diff --git a/library/alloc/src/fmt.rs b/library/alloc/src/fmt.rs
index 501a6353b2c..73b75ea4d83 100644
--- a/library/alloc/src/fmt.rs
+++ b/library/alloc/src/fmt.rs
@@ -221,10 +221,12 @@
 //!
 //! 3. An asterisk `.*`:
 //!
-//!    `.*` means that this `{...}` is associated with *two* format inputs rather than one: the
-//!    first input holds the `usize` precision, and the second holds the value to print. Note that
-//!    in this case, if one uses the format string `{<arg>:<spec>.*}`, then the `<arg>` part refers
-//!    to the *value* to print, and the `precision` must come in the input preceding `<arg>`.
+//!    `.*` means that this `{...}` is associated with *two* format inputs rather than one:
+//!    - If a format string in the fashion of `{:<spec>.*}` is used, then the first input holds
+//!      the `usize` precision, and the second holds the value to print.
+//!    - If a format string in the fashion of `{<arg>:<spec>.*}` is used, then the `<arg>` part
+//!      refers to the value to print, and the `precision` is taken like it was specified with an
+//!      omitted positional parameter (`{}` instead of `{<arg>:}`).
 //!
 //! For example, the following calls all print the same thing `Hello x is 0.01000`:
 //!
@@ -238,15 +240,19 @@
 //! // Hello {arg 0 ("x")} is {arg 2 (0.01) with precision specified in arg 1 (5)}
 //! println!("Hello {0} is {2:.1$}", "x", 5, 0.01);
 //!
-//! // Hello {next arg ("x")} is {second of next two args (0.01) with precision
-//! //                          specified in first of next two args (5)}
+//! // Hello {next arg -> arg 0 ("x")} is {second of next two args -> arg 2 (0.01) with precision
+//! //                          specified in first of next two args -> arg 1 (5)}
 //! println!("Hello {} is {:.*}",    "x", 5, 0.01);
 //!
-//! // Hello {next arg ("x")} is {arg 2 (0.01) with precision
-//! //                          specified in its predecessor (5)}
+//! // Hello {arg 1 ("x")} is {arg 2 (0.01) with precision
+//! //                          specified in next arg -> arg 0 (5)}
+//! println!("Hello {1} is {2:.*}",  5, "x", 0.01);
+//!
+//! // Hello {next arg -> arg 0 ("x")} is {arg 2 (0.01) with precision
+//! //                          specified in next arg -> arg 1 (5)}
 //! println!("Hello {} is {2:.*}",   "x", 5, 0.01);
 //!
-//! // Hello {next arg ("x")} is {arg "number" (0.01) with precision specified
+//! // Hello {next arg -> arg 0 ("x")} is {arg "number" (0.01) with precision specified
 //! //                          in arg "prec" (5)}
 //! println!("Hello {} is {number:.prec$}", "x", prec = 5, number = 0.01);
 //! ```
@@ -304,7 +310,7 @@
 //! ```text
 //! format_string := text [ maybe_format text ] *
 //! maybe_format := '{' '{' | '}' '}' | format
-//! format := '{' [ argument ] [ ':' format_spec ] '}'
+//! format := '{' [ argument ] [ ':' format_spec ] [ ws ] * '}'
 //! argument := integer | identifier
 //!
 //! format_spec := [[fill]align][sign]['#']['0'][width]['.' precision]type
@@ -317,7 +323,12 @@
 //! count := parameter | integer
 //! parameter := argument '$'
 //! ```
-//! In the above grammar, `text` must not contain any `'{'` or `'}'` characters.
+//! In the above grammar,
+//! - `text` must not contain any `'{'` or `'}'` characters,
+//! - `ws` is any character for which [`char::is_whitespace`] returns `true`, has no semantic
+//!   meaning and is completely optional,
+//! - `integer` is a decimal integer that may contain leading zeroes and
+//! - `identifier` is an `IDENTIFIER_OR_KEYWORD` (not an `IDENTIFIER`) as defined by the [Rust language reference](https://doc.rust-lang.org/reference/identifiers.html).
 //!
 //! # Formatting traits
 //!
@@ -358,9 +369,9 @@
 //! ```
 //!
 //! Your type will be passed as `self` by-reference, and then the function
-//! should emit output into the `f.buf` stream. It is up to each format trait
-//! implementation to correctly adhere to the requested formatting parameters.
-//! The values of these parameters will be listed in the fields of the
+//! should emit output into the Formatter `f` which implements `fmt::Write`. It is up to each
+//! format trait implementation to correctly adhere to the requested formatting parameters.
+//! The values of these parameters can be accessed with methods of the
 //! [`Formatter`] struct. In order to help with this, the [`Formatter`] struct also
 //! provides some helper methods.
 //!
@@ -449,7 +460,7 @@
 //!
 //! ```ignore (only-for-syntax-highlight)
 //! format!      // described above
-//! write!       // first argument is a &mut io::Write, the destination
+//! write!       // first argument is either a &mut io::Write or a &mut fmt::Write, the destination
 //! writeln!     // same as write but appends a newline
 //! print!       // the format string is printed to the standard output
 //! println!     // same as print but appends a newline
@@ -460,11 +471,11 @@
 //!
 //! ### `write!`
 //!
-//! This and [`writeln!`] are two macros which are used to emit the format string
+//! [`write!`] and [`writeln!`] are two macros which are used to emit the format string
 //! to a specified stream. This is used to prevent intermediate allocations of
 //! format strings and instead directly write the output. Under the hood, this
 //! function is actually invoking the [`write_fmt`] function defined on the
-//! [`std::io::Write`] trait. Example usage is:
+//! [`std::io::Write`] and the [`std::fmt::Write`] trait. Example usage is:
 //!
 //! ```
 //! # #![allow(unused_must_use)]
@@ -491,7 +502,7 @@
 //!
 //! ### `format_args!`
 //!
-//! This is a curious macro used to safely pass around
+//! [`format_args!`] is a curious macro used to safely pass around
 //! an opaque object describing the format string. This object
 //! does not require any heap allocations to create, and it only
 //! references information on the stack. Under the hood, all of
@@ -529,10 +540,12 @@
 //! [`to_string`]: crate::string::ToString::to_string "ToString::to_string"
 //! [`write_fmt`]: ../../std/io/trait.Write.html#method.write_fmt
 //! [`std::io::Write`]: ../../std/io/trait.Write.html
+//! [`std::fmt::Write`]: ../../std/fmt/trait.Write.html
 //! [`print!`]: ../../std/macro.print.html "print!"
 //! [`println!`]: ../../std/macro.println.html "println!"
 //! [`eprint!`]: ../../std/macro.eprint.html "eprint!"
 //! [`eprintln!`]: ../../std/macro.eprintln.html "eprintln!"
+//! [`format_args!`]: ../../std/macro.format_args.html "format_args!"
 //! [`fmt::Arguments`]: Arguments "fmt::Arguments"
 //! [`format`]: format() "fmt::format"