{"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\/ro\/blog\/administrirovanie\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","title":{"rendered":"Nou record mondial la calcularea num\u0103rului \u03c0: 31,4 trilioane de cifre","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"Nou
\n
\nFormula Bailey-Borwein-Plouffe, which allows extracting any specific hexadecimal or binary digit of the number pi without calculating the previous ones (the current record was set on the Chudnovsky algorithm, see below)<\/i><\/p>\n

The Google Compute Engine computational cluster calculated the largest number of digits in pi over 121 days on 25 virtual machines, setting a new world record: 31.4 trillion digits after the decimal point. This is the first time public cloud software has been used to compute pi to such an extent.<\/p>\n

The record will be attributed to Emma Haruka Iwao from the high-performance computing division at Google. She utilized Google Cloud infrastructure for the computations. 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 her employer.
\n<\/a><\/noindex>
\nLike Truong, the Google engineer applied y-cruncher for the calculation. This program uses the Chudnovsky algorithm<\/a><\/noindex>, a fast algorithm for calculating pi. Even 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 fast convergence property of the hypergeometric series:<\/p>\n

\"Nou
\n
\nEmma Haruka Iwao became fascinated with the 'magic' number after learning about it in a math class at school, scrie<\/a><\/noindex> Wired<\/i>. At university, one of her professors, Daisuke Takahashi, was the record holder for the number of calculated digits of pi using a supercomputer. Today, almost any interested engineer with access to robust computational resources and ample storage (to hold the results of the calculations) can set a record. The program created in 2009, y-cruncher<\/a><\/noindex> , is designed to calculate mathematical constants like pi. It supports massive multithreading and trillion-digit ranges. This program effectively commoditized constant calculations.<\/p>\n

\u201eAi nevoie de un computer destul de mare pentru a bate recordul mondial\u201c, spune Ivao. \u201eNu po\u021bi face asta pe un computer din magazin, a\u0219a c\u0103, \u00een trecut, oamenii \u00ee\u0219i construiau ma\u0219ini personalizate.\u201d \u00cen septembrie 2018, Ivao a \u00eenceput s\u0103 analizeze cum va func\u021biona tehnic procesul de calculare dincolo de gama recordului. A devenit imediat evident c\u0103 principala problem\u0103 va fi volumul datelor de stocare. \u00cen final, s-a constatat c\u0103 rezultatul calculat ocup\u0103 170 de terabytes. \u00cen loc s\u0103 construiasc\u0103 un server personalizat, ca predecesorii s\u0103i, fata a folosit infrastructura Google Cloud.<\/p>\n

\"NouIvao a lansat 25 de ma\u0219ini virtuale: \u201eDar \u00een loc s\u0103 apas pe acel buton al ma\u0219inii virtuale de 25 de ori, l-am automatizat\u201c, explic\u0103 ea. \u201ePo\u021bi face asta \u00eentr-un minut, dar dac\u0103 ai nevoie de at\u00e2t de multe computere, \u00ee\u021bi va lua c\u00e2teva zile s\u0103 configurezi totul.\u201d Apoi, timp de 121 de zile ne\u00eentrerupte, Ivao a gestionat func\u021bionarea y-cruncher pe aceste 25 de ma\u0219ini virtuale. <\/p>\n

Pentru corectitudinea calculilor, ma\u0219inile virtuale trebuiau s\u0103 func\u021bioneze constant. Inginerul a instalat un sistem de monitorizare care o avertiza dac\u0103 ceva nu mergea bine, de exemplu, despre o defectare brusc\u0103 a uneia dintre ma\u0219inile virtuale. O singur\u0103 defec\u021biune - chiar \u0219i pentru c\u00e2teva minute - ar fi putut compromite \u00eentregul proces de calculare, dac\u0103 nu ar fi avut un sistem de rezerv\u0103.<\/p>\n

\u201e\u00cen cruncher \u0219i Google Cloud exist\u0103 sisteme de rezerv\u0103, iar eu le-am configurat astfel \u00eenc\u00e2t s\u0103 po\u021bi crea instantaneu copii ale acestor discuri, f\u0103r\u0103 a opri calcul\u0103rile\u201c, spune Ivao. Aceste date erau apoi copiate \u0219i stocate de extern, pe alte discuri, sub form\u0103 de instantanee.<\/p>\n

\u201eLa \u00eenceput, au fost c\u00e2teva parametrii pe care i-am modificat, de exemplu, c\u00e2t de multe date puteai citi sau scrie simultan \u0219i cum se vor schimba limitele pe m\u0103sur\u0103 ce se m\u0103resc\u201c, spune Ivao.<\/p>\n

Pe m\u0103sur\u0103 ce num\u0103rul cifrelor a crescut, volumul fi\u0219ierelor a devenit mai mare, iar complexitatea calculilor a crescut neliniar. Acest lucru a complicat foarte multe calculul ini\u021bial, c\u00e2nd Ivao \u00eencerca s\u0103 estimeze ce resurse ale ma\u0219inilor virtuale ar fi necesare pentru proiect.<\/p>\n

Acum s-au finalizat at\u00e2t calculele, c\u00e2t \u0219i verificarea rezultatului: \u00een y-cruncher sunt integrate dou\u0103 algoritmi de baz\u0103 - unul pentru calcularea cifrei pi \u0219i altul pentru verificare. Algoritmul de verificare func\u021bioneaz\u0103 paralel cu calculul, dar calculeaz\u0103 doar o singur\u0103 cifr\u0103, astfel \u00eenc\u00e2t recordul poate fi \u00eenregistrat oficial.<\/p>\n

\nTeoretic, un nou record mondial poate fi stabilit dac\u0103 se ia pur \u0219i simplu fi\u0219ierul anterior \u0219i se aplic\u0103 formula Bailey \u2013 Borwein \u2013 Plouffe pentru a calcula \u00eenc\u0103 o cifr\u0103. Dar cu siguran\u021b\u0103 aceasta va contraveni regulilor de \u00eenregistrare a acestor recorduri mondiale: cel mai probabil, fiecare pretendent trebuie s\u0103 \u00eenceap\u0103 calculul de la zero. Ca alternativ\u0103: \u00eembun\u0103t\u0103\u021bi\u021bi realizarea anterioar\u0103 cu N%, lucru ce nu va fi posibil cu formula Bailey \u2013 Borwein \u2013 Plouffe.<\/p>\n

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

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