On 01/11/2014 19:59, [email protected] wrote: > James <[email protected]> [14-11-01 18:16]: >> <meino.cramer <at> gmx.de> writes: >> >> >>> I have a lot of files with digits of PI. The digits >>> are the characters of 0-9. Currently they are ZIPped, >>> which I think is not the best way to do that. >> >> Hello Meino, >> >> It's a bit of effort, but the world's recognized authority >> on algorithms is Don Knuth. [1] He's old now, but his >> pioneering attempt at categorizing most algorithms: >> "The art of computer programming" and his MMIX alogrithm >> implementations (kinda like assembler) are certainly >> part of many first-step research efforts on algorithms >> and their implementations. >> >> It's not a cookbook; more of a scholarly (high_brow) reference, >> just to supplement all the good postings by your peers on gentoo user. >> >> Alan may loan you his copy? >> (ha ha ha)? >> >> >> >> hth, >> James >> >> [1] http://www-cs-faculty.stanford.edu/~uno/ >> > > Hello james, > > Don Knuth ... oh YES! :) > For a long time I am using and prefering TeX over anything else > (ok...for ASCII I use vim... ;). > > And beside his computer wisdom I also like his kind of humor a lot... > for example this one: > https://www.youtube.com/watch?v=eKaI78K_rgA&list=PLUu0XRts4lK6Ri7-xaCNYqTHx7We95Rk8&index=10 > > But my initial question was more targeted to "practical computing" as > to groundshakeing and fundamental research topics. > > More like "what tool to pick?"... > > I did some compression tests myself and currently I have this: >>From http://piworld.calico.jp/ (http://piworld.calico.jp/estart.html) > I got zipped package of > 1000 million places of PI each (~57MB for one ZIP). > > I unpacked the first package and recompressed it with different > methods of 7zip, gzip and bzip2. For gzip and bzip2 I used the highest > compression mode (-9). When a files name matches /.*ultra.*/, I used > the highest compression mode (-mx=9), else I only set the compression > method and leave the rest untouched (defaults). > > > 119888896 2014-10-31 16:44 pi-0001.txt > 57105419 2014-10-31 16:47 pi-0001.txt.gz > 52632832 2014-10-31 16:48 pi-0001.txt.bz2 > 52045827 2014-10-31 16:54 pi-0001.txt.ppmd.7z > 57110291 2014-10-31 17:23 pi-0001.zip > 51766683 2014-10-31 17:26 pi-0001.txt.lzma.7z > 51668838 2014-10-31 17:34 pi-0001.txt.lzma.ultra.7z > 52862115 2014-10-31 17:36 pi-0001.txt.ppmd.ultra.7z > 51668838 2014-10-31 17:39 pi-0001.txt.ultra.7z > > 7zip's lzma wins here, which is also the default method of 7zip. I set > the ultra mode for this by hand. > >>From other sites which offer PI for download I know of methods, which > store the ASCII-digits in binary and compresses then. Would be > interesting, whether this creates a more "handy" input from 7zips > point of view... > > Ah! By the way...I was astonished to read, that the digits of PI are > called random on the one hand and on the other hand there is a formula [1] > to calculate a certain digit of PI without calculation of the previous > digits... > Calculated random? Are nature constants the purest form of PRNGs ??? ;) > (Quantum physics is everywhere... ;;)) > > [1]: > http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
The sequence of digits that make up pi are a random sequence - you can analyze the order any way you want and you'll find no inherent pattern. However, any given digit in the sequence is 100% predictable, as you just showed :-) Randomness has got to be the second most mind-boggling thing out there, first being quantumness (that's not a waord, I just made it up. You you should get the meaning OK from context ;-) ) -- Alan McKinnon [email protected]
