WP 34S vs. DM42 decimal128 differences?

[Claudio L.]

(03-30-2018 12:11 PM)Nigel (UK) Wrote:  Incidentally, calculating \(\sin(\pi)\) with a 34-digit value of \(\pi\), using newRPL with 34 digits of precision, gives an answer also correct to 34 digits. Well done Claudio!

Nigel (UK)

Thanks, but there's not much glory on that achievement. It simply uses \(\pi\) with twice the current precision, so the range reduction produces the angle with full required precision. It's easy to achieve when the whole system has variable precision.
Now if you set the system to maximum precision:

Code:


2000 SETPREC
π0 0 +       @ TO ROUND π0 TO 2000 DIGITS, JUST ADD ZERO
SIN

Now what do you see? Only 22 good digits (thanks to a few extra guard digits beyond 2000), but certainly not 2000 good digits as you would've expected. At the limit of the system precision, newRPL has the same issues of the wp34s. The only solution I found was to use 4000 digits for pi, but what's the point: if the system works with 4000 digits, then I'd rather let the user use them all, just warning them that if you use more than half of that, don't expect all corner cases to be accurate. Due to memory limitations, I chose 2000 digits as the system limit. If you use 1000 digits or less, all functions are guaranteed to give you correctly rounded results in all corner cases with the 1000 digits precision you expect.
On the wp34s it's exactly the same: they used double precision to guarantee single precision on all corner cases. But since it's available, why not let the user access it? after all it's good for 99% of the cases. Now people want perfect results at double precision, so Paul needs quad precision, and then why not let the user use quad?... and here we go again.