A quick precision test

[Dieter]

(06-05-2014 11:03 AM)Claudio L. Wrote:  The last digit is not what we expected, so what? the number is still accurate within ~0.5 ULP

This exactly is the point: there is no way to be absolutely sure the error does not exceed half a ULP. Not even HP can or will guarantee this level of accuracy. A nice overview on this can be found in the HP-15C Advanced Functions Handbook.

That's why my personal accuracy target for "machince precision" is 0,6 ULP or 1 unit in the n+1st significant digit. This is what can be expected on a 15C or 41C for the trig functions, and if it's good enough there, it's good enough for me either.

BTW there are much larger errors in other functions on regular HP calculators that can be off by several ULP, or the error may even spoil last two digits. So ±0,6 or sometimes even ±1 ULP is fine by me.

Dieter