{"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\/cs\/blog\/administrirovanie\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","title":{"rendered":"Nov\u00fd sv\u011btov\u00fd rekord v po\u010d\u00edt\u00e1n\u00ed \u010d\u00edsla p\u00ed: 31,4\u00a0bilionu znak\u016f","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"Nov\u00fd
\n
\nBailey-Borwein-Plouffeho vzorec umo\u017e\u0148uje z\u00edskat jakoukoli konkr\u00e9tn\u00ed hexadecim\u00e1ln\u00ed nebo bin\u00e1rn\u00ed \u010d\u00edslici \u010d\u00edsla p\u00ed, ani\u017e by bylo nutn\u00e9 po\u010d\u00edtat p\u0159edchoz\u00ed (aktu\u00e1ln\u00ed rekord byl stanoven algoritmem Chudnovsk\u00e9ho, viz n\u00ed\u017ee).<\/i><\/p>\n

V\u00fdpo\u010detn\u00ed cluster Google Compute Engine za 121 dn\u00ed na 25 virtu\u00e1ln\u00edch stroj\u00edch vypo\u010d\u00edtal nejv\u011bt\u0161\u00ed mno\u017estv\u00ed \u010d\u00edslic v \u010d\u00edsle p\u00ed, co\u017e stanovilo nov\u00fd sv\u011btov\u00fd rekord: 31,4 trilionu \u010d\u00edslic za desetinnou \u010d\u00e1rkou. To je poprv\u00e9, co bylo ke v\u00fdpo\u010dtu takov\u00e9ho mno\u017estv\u00ed \u010d\u00edsla p\u00ed pou\u017eito ve\u0159ejn\u011b dostupn\u00e9 cloudov\u00e9 softwarov\u00e9 \u0159e\u0161en\u00ed.<\/p>\n

Rekord bude zaps\u00e1n na jm\u00e9no Emmy Haruky Iwao z odd\u011blen\u00ed vysoce v\u00fdkonn\u00fdch v\u00fdpo\u010dt\u016f v Googlu. Ta pou\u017eila infrastrukturu Google Cloud k v\u00fdpo\u010dt\u016fm. P\u0159edchoz\u00ed sv\u011btov\u00fd rekord stanovil Peter Tschichold v roce 2016, kdy vypo\u010d\u00edtal \u010d\u00edslo do 22,4 trilionu \u010d\u00edslic. na speci\u00e1ln\u011b vyroben\u00e9m serveru<\/a><\/noindex>, kter\u00fd rovn\u011b\u017e sponsoroval zam\u011bstnavatel.
\n<\/a><\/noindex>
\nStejn\u011b jako Tschichold, in\u017een\u00fdrka Googlu pou\u017eila k v\u00fdpo\u010dtu y-cruncher. Tento program pou\u017e\u00edv\u00e1 algoritmus Chudnovsk\u00e9ho<\/a><\/noindex>, rychl\u00fd algoritmus pro v\u00fdpo\u010det \u010d\u00edsla p\u00ed. Ji\u017e v 80. letech brat\u0159i Chudnov\u0161t\u00ed<\/a><\/noindex> s jeho pomoc\u00ed vypo\u010d\u00edtali miliardu \u010d\u00edslic za desetinnou \u010d\u00e1rkou.<\/p>\n

Samotn\u00fd algoritmus vych\u00e1z\u00ed z vlastnosti rychl\u00e9 konvergence hypergeometrick\u00e9ho \u0159adu:<\/p>\n

\"Nov\u00fd
\n
\nEmma Haruka Iwao se fascinovala \u201ekouzeln\u00fdm\u201c \u010d\u00edslem, kdy\u017e se o n\u011bm dozv\u011bd\u011bla na hodin\u011b matematiky ve \u0161kole, p\u00ed\u0161e<\/a><\/noindex> Wired<\/i>. Na univerzit\u011b byl jedn\u00edm z jej\u00edch profesor\u016f Daisuke Takahashi, kter\u00fd byl rekordmanem v po\u010dtu vypo\u010d\u00edtan\u00fdch \u010d\u00edslic \u010d\u00edsla pomoc\u00ed superpo\u010d\u00edta\u010de. Dnes m\u016f\u017ee rekord stanovit prakticky jak\u00fdkoli zainteresovan\u00fd in\u017een\u00fdr, kter\u00fd m\u00e1 p\u0159\u00edstup k v\u00e1\u017en\u00fdm v\u00fdpo\u010detn\u00edm zdroj\u016fm a velk\u00e9mu \u00falo\u017en\u00e9mu prostoru (k uchov\u00e1n\u00ed v\u00fdsledk\u016f v\u00fdpo\u010dt\u016f). Program vytvo\u0159en\u00fd v roce 2009 y-cruncher<\/a><\/noindex> je ur\u010den pro v\u00fdpo\u010det matematick\u00fdch konstant, jako je p\u00ed. Podporuje masivn\u00ed v\u00edcerozm\u011brnost a trilionov\u00e9 rozsahy. Tento program vlastn\u011b zkomoditizoval v\u00fdpo\u010dty konstant.<\/p>\n

\u201ePot\u0159ebujete docela v\u00fdkonn\u00fd po\u010d\u00edta\u010d, abyste p\u0159ekonali sv\u011btov\u00fd rekord,\u201c \u0159\u00edk\u00e1 Ivao. \u201eNen\u00ed mo\u017en\u00e9 to ud\u011blat na b\u011b\u017en\u00e9m po\u010d\u00edta\u010di z obchodu, proto si lid\u00e9 d\u0159\u00edve stav\u011bli vlastn\u00ed stroje.\u201c V z\u00e1\u0159\u00ed 2018 Ivao za\u010dala zkoumat, jak technicky funguje v\u00fdpo\u010det v rozsahu za hranicemi rekordn\u00edho rozsahu. Okam\u017eit\u011b bylo jasn\u00e9, \u017ee hlavn\u00edm probl\u00e9mem bude objem dat k ulo\u017een\u00ed. Nakonec to dopadlo tak, \u017ee vypo\u010d\u00edtan\u00fd v\u00fdsledek zabere 170 terabajt\u016f. M\u00edsto sestaven\u00ed vlastn\u00edho serveru, jako jej\u00ed p\u0159edch\u016fdci, vyu\u017eila infrastrukturu Google Cloud.<\/p>\n

\"Nov\u00fdIvao vzty\u010dila 25 virtu\u00e1ln\u00edch stroj\u016f: \u201eAle m\u00edsto toho, abych na tla\u010d\u00edtko virtu\u00e1ln\u00edho stroje klikla 25kr\u00e1t, jsem to automatizovala,\u201c vysv\u011btluje. \u201eM\u016f\u017ee\u0161 to ud\u011blat za p\u00e1r minut, ale pokud pot\u0159ebuje\u0161 tolik po\u010d\u00edta\u010d\u016f, potrv\u00e1 n\u011bkolik dn\u00ed, ne\u017e v\u0161echno nastav\u00ed\u0161.\u201c Pak Ivao nep\u0159etr\u017eit\u011b po dobu 121 dn\u00ed spravovala pr\u00e1ci y-cruncher na t\u011bchto 25 virtu\u00e1ln\u00edch stroj\u00edch. <\/p>\n

Aby byly v\u00fdpo\u010dty p\u0159esn\u00e9, musely virtu\u00e1ln\u00ed stroje fungovat nep\u0159etr\u017eit\u011b. In\u017een\u00fdrka nastavila monitorovac\u00ed syst\u00e9m, kter\u00fd ji varoval, pokud do\u0161lo k n\u011bjak\u00e9 chyb\u011b, nap\u0159\u00edklad p\u0159i n\u00e1hl\u00e9m v\u00fdpadku jednoho z virtu\u00e1ln\u00edch stroj\u016f. Jen jedna nehoda \u2014 i na p\u00e1r minut \u2014 mohla ohrozit cel\u00fd proces v\u00fdpo\u010dtu, pokud by nebylo z\u00e1lohov\u00e1n\u00ed.<\/p>\n

\u201eV crunchu a Google Cloudu jsou k dispozici z\u00e1lohovac\u00ed syst\u00e9my, a j\u00e1 jsem je nastavila tak, abyste mohli okam\u017eit\u011b vytv\u00e1\u0159et z\u00e1lohy t\u011bchto disk\u016f, ani\u017e byste p\u0159eru\u0161ili v\u00fdpo\u010dty,\u201c \u0159\u00edk\u00e1 Ivao. Tato data byla pot\u00e9 kop\u00edrov\u00e1na a ukl\u00e1d\u00e1na extern\u011b, na jin\u00e9 disc\u00edch, ve form\u011b sn\u00edmk\u016f.<\/p>\n

\u201eNa za\u010d\u00e1tku bylo n\u011bkolik parametr\u016f, kter\u00e9 jsem zm\u011bnila, nap\u0159\u00edklad kolik dat jste mohli \u010d\u00edst nebo zapisovat najednou, a jak se hranice budou m\u011bnit s n\u00e1r\u016fstem,\u201c \u0159\u00edk\u00e1 Ivao.<\/p>\n

S rostouc\u00edm po\u010dtem \u010d\u00edslic se objem soubor\u016f zvy\u0161oval a slo\u017eitost v\u00fdpo\u010dt\u016f rostla neliner\u00e1rn\u011b. To velmi zkomplikovalo po\u010d\u00e1te\u010dn\u00ed v\u00fdpo\u010det, kdy\u017e Ivao zkou\u0161ela spo\u010d\u00edtat, jak\u00e9 zdroje virtu\u00e1ln\u00edch stroj\u016f bude pro projekt pot\u0159ebovat.<\/p>\n

Nyn\u00ed jsou dokon\u010deny jak v\u00fdpo\u010dty, tak kontrola v\u00fdsledku: v y-cruncher jsou zabudov\u00e1ny dva z\u00e1kladn\u00ed algoritmy \u2013 jeden pro v\u00fdpo\u010det samotn\u00e9ho p\u00ed a druh\u00fd pro kontrolu. Kontroln\u00ed algoritmus pracuje paraleln\u011b s v\u00fdpo\u010dtem, ale po\u010d\u00edt\u00e1 pouze jednu cifra, tak\u017ee rekord m\u016f\u017ee b\u00fdt ofici\u00e1ln\u011b zaregistrov\u00e1n.<\/p>\n

\nTeoreticky je mo\u017en\u00e9 nastavit nov\u00fd sv\u011btov\u00fd rekord, pokud prost\u011b vezmete p\u0159edchoz\u00ed soubor a pou\u017eijete vzorec Bailey \u2013 Borwein \u2013 Plouffe pro v\u00fdpo\u010det dal\u0161\u00edho \u010d\u00edsla. Ale to jist\u011b odporuje pravidl\u016fm pro registraci takov\u00fdch sv\u011btov\u00fdch rekord\u016f: pravd\u011bpodobn\u011b ka\u017ed\u00fd uchaze\u010d mus\u00ed za\u010d\u00edt v\u00fdpo\u010det od za\u010d\u00e1tku. Jako alternativu: zlep\u0161it p\u0159edchoz\u00ed dosa\u017een\u00ed o N%, co\u017e podle vzorce Bailey \u2013 Borwein \u2013 Plouffe nelze prov\u00e9st.<\/p>\n

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

\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0411\u044d\u0439\u043b\u0438 \u2014 \u0411\u043e\u0440\u0443\u044d\u0439\u043d\u0430 \u2014 \u041f\u043b\u0430\u0444\u0444\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0438\u0437\u0432\u043b\u0435\u0447\u044c \u043b\u044e\u0431\u0443\u044e \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0443\u044e \u0448\u0435\u0441\u0442\u043d\u0430\u0434\u0446\u0430\u0442\u0435\u0440\u0438\u0447\u043d\u0443\u044e \u0438\u043b\u0438 \u0434\u0432\u043e\u0438\u0447\u043d\u0443\u044e \u0446\u0438\u0444\u0440\u0443 \u0447\u0438\u0441\u043b\u0430 \u043f\u0438 \u0431\u0435\u0437 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u0445 (\u043d\u044b\u043d\u0435\u0448\u043d\u0438\u0439 \u0440\u0435\u043a\u043e\u0440\u0434 \u0431\u044b\u043b \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u043b\u0435\u043d \u043d\u0430 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0435 \u0427\u0443\u0434\u043d\u043e\u0432\u0441\u043a\u043e\u0433\u043e, \u0441\u043c. \u043f\u043e\u0434 \u043a\u0430\u0442\u043e\u043c) \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043a\u043b\u0430\u0441\u0442\u0435\u0440 Google Compute Engine \u0437\u0430 121 \u0434\u0435\u043d\u044c \u043d\u0430 25 \u0432\u0438\u0440\u0442\u0443\u0430\u043b\u044c\u043d\u044b\u0445 \u043c\u0430\u0448\u0438\u043d\u0430\u0445 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u043b \u043d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0435\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0446\u0438\u0444\u0440 \u0432 \u0447\u0438\u0441\u043b\u0435 \u043f\u0438, \u0443\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0432 \u043d\u043e\u0432\u044b\u0439 \u043c\u0438\u0440\u043e\u0432\u043e\u0439 \u0440\u0435\u043a\u043e\u0440\u0434: 31,4\u00a0\u0442\u0440\u0438\u043b\u043b\u0438\u043e\u043d\u0430 \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\udd47Nov\u00fd sv\u011btov\u00fd rekord v po\u010d\u00edt\u00e1n\u00ed \u010d\u00edsla p\u00ed: 31,4 bilionu \u010d\u00edslic | ProHoster","description":"Vzorec Bailey \u2013 Borwein \u2013.","canonical_url":"https:\/\/prohoster.info\/cs\/blog\/administrirovanie\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":null,"og:locale":"cs_CZ","og:site_name":"ProHoster | \u041a\u0443\u043f\u0438\u0442\u044c \u043d\u0430\u0434\u0435\u0436\u043d\u044b\u0439 \u0445\u043e\u0441\u0442\u0438\u043d\u0433 \u0434\u043b\u044f \u0441\u0430\u0439\u0442\u043e\u0432 \u0441 \u0437\u0430\u0449\u0438\u0442\u043e\u0439 \u043e\u0442 DDoS, VPS VDS \u0441\u0435\u0440\u0432\u0435\u0440\u044b","og:type":"article","og:title":"\ud83e\udd47\u041d\u043e\u0432\u044b\u0439 \u043c\u0438\u0440\u043e\u0432\u043e\u0439 \u0440\u0435\u043a\u043e\u0440\u0434 \u043f\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044e \u0447\u0438\u0441\u043b\u0430 \u043f\u0438: 31,4 \u0442\u0440\u043b\u043d \u0437\u043d\u0430\u043a\u043e\u0432 | 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