20201208, 10:59  #45  
"Robert Gerbicz"
Oct 2005
Hungary
10110111100_{2} Posts 
Quote:
For comparison in this record size the BBP takes less than a single day, while the whole record computation took 303 days. (ref. https://en.wikipedia.org/wiki/Chrono...tion_of_%CF%80). So with a 50% probability your record claim would fail in a single day. What is not that bad. ps. Or with a much larger probability if we'd ask at each position not a single bit but say 20 consecutive bits, this is not increasing the BBP time too much but you'd fail with much larger chance. 

20201208, 11:18  #46  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,143 Posts 
Quote:
So you ask for your 20 positional digits. A day later the reply gives the digits. You check them and see no error. Still doesn't prove the claimant computed all the other digits. Only a hash of them all after a full recomputation can do that. 

20201208, 12:25  #47  
"Robert Gerbicz"
Oct 2005
Hungary
2^{2}·367 Posts 
Quote:
"if you're claiming a world record then I would choose 1 million random positions and you should give the bits for each of these positions. The check: select say 2025 positions and verify the bits with BBP. You have an extremely small probability to fake me." I'm requesting the bits for 1 million positions and after receiving your file with bits, checking random(!!!) 2025 positions. If you'd do this with BBP then the overall computation time would be 2500 times larger than what a direct computation of pi would use. You can still select some positions from the list and use BBP for these and/or use known bits of pi (for small positions), but you wouldn't pass the test. Last fiddled with by R. Gerbicz on 20201208 at 12:28 Reason: small typo 

20201208, 12:29  #48  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,143 Posts 
Quote:


20201209, 03:06  #49 
Romulan Interpreter
Jun 2011
Thailand
22354_{8} Posts 
How do you figure? Is BBP so slow that computing one million bits with it (in fact, you compute 4 bits every time, iirc), is 2500 times slower than computing (what's the record? two terradigits?) of pi by the fastest method? (probably some variation of Ramanujan formula?, well, it seems odd to me, but yes, I didn't make any calculation, just gut feeling, and just asking).
Last fiddled with by LaurV on 20201209 at 03:12 
20210106, 17:47  #50  
Sep 2016
332_{10} Posts 
Quote:
 There's some preliminary research into a hybrid BBP+Binary Splitting algorithm that may allow M consecutive digits starting from the N'th digit to be computed faster than O(M * N log(N)). (binary digits of course) Such an algorithm could potentially allow for a lowmemory distributed computation of Pi  but only the binary digits and at the cost of a much larger BigO than the classic algorithms. If such an algorithm does come to fruit, then asking for a million digits starting from N may not be sufficient. Last fiddled with by Mysticial on 20210106 at 17:53 

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