Riemann's Zeta Function - another approach (RPL)

[Dieter]

(07-31-2017 03:59 PM)Gerson W. Barbosa Wrote:  I've tested it on Emu42 set to "Authentic Calculator Speed". The number of terms hasn't been adjusted yet, thus accuracy differences between both can be highlighted:

Hmmm... x=0 should return exactly –0,5 because the coefficients are designed accordingly. So I wonder why you get –0,500000000004. This would mean that one of the coefficients is off by 4 E-12. ?!?

BTW the optimized coefficient set has two slight changes in the last digit:
line 123: -8.47149 E-7
line 131: 3.42683395 E-4

And the error check for x<0 (SQRT in line 29) can be omitted here. ;-)

But remember, the two polynomial approximations are intended for 10 digit calculators. While the approximation for 1<x≤2 has an error less than 1 unit in the 12th digit and thus is useable for the 42s, the one for 0≤x<1 may be off by 4 ULP, so here one more term would make sense. Looking at your examples, indeed the largest error between –1 and +2 is 2 ULP.

Dieter