Consistent big O notation

RELEASES.md

@@ -4985,7 +4985,7 @@ Libraries
 - [Upgrade to Unicode 10.0.0][42999]
 - [Reimplemented `{f32, f64}::{min, max}` in Rust instead of using CMath.][42430]
 - [Skip the main thread's manual stack guard on Linux][43072]
-- [Iterator::nth for `ops::{Range, RangeFrom}` is now done in O(1) time][43077]
+- [Iterator::nth for `ops::{Range, RangeFrom}` is now done in *O*(1) time][43077]
 - [`#[repr(align(N))]` attribute max number is now 2^31 - 1.][43097] This was
   previously 2^15.
 - [`{OsStr, Path}::Display` now avoids allocations where possible][42613]
@@ -8288,7 +8288,7 @@ Libraries
   algorithm][s].
 * [`std::io::copy` allows `?Sized` arguments][cc].
 * The `Windows`, `Chunks`, and `ChunksMut` iterators over slices all
-  [override `count`, `nth` and `last` with an O(1)
+  [override `count`, `nth` and `last` with an *O*(1)
   implementation][it].
 * [`Default` is implemented for arrays up to `[T; 32]`][d].
 * [`IntoRawFd` has been added to the Unix-specific prelude,
@@ -8810,7 +8810,7 @@ Libraries
 * The `Default` implementation for `Arc` [no longer requires `Sync +
   Send`][arc].
 * [The `Iterator` methods `count`, `nth`, and `last` have been
-  overridden for slices to have O(1) performance instead of O(n)][si].
+  overridden for slices to have *O*(1) performance instead of *O*(*n*)][si].
 * Incorrect handling of paths on Windows has been improved in both the
   compiler and the standard library.
 * [`AtomicPtr` gained a `Default` implementation][ap].

compiler/rustc_data_structures/src/graph/scc/mod.rs

@@ -3,7 +3,7 @@
 //! Also computes as the resulting DAG if each SCC is replaced with a
 //! node in the graph. This uses [Tarjan's algorithm](
 //! https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm)
-//! that completes in *O(n)* time.
+//! that completes in *O*(*n*) time.
 
 use crate::fx::FxHashSet;
 use crate::graph::vec_graph::VecGraph;

compiler/rustc_data_structures/src/sorted_map.rs

@@ -9,7 +9,7 @@ mod index_map;
 pub use index_map::SortedIndexMultiMap;
 
 /// `SortedMap` is a data structure with similar characteristics as BTreeMap but
-/// slightly different trade-offs: lookup, insertion, and removal are O(log(N))
+/// slightly different trade-offs: lookup, insertion, and removal are *O*(log(*n*))
 /// and elements can be iterated in order cheaply.
 ///
 /// `SortedMap` can be faster than a `BTreeMap` for small sizes (<50) since it

library/alloc/src/collections/binary_heap.rs

@@ -3,7 +3,7 @@
 //! Insertion and popping the largest element have *O*(log(*n*)) time complexity.
 //! Checking the largest element is *O*(1). Converting a vector to a binary heap
 //! can be done in-place, and has *O*(*n*) complexity. A binary heap can also be
-//! converted to a sorted vector in-place, allowing it to be used for an *O*(*n* \* log(*n*))
+//! converted to a sorted vector in-place, allowing it to be used for an *O*(*n* * log(*n*))
 //! in-place heapsort.
 //!
 //! # Examples
@@ -243,9 +243,9 @@ use super::SpecExtend;
 ///
 /// # Time complexity
 ///
-/// | [push] | [pop]     | [peek]/[peek\_mut] |
-/// |--------|-----------|--------------------|
-/// | O(1)~  | *O*(log(*n*)) | *O*(1)               |
+/// | [push]  | [pop]         | [peek]/[peek\_mut] |
+/// |---------|---------------|--------------------|
+/// | *O*(1)~ | *O*(log(*n*)) | *O*(1)             |
 ///
 /// The value for `push` is an expected cost; the method documentation gives a
 /// more detailed analysis.

library/alloc/src/vec/mod.rs

@@ -1,8 +1,8 @@
 //! A contiguous growable array type with heap-allocated contents, written
 //! `Vec<T>`.
 //!
-//! Vectors have `O(1)` indexing, amortized `O(1)` push (to the end) and
-//! `O(1)` pop (from the end).
+//! Vectors have *O*(1) indexing, amortized *O*(1) push (to the end) and
+//! *O*(1) pop (from the end).
 //!
 //! Vectors ensure they never allocate more than `isize::MAX` bytes.
 //!
@@ -1268,7 +1268,7 @@ impl<T, A: Allocator> Vec<T, A> {
     ///
     /// The removed element is replaced by the last element of the vector.
     ///
-    /// This does not preserve ordering, but is O(1).
+    /// This does not preserve ordering, but is *O*(1).
     ///
     /// # Panics
     ///

library/core/src/iter/traits/iterator.rs

@@ -1798,10 +1798,11 @@ pub trait Iterator {
     /// The relative order of partitioned items is not maintained.
     ///
     /// # Current implementation
+    ///
     /// Current algorithms tries finding the first element for which the predicate evaluates
     /// to false, and the last element for which it evaluates to true and repeatedly swaps them.
     ///
-    /// Time Complexity: *O*(*N*)
+    /// Time complexity: *O*(*n*)
     ///
     /// See also [`is_partitioned()`] and [`partition()`].
     ///

library/std/src/collections/mod.rs

@@ -97,11 +97,11 @@
 //!
 //! ## Sequences
 //!
-//! |                | get(i)         | insert(i)       | remove(i)      | append | split_off(i)   |
-//! |----------------|----------------|-----------------|----------------|--------|----------------|
-//! | [`Vec`]        | O(1)           | O(n-i)*         | O(n-i)         | O(m)*  | O(n-i)         |
-//! | [`VecDeque`]   | O(1)           | O(min(i, n-i))* | O(min(i, n-i)) | O(m)*  | O(min(i, n-i)) |
-//! | [`LinkedList`] | O(min(i, n-i)) | O(min(i, n-i))  | O(min(i, n-i)) | O(1)   | O(min(i, n-i)) |
+//! |                | get(i)                 | insert(i)               | remove(i)              | append    | split_off(i)           |
+//! |----------------|------------------------|-------------------------|------------------------|-----------|------------------------|
+//! | [`Vec`]        | *O*(1)                 | *O*(*n*-*i*)*           | *O*(*n*-*i*)           | *O*(*m*)* | *O*(*n*-*i*)           |
+//! | [`VecDeque`]   | *O*(1)                 | *O*(min(*i*, *n*-*i*))* | *O*(min(*i*, *n*-*i*)) | *O*(*m*)* | *O*(min(*i*, *n*-*i*)) |
+//! | [`LinkedList`] | *O*(min(*i*, *n*-*i*)) | *O*(min(*i*, *n*-*i*))  | *O*(min(*i*, *n*-*i*)) | *O*(1)    | *O*(min(*i*, *n*-*i*)) |
 //!
 //! Note that where ties occur, [`Vec`] is generally going to be faster than [`VecDeque`], and
 //! [`VecDeque`] is generally going to be faster than [`LinkedList`].
@@ -110,10 +110,10 @@
 //!
 //! For Sets, all operations have the cost of the equivalent Map operation.
 //!
-//! |              | get       | insert    | remove    | range     | append |
-//! |--------------|-----------|-----------|-----------|-----------|--------|
-//! | [`HashMap`]  | O(1)~     | O(1)~*    | O(1)~     | N/A       | N/A    |
-//! | [`BTreeMap`] | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n+m) |
+//! |              | get           | insert        | remove        | range         | append       |
+//! |--------------|---------------|---------------|---------------|---------------|--------------|
+//! | [`HashMap`]  | *O*(1)~       | *O*(1)~*      | *O*(1)~       | N/A           | N/A          |
+//! | [`BTreeMap`] | *O*(log(*n*)) | *O*(log(*n*)) | *O*(log(*n*)) | *O*(log(*n*)) | *O*(*n*+*m*) |
 //!
 //! # Correct and Efficient Usage of Collections
 //!

library/std/src/ffi/mod.rs

@@ -43,8 +43,8 @@
 //! terminator, so the buffer length is really `len+1` characters.
 //! Rust strings don't have a nul terminator; their length is always
 //! stored and does not need to be calculated. While in Rust
-//! accessing a string's length is a `O(1)` operation (because the
-//! length is stored); in C it is an `O(length)` operation because the
+//! accessing a string's length is an *O*(1) operation (because the
+//! length is stored); in C it is an *O*(*n*) operation because the
 //! length needs to be computed by scanning the string for the nul
 //! terminator.
 //!

src/tools/clippy/clippy_lints/src/methods/mod.rs

@@ -995,7 +995,7 @@ declare_clippy_lint! {
 declare_clippy_lint! {
     /// ### What it does
     /// Checks for use of `.iter().nth()` (and the related
-    /// `.iter_mut().nth()`) on standard library types with O(1) element access.
+    /// `.iter_mut().nth()`) on standard library types with *O*(1) element access.
     ///
     /// ### Why is this bad?
     /// `.get()` and `.get_mut()` are more efficient and more