Integer roots: Difference between revisions

=={{header|F#}}==

{{trans|C#}}

<lang fsharp>open System

let iroot (base_ : bigint) n =

if base_ < bigint.Zero || n <= 0 then

raise (ArgumentException "Bad parameter")

let n1 = n - 1

let n2 = bigint n

let n3 = bigint n1

let mutable c = bigint.One

let mutable d = (n3 + base_) / n2

let mutable e = ((n3 * d) + (base_ / bigint.Pow(d, n1))) / n2

while c <> d && c <> e do

c <- d

d <- e

e <- (n3 * e + base_ / bigint.Pow(e, n1)) / n2

if d < e then

d

else

e

[<EntryPoint>]

let main _ =

Console.WriteLine("3rd integer root of 8 = {0}", (iroot (bigint 8) 3))

Console.WriteLine("3rd integer root of 9 = {0}", (iroot (bigint 9) 3))

let b = bigint.Pow(bigint 100, 2000) * (bigint 2)

Console.WriteLine("First 2001 digits of the sqaure root of 2: {0}", (iroot b 2))

0 // return an integer exit code</lang>

{{out}}

<pre>3rd integer root of 8 = 2

3rd integer root of 9 = 2

First 2001 digits of the sqaure root of 2: 141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008</pre>