Riemann's Zeta Function - another approach (RPL)

[DavidM]

(07-12-2017 02:47 AM)Gerson W. Barbosa Wrote:  SysRPL handles 15 digits, in case someone wants to try, but I don't think it won't be necessary. Even (old) HP would tolerate some inaccuracy in the last digit in more simple transcendental functions.

File the following in the "for what it's worth" category. No surprises here.

Don't look too closely at this, as the %'s will make your head spin...

Code:

::
   CK1NOLASTWD
   CK&DISPATCH1
   real ::
      %>%% %%1 %%-
      %% 1.418226E-7 OVER %%*
      %% 2.669693E-7 %%- OVER %%*
      %% 6.5523865E-6 %%- OVER %%*
      %% 9.6919523E-5 %%+ OVER %%*
      %% 3.4229834E-4 %%- OVER %%*
      %% 4.845180903E-3 %%- OVER %%*
      %% 7.28158454506E-2 %%+ OVER %%*
      %% 5.77215664896E-1 %%+
      SWAP ERRSET :: %%1/ %%+ ; ERRTRAP :: DROP %MAXREAL %>%% ;
      %%>%
   ;
;

...results in the following on a 50g:

Code:

0.0:  -.5
0.1:  -.603037519856
0.2:  -.733920924896
0.3:  -.904559257254
0.4:  -1.13479778387
0.5:  -1.46035450881
0.6:  -1.95266144822
0.7:  -2.77838844555
0.8:  -4.43753841589
0.9:  -9.4301140194
1.0:  9.99999999999E499
1.05: 20.580844302
1.1:  10.584448465

If I remove the final conversion step from extended real -> real, the extra digits are visible:

Code:

0.0:  -.5
0.1:  -.603037519856 217
0.2:  -.733920924896 446
0.3:  -.904559257253 991
0.4:  -1.13479778386 675
0.5:  -1.46035450880 966
0.6:  -1.95266144822 460
0.7:  -2.77838844555 380
0.8:  -4.43753841589 442
0.9:  -9.43011401940 255
1.0:  9.99999999999E499
1.05: 20.5808443020 327
1.1:  10.5844484649 599

Hopefully my transcription of Dieter's approximation didn't introduce any problems. Any errors are definitely mine, not his.