sin(x) & cos(x) for x = 10²² in radians

[J-F Garnier]

(10-05-2023 09:20 PM)Albert Chan Wrote:  

(10-03-2023 12:56 AM)Albert Chan Wrote:  I wonder how big is [HP71B] lookup table to get this good ...

I should just try it! No table, just many digits of pi.

>sin(1e22)
-.852200849762
>sin(1e33)
-5.11830428837E-2

Using rpn.exe, HP71B stored 32 digits of pi (note, next digit of pi is 0)

Actually, the Saturn machines are using the PI/4 constant with 31 digits.

The main goal of the PI/4 double precision value was not to manage huge exact arguments, since this has no real-life interest and there will always be a limit unless storing 500 digits, but to guarantee 12-digit accuracy trig results for all "realistic" arguments, especially SIN(X) with X close to PI.

J-F