HP-35: Sin and cos function formulas, another point of view

[Thomas Klemm]

(08-16-2018 08:46 AM)sasa Wrote:  Due extreme space limitation, I'm almost certain it is used implemented sqrt and reciprocal routine.

Not only this. Since digit by digit methods are used for CORDIC, multiplication, division and square root all of them take roughly the same time.
This time depends on the sum of the digits but on average it's constant.

Thus each of these steps takes about the same time:

• \(\tan(x)\) (CORDIC)
• \(\cot(x)\) (division)
• \(\cot^2(x)\) (multiplication)
• \(\sqrt{1+\cot^2(x)}\) (square root)
• \(\frac{\cot(x)}{\sqrt{1+\cot^2(x)}}\) (division)
  

Newton's method uses a multiplication in each step which is expensive on this CPU.
Thus we wouldn't benefit much, maybe even lose in some cases.

Cheers
Thomas