# Objective
- Add Time-Adjusted Rolling EMA-based smoothing to diagnostics.
- Closes#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 #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`.
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## 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.
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