On: Why the CORDIC algorithm lives rent-free in my hea...

[1oooqooq]

so, it's a https://en.wikipedia.org/wiki/Farey_sequence (aka mediant, aka naive fraction sum for approximation) but for angles?

[ykonstant → 1oooqooq]

It is not, because the subdivisions in CORDIC do not possess the best approximation properties of Farey fractions. For that, you would have to partition the circle into major/minor arcs instead, in the sense of Hardy-Littlewood's circle method. But that would be computationally very expensive, whereas this binary subdivision is fast, and is made faster using the shift-add tricks.

[1oooqooq → ykonstant]

i see. thanks. assumed it was just bit shift tricks implementation. but indeed, no mediant.

[kevindamm → 1oooqooq]

More like a binary search, but instead of adjusting an array index you're iterating an orthonormal matrix which represents rotation about the origin.

[tapatio → kevindamm]

Or a second order step response.

[nico → 1oooqooq]

That’s super cool

Thank you for that link, very interesting diagrams and structures

They look very similar to what a neural network might be in certain cases, and it seems like the structures are trying to map some sort of duality