Avoid sorting all paths in the format command (#8181)

## Summary

Related to #8135.

If we're not printing a `--diff`, or a summary of `--check` changes, we
can avoid sorting the list of results. Further, when sorting, we only
need to sort a small subset of the entries, in the common case (i.e., in
general, it's much more likely that a file is formatted than not).

## Test Plan

Local benchmarks suggest a 5-10% speedup on the cached behavior:

```
❯ hyperfine --warmup 3 "./target/release/ruff format ../airflow" "./target/release/sort format ../airflow"
Benchmark 1: ./target/release/ruff format ../airflow
  Time (mean ± σ):      70.3 ms ±   5.2 ms    [User: 52.1 ms, System: 59.0 ms]
  Range (min … max):    68.3 ms … 101.7 ms    42 runs

  Warning: Statistical outliers were detected. Consider re-running this benchmark on a quiet PC without any interferences from other programs. It might help to use the '--warmup' or '--prepare' options.

Benchmark 2: ./target/release/sort format ../airflow
  Time (mean ± σ):      66.0 ms ±   1.4 ms    [User: 48.3 ms, System: 58.4 ms]
  Range (min … max):    64.7 ms …  71.8 ms    44 runs

  Warning: Statistical outliers were detected. Consider re-running this benchmark on a quiet PC without any interferences from other programs. It might help to use the '--warmup' or '--prepare' options.

Summary
  './target/release/sort format ../airflow' ran
    1.07 ± 0.08 times faster than './target/release/ruff format ../airflow'
```

crates/ruff_cli/src/commands/format.rs

@@ -107,7 +107,7 @@ pub(crate) fn format(
     };
 
     let start = Instant::now();
-    let (mut results, mut errors): (Vec<_>, Vec<_>) = paths
+    let (results, mut errors): (Vec<_>, Vec<_>) = paths
         .par_iter()
         .filter_map(|entry| {
             match entry {
@@ -168,27 +168,6 @@ pub(crate) fn format(
         });
     let duration = start.elapsed();
 
-    // Make output deterministic, at least as long as we have a path
-    results.sort_unstable_by(|x, y| x.path.cmp(&y.path));
-    errors.sort_by(|x, y| {
-        fn get_key(error: &FormatCommandError) -> Option<&PathBuf> {
-            match &error {
-                FormatCommandError::Ignore(ignore) => {
-                    if let ignore::Error::WithPath { path, .. } = ignore {
-                        Some(path)
-                    } else {
-                        None
-                    }
-                }
-                FormatCommandError::Panic(path, _)
-                | FormatCommandError::Read(path, _)
-                | FormatCommandError::Format(path, _)
-                | FormatCommandError::Write(path, _) => path.as_ref(),
-            }
-        }
-        get_key(x).cmp(&get_key(y))
-    });
-
     debug!(
         "Formatted {} files in {:.2?}",
         results.len() + errors.len(),
@@ -198,15 +177,21 @@ pub(crate) fn format(
     caches.persist()?;
 
     // Report on any errors.
+    errors.sort_unstable_by(|a, b| a.path().cmp(&b.path()));
+
     for error in &errors {
         error!("{error}");
     }
 
-    results.sort_unstable_by(|a, b| a.path.cmp(&b.path));
     let results = FormatResults::new(results.as_slice(), mode);
-
-    if mode.is_diff() {
-        results.write_diff(&mut stdout().lock())?;
+    match mode {
+        FormatMode::Write => {}
+        FormatMode::Check => {
+            results.write_changed(&mut stdout().lock())?;
+        }
+        FormatMode::Diff => {
+            results.write_diff(&mut stdout().lock())?;
+        }
     }
 
     // Report on the formatting changes.
@@ -470,42 +455,62 @@ impl<'a> FormatResults<'a> {
         })
     }
 
+    /// Write a diff of the formatting changes to the given writer.
     fn write_diff(&self, f: &mut impl Write) -> io::Result<()> {
-        for result in self.results {
-            if let FormatResult::Diff {
-                unformatted,
-                formatted,
-            } = &result.result
-            {
-                let text_diff =
-                    TextDiff::from_lines(unformatted.source_code(), formatted.source_code());
-                let mut unified_diff = text_diff.unified_diff();
-                unified_diff.header(
-                    &fs::relativize_path(&result.path),
-                    &fs::relativize_path(&result.path),
-                );
-                unified_diff.to_writer(&mut *f)?;
-            }
+        for (path, unformatted, formatted) in self
+            .results
+            .iter()
+            .filter_map(|result| {
+                if let FormatResult::Diff {
+                    unformatted,
+                    formatted,
+                } = &result.result
+                {
+                    Some((result.path.as_path(), unformatted, formatted))
+                } else {
+                    None
+                }
+            })
+            .sorted_unstable_by_key(|(path, _, _)| *path)
+        {
+            let text_diff =
+                TextDiff::from_lines(unformatted.source_code(), formatted.source_code());
+            let mut unified_diff = text_diff.unified_diff();
+            unified_diff.header(&fs::relativize_path(path), &fs::relativize_path(path));
+            unified_diff.to_writer(&mut *f)?;
+        }
+
+        Ok(())
+    }
+
+    /// Write a list of the files that would be changed to the given writer.
+    fn write_changed(&self, f: &mut impl Write) -> io::Result<()> {
+        for path in self
+            .results
+            .iter()
+            .filter_map(|result| {
+                if result.result.is_formatted() {
+                    Some(result.path.as_path())
+                } else {
+                    None
+                }
+            })
+            .sorted_unstable()
+        {
+            writeln!(f, "Would reformat: {}", fs::relativize_path(path).bold())?;
         }
 
         Ok(())
     }
 
+    /// Write a summary of the formatting results to the given writer.
     fn write_summary(&self, f: &mut impl Write) -> io::Result<()> {
         // Compute the number of changed and unchanged files.
         let mut changed = 0u32;
         let mut unchanged = 0u32;
         for result in self.results {
             match &result.result {
                 FormatResult::Formatted => {
-                    // If we're running in check mode, report on any files that would be formatted.
-                    if self.mode.is_check() {
-                        writeln!(
-                            f,
-                            "Would reformat: {}",
-                            fs::relativize_path(&result.path).bold()
-                        )?;
-                    }
                     changed += 1;
                 }
                 FormatResult::Unchanged => unchanged += 1,
@@ -564,6 +569,24 @@ pub(crate) enum FormatCommandError {
     Write(Option<PathBuf>, SourceError),
 }
 
+impl FormatCommandError {
+    fn path(&self) -> Option<&Path> {
+        match self {
+            Self::Ignore(err) => {
+                if let ignore::Error::WithPath { path, .. } = err {
+                    Some(path.as_path())
+                } else {
+                    None
+                }
+            }
+            Self::Panic(path, _)
+            | Self::Read(path, _)
+            | Self::Format(path, _)
+            | Self::Write(path, _) => path.as_deref(),
+        }
+    }
+}
+
 impl Display for FormatCommandError {
     fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
         match self {