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I was wondering how python calculates base to power of exp so fast, if python is written in C then it should use pow() for calculating power, meanwhile the output of pow in C for a number like 2^10000 is like below :

#include <stdio.h>
#include <math.h>

int main()
{
    int base_num = 2;
    int exp_num = 10000;

    printf("%lf\n", pow(base_num,exp_num) );

    return 0;
}

the result is : inf

but when i execute this code in python :

>>> print( 2**10000 )

it results the large number below : 

19950631168807583848837421626835850838234968318861924548520089498529438830221946631919961684036194597899331129423209124271556491349413781117593785932096323957855730046793794526765246551266059895520550086918193311542508608460618104685509074866089624888090489894838009253941633257850621568309473902556912388065225096643874441046759871626985453222868538161694315775629640762836880760732228535091641476183956381458969463899410840960536267821064621427333394036525565649530603142680234969400335934316651459297773279665775606172582031407994198179607378245683762280037302885487251900834464581454650557929601414833921615734588139257095379769119277800826957735674444123062018757836325502728323789270710373802866393031428133241401624195671690574061419654342324638801248856147305207431992259611796250130992860241708340807605932320161268492288496255841312844061536738951487114256315111089745514203313820202931640957596464756010405845841566072044962867016515061920631004186422275908670900574606417856951911456055068251250406007519842261898059237118054444788072906395242548339221982707404473162376760846613033778706039803413197133493654622700563169937455508241780972810983291314403571877524768509857276937926433221599399876886660808368837838027643282775172273657572744784112294389733810861607423253291974813120197604178281965697475898164531258434135959862784130128185406283476649088690521047580882615823961985770122407044330583075869039319604603404973156583208672105913300903752823415539745394397715257455290510212310947321610753474825740775273986348298498340756937955646638621874569499279016572103701364433135817214311791398222983845847334440270964182851005072927748364550578634501100852987812389473928699540834346158807043959118985815145779177143619698728131459483783202081474982171858011389071228250905826817436220577475921417653715687725614904582904992461028630081535583308130101987675856234343538955409175623400844887526162643568648833519463720377293240094456246923254350400678027273837755376406726898636241037491410966718557050759098100246789880178271925953381282421954028302759408448955014676668389697996886241636313376393903373455801407636741877711055384225739499110186468219696581651485130494222369947714763069155468217682876200362777257723781365331611196811280792669481887201298643660768551639860534602297871557517947385246369446923087894265948217008051120322365496288169035739121368338393591756418733850510970271613915439590991598154654417336311656936031122249937969999226781732358023111862644575299135758175008199839236284615249881088960232244362173771618086357015468484058622329792853875623486556440536962622018963571028812361567512543338303270029097668650568557157505516727518899194129711337690149916181315171544007728650573189557450920330185304847113818315407324053319038462084036421763703911550639789000742853672196280903477974533320468368795868580237952218629120080742819551317948157624448298518461509704888027274721574688131594750409732115080498190455803416826949787141316063210686391511681774304792596709376

and because :

10000 x log(2) + 1 = 3011

so it's absolutely correct ! because it has 3011 digits.

so i was wondering how can it really act so fast to raise 2 to the power 10000 in less than a second, while the C itself cannot calculate 2^10000 and returns inf

what formula does it use to calculate so fast, also i have tested 2^1000000 and it resulted in less than 2 seconds

Erfan Mola
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    Probably uses exponentation by squaring. Do Google it. C can evaluate that if you empower it with a multiprecision library. (Personally I'm surprised it takes it so long.) – Bathsheba Nov 14 '19 at 17:46
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    The int type in C is some small fixed number of bytes (depending on implementation). The int type in Python is an arbitrary size, so it can store a silly big number like that. – khelwood Nov 14 '19 at 17:47
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    This may be of interest: [Python internals: Arbitrary-precision integer implementation](https://rushter.com/blog/python-integer-implementation/) – Ted Lyngmo Nov 14 '19 at 17:51
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    Possible duplicate: https://stackoverflow.com/questions/5246856/how-did-python-implement-the-built-in-function-pow – zweistein Nov 14 '19 at 17:55
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    *if python is written in C then it should use pow() for calculating power...* This is an oversimplification of python's arithmetic. Python's `int` type has arbitrary precision. There is no analogue of this type in C, so python has to define and implement its own algorithms for operations with exclusively `int` operands. – President James K. Polk Nov 14 '19 at 20:59
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    *so i was wondering how can it really act so fast to raise 2 to the power 10000 in less than a second*. Is that fast? Or is it really slow? Without understanding the underlying algorithms I don't see how you can have developed an expectation of performance. – President James K. Polk Nov 14 '19 at 21:02

0 Answers0