HP41: accuracy of 13-digit routines

[Ángel Martin]

(09-03-2015 12:36 PM)Dieter Wrote:  

(09-03-2015 06:22 AM)Ángel Martin Wrote:  the X! on the 15C is the gamma function, right? So there you also have it to test for the accuracy to the 10th decimal digit.

Yes, on the 15C x! actually evaluates Gamma(x+1), just like the 34C did before. The 15C AFH says that the last digit may be off by 1 ULP, maybe 2 for large results.

(09-03-2015 06:22 AM)Ángel Martin Wrote:  As far as GAMMA in the SandMath I checked the accuracy for the natural arguments were ok (see the table in its manual) but didn't do any further checks for non-integer arguments.

Here and there the result may be off in the last digit, but the cases I found were just 1 ULP high or low. So it seems on par with the 15C. ;-)

Great!

(09-03-2015 12:36 PM)Dieter Wrote:  BTW, have you read the recent thread on Spouge's Gamma approximation in the HP41 software library? Les and I have been talking about an improved Lanczos method, and I posted a set of coefficents resulting in a relative error less than 2 E–11 up to Gamma(71), and this with even two terms less than the current Sandmath implementation.

I need to check how that one will pan out - how many coefficients are you using in the inproved version? I haven't really looked into the details yet... but if it's equal or better than the current implementation (up to 10 digits, remember...) then it'll be worth replacing it with the new set.


PS. ok there are 4 coefficients instead of 7 - so far so good, but what about the rest of the formula? c replaces the arbitrary "5" value, but does the rest remain unchanged??

Pls. let me know which of the formulas on Viktor's page would be the applicable one for the new coefficient set:
http://www.rskey.org/CMS/index.php/the-library/11

ÁM