Accurate Bernoulli numbers on the 41C, or "how close can you get"?

[Dieter]

(03-20-2014 06:46 AM)Ángel Martin Wrote:  On V41 using the default settings: qf(0.01) = -2,326522873, in 1.5 seconds.
On a 41CL using TURBO=zero the same calculation takes 2.35 seconds.

That's fast ...but the true value is 2,326347874. That's also what my FOCAL program returns in 9,5 seconds. ?!?

(03-20-2014 06:46 AM)Ángel Martin Wrote:  cf. the paper by Mike Giles posted at:
http://people.maths.ox.ac.uk/gilesm/file...erfinv.pdf

Ah, I happened to come across that paper a few days ago. ;-) Table 5 shows the CUDA code for single precision (approx. 7 digits), which is a set of two 8th degree polynomials, requiring 18 nine-digit constants just for the coefficients.

(03-20-2014 06:46 AM)Ángel Martin Wrote:  Edited: I checked my files looking for the double-precision source code paper. It appears the link has been re-directed to another subject, so I cannot find it on-line. Unfortunately I didn't keep an electronic copy of the document so would need to go to the actual "paper vault" , I hope to find it or else would have to reverse-engineer my own MCODE

Never mind. I just would like to know the basic idea. Is it really a series expansion, or the usual polynomial/rational approximation, or something else?

Dieter