# Problem

I didn’t expect `sleep(seconds)`

to be super accurate, but I must admit I was surprised over how inaccurate it is. See a benchmark below. Relative error of 10% for sleep times under 0.01 seconds is quite a lot, and may cause potential issues in, e.g., real-time control loops.

```
using Plots
function testsleep()
sleeptimes = logspace(-3,1,50)
actual_sleeptimes = map(sleeptimes) do st
@elapsed sleep(st)
end
sleeptimes, actual_sleeptimes
end
sleeptimes, actual_sleeptimes = testsleep()
diff = actual_sleeptimes-sleeptimes
plot(sleeptimes, [diff diff./sleeptimes], xlabel="Sleeptimes", ylabel=["Absolute difference" "Relative difference"],
xscale=:log10, yscale=[:linear :log10], ylims=[(0,1e-2) :auto], layout=2, legend=false)
```

# Compensation

One can potentially model the time difference and compensate for it. For sleeptimes close to the lower limit of `1e-3`

s, preliminary testing indicates that one can reduce the relative error about one order of magnitude with a simple polynomial model:

```
A = log.(sleeptimes).^(0:2)' # Regressor matrix
x = A\log.(actual_sleeptimes) # Polynomial coeffs
e = log.(actual_sleeptimes) - A*x
predicted_time(t) = exp((log(t).^(0:2)')*x)
predicted_difference(t) = predicted_time(t)-t
plot(sleeptimes, [actual_sleeptimes predicted_time.(sleeptimes)], lab=["Actual", "Predicted"], xlabel="Sleeptime", yscale=:log10, xscale=:log10)
plot(sleeptimes, [abs.(diff-predicted_difference.(sleeptimes)) abs.(diff-predicted_difference.(sleeptimes))./sleeptimes],
xlabel="Sleeptimes", ylabel=["Absolute prediction error" "Relative prediction error"],
xscale=:log10, yscale=[:linear :log10], ylims=[(0,1e-2) :auto],
layout=2, legend=false)
# Estimated parameters stat. significant?
σ² = var(e) # Prediction error variance
Σ = σ²*inv(A'A) # Parameter covariance
p05 = abs.(x)./sqrt.(diag(Σ)) .> 1.96 # Significant?
5-element BitArray{1}:
false
true
false
false
true
```

# Question

Does anyone have experience with this before and have suggestions on a more accurate strategy. I’ll see how reproducible the results are on a different system tomorrow and try to improve upon my quick and dirty high-order polynomial model.