{"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\/sl\/blog\/administrirovanie\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","title":{"rendered":"Nov svetovni rekord pri izra\u010dunu \u0161tevila pi: 31,4 triljona znakov","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"Nov
\n
\nBailey-Borwein-Plouffejeva formula, which allows extracting any specific hexadecimal or binary digit of pi without calculating previous ones (the current record was set using the Chudnovsky algorithm, see below)<\/i><\/p>\n

Google Compute Engine computational cluster calculated the largest number of digits of pi in 121 days using 25 virtual machines, setting a new world record: 31.4 trillion digits after the decimal point. This is the first time that publicly available cloud software has been used to calculate pi to such magnitude.<\/p>\n

The record will be credited to Emma Haruka Iwao from the high-performance computing division at Google. She used Google Cloud infrastructure for the calculations. The previous world record was set by Peter Truong in 2016, who calculated pi to 22.4 trillion digits. on a specially made server<\/a><\/noindex>, which was also sponsored by the employer.
\n<\/a><\/noindex>
\nLike Truong, the Google engineer used y-cruncher for the calculation. This program employs the Chudnovsky algorithm<\/a><\/noindex>, a fast algorithm for computing pi. Back in the 80s, the Chudnovsky brothers<\/a><\/noindex> used it to calculate a billion digits after the decimal point.<\/p>\n

In turn, the algorithm is based on the rapidly converging properties of the hypergeometric series:<\/p>\n

\"Nov
\n
\nEmma Haruka Iwao became fascinated by the 'magic' number after learning about it in a mathematics class at school, , that multimodelity is a sine qua non condition primarily for<\/a><\/noindex> Wired<\/i>. At university, one of her professors, Daisuke Takahashi, held the record for the most digits calculated using a supercomputer. Nowadays, practically anyone with access to serious computational resources and ample disk storage (for storing the calculation results) can set a record. The program created in 2009, y-cruncher<\/a><\/noindex> , is designed for calculating mathematical constants such as pi. It supports massive multithreading and trillion-digit ranges. This program has effectively commoditized the calculation of constants.<\/p>\n

\u201ePotrebujete precej mo\u010dnej\u0161i ra\u010dunalnik, da osvojite svetovni rekord,\u201c pravi Ivao. \u201eNekako ne morete dose\u010di tega na ra\u010dunalniku iz trgovine, zato so ljudje prej gradili prilagojene naprave.\u201c Septembra 2018 je Ivao za\u010dela razmi\u0161ljati, kako tehni\u010dno izvesti proces ra\u010duna izven rekorda. Takoj je bilo jasno, da bo glavni problem obseg podatkov za shranjevanje. Na koncu se je izkazalo, da izbrani rezultat zavzema 170 terabajtov. Namesto gradnje prilagojenega stre\u017enika, kot so to po\u010deli njegovi predhodniki, je deklica uporabila infrastrukturo Google Cloud.<\/p>\n

\"NovIvao je zagnala 25 virtualnih strojev: \u201eAmpak namesto da bi to\u010dno 25-krat pritisnila gumb za virtualni stroj, sem to avtomatizirala,\u201c razlaga. \u201eLahko to naredite v nekaj minutah, vendar \u010de potrebujete toliko ra\u010dunalnikov, bo \u0161e vedno trajalo nekaj dni, da vse nastavite.\u201c Nato je neprekinjeno 121 dni upravljala delo y-cruncherja na teh 25 virtualnih strojih. <\/p>\n

Za pravilnost izra\u010dunov so morali virtualni stroji delovati neprekinjeno. In\u017eenirka je namestila sistem spremljanja, ki jo je opozoril, \u010de bi bilo kaj narobe, na primer ob nenadnem padcu enega izmed virtualnih strojev. Le ena okvara \u2013 celo za nekaj minut \u2013 bi lahko ogrozila celoten proces izra\u010dunov, \u010de ne bi bilo varnostne kopije.<\/p>\n

\u201eV cruncherju in Google Cloud obstajajo varnostni sistemi, in jih je nastavila tako, da lahko takoj naredite varnostne kopije teh diskov, ne da bi ustavili izra\u010dune,\u201c pravi Ivao. Ti podatki so bili nato kopirani in shranjeni z zunanjega dela, na drugih diskih, v obliki posnetkov.<\/p>\n

\u201eNa za\u010detku je bilo ve\u010d parametrov, ki sem jih spremenila, kot so koliko podatkov ste lahko prebrali ali zapisali naenkrat, in kako se bodo meje spreminjale z nara\u0161\u010danjem,\u201c pravi Ivao.<\/p>\n

Z nara\u0161\u010danjem \u0161tevila \u0161tevilk se je obseg datotek pove\u010deval, kompleksnost izra\u010dunov pa je nelinearno nara\u0161\u010dala. To je zelo ote\u017eilo za\u010detni izra\u010dun, ko je Ivao posku\u0161ala ugotoviti, kak\u0161ne vire virtualnih strojev bo potrebovala za projekt.<\/p>\n

Zdaj so zaklju\u010deni tako izra\u010duni kot preverjanje rezultata: v y-cruncher so vgrajeni dva osnovna algoritma - eden za izra\u010dun \u03c0, drugi pa za preverjanje. Algoritem za preverjanje deluje vzporedno z izra\u010dunom, vendar izra\u010duna le eno \u0161tevilko, kar omogo\u010da uradno registracijo rekorda.<\/p>\n

\nTeoreti\u010dno je mo\u017eno postaviti nov svetovni rekord, \u010de preprosto vzamemo prej\u0161njo datoteko in uporabimo formulacijo Bailey \u2013 Borwein \u2013 Plouffe za izra\u010dun \u0161e ene \u0161tevilke. Vendar to zagotovo kr\u0161i pravila za registracijo tovrstnih svetovnih rekordov: verjetno mora vsak kandidat za\u010deti izra\u010dun od za\u010detka. Ena mo\u017enost: izbolj\u0161ati prej\u0161nji dose\u017eek za N%, kar s formulo Bailey \u2013 Borwein \u2013 Plouffe ne bo mogo\u010de.<\/p>\n

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

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