[time-nuts] Re: pulling some crystals

[Jim Lux]

Generically, this is known as the Cordic method. 
There are some techniques for managing the truncation error and magnitude that Detlef mentions, but I can’t remember them off the top of my head. I’m sure they’re in the literature. The trick is in making them simple and deterministic in time.


On Fri, 29 Dec 2023 12:28:20 +0100, dschuecker via time-nuts <time-nuts at lists.febo.com> wrote:

Hi,

I generate Sin/Cos without a table by rotating complex numbers
(a+i*b)*(u+i*v)

a,b,u,v may be 16Bit integers, for most appplications this prooved
sufficient for me. a is the cos-component, b is the sine component.
(a+i*b) is rotated by the angle of (u+i*v). For integer calculation
|u+i*v| = sqrt(u*u+v*v) is normalized to ,say 2^16 and followed by a
rightshift of 16Bit. It is necessary to watch |a+i*b|=sqrt(a*a+b*b)
because vectorlength is shrinking or expanding due to calculation noise.

Cheers Detlef



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