Periodic distances between two angle tensors

Given two tensors X, Y with each component interpreted as an angle within [-pi, pi], I am trying to compute their periodic distance in following way:

d = root of (summation of d_i^2)

where d_i = min (abs(x_i -y_i), abs(x_i -y_i + 2 pi), abs(x_i -y_i - 2 pi))

does anyone know what would be a good way to implement this and would there be any problem with backprop when using min function?

Thank you!

something like sin((x_i - y_i)/2) ?

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That’s right, maybe arcsin(sin(x_i-y_i)). Thanks!