HP41: accuracy of 13-digit routines

[Dieter]

It is well known that the HP41 internally uses extended precision routines with 13 significant digits, so that the finally returned 10-digit result usually can be considered accurate in all its ten digits.

But what about the 13-digit routines? I read Ángel Martin's PDF on the "HP41 13-digit OS routines", but while I found lots of useful information, nothing was said about the actual accuracy of these routines. In other words: do they really provide correctly rounded 13-digit results under all circumstances? Or may the results be truncated instead of rounded? Or maybe even the last digit may be slightly off?

Here I remember the good old TI58/59 with their 13-digit precision ...but not always 13-digit accuracy. I also own a non-HP RPN calculator (an SR-54NC) with 12-digit precision (and display), but the result sometimes does not carry more than 11 or even 10 valid digits. So my question is: how does the HP41 perform in this regard?

Dieter