Integer roots: Difference between revisions

Content added Content deleted
m (→‎{{header|F#}}: fix heading, as suggested on the Count examples/Full list/Tier 4 talk page)
m (syntax highlighting fixup automation)
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{{trans|D}}
{{trans|D}}


<lang 11l>F iRoot(BigInt b, Int n)
<syntaxhighlight lang="11l">F iRoot(BigInt b, Int n)
I b < 2 {R b}
I b < 2 {R b}
V n1 = n - 1
V n1 = n - 1
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print(‘3rd root of 8 = ’iRoot(8, 3))
print(‘3rd root of 8 = ’iRoot(8, 3))
print(‘3rd root of 9 = ’iRoot(9, 3))
print(‘3rd root of 9 = ’iRoot(9, 3))
print(‘First 2001 digits of the square root of 2: ’iRoot(BigInt(100) ^ 2000 * 2, 2))</lang>
print(‘First 2001 digits of the square root of 2: ’iRoot(BigInt(100) ^ 2000 * 2, 2))</syntaxhighlight>


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{{trans|D}}
{{trans|D}}


<lang rebol>iroot: function [b n][
<syntaxhighlight lang="rebol">iroot: function [b n][
if b<2 -> return b
if b<2 -> return b
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print ["3rd root of 8:" iroot 8 3]
print ["3rd root of 8:" iroot 8 3]
print ["3rd root of 9:" iroot 9 3]
print ["3rd root of 9:" iroot 9 3]
print ["First 2001 digits of the square root of 2:" iroot (100^2000)*2 2]</lang>
print ["First 2001 digits of the square root of 2:" iroot (100^2000)*2 2]</syntaxhighlight>


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=={{header|BASIC256}}==
=={{header|BASIC256}}==
{{trans|FreeBASIC}}
{{trans|FreeBASIC}}
<lang BASIC256>function root(n, x)
<syntaxhighlight lang="basic256">function root(n, x)
for nr = floor(sqr(x)) to 1 step -1
for nr = floor(sqr(x)) to 1 step -1
if (nr ^ n) <= x then return nr
if (nr ^ n) <= x then return nr
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print root(4, 167)
print root(4, 167)
print root(2, 2e18)
print root(2, 2e18)
end</lang>
end</syntaxhighlight>
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<pre>
<pre>
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=={{header|C}}==
=={{header|C}}==
{{trans|C++}}
{{trans|C++}}
<lang C>#include <stdio.h>
<syntaxhighlight lang="c">#include <stdio.h>
#include <math.h>
#include <math.h>


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return 0;
return 0;
}</lang>
}</syntaxhighlight>
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<pre>3rd root of 8 = 2
<pre>3rd root of 8 = 2
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=={{header|C sharp|C#}}==
=={{header|C sharp|C#}}==
{{trans|Java}}
{{trans|Java}}
<lang csharp>using System;
<syntaxhighlight lang="csharp">using System;
using System.Numerics;
using System.Numerics;


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}
}
}
}
}</lang>
}</syntaxhighlight>
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<pre>3rd integer root of 8 = 2
<pre>3rd integer root of 8 = 2
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=={{header|C++}}==
=={{header|C++}}==
<lang cpp>#include <iostream>
<syntaxhighlight lang="cpp">#include <iostream>
#include <math.h>
#include <math.h>


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return 0;
return 0;
}</lang>
}</syntaxhighlight>
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<pre>3rd root of 8 = 2
<pre>3rd root of 8 = 2
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=={{header|D}}==
=={{header|D}}==
{{trans|Kotlin}}
{{trans|Kotlin}}
<lang D>import std.bigint;
<syntaxhighlight lang="d">import std.bigint;
import std.stdio;
import std.stdio;


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b = BigInt(100)^^2000*2;
b = BigInt(100)^^2000*2;
writeln("First 2001 digits of the square root of 2: ", b.iRoot(2));
writeln("First 2001 digits of the square root of 2: ", b.iRoot(2));
}</lang>
}</syntaxhighlight>
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<pre>3rd root of 8 = 2
<pre>3rd root of 8 = 2
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=={{header|Elixir}}==
=={{header|Elixir}}==
{{trans|Ruby}}
{{trans|Ruby}}
<lang elixir>defmodule Integer_roots do
<syntaxhighlight lang="elixir">defmodule Integer_roots do
def root(_, b) when b<2, do: b
def root(_, b) when b<2, do: b
def root(a, b) do
def root(a, b) do
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end
end


Integer_roots.task</lang>
Integer_roots.task</syntaxhighlight>


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=={{header|F_Sharp|F#}}==
=={{header|F_Sharp|F#}}==
{{trans|C#}}
{{trans|C#}}
<lang fsharp>open System
<syntaxhighlight lang="fsharp">open System


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


0 // return an integer exit code</lang>
0 // return an integer exit code</syntaxhighlight>
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<pre>3rd integer root of 8 = 2
<pre>3rd integer root of 8 = 2
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=={{header|Factor}}==
=={{header|Factor}}==
{{trans|Sidef}}
{{trans|Sidef}}
<lang factor>USING: io kernel locals math math.functions math.order
<syntaxhighlight lang="factor">USING: io kernel locals math math.functions math.order
prettyprint sequences ;
prettyprint sequences ;


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"First 2,001 digits of the square root of two:" print
"First 2,001 digits of the square root of two:" print
2 100 2000 ^ 2 * root .</lang>
2 100 2000 ^ 2 * root .</syntaxhighlight>
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<pre>
<pre>
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=={{header|FreeBASIC}}==
=={{header|FreeBASIC}}==
{{trans|Ring}}
{{trans|Ring}}
<lang freebasic>#define floor(x) ((x*2.0-0.5) Shr 1)
<syntaxhighlight lang="freebasic">#define floor(x) ((x*2.0-0.5) Shr 1)


Function root(n As Uinteger, x As Uinteger) As Uinteger
Function root(n As Uinteger, x As Uinteger) As Uinteger
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Print root(2, 2e18)
Print root(2, 2e18)


Sleep</lang>
Sleep</syntaxhighlight>
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<pre>2
<pre>2
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=={{header|Go}}==
=={{header|Go}}==
===int===
===int===
<lang go>package main
<syntaxhighlight lang="go">package main


import "fmt"
import "fmt"
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r += Δr
r += Δr
}
}
}</lang>
}</syntaxhighlight>
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<pre>
<pre>
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</pre>
</pre>
===big.Int===
===big.Int===
<lang go>package main
<syntaxhighlight lang="go">package main


import (
import (
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r.Add(r, &Δr)
r.Add(r, &Δr)
}
}
}</lang>
}</syntaxhighlight>
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<pre>
<pre>
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=={{header|Haskell}}==
=={{header|Haskell}}==
{{trans|Python}}
{{trans|Python}}
<lang haskell>root :: Integer -> Integer -> Integer
<syntaxhighlight lang="haskell">root :: Integer -> Integer -> Integer
root a b = findAns $ iterate (\x -> (a1 * x + b `div` (x ^ a1)) `div` a) 1
root a b = findAns $ iterate (\x -> (a1 * x + b `div` (x ^ a1)) `div` a) 1
where
where
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print $ root 3 8
print $ root 3 8
print $ root 3 9
print $ root 3 9
print $ root 2 (2 * 100 ^ 2000) -- first 2001 digits of the square root of 2</lang>
print $ root 2 (2 * 100 ^ 2000) -- first 2001 digits of the square root of 2</syntaxhighlight>


Or equivalently, in terms of an applicative expression:
Or equivalently, in terms of an applicative expression:


<lang haskell>integerRoot :: Integer -> Integer -> Integer
<syntaxhighlight lang="haskell">integerRoot :: Integer -> Integer -> Integer
integerRoot n x =
integerRoot n x =
go $ iterate ((`div` n) . ((+) . (pn *) <*> (x `div`) . (^ pn))) 1
go $ iterate ((`div` n) . ((+) . (pn *) <*> (x `div`) . (^ pn))) 1
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main :: IO ()
main :: IO ()
main = mapM_ (print . uncurry integerRoot) [(3, 8), (3, 9), (2, 2 * 100 ^ 2000)]</lang>
main = mapM_ (print . uncurry integerRoot) [(3, 8), (3, 9), (2, 2 * 100 ^ 2000)]</syntaxhighlight>


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For example, If you use "3 <.@%: (2*10x^2*200'''0''')" instead of "3 <.@%: (2*10x^2*200'''1''')", you will get an output starting with "271441761659490657151808946...", which are the first digits of the cube root of 20, not 2.
For example, If you use "3 <.@%: (2*10x^2*200'''0''')" instead of "3 <.@%: (2*10x^2*200'''1''')", you will get an output starting with "271441761659490657151808946...", which are the first digits of the cube root of 20, not 2.


<lang J> 9!:37]0 4096 0 222 NB. set display truncation sufficiently high for our results
<syntaxhighlight lang="j"> 9!:37]0 4096 0 222 NB. set display truncation sufficiently high for our results


2 <.@%: (2*10x^2*2000)
2 <.@%: (2*10x^2*2000)
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114869835499703500679862694677792758944385088909779750551371111849360320625351305681147311301150847391457571782825280872990018972855371267615994917020637676959403854539263226492033301322122190625130645468320078386350285806907949085127708283982797043969640382563667945344431106523789654147255972578315704103326302050272017414235255993151553782375173884359786924137881735354092890268530342009402133755822717151679559278360263800840317501093689917495888199116488588871447782240220513546797235647742625493141141704109917646404017146978939243424915943739448283626010758721504375406023613552985026793701507511351368254645700768390780390334017990233124030682358360249760098999315658413563173197024899154512108923313999675829872581317721346549115423634135836394159076400636688679216398175376716152621781331348
114869835499703500679862694677792758944385088909779750551371111849360320625351305681147311301150847391457571782825280872990018972855371267615994917020637676959403854539263226492033301322122190625130645468320078386350285806907949085127708283982797043969640382563667945344431106523789654147255972578315704103326302050272017414235255993151553782375173884359786924137881735354092890268530342009402133755822717151679559278360263800840317501093689917495888199116488588871447782240220513546797235647742625493141141704109917646404017146978939243424915943739448283626010758721504375406023613552985026793701507511351368254645700768390780390334017990233124030682358360249760098999315658413563173197024899154512108923313999675829872581317721346549115423634135836394159076400636688679216398175376716152621781331348
7 <.@%: (2*10x^2*2002)
7 <.@%: (2*10x^2*2002)
1104089513673812337649505387623344721325326600780124165514532464142106322880380980716598289886302005146897159065579931253969214680430855796510648058388081961639198643922155838145512343974763395078906646859029211806139421440562835192195007740110439139292223389537903767320705032063903809884944457070845279252405827307254864679671836816589429995916822424590361601902611505690284386526869351720866524568004847701822070064334667580822044823960984514550922242408608825451442062850448298384317793721518676765230683406727811327252052334859250776811047221310365241746671294399050316</lang>
1104089513673812337649505387623344721325326600780124165514532464142106322880380980716598289886302005146897159065579931253969214680430855796510648058388081961639198643922155838145512343974763395078906646859029211806139421440562835192195007740110439139292223389537903767320705032063903809884944457070845279252405827307254864679671836816589429995916822424590361601902611505690284386526869351720866524568004847701822070064334667580822044823960984514550922242408608825451442062850448298384317793721518676765230683406727811327252052334859250776811047221310365241746671294399050316</syntaxhighlight>


=={{header|Java}}==
=={{header|Java}}==
{{trans|Kotlin}}
{{trans|Kotlin}}
<lang Java>import java.math.BigInteger;
<syntaxhighlight lang="java">import java.math.BigInteger;


public class IntegerRoots {
public class IntegerRoots {
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System.out.println(iRoot(b, 2));
System.out.println(iRoot(b, 2));
}
}
}</lang>
}</syntaxhighlight>
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<pre>3rd integer root of 8 = 2
<pre>3rd integer root of 8 = 2
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'''Works with gojq, the Go implementation of jq'''
'''Works with gojq, the Go implementation of jq'''
<lang jq># To take advantage of gojq's arbitrary-precision integer arithmetic:
<syntaxhighlight lang="jq"># To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);


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# The task:
# The task:
"First 2,001 digits of the square root of two:",
"First 2,001 digits of the square root of two:",
iroot(2; 2 * (100 | power(2000)))</lang>
iroot(2; 2 * (100 | power(2000)))</syntaxhighlight>
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Exactly as for [[#Julia|Julia]].
Exactly as for [[#Julia|Julia]].
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{{trans|Python}}
{{trans|Python}}


<lang julia>function iroot(a, b)
<syntaxhighlight lang="julia">function iroot(a, b)
b < 2 && return b
b < 2 && return b
a1, c = a - 1, 1
a1, c = a - 1, 1
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end
end


println("First 2,001 digits of the square root of two:\n", iroot(2, 2 * big(100) ^ 2000))</lang>
println("First 2,001 digits of the square root of two:\n", iroot(2, 2 * big(100) ^ 2000))</syntaxhighlight>


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=={{header|Kotlin}}==
=={{header|Kotlin}}==
{{trans|Python}}
{{trans|Python}}
<lang scala>// version 1.1.2
<syntaxhighlight lang="scala">// version 1.1.2


import java.math.BigInteger
import java.math.BigInteger
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println("First 2001 digits of the square root of 2:")
println("First 2001 digits of the square root of 2:")
println(b.iRoot(2))
println(b.iRoot(2))
}</lang>
}</syntaxhighlight>


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=={{header|Lua}}==
=={{header|Lua}}==
{{trans|C}}
{{trans|C}}
<lang lua>function root(base, n)
<syntaxhighlight lang="lua">function root(base, n)
if base < 2 then return base end
if base < 2 then return base end
if n == 0 then return 1 end
if n == 0 then return 1 end
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print("3rd root of 8 = " .. root(8, 3))
print("3rd root of 8 = " .. root(8, 3))
print("3rd root of 9 = " .. root(9, 3))
print("3rd root of 9 = " .. root(9, 3))
print("2nd root of " .. b .. " = " .. root(b, 2))</lang>
print("2nd root of " .. b .. " = " .. root(b, 2))</syntaxhighlight>
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<pre>3rd root of 8 = 2
<pre>3rd root of 8 = 2
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=={{header|Modula-2}}==
=={{header|Modula-2}}==
<lang modula2>MODULE IntegerRoot;
<syntaxhighlight lang="modula2">MODULE IntegerRoot;
FROM FormatString IMPORT FormatString;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,ReadChar;
FROM Terminal IMPORT WriteString,ReadChar;
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ReadChar
ReadChar
END IntegerRoot.</lang>
END IntegerRoot.</syntaxhighlight>


=={{header|Nim}}==
=={{header|Nim}}==
{{trans|Kotlin}}
{{trans|Kotlin}}
{{libheader|bignum}}
{{libheader|bignum}}
<lang Nim>import bignum
<syntaxhighlight lang="nim">import bignum


proc root(x: Int; n: int): Int =
proc root(x: Int; n: int): Int =
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echo "First 2001 digits of the square root of 2:"
echo "First 2001 digits of the square root of 2:"
let s = $x.root(2)
let s = $x.root(2)
for i in countup(0, s.high, 87): echo s.substr(i, i + 86)</lang>
for i in countup(0, s.high, 87): echo s.substr(i, i + 86)</syntaxhighlight>


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=={{header|PARI/GP}}==
=={{header|PARI/GP}}==
<lang parigp>sqrtnint(8,3)
<syntaxhighlight lang="parigp">sqrtnint(8,3)
sqrtnint(9,3)
sqrtnint(9,3)
sqrtnint(2*100^2000,2)</lang>
sqrtnint(2*100^2000,2)</syntaxhighlight>
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<pre>%1 = 2
<pre>%1 = 2
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=={{header|Perl}}==
=={{header|Perl}}==
{{trans|Ruby}}
{{trans|Ruby}}
<lang perl>use bigint;
<syntaxhighlight lang="perl">use bigint;


sub integer_root {
sub integer_root {
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print integer_root( 3, 8), "\n";
print integer_root( 3, 8), "\n";
print integer_root( 3, 9), "\n";
print integer_root( 3, 9), "\n";
print integer_root( 2, 2 * 100 ** 2000), "\n";</lang>
print integer_root( 2, 2 * 100 ** 2000), "\n";</syntaxhighlight>
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<pre>2
<pre>2
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===Using a module===
===Using a module===
If using bigints, we can do this directly, which will be much faster than the method above:
If using bigints, we can do this directly, which will be much faster than the method above:
<lang perl>use bigint;
<syntaxhighlight lang="perl">use bigint;
print 8->babs->broot(3),"\n";
print 8->babs->broot(3),"\n";
print 9->babs->broot(3),"\n";
print 9->babs->broot(3),"\n";
print +(2*100**2000)->babs->broot(2),"\n";</lang>
print +(2*100**2000)->babs->broot(2),"\n";</syntaxhighlight>


The <code>babs</code> calls are only necessary if the input might be non-negative.
The <code>babs</code> calls are only necessary if the input might be non-negative.


Even faster, using a module:
Even faster, using a module:
<lang perl>use bigint;
<syntaxhighlight lang="perl">use bigint;
use ntheory "rootint";
use ntheory "rootint";
print rootint(8,3),"\n";
print rootint(8,3),"\n";
print rootint(9,3),"\n";
print rootint(9,3),"\n";
print rootint(2*100**2000,2),"\n";</lang>
print rootint(2*100**2000,2),"\n";</syntaxhighlight>


Both generate the same output as above.
Both generate the same output as above.
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=={{header|Phix}}==
=={{header|Phix}}==
{{libheader|Phix/mpfr}}
{{libheader|Phix/mpfr}}
<!--<lang Phix>(phixonline)-->
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First digits of the cube root of 2: %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"First digits of the cube root of 2: %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)})</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)</span>
<!--</lang>-->
<!--</syntaxhighlight>-->
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<pre>
<pre>
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=={{header|Python}}==
=={{header|Python}}==
<lang python>def root(a, b):
<syntaxhighlight lang="python">def root(a, b):
if b < 2:
if b < 2:
return b
return b
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print("First 2,001 digits of the square root of two:\n{}".format(
print("First 2,001 digits of the square root of two:\n{}".format(
root(2, 2 * 100 ** 2000)
root(2, 2 * 100 ** 2000)
))</lang>
))</syntaxhighlight>


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=={{header|Quackery}}==
=={{header|Quackery}}==
{{trans|Python}}
{{trans|Python}}
<lang Quackery> [ stack ] is a-1 ( --> s )
<syntaxhighlight lang="quackery"> [ stack ] is a-1 ( --> s )
[ stack ] is b ( --> s )
[ stack ] is b ( --> s )


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say "3rd root of 9 = " 9 3 root echo cr
say "3rd root of 9 = " 9 3 root echo cr
say "First 2001 digits of the square root of 2: "
say "First 2001 digits of the square root of 2: "
2 100 2000 ** * 2 root echo cr</lang>
2 100 2000 ** * 2 root echo cr</syntaxhighlight>


{{out}}
{{out}}
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(formerly Perl 6)
(formerly Perl 6)
{{trans|Python}}
{{trans|Python}}
<lang perl6>sub integer_root ( Int $p where * >= 2, Int $n --> Int ) {
<syntaxhighlight lang="raku" line>sub integer_root ( Int $p where * >= 2, Int $n --> Int ) {
my Int $d = $p - 1;
my Int $d = $p - 1;
my $guess = 10**($n.chars div $p);
my $guess = 10**($n.chars div $p);
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}
}


say integer_root( 2, 2 * 100 ** 2000 );</lang>
say integer_root( 2, 2 * 100 ** 2000 );</syntaxhighlight>
{{out}}
{{out}}
<pre>141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008
<pre>141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008
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<br>multiply the guess ['''G'''] by unity, &nbsp; and no need to compute the guess to the 1<sup>st</sup> power, &nbsp; bypassing some trivial arithmetic).
<br>multiply the guess ['''G'''] by unity, &nbsp; and no need to compute the guess to the 1<sup>st</sup> power, &nbsp; bypassing some trivial arithmetic).
===integer result only===
===integer result only===
<lang rexx>/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/
<syntaxhighlight lang="rexx">/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/
parse arg num root digs . /*obtain the optional arguments from CL*/
parse arg num root digs . /*obtain the optional arguments from CL*/
if num=='' | num=="," then num= 2 /*Not specified? Then use the default.*/
if num=='' | num=="," then num= 2 /*Not specified? Then use the default.*/
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if m==1 then do until old==g; old=g; g=(g + z % g ) % root; end
if m==1 then do until old==g; old=g; g=(g + z % g ) % root; end
else do until old==g; old=g; g=(g*m + z % (g**m) ) % root; end
else do until old==g; old=g; g=(g*m + z % (g**m) ) % root; end
return left(g,p) /*return the Nth root of Z to invoker.*/</lang>
return left(g,p) /*return the Nth root of Z to invoker.*/</syntaxhighlight>
'''output''' &nbsp; when the defaults are being used:
'''output''' &nbsp; when the defaults are being used:
<pre>
<pre>
Line 1,044: Line 1,044:
===true results===
===true results===
<br>Negative and complex roots are supported. &nbsp; The expressed root may have a decimal point.
<br>Negative and complex roots are supported. &nbsp; The expressed root may have a decimal point.
<lang rexx>/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/
<syntaxhighlight lang="rexx">/*REXX program calculates the Nth root of a number to a specified number of decimal digs*/
parse arg num root digs . /*obtain the optional arguments from CL*/
parse arg num root digs . /*obtain the optional arguments from CL*/
if num=='' | num=="," then num= 2 /*Not specified? Then use the default.*/
if num=='' | num=="," then num= 2 /*Not specified? Then use the default.*/
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numeric digits od /*set numeric digits to the original.*/
numeric digits od /*set numeric digits to the original.*/
if oy<0 then return (1/_)i /*Is the root negative? Use reciprocal*/
if oy<0 then return (1/_)i /*Is the root negative? Use reciprocal*/
return (_/1)i /*return the Yth root of X to invoker.*/</lang>
return (_/1)i /*return the Yth root of X to invoker.*/</syntaxhighlight>
'''output''' &nbsp; when the defaults are being used:
'''output''' &nbsp; when the defaults are being used:
<pre>
<pre>
Line 1,118: Line 1,118:


=={{header|Ring}}==
=={{header|Ring}}==
<lang ring>
<syntaxhighlight lang="ring">
# Project : Integer roots
# Project : Integer roots


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ok
ok
next
next
</syntaxhighlight>
</lang>
Output:
Output:
<pre>
<pre>
Line 1,142: Line 1,142:
=={{header|Ruby}}==
=={{header|Ruby}}==
{{trans|Python, zkl}}
{{trans|Python, zkl}}
<lang ruby>def root(a,b)
<syntaxhighlight lang="ruby">def root(a,b)
return b if b<2
return b if b<2
a1, c = a-1, 1
a1, c = a-1, 1
Line 1,154: Line 1,154:
puts "First 2,001 digits of the square root of two:"
puts "First 2,001 digits of the square root of two:"
puts root(2, 2*100**2000)
puts root(2, 2*100**2000)
</syntaxhighlight>
</lang>
{{out}}<pre>First 2,001 digits of the square root of two:
{{out}}<pre>First 2,001 digits of the square root of two:
14142135623730950488016887242096(...)46758516447107578486024636008</pre>
14142135623730950488016887242096(...)46758516447107578486024636008</pre>
Line 1,160: Line 1,160:
=={{header|Rust}}==
=={{header|Rust}}==
The rug crate provides the functionality required for this task.
The rug crate provides the functionality required for this task.
<lang rust>// [dependencies]
<syntaxhighlight lang="rust">// [dependencies]
// rug = "1.9"
// rug = "1.9"


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let s = Integer::from(x.root(3)).to_string();
let s = Integer::from(x.root(3)).to_string();
println!("First {} digits of the cube root of 2:\n{}", s.len(), shorten(&s, 70));
println!("First {} digits of the cube root of 2:\n{}", s.len(), shorten(&s, 70));
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
Line 1,204: Line 1,204:
=={{header|Scala}}==
=={{header|Scala}}==
===Functional solution, tail recursive, no immutables===
===Functional solution, tail recursive, no immutables===
<lang Scala>import scala.annotation.tailrec
<syntaxhighlight lang="scala">import scala.annotation.tailrec


object IntegerRoots extends App {
object IntegerRoots extends App {
Line 1,231: Line 1,231:
}
}


}</lang>
}</syntaxhighlight>
{{Out}}See it running in your browser by [https://scalafiddle.io/sf/bVwlHfa/0 ScalaFiddle (JavaScript, non JVM)] or by [https://scastie.scala-lang.org/0T93IhLVRGiYfuKpW7DTUg Scastie (JVM)].
{{Out}}See it running in your browser by [https://scalafiddle.io/sf/bVwlHfa/0 ScalaFiddle (JavaScript, non JVM)] or by [https://scastie.scala-lang.org/0T93IhLVRGiYfuKpW7DTUg Scastie (JVM)].


=={{header|Scheme}}==
=={{header|Scheme}}==
{{trans|Python}}
{{trans|Python}}
<lang scheme>(define (root a b)
<syntaxhighlight lang="scheme">(define (root a b)
(define // quotient)
(define // quotient)
(define (y a a1 b c d e)
(define (y a a1 b c d e)
Line 1,251: Line 1,251:
(display "First 2,001 digits of the cube root of two:\n")
(display "First 2,001 digits of the cube root of two:\n")
(display (root 3 (* 2 (expt 1000 2000))))</lang>
(display (root 3 (* 2 (expt 1000 2000))))</syntaxhighlight>


{{out}}
{{out}}
Line 1,259: Line 1,259:
=={{header|Sidef}}==
=={{header|Sidef}}==
{{trans|Ruby}}
{{trans|Ruby}}
<lang ruby>func root(a, b) {
<syntaxhighlight lang="ruby">func root(a, b) {
b < 2 && return(b)
b < 2 && return(b)
var (a1, c) = (a-1, 1)
var (a1, c) = (a-1, 1)
Line 1,272: Line 1,272:


say "First 2,001 digits of the square root of two:"
say "First 2,001 digits of the square root of two:"
say root(2, 2 * 100**2000)</lang>
say root(2, 2 * 100**2000)</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>
Line 1,283: Line 1,283:


On the other hand, everything is very straightforward, no libraries necessary.
On the other hand, everything is very straightforward, no libraries necessary.
<lang tcl>
<syntaxhighlight lang="tcl">
proc root {this n} {
proc root {this n} {
if {$this < 2} {return $this}
if {$this < 2} {return $this}
Line 1,303: Line 1,303:
puts [root 9 3]
puts [root 9 3]
puts [root [expr 2* (100**2000)] 2]
puts [root [expr 2* (100**2000)] 2]
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
Line 1,313: Line 1,313:
=={{header|Visual Basic .NET}}==
=={{header|Visual Basic .NET}}==
{{libheader|System.Numerics}}
{{libheader|System.Numerics}}
From the method described on [https://en.wikipedia.org/wiki/Nth_root_algorithm the Wikipedia page]. Included is an Integer Square Root function to compare results to the Integer Nth Square root function. One must choose the exponents carefully, otherwise one will obtain the digits of the nth root of 20, 200, 2000, etc..., instead of 2. For example, 4008 was chosen because it works for both ''n = 2'' and ''n = 3'', whereas 4004 was chosen for ''n = 7''<lang vbnet>Imports System
From the method described on [https://en.wikipedia.org/wiki/Nth_root_algorithm the Wikipedia page]. Included is an Integer Square Root function to compare results to the Integer Nth Square root function. One must choose the exponents carefully, otherwise one will obtain the digits of the nth root of 20, 200, 2000, etc..., instead of 2. For example, 4008 was chosen because it works for both ''n = 2'' and ''n = 3'', whereas 4004 was chosen for ''n = 7''<syntaxhighlight lang="vbnet">Imports System
Imports System.Numerics
Imports System.Numerics
Imports Microsoft.VisualBasic.Strings
Imports Microsoft.VisualBasic.Strings
Line 1,361: Line 1,361:


End Module
End Module
</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre style="height:64ex;overflow:scroll">
<pre style="height:64ex;overflow:scroll">
Line 1,379: Line 1,379:
=={{header|Wren}}==
=={{header|Wren}}==
Wren doesn't have arbitrary precision numerics and so can't do the third example in the task description. We therefore do the third C/C++ example instead.
Wren doesn't have arbitrary precision numerics and so can't do the third example in the task description. We therefore do the third C/C++ example instead.
<lang ecmascript>var intRoot = Fn.new { |x, n|
<syntaxhighlight lang="ecmascript">var intRoot = Fn.new { |x, n|
if (!(x is Num && x.isInteger && x >= 0)) {
if (!(x is Num && x.isInteger && x >= 0)) {
Fiber.abort("First argument must be a non-negative integer.")
Fiber.abort("First argument must be a non-negative integer.")
Line 1,394: Line 1,394:
var n = e[1]
var n = e[1]
System.print("%(x) ^ (1/%(n)) = %(intRoot.call(x, n))")
System.print("%(x) ^ (1/%(n)) = %(intRoot.call(x, n))")
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
Line 1,406: Line 1,406:
=={{header|Yabasic}}==
=={{header|Yabasic}}==
{{trans|FreeBASIC}}
{{trans|FreeBASIC}}
<lang yabasic>sub root(n, x)
<syntaxhighlight lang="yabasic">sub root(n, x)
for nr = floor(sqr(x)) to 1 step -1
for nr = floor(sqr(x)) to 1 step -1
if (nr ^ n) <= x then return nr : fi
if (nr ^ n) <= x then return nr : fi
Line 1,415: Line 1,415:
print root(3, 9)
print root(3, 9)
print root(4, 167)
print root(4, 167)
end</lang>
end</syntaxhighlight>




Line 1,421: Line 1,421:
{{trans|Python}}
{{trans|Python}}
Uses GNU GMP library
Uses GNU GMP library
<lang zkl>var [const] BN=Import("zklBigNum");
<syntaxhighlight lang="zkl">var [const] BN=Import("zklBigNum");
fcn root(n,r){
fcn root(n,r){
f:='wrap(z){ (n/z.pow(r-1) + z*(r-1))/r or 1 }; //--> v or 1
f:='wrap(z){ (n/z.pow(r-1) + z*(r-1))/r or 1 }; //--> v or 1
Line 1,427: Line 1,427:
while(c!=d and c!=e){ c,d,e=d,e,f(e) }
while(c!=d and c!=e){ c,d,e=d,e,f(e) }
if(d<e) d else e
if(d<e) d else e
}</lang>
}</syntaxhighlight>
<lang zkl>a:=BN(100).pow(2000)*2;
<syntaxhighlight lang="zkl">a:=BN(100).pow(2000)*2;
println("Does GMP agree: ",root(a,3)==a.root(3));</lang>
println("Does GMP agree: ",root(a,3)==a.root(3));</syntaxhighlight>
{{out}}
{{out}}
<pre>
<pre>