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Big numbers in Python

Numbers in Python can get arbitrarily large. This is pretty fun for things like doing factorials

>>> def fac(n): return reduce(lambda x,y: x*y, range(1,n+1))
... 
>>> fac(1)
1
>>> fac(2)
2
>>> fac(3)
6
>>> fac(4)
24
>>> fac(5)
120
>>> fac(500)
1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000L
You're like Ooooh! I'm a gonna break Python!

>>> fac(5000)

And Python calmly gives you

42285779266055435222010642002335844053907866746266467488497824021813580527081082006908990478717063875370847466573006854458784860666838127363372108937727876312793903630584621606439044789869822398719297088962116126529683217755003992421968370314690726447287878979040475488416221522667192841096923691044956597173635294840022384038112064482023085767110450230617489475542830976178172404080532480992780932878405548619936454829121187625824880218917397790005021321259804363924462646077051135884659510867547058583392465522558903547443598834738317898803463300845863151020909150993565382001093304796574255674193091705517280520023607508599119763522875590790204336974312350691683121192449597155626740752146219898623308862599830285986485757874944596311528697088671004626842364817898990545469086139161321834417414880718623444811483120949036119654687276775561788682872026910481409245641034183597560427645816151317857590166107178254415698088335937272999560337137120047104943765629114248860533529949964230069997220491812010081905943914067505326500477553385089909794510155109148690700440711957233602624336813233021870928769919680665656975279042225826784156108337642578103262920268721107027468139435112860150232619064995917189736417637843649121970910984094451489535895910380417694195665783482207174910551275263914838117205260482696516264271009491939333266103010436053045911701455720958471435372194824668679346737590487226813341020786090365710880637661624974950741310707740168218058594552644517140927746923006269751134604417456794673582878226162958424867515737917294272417878310542985824511757551188450657442482757466080023858837849239624736876150701576772589832112863229553704490251638792512759084179174464046691353104734798446499615459554201399631735747630174003679619291994219076289544565626176704179953816113338731282351153415258130908791588363835166479722591294427065355714251173732380723263295812179791667969232968709692390100325557478905509980748706104723064619598495523965761220867386651417169930755769189790267515734207586479634533844683508596549072732632191050406428971309622450516206466946809886991712212740450402068492326624176013291022786668727030528470945252682549661777249964520669983692591069089408263740104349837159112645582228060636139411534431677176993435366428492829443641476961588199366138825557748770993700459475390784514903443452117456059403991626844469766182138747070532555957793319646099666214537756493547416970856238921477322286550718249043001618614219276045230767062114296176727470412361610722000974375864749275366514953216478084907514633007101669131342066288256261828386583698363210876071042751607334834778841479673242708041086076184128188830711509898213533840661065214708704687476099542747367350945155359976904036735338555105257168265031768240574399341486239233198143257918219332189894045086501361099809838399311099635598132800104973158859631213185380120504678764291066936560043730563343198487904899852470129330078934453286815667976288049553284638602013348026527983694639338499567504999370781474656154343893043138423787898184780288600997108869563298834771186312238278596365311513237793137364739742936941149902875197222799954518261548829895115192668211245135531847220999043535594988729992203506203981601108637623653978217238023784665067362451063503442318731533830821204380471099941922782103974755271741604389016972396130554937184483611980356589606202500909366439936017200738361335440509432907247651890950250772467584198941222465939216311635203814736247952853973208930953342191063570280557662972015655651076778080593345363112182956179288767300280245093212277885296841820826177847695564498038569127578737267804095915871173397110316523267806079812760924617350412018266687426280538527584397916760900774338074842075118511910292196033937628098675366508521286925532153678793252188257410186613705432897373586272537017855880663985135038694403960492825882018041917807364969388580259775839889201438974716546597351085260570623440206963706566012953573404358296147342727580563083951066737534925965951857564693972321827578000325059389530382053969755887051154307392082742244051629970873959976846120624662909811236801257989128480250509402891695976507939543719131137931442740513559963037564221452729434179724618759796407423914783899354156583471615685849903677305661135383336708754890041309198167633074904151033759730724688583924694171554829573075061850588158195952899266022562690343957331345066697295211523066869622792094777997433657447267347140892807141128388808269337737807729310411076751363947620061085804059601963905801576100233746386935222838580143495717812558144586293004247940406573685986200791460459025541392995008804471038475899032654809733816694050008545272371357139490246382030866854180283831752766806427848956100575585999171896678644915406357001449719424987892085973125427556751457520639911815073639748310249079384172565342189427676911659815343008463708776951029541513655173467505401523970604257174600108996844049884598547797790503163256848915655723100649972649872148080018177035770150298300887948724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371367395995678940884705976859514505017241517746017351430990972615509378334720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000L

Another fun thing about such arbitrary length integers in Python is that you can do weird, and fast, bit shifts.

>>> n = 1 << int(250e6)
You just created a 250 million bit array with the last bit set to one! And it's fast too:
In [407]: %timeit n = 1 << int(250e6)
100 loops, best of 3: 12.4 ms per loop

In [408]: %%timeit n = 1 << int(250e6)
   .....: n &= 1
   .....: 
10000000 loops, best of 3: 159 ns per loop

In [409]: %%timeit n = 1 << int(250e6)
n &= 1 << int(200e6)
   .....: 
100 loops, best of 3: 10.5 ms per loop



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