{"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\/hu\/blog\/administrirovanie\/novyj-mirovoj-rekord-po-vychisleniyu-chisla-pi-31-4-trln-znakov","title":{"rendered":"\u00daj vil\u00e1grekord a pi sz\u00e1m kisz\u00e1m\u00edt\u00e1s\u00e1ban: 31,4 trilli\u00f3 jegy","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

\"\u00daj
\n
\nA Bailey-Borwein-Plouffe k\u00e9plet, amely lehet\u0151v\u00e9 teszi b\u00e1rmely adott hexadecim\u00e1lis vagy bin\u00e1ris sz\u00e1mjegy kinyer\u00e9s\u00e9t a pi sz\u00e1m \u00e9rt\u00e9k\u00e9b\u0151l an\u00e9lk\u00fcl, hogy a kor\u00e1bbiak kisz\u00e1m\u00edt\u00e1s\u00e1ra lenne sz\u00fcks\u00e9g (a jelenlegi rekordot a Chudnovsky-algoritmus \u00e1ll\u00edtotta fel, l\u00e1sd lent).<\/i><\/p>\n

A Google Compute Engine sz\u00e1m\u00edt\u00e1si klasztere 121 nap alatt 25 virtu\u00e1lis g\u00e9pen a pi sz\u00e1m legnagyobb sz\u00e1mjegyeit sz\u00e1m\u00edtotta ki, \u00faj vil\u00e1grekordot \u00e1ll\u00edtva fel: 31,4 trilli\u00f3 sz\u00e1mjegy a tizedesvessz\u0151 ut\u00e1n. Ez az els\u0151 alkalom, hogy egy ilyen m\u00e9ret\u0171 pi sz\u00e1m kisz\u00e1m\u00edt\u00e1s\u00e1hoz nyilv\u00e1nos felh\u0151alap\u00fa szoftvert haszn\u00e1ltak.<\/p>\n

A rekordot Emma Haruka Iwao, a Google nagy teljes\u00edtm\u00e9ny\u0171 sz\u00e1m\u00edt\u00e1stechnikai r\u00e9szleg\u00e9nek munkat\u00e1rsa jegyzi. \u0150 haszn\u00e1lta a Google Cloud infrastrukt\u00far\u00e1j\u00e1t a sz\u00e1m\u00edt\u00e1shoz. Az el\u0151z\u0151 vil\u00e1grekordot Peter Trueb \u00e1ll\u00edtotta fel 2016-ban, \u0151 22,4 trilli\u00f3 sz\u00e1mjegyig sz\u00e1m\u00edtotta ki a pi-t. egy speci\u00e1lisan k\u00e9sz\u00edtett szerveren<\/a><\/noindex>, amit a munk\u00e1ltat\u00f3 is szponzor\u00e1lt.
\n<\/a><\/noindex>
\nAhogyan Trueb, a Google m\u00e9rn\u00f6ke is y-crunchert haszn\u00e1lt a sz\u00e1m\u00edt\u00e1shoz. Ez a program a Chudnovsky-algoritmusra<\/a><\/noindex>, egy gyors pi sz\u00e1m\u00edt\u00e1si algoritmusra \u00e9p\u00fcl. M\u00e1r az 1980-as \u00e9vekben maguk a Chudnovsky fiv\u00e9rek<\/a><\/noindex> seg\u00edts\u00e9g\u00e9vel milli\u00e1rd sz\u00e1mjegyig sz\u00e1molt\u00e1k ki a pi-t.<\/p>\n

Az algoritmus viszont a hipergeometrikus sor gyors konverg\u00e1l\u00e1s\u00e1nak tulajdons\u00e1g\u00e1n alapul:<\/p>\n

\"\u00daj
\n
\nEmma Haruka Iwao a \u201evar\u00e1zslatos\u201d sz\u00e1m ir\u00e1nt \u00e9rdekl\u0151d\u00f6tt, miut\u00e1n iskolai matematikai \u00f3r\u00e1n hallott r\u00f3la. Ki vezeti be az IPv6-ot, \u00e9s mi lass\u00edtja annak fejl\u0151d\u00e9s\u00e9t?<\/a><\/noindex> Wired<\/i>. Az egyetemen egyik professzora, Daisuke Takahashi szuperkomputerekkel el\u00e9rt sz\u00e1mjegysz\u00e1m rekordere volt. Ma szinte b\u00e1rmely \u00e9rdekl\u0151d\u0151 m\u00e9rn\u00f6k, akinek komoly sz\u00e1m\u00edt\u00e1si er\u0151forr\u00e1sai \u00e9s nagyobb t\u00e1rol\u00f3kapacit\u00e1sa van (a sz\u00e1m\u00edt\u00e1sok eredm\u00e9nyeinek t\u00e1rol\u00e1s\u00e1ra), fel\u00e1ll\u00edthat rekordot. A 2009-ben l\u00e9trehozott program y-cruncher<\/a><\/noindex> a matematikai \u00e1lland\u00f3k, p\u00e9ld\u00e1ul a pi sz\u00e1m kisz\u00e1m\u00edt\u00e1s\u00e1ra k\u00e9sz\u00fclt. T\u00e1mogatja a massz\u00edv p\u00e1rhuzamos\u00edt\u00e1st \u00e9s trilli\u00f3szoros tartom\u00e1nyokat. Ez a program l\u00e9nyeg\u00e9ben kommerssz\u00e9 tette az \u00e1lland\u00f3k sz\u00e1m\u00edt\u00e1s\u00e1t.<\/p>\n

\u201eEl\u00e9g nagy sz\u00e1m\u00edt\u00f3g\u00e9p kell a vil\u00e1grekord megd\u00f6nt\u00e9s\u00e9hez \u2013 mondja Ivao. \u2013 Ezt nem lehet egy boltban v\u00e1s\u00e1rolt g\u00e9ppel megcsin\u00e1lni, ez\u00e9rt kor\u00e1bban az emberek egyedi g\u00e9peket \u00e9p\u00edtettek.\u201c 2018 szeptember\u00e9ben Ivao elkezdte vizsg\u00e1lni, hogy technikailag hogyan m\u0171k\u00f6dik majd a sz\u00e1m\u00edt\u00e1s a rekordsz\u00e1mok f\u00f6l\u00f6tt. Azonnal vil\u00e1goss\u00e1 v\u00e1lt, hogy a f\u0151 probl\u00e9ma az adatok t\u00e1rol\u00e1sa lesz. V\u00e9g\u00fcl kider\u00fclt, hogy a kisz\u00e1m\u00edtott eredm\u00e9ny 170 terab\u00e1jtot foglal el. Az el\u0151d\u00f6kh\u00f6z hasonl\u00f3an, a l\u00e1ny nem egyedi szervert \u00e9p\u00edtett, hanem a Google Cloud infrastrukt\u00far\u00e1j\u00e1t haszn\u00e1lta.<\/p>\n

\"\u00dajIvao 25 virtu\u00e1lis g\u00e9pet ind\u00edtott: \u201eDe ahelyett, hogy 25-sz\u00f6r megnyomtam volna azt a gombot, automatiz\u00e1ltam azt \u2013 magyar\u00e1zza. \u2013 Ezt megteheted p\u00e1r perc alatt, de ha ennyi sz\u00e1m\u00edt\u00f3g\u00e9pre van sz\u00fcks\u00e9ged, akkor t\u00f6bb napra lesz sz\u00fcks\u00e9ged, hogy mindent be\u00e1ll\u00edts.\u201c Ezt k\u00f6vet\u0151en Ivao 121 napon kereszt\u00fcl folyamatosan ir\u00e1ny\u00edtotta a y-crunchert ezeken a 25 virtu\u00e1lis g\u00e9pen. <\/p>\n

A sz\u00e1m\u00edt\u00e1sok helyess\u00e9ge \u00e9rdek\u00e9ben a virtu\u00e1lis g\u00e9peknek folyamatosan m\u0171k\u00f6dni\u00fck kellett. Az m\u00e9rn\u00f6k egy monitoroz\u00f3 rendszert \u00e1ll\u00edtott be, amely figyelmeztette volna, ha valami baj t\u00f6rt\u00e9nt, p\u00e9ld\u00e1ul egy virtu\u00e1lis g\u00e9p v\u00e1ratlan le\u00e1ll\u00e1sa eset\u00e9n. Mind\u00f6ssze egy baleset \u2013 m\u00e9g p\u00e1r percre is \u2013 vesz\u00e9lyeztethette volna az eg\u00e9sz sz\u00e1m\u00edt\u00e1si folyamatot, ha nem lett volna ment\u00e9s.<\/p>\n

\u201eA cruncherben \u00e9s a Google Cloudban vannak ment\u00e9si rendszerek, \u00e9s \u00e9n \u0151ket \u00fagy \u00e1ll\u00edtottam be, hogy az adatlemezek m\u00e1solat\u00e1t azonnal el lehessen k\u00e9sz\u00edteni an\u00e9lk\u00fcl, hogy le\u00e1ll\u00edtan\u00e1nk a sz\u00e1m\u00edt\u00e1sokat \u2013 mondja Ivao. Ezek az adatok ezut\u00e1n m\u00e1s k\u00fcls\u0151 lemezekre m\u00e1solt\u00e1k \u00e9s snapshot form\u00e1ban lettek t\u00e1rolva.<\/p>\n

\u201eEleinte t\u00f6bb param\u00e9tert v\u00e1ltoztattam, p\u00e9ld\u00e1ul hogy mennyi adatot tudt\u00e1l olvasni vagy \u00edrni egyszerre, \u00e9s hogy a hat\u00e1rok hogyan fognak v\u00e1ltozni a n\u00f6veked\u00e9s sor\u00e1n \u2013 mondja Ivao.<\/p>\n

A sz\u00e1mjegyek sz\u00e1m\u00e1nak n\u00f6veked\u00e9s\u00e9vel a f\u00e1jlok m\u00e9rete n\u0151tt, m\u00edg a sz\u00e1m\u00edt\u00e1sok bonyolults\u00e1ga nemline\u00e1risan emelkedett. Ez nagyon megnehez\u00edtette az els\u0151 sz\u00e1m\u00edt\u00e1st, amikor Ivao megpr\u00f3b\u00e1lta kisz\u00e1m\u00edtani, hogy milyen er\u0151forr\u00e1sokra lesz sz\u00fcks\u00e9ge a virtu\u00e1lis g\u00e9peknek a projekthez.<\/p>\n

Most a sz\u00e1m\u00edt\u00e1sok, mind az eredm\u00e9nyek ellen\u0151rz\u00e9se befejez\u0151d\u00f6tt: a y-cruncherbe k\u00e9t alap algoritmus van be\u00e9p\u00edtve - az egyik a pi kisz\u00e1m\u00edt\u00e1s\u00e1ra, a m\u00e1sik az ellen\u0151rz\u00e9sre. Az ellen\u0151rz\u0151 algoritmus p\u00e1rhuzamosan m\u0171k\u00f6dik a sz\u00e1m\u00edt\u00e1ssal, de csak egy sz\u00e1mjegyet sz\u00e1m\u00edt, \u00edgy a rekord hivatalosan regisztr\u00e1lhat\u00f3.<\/p>\n

\nElm\u00e9letileg \u00faj vil\u00e1grekordot lehetne fel\u00e1ll\u00edtani, ha egyszer\u0171en elvenn\u00e9nk az el\u0151z\u0151 f\u00e1jlt, \u00e9s alkalmazn\u00e1nk a Bailey-Borwein-Plouffe formul\u00e1t egy \u00faj sz\u00e1m kisz\u00e1m\u00edt\u00e1s\u00e1hoz. De ez val\u00f3sz\u00edn\u0171leg ellentmond a hasonl\u00f3 vil\u00e1grekordok regisztr\u00e1l\u00e1s\u00e1nak szab\u00e1lyainak: val\u00f3sz\u00edn\u0171leg minden jel\u00f6ltnek null\u00e1r\u00f3l kell kezdenie a sz\u00e1m\u00edt\u00e1st. Alternat\u00edva: jav\u00edtani a kor\u00e1bbi eredm\u00e9nyt N%-kal, amit a Bailey-Borwein-Plouffe formul\u00e1val nem lehet el\u00e9rni.<\/p>\n

Forr\u00e1s: 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\udd47\u00daj vil\u00e1grekord a pi sz\u00e1m\u00edt\u00e1s\u00e1ban: 31,4 trilli\u00f3 sz\u00e1mjegy | ProHoster","description":"A Bailey-Borwein 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