Algorithms for trig. on scientific calculators ?

[Commie]

(12-06-2024 03:20 AM)brouhaha Wrote:  Which calculator models use the Padé approximant? While I've heard of this method, I've never before heard of it bring used in a calculator. I would have expected the Padé approximant to require too many terms to get the required accuracy for sin over e.g. the domain [0, pi/4].

Hi,

The only calculator, i know of, are the original hp35 and the hp45 which both use cordics and thats a certainty, however, if you check the link for the Pade algorithm on wikipedia, it claims that the Pade algorithm is used extensively in computers, the exact models I'm not sure.

I have used the Pade algorithm in a hp45 clone and it works well. The sine approx., I provided has a range greater than what you specify i.e., [-pi/2, pi/2], pi/2 is worst case approx., the equation I showed/derived becomes more accurate as you get closer to zero, maximum accuracy for the given equation.
Also, due to the symmetry of sine waves, one can double the dynamic range by including an if/then/else construct preceeding the main equation whose range then extends to [-pi,pi] which is a complete wave of 360 deg. or 2.pi. The first step in calculating sine is to remove all the sine circles first.

The best way to use Pade algorithm is to program in a poly subroutine so it can be called multiple times, this way, many transcandential math functions can be called over and over again, reducing rom space and increasing speed.

Cheers
Darren