HP calcs are really not that accurate..

[Claudio L.]

Spoiler alert: shameless plug below. But it's all true nonetheless...

(12-01-2017 09:09 PM)DA74254 Wrote:  In my opinion, there should be no reason that we should not have, say, at least 256 digits/decimal points accuracy. That goes for any device capable of doing "2+2".

How about 2000? Search for newRPL.

(12-01-2017 10:37 PM)brickviking Wrote:  In addition, while computers have gobs of spare memory and awesome (!) floating point processors, calculators do not. Most calculators are not expected to be connected to the wall just to plain work (or charge their batteries after 9 hours of use), they're expected to work after 6 months (or more!) of use just the same as when the battery was first put in. This requires serious compromises in the choices of CPU or multifunction chip so as to make best use of the limited energy resources available from batteries.

Not completely true - see newRPL. Same CPU, battery and RAM requirements as the 39gs/40gs/50g. May not be perfect but does what the OP suggested (>256 digits) without much compromise.

(12-02-2017 10:37 AM)DA74254 Wrote:  I have been lied to, and I don't like it.

Well, some good came out of this. My slight ADHD/ADD, which demands things set square still prefers the "good" answers from the lying calcs, though I myself, upon reading the HP article linked here and the explanations from you, sets things "square" in a better way.

You can have it both ways. If your precision is sufficiently high (as you suggested), but you only display a limited number of digits, it creates the illusion of the perfect answer (2.00000000000000000000000), but if you subtract 2 you'll still see the 1.3E-254 error, which is the "truth" behind the scenes. That will give you the peace of mind that you are not being lied to.
By the way, that number is the actual answer from newRPL with 256 digits setting, doing the 5 iterations of sqrt/sq).
My way of thinking aligns well with yours. If you have enough numerical precision, you don't need to "lie",and you need to worry less about roundoff error propagations after thousands of operations.

I'm not sure I mentioned before in this post, but you should check out newRPL! :-)

PS: My apologies to everybody, I'm really bad at marketing...