(Free42) roundoff for complex SQRT

[Dieter]

(04-03-2018 01:28 PM)Werner Wrote:  Free42 shows 2+i2, which SHOW reveals to be really 2+i(2-1E-33).
Almost any b you throw at it has a rounding error like that, in the real or complex part.
The 12-digit 42S gets the exact result - it must have special code for a=0, and return SQRT(ABS(b)/2)*(1+i*SIGN(b)) in that case - even when b/2 would underflow.

I assume (!) that the reason why a physical 42s returns an exact result simply is its three guard digits: the function is calculated to 15 digits, and if this yields 2,00000000000012 + 1,99999999999996 i this does not become visible as it is rounded to 12 digits before it is returned to the user.

I wonder if Free42 (or DM42) make use of such guard digits. Is it possible that here these calculations are performed with the same 34 digits that are finally returned? This would explain slight errors in the last digit. Or are there really some additional digits that would cover roundoff errors like the ones discussed here?

Edit: I just noticed that the use of guard digits has already been mentioned in your later post.

Dieter