Algorithm accuracy vs calculator precision

[Claudio L.]

(11-13-2024 04:59 AM)brouhaha Wrote:  Whether they are faster or slower depends _greatly_ on the processor architecture. On a multi-digit BCD word architecture, like either the 1970s-1990s HP and TI calculators, CORDIC is _MUCH_ faster than a polynomial algorithm. Even if HP or TI had more ROM available, they almost certainly would still have used CORDIC.

With regard to HP calcualtors, this isn't just my opinion. In at least one article about the origin of HP calculators, an HP employe specifically stated they that chose CORDIC for speed. I don't recall which specific article.

Even on short-word-length binary processors, and processors without any efficient floating point add and multiply hardware, CORDIC is often faster than polynomial.

However, on all modern general-purpose processors (x86, high-end ARM, etc.), with efficient floating point hardware, polynomial is much faster than even hardware CORDIC.

I agree. Even on the ARM9 platform used on the 50g, CORDIC was faster. When I wrote the arbitrary precision library for newRPL, CORDIC was faster again. In the end, I decided to go for the polynomial at a 20 to 30% penalty in speed because the tables for CORDIC at 2000 digits took way too much space and would've eliminated the 39g as a hardware platform for newRPL.