{"id":42130,"date":"2019-03-18T00:00:00","date_gmt":"2019-03-17T21:00:00","guid":{"rendered":"https:\/\/prohoster.info\/blog\/blog_prohoster\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov"},"modified":"2020-02-18T13:44:56","modified_gmt":"2020-02-18T10:44:56","slug":"novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","status":"publish","type":"post","link":"https:\/\/prohoster.info\/hr\/blog\/administrirovanie\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","title":{"rendered":"Novi svjetski rekord u izra\u010dunu broja pi: 31,4 bilijuna znamenki","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"Novi
\n
\nBailey-Borwein-Plouffeova formula omogu\u0107uje izra\u010dun bilo koje konkretne heksadecimale ili binarne znamenke broja pi bez izra\u010dunavanja prethodnih (trenutni rekord postavljen je algoritmom Chudnovsky, pogledajte dolje)<\/i><\/p>\n

Izra\u010dunatski klaster Google Compute Engine u 121 danu na 25 virtualnih strojeva izra\u010dunao je najve\u0107i broj znamenki u broju pi, postaviv\u0161i novi svjetski rekord: 31,4 trilijuna znamenki nakon decimalne to\u010dke. Ovo je prvi put da je za izra\u010dun broja pi te veli\u010dine kori\u0161tena javna cloud softverska rje\u0161enja.<\/p>\n

Rekord \u0107e biti zabilje\u017een na ime Emme Haruka Iwao iz sektora visokih performansi u Googleu. Ona je iskoristila infrastrukturu Google Clouda za izra\u010dune. Prethodni svjetski rekord postavio je Peter Treadway 2016. godine, izra\u010dunav\u0161i broj do 22,4 triliona znamenki. na specijalno izra\u0111enom serveru<\/a><\/noindex>, kojeg tako\u0111er sponzorira poslodavac.
\n<\/a><\/noindex>
\nPoput Treadway-a, Googleova in\u017eenjerka je koristila y-cruncher za izra\u010dun. Ovaj program koristi Chudnovskyjev algoritam<\/a><\/noindex>, brz algoritam za izra\u010dun broja pi. Jo\u0161 u 80-im godinama sami braca Chudnovsky<\/a><\/noindex> su njegovim pomo\u010d u\u010dinili milijardu znamenki nakon decimalne to\u010dke.<\/p>\n

Ovaj algoritam se temelji na svojstvu brze konvergencije hipergeometrijskog niza:<\/p>\n

\"Novi
\n
\nEmma Haruka Iwao je postala strastvena prema \"\u010darobnom\" broju nakon \u0161to je saznala o njemu na satu matematike u \u0161koli, pi\u0161e<\/a><\/noindex> Wired<\/i>. Na sveu\u010dili\u0161tu je jedan od njezinih profesora, Daisuke Takahashi, bio rekordman po broju izra\u010dunatih znamenki uz pomo\u0107 superra\u010dunala. Danas rekord mo\u017ee postaviti prakti\u010dki svaki zainteresirani in\u017eenjer koji ima pristup ozbiljnim ra\u010dunalnim resursima i velikom skladi\u0161tu podataka (za pohranu rezultata izra\u010duna). Program y-cruncher<\/a><\/noindex> namijenjen je izra\u010dunu matemati\u010dkih konstanti, poput pi. Podr\u017eava masivnu vi\u0161edretvenost i trilijunske domete. Ovaj program zapravo je komodificirao izra\u010dune konstanti.<\/p>\n

\u201eTreba vam prili\u010dno mo\u0107an ra\u010dunar da oborite svetski rekord\u201c, ka\u017ee Ivao. \u201eNe mo\u017eete to uraditi sa ra\u010dunarom iz radnje, pa su ljudi ranije gradili prilago\u0111ene ma\u0161ine.\u201c U septembru 2018. godine, Ivao je po\u010dela razmatrati kako \u0107e tehni\u010dki raditi proces izra\u010dunavanja van rekordnog opsega. Odmah je postalo jasno da \u0107e glavni problem biti obim podataka za skladi\u0161tenje. Na kraju, izra\u010dunati rezultat zauzima 170 terabajta. Umesto da sastavi prilago\u0111eni server, kao \u0161to su to radili njeni prethodnici, koristila je infrastrukturu Google Clouda.<\/p>\n

\"NoviIvao je podigla 25 virtuelnih ma\u0161ina: \u201eAli umesto da pritisnem ovu dugmad virtuelne ma\u0161ine 25 puta, automatizovala sam je\u201c, obja\u0161njava ona. \u201eMo\u017ee\u0161 to uraditi za nekoliko minuta, ali ako ti treba toliko mnogo ra\u010dunara, bi\u0107e potrebno nekoliko dana da sve postavi\u0161.\u201c Potom je neprekidno, tokom 121 dana, Ivao upravljala radom y-cruncher-a na ovih 25 virtuelnih ma\u0161ina. <\/p>\n

Da bi izra\u010dunavanja bila ta\u010dna, virtuelne ma\u0161ine morale su raditi neprekidno. In\u017eenjerka je postavila sistem pra\u0107enja koji bi je upozorio ako ne\u0161to krene po zlu, na primer, o iznenadnom kvaru na jednoj od virtuelnih ma\u0161ina. Samo jedan kvar \u2014 \u010dak i na nekoliko minuta \u2014 mogao bi ugroziti ceo proces izra\u010dunavanja, da nije bilo rezervne kopije.<\/p>\n

\u201eU kran\u010deru i Google Cloudu postoje sistemi rezervnih kopija, i postavila sam ih tako da mo\u017eete odmah praviti kopije tih diskova, ne zaustavljaju\u0107i izra\u010dunavanja\u201c, ka\u017ee Ivao. Ovi podaci su zatim kopirani i \u010duvani spolja, na drugim diskovima, u obliku trenutnih snimaka.<\/p>\n

\u201eNa po\u010detku je bilo nekoliko parametara koje sam promenila, na primer, koliko podataka mo\u017eete \u010ditati ili pisati odjednom, i kako \u0107e se granice menjati kako se pove\u0107avaju\u201c, ka\u017ee Ivao.<\/p>\n

Sa pove\u0107anjem broja cifara, obim datoteka se pove\u0107avao, a slo\u017eenost izra\u010dunavanja rasla je nelinearno. To je zna\u010dajno ote\u017ealo prvobitno izra\u010dunavanje, kada je Ivao poku\u0161avala da izra\u010duna koja resursa virtuelnih ma\u0161ina \u0107e joj biti potrebna za projekat.<\/p>\n

Sada su zavr\u0161eni i izra\u010duni i provjera rezultata: y-cruncher ima ugra\u0111ena dva osnovna algoritma - jedan za izra\u010dunavanje pi, a drugi za provjeru. Algoritam provjere radi paralelno s izra\u010dunom, ali izra\u010dunava samo jednu znamenku, tako da se rekord mo\u017ee slu\u017ebeno registrirati.<\/p>\n

\nTeoretski, novi svjetski rekord mo\u017ee se postaviti ako jednostavno uzmete prethodnu datoteku i primijenite Bailey\u2013Borwein\u2013Plouffeov okvir za izra\u010dunavanje jo\u0161 jednog broja. No to sigurno kr\u0161i pravila registracije takvih svjetskih rekorda: vjerojatno svaki kandidat mora zapo\u010deti izra\u010dun od po\u010detka. Kao opcija: pobolj\u0161ati prethodni rezultat za N%, \u0161to prema Bailey\u2013Borwein\u2013Plouffeovoj formuli nije mogu\u0107e.<\/p>\n

Izvor: habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

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\u0437\u043d\u0430\u043a\u043e\u0432 […]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":42131,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[688],"tags":[],"class_list":["post-42130","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-administrirovanie"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\n","aioseo_head_json":{"title":"\ud83e\udd47Novi svjetski rekord u izra\u010dunavanju broja pi: 31,4 trilijuna znamenki | ProHoster","description":"Bailey\u2013Borwein\u2013Plouffeova 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