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Tyler
windwakr wrote: For lazy people.... 

13 Aug 2010, 05:38 

windwakr
Another pointless post in a pointless thread.
Played around a little with Pari/gp and the lindep function, and found this variation of the BBP Pi formula: I think it's interesting. Except for the 16 in there, everything is a multiple of 5. EDIT: Lol, didn't even notice something. It's just the normal formula, except that every number except the (1/16^k) is multiplied by 5. Weird. 

17 Aug 2010, 01:13 

bitRAKE
I've implemented it here:
http://board.flatassembler.net/topic.php?t=7816 

19 Aug 2010, 07:00 

windwakr
Neat, bitRAKE.
Here comes yet another dumb post by me. I know that sadly there's no decimal BBP Pi algorithm, but what about Pi approximations? Take the vector: Code: [5, 34, 29, 43, 6, 10, 7, 26, 12, 18, 0, 32, 7, 49, 19, 11, 32, 32, 13, 7, 28, 2, 30, 3, 27, 4, 25, 42, 13, 1, 21, 7, 42, 3, 4, 35, 32, 64, 25, 32, 27, 4]~ Now S1+S2+S3...S46, where Si = Code: oo  S = v[i] * \ 1 i /   (10^k)*48k+i k=0 You now have an approximation of Pi to ~80 digits, and you are able to extract digits from it. I had one that was good to around 300 digits, but lost it. Maybe someone could find an approximation that has millions/billions/trillions of digits? Last edited by windwakr on 20 Aug 2010, 21:40; edited 1 time in total 

20 Aug 2010, 20:43 

LocoDelAssembly
It is OK if I move the posts from here to Heap?


20 Aug 2010, 21:14 

windwakr
I don't care.


20 Aug 2010, 21:21 

bitRAKE
For me the interesting thing about BBPlike algorithms is the "compression" of information. Many algorithms are possible which don't reduce the spacetime complexity. BBP seems to packetize the space requirements and dependencies  which the "possibility of" is completely outside of obvious.
wikipedia wrote: This process is similar to performing long multiplication, but only having to perform the summation of some middle columns. While there are some carries that are not counted, computers usually perform arithmetic for many bits (32 or 64) and they round and we are only interested in the most significant digit(s). There is a vanishingly small possibility that a particular computation will be akin to failing to add a small number (e.g. 1) to the number 999999999999999 and that the error will propagate to the most significant digit, but being near this situation is obvious in the final value produced. 

21 Aug 2010, 02:22 

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