(12C Platinum) Internal Precision Test

[Dieter]

(12-31-2018 01:52 PM)Albert Chan Wrote:  IIRC, 12C internal precision digits are rounded-away after each operation.
Only 10 sig. digits remains (what you see is what you get).

No, the 12C Platinum does not finally round to 10 digits. We have verified this in an earlier thread.

Also let's be accurate about the term "internal precision". This usually referns to the precision of the calculator's internal (sic!) calculations. On HP calculators these are typically three more digits than what is exposed to the user, i.e. 13 dgits for 10-digit calculators or 15 digits for 12-digit devices.

What we are talking about here is something different. The 12C Platinums works with 12 digits while the hardware can only display 10 of these. In a way that's similar to, say, the TI-58/59: you see 10 digits but 13 are present.

So while the 12C Platinum displays √2 as 1,414213562 there calculated result is 1,41421356237. Which can be shown by subtracting the displayed value, this should yield 3,7E–10.

So...

(12-31-2018 01:52 PM)Albert Chan Wrote:  2
2.5
2.666666667
2.708333334

...I am pretty sure the 12C Platinum wil show 2,708333333 at this point, avoiding the 10-digit roundoff error.

(12-31-2018 01:52 PM)Albert Chan Wrote:  If the same applied to 12C Platinum, why did it need more terms to reach 10 digits of e ?
I would guess it would need about the same iterations:

The additional iterations occur because at the end there are two values that look the same (the first 10 digits agree) while the test in the program detects that they are still different, so the iteration continues until they match in all 12 digits.

Since I don't have a 12C Platinum at hand I have tried this on the 12-digit HP35s. Set to 10 displayed digits, the result eventually reaches 2,718281828. But the iteration does not stop here because the 12-digit value at this point is 2,71828182829 which is compared to the 12-digit true value of e, 2,71828182846. The next iteration yields 2,71828182845 and finally 2,71828182846. These are the mentioned two additional iterations. Gamo said it's three more iterations on the Platinum, but this is caused by roundoff errors in the standard 12C: The last value in your table actually should be 2,718281826 when evaluated exactly, which means one more iteration. It should be 12 and 14 instead of 11 and 14.

(12-31-2018 01:52 PM)Albert Chan Wrote:  BTW, getting it converge to 10-digits of e is just lucky. Last digit might be off due to rounding error.
Example, next iteration of above is 2.71828183

Yes, with 10 digit precision the iteration converges to 2,718281830. That's also caused by the mentioned roundoff errors.

Dieter