diff --git a/library/core/src/num/f128.rs b/library/core/src/num/f128.rs
index 08c34e852da4..d3d1eebc2275 100644
--- a/library/core/src/num/f128.rs
+++ b/library/core/src/num/f128.rs
@@ -224,14 +224,16 @@ impl f128 {
 
     /// Not a Number (NaN).
     ///
-    /// Note that IEEE 754 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.
+    /// Note that IEEE 754 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)
+    /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
+    /// info.
+    ///
+    /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
+    /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
+    /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
+    /// The concrete bit pattern may change across Rust versions and target platforms.
     #[allow(clippy::eq_op)]
     #[rustc_diagnostic_item = "f128_nan"]
     #[unstable(feature = "f128", issue = "116909")]
diff --git a/library/core/src/num/f16.rs b/library/core/src/num/f16.rs
index a33e5f530146..dceb30177e66 100644
--- a/library/core/src/num/f16.rs
+++ b/library/core/src/num/f16.rs
@@ -219,14 +219,16 @@ impl f16 {
 
     /// Not a Number (NaN).
     ///
-    /// Note that IEEE 754 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.
+    /// Note that IEEE 754 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)
+    /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
+    /// info.
+    ///
+    /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
+    /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
+    /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
+    /// The concrete bit pattern may change across Rust versions and target platforms.
     #[allow(clippy::eq_op)]
     #[rustc_diagnostic_item = "f16_nan"]
     #[unstable(feature = "f16", issue = "116909")]
diff --git a/library/core/src/num/f32.rs b/library/core/src/num/f32.rs
index e473fac03935..c97dbfb63ae1 100644
--- a/library/core/src/num/f32.rs
+++ b/library/core/src/num/f32.rs
@@ -470,14 +470,16 @@ impl f32 {
 
     /// Not a Number (NaN).
     ///
-    /// Note that IEEE 754 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.
+    /// Note that IEEE 754 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)
+    /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
+    /// info.
+    ///
+    /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
+    /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
+    /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
+    /// The concrete bit pattern may change across Rust versions and target platforms.
     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
     #[rustc_diagnostic_item = "f32_nan"]
     #[allow(clippy::eq_op)]
diff --git a/library/core/src/num/f64.rs b/library/core/src/num/f64.rs
index 6522a80b0b7e..91affdb3794b 100644
--- a/library/core/src/num/f64.rs
+++ b/library/core/src/num/f64.rs
@@ -469,14 +469,16 @@ impl f64 {
 
     /// Not a Number (NaN).
     ///
-    /// Note that IEEE 754 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.
+    /// Note that IEEE 754 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)
+    /// and its sign. See the [specification of NaN bit patterns](f32#nan-bit-patterns) for more
+    /// info.
+    ///
+    /// This constant is guaranteed to be a quiet NaN (on targets that follow the Rust assumptions
+    /// that the quiet/signaling bit being set to 1 indicates a quiet NaN). Beyond that, nothing is
+    /// guaranteed about the specific bit pattern chosen here: both payload and sign are arbitrary.
+    /// The concrete bit pattern may change across Rust versions and target platforms.
     #[rustc_diagnostic_item = "f64_nan"]
     #[stable(feature = "assoc_int_consts", since = "1.43.0")]
     #[allow(clippy::eq_op)]