@Thomas Klemm -> CORDIC Article

[Paul Dale]

(06-01-2014 11:57 AM)Tugdual Wrote:  Interesting, I wonder what justified the choice.
A matter of patent?

I honestly don't remember why I chose this approach over others. My guess would be a matter of expediency, I had a lot to implement quickly. A taylor expansion is easy to write and generally quite small. They aren't always the most numerically stable methods. There aren't patent issues for these series that I'm aware of -- too well known to an expert in the field.

Quote:What is the most efficient approach in terms of speed and accuracy between CORDIC and Taylor?

Taylor series generally can be made as accurate as you want by adding additional terms -- this being important early on when the working precision wasn't set in stone. CORDIC requires a bit more effort to increase its accuracy, more iterations and more constants. Speed wise, I doubt there is much difference a lot of the time -- at the least, I don't have a good feel for the differences. However, remember the 34S CPU can do integer multiplies which helps a lot. CORDIC assumes only additions and shifts are possible and wouldn't directly benefit from multiplication.

If I was going to go back and revisit these, I'd be looking harder at specially designed rational approximations that gave results roughly at the desired working precision.

Quote:Or may be CORDIC was the right choice for old calculators with little ROM?

CORDIC has the big advantage that is can produce trigonometric, inverse trigonometric, logarithmic, exponential, hyperbolic and interse hyperbolic functions using essentially the same algorithm. I.e. very code space efficient. This was vital for the older devices with tiny amounts of ROM.

It really is difficult to foresee any other algorithms fitting into so few resources yet still providing such functionality.


Pauli