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It would be interesting to see your C# examples side-by-side against the same problems solved in F#
"There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that there are no obvious deficiencies. The first method is far more difficult." - C.A.R. Hoare
OH I like big fibs and I cannot lie, here's a nice trick if you don't mind some BigInteger hackery,
Take some nice prime p such that p ≡ 3 mod 4 (this congruence is not strictly required but makes the next part easier). For example p = 45427892858481394071686190649738831656137145778469793250959984709250004157335359
Then calculate the square root of 5 = BigInteger.ModPow(5, (p + 1) / 4, p) (this simple formula works before p was chosen with p ≡ 3 mod 4).
I suspect that you clicked the wrong comment in the wrong discussion when you wrote your followup.
Nevertheless, I would like to comment on your question:
In my student days (long ago), a fellow student in theoretical physics was working on an analytical model of what happens when two waves collide. He did some numerical simulations, but his results displayed discontinuieties which he traced down to limited precision (72 bits double precision on a Univac mainframe). We wrote him a library for arbitrary precision floating point calculations (they weren't readily available on the Internet in those days), and he set out with 200 decimal digits of precision. This reduced the problems significantly, but not entirely.
Here comes the important stuff: As a student of theoretical physics, math is not hampered by issues like "limited precision". Our fellow student refused to relate to such mundane things. After two others have failed to make him understand that when adding the elements of a series expansion, it does matter if you add them from the one end or from the other one, I came in as the third one and finally made him accept (I wouldn't say "willingly"...) that adding "from the small end" could make an essential difference. It actually turned out that by adding from the small end, he never needed the exended precision library at all.
Numerical methods, error propagation and stuff like that are certainly not subjects taught to theoretical physicists or anyone else who simply use a computer as a tool to procuce some results. If the users think in math terms, like this student, you need all the precision that can be provided to make computer math behave as closely to real math as possible.
In mathematical theory, you may of course encounter people who really explore extremes of the concepts of numbers. They may even care for integers of 100,000,000 digits - not because they need the precision, but they really handle numbers of that range. The numbers are certainly not needed for any industrial or financial application, only for the number theory. Say, if a mathmatician is studying the possibility of there being a largest possible prime number, he might very well end up in those number ranges.
(Disclaimer: For all I know, it may have been proven that there is no such largest possible prime number. I am not a mathmatician; I simply made it up as a possible example.)
After a failed build on our Windows build server with Visual Studio 2017, it turned out that the C: drive had run out of space. Freeing up space in the usual way with "Disk Cleanup" did not help much. Only after inspection of directories my eye fell on C:\ProgramData\Package Cache which was over 9 Gb in size !
After Googling a bit I found this helpful link: Move C:\ProgramData\Package Cache\ to D:\ – Knowledgebase[^]
Following the instructions I could move the data to the D: drive and created a "filesystem junction" to point to the new location.
Everything seemed to work fine after that, but beware that problems can occur when updating or repairing with the Visual Studio installer