Torture tests: what do they mean?

[Dieter]

(05-14-2014 07:47 AM)Manolo Sobrino Wrote:  A machine that can give you x accurate digits for all the domain is not working internally with just x digits. As was discussed in another thread, the HPs are likely using 2x significant digits in their trigonometrics.

Most HP calculators since the HP-91 work with three additional digits. For internal calculations, that is. These digits are not presented to the user. The input has always just the number of digits you can enter. That's the crucial point here: you would need a 20-digit input for 355/226 in order to get the output (the tangent) correct to 12 digits. As already stated, you cannot trust the last eight digits.

Quote:There you go. You need at least 19 significant digits to get that.

Let's make this 20. See my previous post and, even better, Pauli's table with all results from 8 to 20 digits. The tangent of the 19-digit respresentation of 355/226 is off by 3 units in the 12th digit.

Dieter