HP41: accuracy of 13-digit routines

[Thomas Klemm]

(09-01-2015 09:23 PM)Dieter Wrote:  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?

This depends a little on the definition of "correctly rounded".
You may try 104985/9999 which is:

10.499549954995...

Correctly rounded to 13 digits would give us:

10.49954995500

If we'd round this to 10 digits we'd get:

10.49954996

But that's not what we get. Instead we get:

10.49954995

Thus the internal 13-digit result isn't rounded correctly but cut off.

As far as I remeber rounding is just adding 500 to the 13-digit mantissa.
Thus in the example from above:

Code:

10.49954995499
+          500
10.49954995999

From this only the first 10 digits are used.

HTH
Thomas