![]() ![]() A relatively straightforward application of dynamic programming goes up to maybe 12×12 or so. Brute force enumeration falls flat at about a 5×5 board. This is a mere 171 digit number but quite intricate to compute. To make this more concrete I was involved in the efforts to compute the exact number of legal positions on a 19×19 go board. And the core to making the journey worthwhile is finding new algorithms, not only computing something nobody did before but something nobody was even able to compute before. It’s very much a case of the journey is everything, proving that you can compute something that nobody did before. I’m sure MPFR lib has no such limit internally.Īnother thing to note is that in these kinds of problems the actual result is generally the least interesting aspect it will just be a long sequence of digits that nobody can do anything useful with. This is sad that this beautiful language has this ugly limit built-in. I think Julia developers should consider removing the 2^31 precision limit in Julia. Maybe you right that I need to join math forums first and to ask mathematicians about possible algorithms able to solve my task. I’m not sure is it even possible to calculate pi^pi^pi directly without doing it step by step with limited precision in each step. To do this I only need to use One function, only One - “non-integer power”īecause I do not need a function to calculate pi - I can use 圜runcher or download already calculated Pi up to Trillions of digits.īecause of that, I think that I need only one function: pow(float, float) calculate pi with high precision → final result after 3 steps.calculate pi with high precision → save result 2.calculate pi with high precision → save result 1.I cannot imagine how can I try to invent a new algorithm to calc pi^pi^pi besides standard step by step classic calculations. I think I can try to use both libs MPFR and LibBF using their standard methods of calculation. I also found another math lib by amazing guy Fabrice Bellardītw, he is an author of even faster formula to calculate N-th binary number of Pi: Look at the book and how complex it was even in 2010. Maybe it is possible to imagine the existence of a faster solution to calculate pi^pi^pi besides currently available standard methods but I even cannot fully understand the amazing complexity of today’s already existing math algorithms. Oh, it looks so hard/so complex from the outside. “Modern Computer Arithmetic, Richard Brent and Paul Zimmermann, Cambridge University Press, 2010.” I found a book about modern math algoritms and its computer realizations: ![]() Oh man! I just realized IT IS YOU who wrote the article because of which I downloaded Julia)ĭear Mosè, thank you so much! Your code motivated me to try Julia ) I believe you have your priorities in the wrong order. I cannot understand how it works! And I want to figure out and do a super high precision calculation) Moreover, in the case of pi^pi - we need to multiply pi, which is an infinitely-precise number, to itself a non-integer number of times! How it is possible guys?! But somehow - when I enter to calculator pi^pi - it gives me an answer. Very easy to understand.īut how it is possible to be able to calculate 2^2.3? How it is possible to multiply 2 by itself non-integer number of times? I cannot understand it. With my brain I can understand how to calculate, for example, 2^20 - just multiply 2 to itself 20 times. Honestly, I, with my normal human brain, cannot understand or even imagine - how it is possible to be able to multiply a number to itself not-integer number of times?! Somebody can understand how it is possible?īut somehow they created algorithms for this. The problem in pi^pi - it is a “non-integer power”. YCruncher can do many types of Pi-formulas, but last records were set by using Chudnovsky formula. I was impressed by the shortness and beauty of Julia’s code and decided to try. You mentioned the link because of what - I did download the Julia language and registered on this forum) ![]()
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