[VA] SRC#006- Pi Day 2020 Special: A New Fast Way to Compute Pi

[Valentin Albillo]

.
Hi, all:

Thanks for your interest in my SRC#006, much appreciated. As for fast computation of sin(x), these papers and link are interesting and relevant:

      E. Karatsuba. "Fast evaluation of transcendental functions (1991)"
      B. Haible & T. Papanikolaou. "Fast multiprecision evaluation of series of rational numbers"
      Binary Splitting

Remember that no general implementation of sin(x) is required, just an optimized one for suitably small x in a very short interval.

EdS2 Wrote:For the rnd/rnd method I found I had to adjust the program - is there a typo in there?

No, there isn't. I always check the code I post by keying it in anew from the [Preview Post] listing and running it, so that I can check the results before hitting [Post]. I did that once again and it runs fine so no typo. I suggest you check what you keyed in, if there's a typo it certainly is on your side.

Also, I saw you mentioned my fast program here ...

https://stardot.org.uk/forums/viewtopic....2&p=262553

... but you modified the code to start from X₀=1 as the first approximation, so it takes longer to converge. You shouldn't do that just because you feel like it, you should leave my original code alone and start from X₀=3. The fact that it also converges when starting at X₀=1 (albeit taking extra unnecessary iterations) is ancillary, the correct starting value X₀ must be such that Abs(Pi-X₀) < 1, and the simplest such value is X₀ = 3. Arbitrarily chaging it to 1, as you did, does not meet the condition.

In the future, I would appreciate it if, when giving me credit for some code I wrote, you don't modify my code in any way (apart from adapting it to some particular programming language) without clearly stating that you modified my original code and what modifications you made (in this particular case, changing the starting value, which I don't approve of).

Thanks in advance.

Regards.
V.