We had the algorithm for the hexadecimal digits in 1997, and this post refers to it as reference 2. That algorithm runs in constant time, which is a pretty big deal.
This algorithm here runs in O(n^2). I'm not sure how impressed I should be. Bellard himself wrote this paper [1] in 2010 where he showed how he calculated 2.7 trillion decimal digits of pi. The algorithm was essentially linear (with some logs and powers of logs thrown in there, like in all self-respecting algorithms). Of course, 2010 was 13 years after 1997, maybe in 1997 O(n^2) was the best someone could get. I'm getting the impression however that the ingredients for the 2010 record were all there since the record established by the Chudnovsky brothers in 1988 [2].
This algorithm here runs in O(n^2). I'm not sure how impressed I should be. Bellard himself wrote this paper [1] in 2010 where he showed how he calculated 2.7 trillion decimal digits of pi. The algorithm was essentially linear (with some logs and powers of logs thrown in there, like in all self-respecting algorithms). Of course, 2010 was 13 years after 1997, maybe in 1997 O(n^2) was the best someone could get. I'm getting the impression however that the ingredients for the 2010 record were all there since the record established by the Chudnovsky brothers in 1988 [2].
[1] https://bellard.org/pi/pi2700e9/pipcrecord.pdf
[2] https://en.wikipedia.org/wiki/Chudnovsky_algorithm