Add Exponential Moving Average into diagnostics (bevyengine#4992)

# Objective

- Add Time-Adjusted Rolling EMA-based smoothing to diagnostics.
- Closes bevyengine#4983; see that issue for more more information.

## Terms

- EMA - [Exponential Moving Average](https://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average)
- SMA - [Simple Moving Average](https://en.wikipedia.org/wiki/Moving_average#Simple_moving_average)

## Solution

- We use a fairly standard approximation of a true EMA where $EMA_{\text{frame}} = EMA_{\text{previous}} + \alpha \left( x_{\text{frame}} - EMA_{\text{previous}} \right)$ where $\alpha = \Delta t / \tau$ and $\tau$ is an arbitrary smoothness factor. (See bevyengine#4983 for more discussion of the math.)
- The smoothness factor is here defaulted to $2 / 21$; this was chosen fairly arbitrarily as supposedly related to the existing 20-bucket SMA.
- The smoothness factor can be set on a per-diagnostic basis via `Diagnostic::with_smoothing_factor`.

---

## Changelog

### Added

- `Diagnostic::smoothed` - provides an exponentially smoothed view of a recorded diagnostic, to e.g. reduce jitter in frametime readings.

### Changed
- `LogDiagnosticsPlugin` now records the smoothed value rather than the raw value.
  - For diagnostics recorded less often than every 0.1 seconds, this change to defaults will have no visible effect.
  - For discrete diagnostics where this smoothing is not desirable, set a smoothing factor of 0 to disable smoothing.
  - The average of the recent history is still shown when available.

crates/bevy_diagnostic/src/diagnostic.rs

@@ -37,6 +37,8 @@ pub struct Diagnostic {
     pub suffix: Cow<'static, str>,
     history: VecDeque<DiagnosticMeasurement>,
     sum: f64,
+    ema: f64,
+    ema_smoothing_factor: f64,
     max_history_length: usize,
     pub is_enabled: bool,
 }
@@ -45,6 +47,15 @@ impl Diagnostic {
     /// Add a new value as a [`DiagnosticMeasurement`]. Its timestamp will be [`Instant::now`].
     pub fn add_measurement(&mut self, value: f64) {
         let time = Instant::now();
+
+        if let Some(previous) = self.measurement() {
+            let delta = (time - previous.time).as_secs_f64();
+            let alpha = (delta / self.ema_smoothing_factor).clamp(0.0, 1.0);
+            self.ema += alpha * (value - self.ema);
+        } else {
+            self.ema = value;
+        }
+
         if self.max_history_length > 1 {
             if self.history.len() == self.max_history_length {
                 if let Some(removed_diagnostic) = self.history.pop_front() {
@@ -57,6 +68,7 @@ impl Diagnostic {
             self.history.clear();
             self.sum = value;
         }
+
         self.history
             .push_back(DiagnosticMeasurement { time, value });
     }
@@ -83,6 +95,8 @@ impl Diagnostic {
             history: VecDeque::with_capacity(max_history_length),
             max_history_length,
             sum: 0.0,
+            ema: 0.0,
+            ema_smoothing_factor: 2.0 / 21.0,
             is_enabled: true,
         }
     }
@@ -94,6 +108,22 @@ impl Diagnostic {
         self
     }
 
+    /// The smoothing factor used for the exponential smoothing used for
+    /// [`smoothed`](Self::smoothed).
+    ///
+    /// If measurements come in less fequently than `smoothing_factor` seconds
+    /// apart, no smoothing will be applied. As measurements come in more
+    /// frequently, the smoothing takes a greater effect such that it takes
+    /// approximately `smoothing_factor` seconds for 83% of an instantaneous
+    /// change in measurement to e reflected in the smoothed value.
+    ///
+    /// A smoothing factor of 0.0 will effectively disable smoothing.
+    #[must_use]
+    pub fn with_smoothing_factor(mut self, smoothing_factor: f64) -> Self {
+        self.ema_smoothing_factor = smoothing_factor;
+        self
+    }
+
     /// Get the latest measurement from this diagnostic.
     #[inline]
     pub fn measurement(&self) -> Option<&DiagnosticMeasurement> {
@@ -105,7 +135,7 @@ impl Diagnostic {
         self.measurement().map(|measurement| measurement.value)
     }
 
-    /// Return the mean (average) of this diagnostic's values.
+    /// Return the simple moving average of this diagnostic's recent values.
     /// N.B. this a cheap operation as the sum is cached.
     pub fn average(&self) -> Option<f64> {
         if !self.history.is_empty() {
@@ -115,6 +145,19 @@ impl Diagnostic {
         }
     }
 
+    /// Return the exponential moving average of this diagnostic.
+    ///
+    /// This is by default tuned to behave reasonably well for a typical
+    /// measurement that changes every frame such as frametime. This can be
+    /// adjusted using [`with_smoothing_factor`](Self::with_smoothing_factor).
+    pub fn smoothed(&self) -> Option<f64> {
+        if !self.history.is_empty() {
+            Some(self.ema)
+        } else {
+            None
+        }
+    }
+
     /// Return the number of elements for this diagnostic.
     pub fn history_len(&self) -> usize {
         self.history.len()

crates/bevy_diagnostic/src/frame_time_diagnostics_plugin.rs

@@ -25,7 +25,8 @@ impl FrameTimeDiagnosticsPlugin {
     pub fn setup_system(mut diagnostics: ResMut<Diagnostics>) {
         diagnostics.add(Diagnostic::new(Self::FRAME_TIME, "frame_time", 20).with_suffix("ms"));
         diagnostics.add(Diagnostic::new(Self::FPS, "fps", 20));
-        diagnostics.add(Diagnostic::new(Self::FRAME_COUNT, "frame_count", 1));
+        diagnostics
+            .add(Diagnostic::new(Self::FRAME_COUNT, "frame_count", 1).with_smoothing_factor(0.0));
     }
 
     pub fn diagnostic_system(

crates/bevy_diagnostic/src/log_diagnostics_plugin.rs

@@ -53,16 +53,16 @@ impl LogDiagnosticsPlugin {
     }
 
     fn log_diagnostic(diagnostic: &Diagnostic) {
-        if let Some(value) = diagnostic.value() {
+        if let Some(value) = diagnostic.smoothed() {
             if diagnostic.get_max_history_length() > 1 {
                 if let Some(average) = diagnostic.average() {
                     info!(
                         target: "bevy diagnostic",
-                        // Suffix is only used for 's' as in seconds currently,
-                        // so we reserve one column for it; however,
-                        // Do not reserve one column for the suffix in the average
+                        // Suffix is only used for 's' or 'ms' currently,
+                        // so we reserve two columns for it; however,
+                        // Do not reserve columns for the suffix in the average
                         // The ) hugging the value is more aesthetically pleasing
-                        "{name:<name_width$}: {value:>11.6}{suffix:1} (avg {average:>.6}{suffix:})",
+                        "{name:<name_width$}: {value:>11.6}{suffix:2} (avg {average:>.6}{suffix:})",
                         name = diagnostic.name,
                         suffix = diagnostic.suffix,
                         name_width = crate::MAX_DIAGNOSTIC_NAME_WIDTH,

examples/stress_tests/bevymark.rs

@@ -96,35 +96,28 @@ fn setup(mut commands: Commands, asset_server: Res<AssetServer>) {
 
     let texture = asset_server.load("branding/icon.png");
 
+    let text_section = move |color, value: &str| {
+        TextSection::new(
+            value,
+            TextStyle {
+                font: asset_server.load("fonts/FiraSans-Bold.ttf"),
+                font_size: 40.0,
+                color,
+            },
+        )
+    };
+
     commands.spawn(Camera2dBundle::default());
     commands.spawn((
         TextBundle::from_sections([
-            TextSection::new(
-                "Bird Count: ",
-                TextStyle {
-                    font: asset_server.load("fonts/FiraSans-Bold.ttf"),
-                    font_size: 40.0,
-                    color: Color::rgb(0.0, 1.0, 0.0),
-                },
-            ),
-            TextSection::from_style(TextStyle {
-                font: asset_server.load("fonts/FiraSans-Bold.ttf"),
-                font_size: 40.0,
-                color: Color::rgb(0.0, 1.0, 1.0),
-            }),
-            TextSection::new(
-                "\nAverage FPS: ",
-                TextStyle {
-                    font: asset_server.load("fonts/FiraSans-Bold.ttf"),
-                    font_size: 40.0,
-                    color: Color::rgb(0.0, 1.0, 0.0),
-                },
-            ),
-            TextSection::from_style(TextStyle {
-                font: asset_server.load("fonts/FiraSans-Bold.ttf"),
-                font_size: 40.0,
-                color: Color::rgb(0.0, 1.0, 1.0),
-            }),
+            text_section(Color::GREEN, "Bird Count"),
+            text_section(Color::CYAN, ""),
+            text_section(Color::GREEN, "\nFPS (raw): "),
+            text_section(Color::CYAN, ""),
+            text_section(Color::GREEN, "\nFPS (SMA): "),
+            text_section(Color::CYAN, ""),
+            text_section(Color::GREEN, "\nFPS (EMA): "),
+            text_section(Color::CYAN, ""),
         ])
         .with_style(Style {
             position_type: PositionType::Absolute,
@@ -261,8 +254,14 @@ fn counter_system(
     }
 
     if let Some(fps) = diagnostics.get(FrameTimeDiagnosticsPlugin::FPS) {
-        if let Some(average) = fps.average() {
-            text.sections[3].value = format!("{average:.2}");
+        if let Some(raw) = fps.value() {
+            text.sections[3].value = format!("{raw:.2}");
+        }
+        if let Some(sma) = fps.average() {
+            text.sections[5].value = format!("{sma:.2}");
+        }
+        if let Some(ema) = fps.smoothed() {
+            text.sections[7].value = format!("{ema:.2}");
         }
     };
 }

examples/ui/text.rs

@@ -93,9 +93,9 @@ fn text_color_system(time: Res<Time>, mut query: Query<&mut Text, With<ColorText
 fn text_update_system(diagnostics: Res<Diagnostics>, mut query: Query<&mut Text, With<FpsText>>) {
     for mut text in &mut query {
         if let Some(fps) = diagnostics.get(FrameTimeDiagnosticsPlugin::FPS) {
-            if let Some(average) = fps.average() {
+            if let Some(value) = fps.smoothed() {
                 // Update the value of the second section
-                text.sections[1].value = format!("{average:.2}");
+                text.sections[1].value = format!("{value:.2}");
             }
         }
     }

examples/ui/text_debug.rs

@@ -157,16 +157,16 @@ fn change_text_system(
     for mut text in &mut query {
         let mut fps = 0.0;
         if let Some(fps_diagnostic) = diagnostics.get(FrameTimeDiagnosticsPlugin::FPS) {
-            if let Some(fps_avg) = fps_diagnostic.average() {
-                fps = fps_avg;
+            if let Some(fps_smoothed) = fps_diagnostic.smoothed() {
+                fps = fps_smoothed;
             }
         }
 
         let mut frame_time = time.delta_seconds_f64();
         if let Some(frame_time_diagnostic) = diagnostics.get(FrameTimeDiagnosticsPlugin::FRAME_TIME)
         {
-            if let Some(frame_time_avg) = frame_time_diagnostic.average() {
-                frame_time = frame_time_avg;
+            if let Some(frame_time_smoothed) = frame_time_diagnostic.smoothed() {
+                frame_time = frame_time_smoothed;
             }
         }