Use radsort for Transparent2d PhaseItem sorting (#9882)

# Objective

Fix a performance regression in the "[bevy vs
pixi](https://github.com/SUPERCILEX/bevy-vs-pixi)" benchmark.

This benchmark seems to have a slightly pathological distribution of `z`
values -- Sprites are spawned with a random `z` value with a child
sprite at `f32::EPSILON` relative to the parent.

See discussion here:
#8100 (comment)

## Solution

Use `radsort` for sorting `Transparent2d` `PhaseItem`s.

Use random `z` values in bevymark to stress the phase sort. Add an
`--ordered-z` option to `bevymark` that uses the old behavior.

## Benchmarks

mac m1 max

| benchmark | fps before | fps after | diff |
| - | - | - | - |
| bevymark --waves 120 --per-wave 1000 --random-z | 42.16 | 47.06 | 🟩
+11.6% |
| bevymark --waves 120 --per-wave 1000 | 52.50 | 52.29 | 🟥 -0.4% |
| bevymark --waves 120 --per-wave 1000 --mode mesh2d --random-z | 9.64 |
10.24 | 🟩 +6.2% |
| bevymark --waves 120 --per-wave 1000 --mode mesh2d | 15.83 | 15.59 | 🟥
-1.5% |
| bevy-vs-pixi | 39.71 | 59.88 | 🟩 +50.1% |

## Discussion

It's possible that `TransparentUi` should also change. We could probably
use `slice::sort_unstable_by_key` with the current sort key though, as
its items are always sorted and unique. I'd prefer to follow up later to
look into that.

Here's a survey of sorts used by other `PhaseItem`s

#### slice::sort_by_key
`Transparent2d`, `TransparentUi`

#### radsort
`Opaque3d`, `AlphaMask3d`, `Transparent3d`, `Opaque3dPrepass`,
`AlphaMask3dPrepass`, `Shadow`

I also tried `slice::sort_unstable_by_key` with a compound sort key
including `Entity`, but it didn't seem as promising and I didn't test it
as thoroughly.

---------

Co-authored-by: Alice Cecile <alice.i.cecile@gmail.com>
Co-authored-by: Robert Swain <robert.swain@gmail.com>

crates/bevy_core_pipeline/src/core_2d/mod.rs

@@ -106,7 +106,8 @@ impl PhaseItem for Transparent2d {
 
     #[inline]
     fn sort(items: &mut [Self]) {
-        items.sort_by_key(|item| item.sort_key());
+        // radsort is a stable radix sort that performed better than `slice::sort_by_key` or `slice::sort_unstable_by_key`.
+        radsort::sort_by_key(items, |item| item.sort_key().0);
     }
 
     #[inline]

crates/bevy_sprite/Cargo.toml

@@ -31,3 +31,4 @@ guillotiere = "0.6.0"
 thiserror = "1.0"
 rectangle-pack = "0.4"
 bitflags = "2.3"
+radsort = "0.1"

examples/stress_tests/bevymark.rs

@@ -60,6 +60,10 @@ struct Args {
     /// the number of different textures from which to randomly select the material color. 0 means no textures.
     #[argh(option, default = "1")]
     material_texture_count: usize,
+
+    /// generate z values in increasing order rather than randomly
+    #[argh(switch)]
+    ordered_z: bool,
 }
 
 #[derive(Default, Clone)]
@@ -163,6 +167,7 @@ struct BirdResources {
     color_rng: StdRng,
     material_rng: StdRng,
     velocity_rng: StdRng,
+    transform_rng: StdRng,
 }
 
 #[derive(Component)]
@@ -204,6 +209,7 @@ fn setup(
         color_rng: StdRng::seed_from_u64(42),
         material_rng: StdRng::seed_from_u64(42),
         velocity_rng: StdRng::seed_from_u64(42),
+        transform_rng: StdRng::seed_from_u64(42),
     };
 
     let text_section = move |color, value: &str| {
@@ -360,7 +366,12 @@ fn spawn_birds(
         Mode::Sprite => {
             let batch = (0..spawn_count)
                 .map(|count| {
-                    let bird_z = (current_count + count) as f32 * 0.00001;
+                    let bird_z = if args.ordered_z {
+                        (current_count + count) as f32 * 0.00001
+                    } else {
+                        bird_resources.transform_rng.gen::<f32>()
+                    };
+
                     let (transform, velocity) = bird_velocity_transform(
                         half_extents,
                         Vec3::new(bird_x, bird_y, bird_z),
@@ -398,7 +409,12 @@ fn spawn_birds(
         Mode::Mesh2d => {
             let batch = (0..spawn_count)
                 .map(|count| {
-                    let bird_z = (current_count + count) as f32 * 0.00001;
+                    let bird_z = if args.ordered_z {
+                        (current_count + count) as f32 * 0.00001
+                    } else {
+                        bird_resources.transform_rng.gen::<f32>()
+                    };
+
                     let (transform, velocity) = bird_velocity_transform(
                         half_extents,
                         Vec3::new(bird_x, bird_y, bird_z),