Hi Jorge --

I agree, it'd be interesting to apply a Riemann Sum algorithm using
arbitrary precision as the number crunching type, versus IEEE754.

Freed from FORTRAN, you would have that option.  I'll do it now...

[ sometime later ]

Here's a sandbox version:
https://repl.it/@kurner/computepi

I'm comparing the convergent Rsum you give with one of Ramanujan's:

pi = 3.141591653589626571795976716612836217532486859692
start_time = 23183.62579051
end_time = 23205.729972367
elapsed time = 22.104181857001095 seconds

Ramanujan's converges really quickly, after 100 terms:

pi = 3.141592653589793238462643383279502884197169399375
start_time = 23205.731066136
end_time = 23205.838047055
elapsed time = 0.10698091900121653 seconds

That 2nd answer is correct as far as I'm showing it.  One may tweak the
repl to get even more precision.

I wonder how fast REPL.it is compared to my R-Pi.  I'll be checking that
later.

You're getting into clustering, cool!

That's a deep topic, with or without converging to Pi, wish I knew more.

Kirby

On Fri, Jan 31, 2020 at 8:30 PM <calcp...@aol.com> wrote:

> Hi Kirby,
>
> Love your post about arbitrary precision. I wish I had seen it before I
> started a project with my students computing PI on a Linux Cluster.
> Here's my blog post about our project so far if anyone is interested,
>
> https://shadowfaxrant.blogspot.com/2019/12/cistheta-2019-2020-meeting-7-121519.html
>
> Regards,
> A. Jorge Garcia
> Teacher and Professor
> Applied Math, Physics and Computer Science
> http://shadowfaxrant.blogspot.com
> http://www.youtube.com/calcpage2009
>
>
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