian.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1114,6 +1152,9 @@ impl f32 {
     /// [`from_be_bytes`]: f32::from_be_bytes
     /// [`from_le_bytes`]: f32::from_le_bytes
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
diff --git a/core/src/num/f64.rs b/core/src/num/f64.rs
index b8780235e..75c92c2f8 100644
--- a/core/src/num/f64.rs
+++ b/core/src/num/f64.rs
@@ -392,6 +392,15 @@ impl f64 {
     pub const MAX_10_EXP: i32 = 308;
 
     /// Not a Number (NaN).
+    ///
+    /// Note that IEEE-745 doesn't define just a single NaN value;
+    /// a plethora of bit patterns are considered to be NaN.
+    /// Furthermore, the standard makes a difference
+    /// between a "signaling" and a "quiet" NaN,
+    /// and allows inspecting its "payload" (the unspecified bits in the bit pattern).
+    /// This constant isn't guaranteed to equal to any specific NaN bitpattern,
+    /// and the stability of its representation over Rust versions
+    /// and target platforms isn't guaranteed.
     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
     pub const NAN: f64 = 0.0_f64 / 0.0_f64;
     /// Infinity (∞).
@@ -401,7 +410,7 @@ impl f64 {
     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
     pub const NEG_INFINITY: f64 = -1.0_f64 / 0.0_f64;
 
-    /// Returns `true` if this value is `NaN`.
+    /// Returns `true` if this value is NaN.
     ///
     /// ```
     /// let nan = f64::NAN;
@@ -456,7 +465,7 @@ impl f64 {
         (self == f64::INFINITY) | (self == f64::NEG_INFINITY)
     }
 
-    /// Returns `true` if this number is neither infinite nor `NaN`.
+    /// Returns `true` if this number is neither infinite nor NaN.
     ///
     /// ```
     /// let f = 7.0f64;
@@ -507,7 +516,7 @@ impl f64 {
     }
 
     /// Returns `true` if the number is neither zero, infinite,
-    /// [subnormal], or `NaN`.
+    /// [subnormal], or NaN.
     ///
     /// ```
     /// let min = f64::MIN_POSITIVE; // 2.2250738585072014e-308f64
@@ -614,8 +623,12 @@ impl f64 {
         }
     }
 
-    /// Returns `true` if `self` has a positive sign, including `+0.0`, `NaN`s with
-    /// positive sign bit and positive infinity.
+    /// Returns `true` if `self` has a positive sign, including `+0.0`, NaNs with
+    /// positive sign bit and positive infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_positive` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
     ///
     /// ```
     /// let f = 7.0_f64;
@@ -641,8 +654,12 @@ impl f64 {
         self.is_sign_positive()
     }
 
-    /// Returns `true` if `self` has a negative sign, including `-0.0`, `NaN`s with
-    /// negative sign bit and negative infinity.
+    /// Returns `true` if `self` has a negative sign, including `-0.0`, NaNs with
+    /// negative sign bit and negative infinity. Note that IEEE-745 doesn't assign any
+    /// meaning to the sign bit in case of a NaN, and as Rust doesn't guarantee that
+    /// the bit pattern of NaNs are conserved over arithmetic operations, the result of
+    /// `is_sign_negative` on a NaN might produce an unexpected result in some cases.
+    /// See [explanation of NaN as a special value](f32) for more info.
     ///
     /// ```
     /// let f = 7.0_f64;
@@ -724,10 +741,12 @@ impl f64 {
         self * (value / 180.0)
     }
 
-    /// Returns the maximum of the two numbers.
+    /// Returns the maximum of the two numbers, ignoring NaN.
     ///
-    /// Follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs.
-    /// This matches the behavior of libm’s fmax.
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for maxNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids maxNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmax.
     ///
     /// ```
     /// let x = 1.0_f64;
@@ -735,8 +754,6 @@ impl f64 {
     ///
     /// assert_eq!(x.max(y), y);
     /// ```
-    ///
-    /// If one of the arguments is NaN, then the other argument is returned.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
@@ -744,10 +761,12 @@ impl f64 {
         intrinsics::maxnumf64(self, other)
     }
 
-    /// Returns the minimum of the two numbers.
+    /// Returns the minimum of the two numbers, ignoring NaN.
     ///
-    /// Follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs.
-    /// This matches the behavior of libm’s fmin.
+    /// If one of the arguments is NaN, then the other argument is returned.
+    /// This follows the IEEE-754 2008 semantics for minNum, except for handling of signaling NaNs;
+    /// this function handles all NaNs the same way and avoids minNum's problems with associativity.
+    /// This also matches the behavior of libm’s fmin.
     ///
     /// ```
     /// let x = 1.0_f64;
@@ -755,8 +774,6 @@ impl f64 {
     ///
     /// assert_eq!(x.min(y), x);
     /// ```
-    ///
-    /// If one of the arguments is NaN, then the other argument is returned.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[stable(feature = "rust1", since = "1.0.0")]
     #[inline]
@@ -764,7 +781,7 @@ impl f64 {
         intrinsics::minnumf64(self, other)
     }
 
-    /// Returns the maximum of the two numbers, propagating NaNs.
+    /// Returns the maximum of the two numbers, propagating NaN.
     ///
     /// This returns NaN when *either* argument is NaN, as opposed to
     /// [`f64::max`] which only returns NaN when *both* arguments are NaN.
@@ -781,6 +798,9 @@ impl f64 {
     /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the greater
     /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
     /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[unstable(feature = "float_minimum_maximum", issue = "91079")]
     #[inline]
@@ -796,7 +816,7 @@ impl f64 {
         }
     }
 
-    /// Returns the minimum of the two numbers, propagating NaNs.
+    /// Returns the minimum of the two numbers, propagating NaN.
     ///
     /// This returns NaN when *either* argument is NaN, as opposed to
     /// [`f64::min`] which only returns NaN when *both* arguments are NaN.
@@ -813,6 +833,9 @@ impl f64 {
     /// If one of the arguments is NaN, then NaN is returned. Otherwise this returns the lesser
     /// of the two numbers. For this operation, -0.0 is considered to be less than +0.0.
     /// Note that this follows the semantics specified in IEEE 754-2019.
+    ///
+    /// Also note that "propagation" of NaNs here doesn't necessarily mean that the bitpattern of a NaN
+    /// operand is conserved; see [explanation of NaN as a special value](f32) for more info.
     #[must_use = "this returns the result of the comparison, without modifying either input"]
     #[unstable(feature = "float_minimum_maximum", issue = "91079")]
     #[inline]
@@ -1007,6 +1030,9 @@ impl f64 {
     /// Return the memory representation of this floating point number as a byte array in
     /// big-endian (network) byte order.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1025,6 +1051,9 @@ impl f64 {
     /// Return the memory representation of this floating point number as a byte array in
     /// little-endian byte order.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1049,6 +1078,9 @@ impl f64 {
     /// [`to_be_bytes`]: f64::to_be_bytes
     /// [`to_le_bytes`]: f64::to_le_bytes
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1073,6 +1105,9 @@ impl f64 {
 
     /// Create a floating point value from its representation as a byte array in big endian.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1089,6 +1124,9 @@ impl f64 {
 
     /// Create a floating point value from its representation as a byte array in little endian.
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
@@ -1112,6 +1150,9 @@ impl f64 {
     /// [`from_be_bytes`]: f64::from_be_bytes
     /// [`from_le_bytes`]: f64::from_le_bytes
     ///
+    /// See [`from_bits`](Self::from_bits) for some discussion of the
+    /// portability of this operation (there are almost no issues).
+    ///
     /// # Examples
     ///
     /// ```
diff --git a/core/src/primitive_docs.rs b/core/src/primitive_docs.rs
index 225a679ef..ac4e66811 100644
--- a/core/src/primitive_docs.rs
+++ b/core/src/primitive_docs.rs
@@ -977,10 +977,22 @@ mod prim_tuple {}
 ///   like `1.0 / 0.0`.
 /// - [NaN (not a number)](#associatedconstant.NAN): this value results from
 ///   calculations like `(-1.0).sqrt()`. NaN has some potentially unexpected
-///   behavior: it is unequal to any float, including itself! It is also neither
-///   smaller nor greater than any float, making it impossible to sort. Lastly,
-///   it is considered infectious as almost all calculations where one of the
-///   operands is NaN will also result in NaN.
+///   behavior:
+///   - It is unequal to any float, including itself! This is the reason `f32`
+///     doesn't implement the `Eq` trait.
+///   - It is also neither smaller nor greater than any float, making it
+///     impossible to sort by the default comparison operation, which is the
+///     reason `f32` doesn't implement the `Ord` trait.
+///   - It is also considered *infectious* as almost all calculations where one
+///     of the operands is NaN will also result in NaN. The explanations on this
+///     page only explicitly document behavior on NaN operands if this default
+///     is deviated from.
+///   - Lastly, there are multiple bit patterns that are considered NaN.
+///     Rust does not currently guarantee that the bit patterns of NaN are
+///     preserved over arithmetic operations, and they are not guaranteed to be
+///     portable or even fully deterministic! This means that there may be some
+///     surprising results upon inspecting the bit patterns,
+///     as the same calculations might produce NaNs with different bit patterns.
 ///
 /// For more information on floating point numbers, see [Wikipedia][wikipedia].
 ///
diff --git a/std/src/f32.rs b/std/src/f32.rs
index 557c59dfb..933b52b4d 100644
--- a/std/src/f32.rs
+++ b/std/src/f32.rs
@@ -29,7 +29,7 @@ pub use core::f32::{
 
 #[cfg(not(test))]
 impl f32 {
-    /// Returns the largest integer less than or equal to a number.
+    /// Returns the largest integer less than or equal to `self`.
     ///
     /// # Examples
     ///
@@ -50,7 +50,7 @@ impl f32 {
         unsafe { intrinsics::floorf32(self) }
     }
 
-    /// Returns the smallest integer greater than or equal to a number.
+    /// Returns the smallest integer greater than or equal to `self`.
     ///
     /// # Examples
     ///
@@ -69,7 +69,7 @@ impl f32 {
         unsafe { intrinsics::ceilf32(self) }
     }
 
-    /// Returns the nearest integer to a number. Round half-way cases away from
+    /// Returns the nearest integer to `self`. Round half-way cases away from
     /// `0.0`.
     ///
     /// # Examples
@@ -89,7 +89,8 @@ impl f32 {
         unsafe { intrinsics::roundf32(self) }
     }
 
-    /// Returns the integer part of a number.
+    /// Returns the integer part of `self`.
+    /// This means that non-integer numbers are always truncated towards zero.
     ///
     /// # Examples
     ///
@@ -110,7 +111,7 @@ impl f32 {
         unsafe { intrinsics::truncf32(self) }
     }
 
-    /// Returns the fractional part of a number.
+    /// Returns the fractional part of `self`.
     ///
     /// # Examples
     ///
@@ -131,8 +132,7 @@ impl f32 {
         self - self.trunc()
     }
 
-    /// Computes the absolute value of `self`. Returns `NAN` if the
-    /// number is `NAN`.
+    /// Computes the absolute value of `self`.
     ///
     /// # Examples
     ///
@@ -160,7 +160,7 @@ impl f32 {
     ///
     /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
     /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
-    /// - `NAN` if the number is `NAN`
+    /// - NaN if the number is NaN
     ///
     /// # Examples
     ///
@@ -184,8 +184,10 @@ impl f32 {
     /// `sign`.
     ///
     /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
-    /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
-    /// `sign` is returned.
+    /// equal to `-self`. If `self` is a NaN, then a NaN with the sign bit of
+    /// `sign` is returned. Note, however, that conserving the sign bit on NaN
+    /// across arithmetical operations is not generally guaranteed.
+    /// See [explanation of NaN as a special value](primitive@f32) for more info.
     ///
     /// # Examples
     ///
@@ -298,7 +300,9 @@ impl f32 {
 
     /// Raises a number to an integer power.
     ///
-    /// Using this function is generally faster than using `powf`
+    /// Using this function is generally faster than using `powf`.
+    /// It might have a different sequence of rounding operations than `powf`,
+    /// so the results are not guaranteed to agree.
     ///
     /// # Examples
     ///
diff --git a/std/src/f64.rs b/std/src/f64.rs
index 6f322aea6..a9aa84f70 100644
--- a/std/src/f64.rs
+++ b/std/src/f64.rs
@@ -29,7 +29,7 @@ pub use core::f64::{
 
 #[cfg(not(test))]
 impl f64 {
-    /// Returns the largest integer less than or equal to a number.
+    /// Returns the largest integer less than or equal to `self`.
     ///
     /// # Examples
     ///
@@ -50,7 +50,7 @@ impl f64 {
         unsafe { intrinsics::floorf64(self) }
     }
 
-    /// Returns the smallest integer greater than or equal to a number.
+    /// Returns the smallest integer greater than or equal to `self`.
     ///
     /// # Examples
     ///
@@ -69,7 +69,7 @@ impl f64 {
         unsafe { intrinsics::ceilf64(self) }
     }
 
-    /// Returns the nearest integer to a number. Round half-way cases away from
+    /// Returns the nearest integer to `self`. Round half-way cases away from
     /// `0.0`.
     ///
     /// # Examples
@@ -89,7 +89,8 @@ impl f64 {
         unsafe { intrinsics::roundf64(self) }
     }
 
-    /// Returns the integer part of a number.
+    /// Returns the integer part of `self`.
+    /// This means that non-integer numbers are always truncated towards zero.
     ///
     /// # Examples
     ///
@@ -110,7 +111,7 @@ impl f64 {
         unsafe { intrinsics::truncf64(self) }
     }
 
-    /// Returns the fractional part of a number.
+    /// Returns the fractional part of `self`.
     ///
     /// # Examples
     ///
@@ -131,8 +132,7 @@ impl f64 {
         self - self.trunc()
     }
 
-    /// Computes the absolute value of `self`. Returns `NAN` if the
-    /// number is `NAN`.
+    /// Computes the absolute value of `self`.
     ///
     /// # Examples
     ///
@@ -160,7 +160,7 @@ impl f64 {
     ///
     /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
     /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
-    /// - `NAN` if the number is `NAN`
+    /// - NaN if the number is NaN
     ///
     /// # Examples
     ///
@@ -184,8 +184,10 @@ impl f64 {
     /// `sign`.
     ///
     /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
-    /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
-    /// `sign` is returned.
+    /// equal to `-self`. If `self` is a NaN, then a NaN with the sign bit of
+    /// `sign` is returned. Note, however, that conserving the sign bit on NaN
+    /// across arithmetical operations is not generally guaranteed.
+    /// See [explanation of NaN as a special value](primitive@f32) for more info.
     ///
     /// # Examples
     ///
@@ -298,7 +300,9 @@ impl f64 {
 
     /// Raises a number to an integer power.
     ///
-    /// Using this function is generally faster than using `powf`
+    /// Using this function is generally faster than using `powf`.
+    /// It might have a different sequence of rounding operations than `powf`,
+    /// so the results are not guaranteed to agree.
     ///
     /// # Examples
     ///
diff --git a/std/src/primitive_docs.rs b/std/src/primitive_docs.rs
index 225a679ef..ac4e66811 100644
--- a/std/src/primitive_docs.rs
+++ b/std/src/primitive_docs.rs
@@ -977,10 +977,22 @@ mod prim_tuple {}
 ///   like `1.0 / 0.0`.
 /// - [NaN (not a number)](#associatedconstant.NAN): this value results from
 ///   calculations like `(-1.0).sqrt()`. NaN has some potentially unexpected
-///   behavior: it is unequal to any float, including itself! It is also neither
-///   smaller nor greater than any float, making it impossible to sort. Lastly,
-///   it is considered infectious as almost all calculations where one of the
-///   operands is NaN will also result in NaN.
+///   behavior:
+///   - It is unequal to any float, including itself! This is the reason `f32`
+///     doesn't implement the `Eq` trait.
+///   - It is also neither smaller nor greater than any float, making it
+///     impossible to sort by the default comparison operation, which is the
+///     reason `f32` doesn't implement the `Ord` trait.
+///   - It is also considered *infectious* as almost all calculations where one
+///     of the operands is NaN will also result in NaN. The explanations on this
+///     page only explicitly document behavior on NaN operands if this default
+///     is deviated from.
+///   - Lastly, there are multiple bit patterns that are considered NaN.
+///     Rust does not currently guarantee that the bit patterns of NaN are
+///     preserved over arithmetic operations, and they are not guaranteed to be
+///     portable or even fully deterministic! This means that there may be some
+///     surprising results upon inspecting the bit patterns,
+///     as the same calculations might produce NaNs with different bit patterns.
 ///
 /// For more information on floating point numbers, see [Wikipedia][wikipedia].
 ///