Integer roots: Difference between revisions
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Line 46:
3rd root of 9 = 2
First 2001 digits of the square root of 2: 141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008
</pre>
=={{header|Ada}}==
<syntaxhighlight lang="ada">
-- Find integer roots
-- J. Carter 2023 Jun
with Ada.Text_IO;
with System;
procedure Integer_Roots is
type Big is mod System.Max_Binary_Modulus;
function Root (N : in Positive; X : in Big) return Big With Pre => N > 1;
-- Returns the largest integer R such that R ** N <= X
-- Derived from Modula-2
function Root (N : in Positive; X : in Big) return Big is
N1 : constant Positive := N - 1;
N2 : constant Big := Big (N);
N3 : constant Big := N2 - 1;
C : Big := 1;
D : Big := (N3 + X) / N2;
E : Big := (N3 * D + X / D ** N1) / N2;
begin -- Root
if X <= 1 then
return X;
end if;
Converge : loop
exit Converge when C = D or C = E;
C := D;
D := E;
E := (N3 * D + X / E ** N1) / N2;
end loop Converge;
return (if D < E then D else E);
end Root;
Large : constant Big := 2 * 10 ** 38;
-- On 64-bit platforms, recent versions of GNAT provide 128-bit integers
-- 10 ** 38 is the largest power of 10 < 2 ** 128
begin -- Integer_Roots
Ada.Text_IO.Put_Line (Item => "Cube root of 8 =" & Root (3, 8)'Image);
Ada.Text_IO.Put_Line (Item => "Cube root of 9 =" & Root (3, 9)'Image);
Ada.Text_IO.Put_Line (Item => "Square root of" & Large'Image & " =" & Root (2, Large)'Image);
end Integer_Roots;
</syntaxhighlight>
{{out}}
<pre>
Cube root of 8 = 2
Cube root of 9 = 2
Square root of 200000000000000000000000000000000000000 = 14142135623730950488
</pre>
Line 263 ⟶ 319:
3rd root of 9 = 2
First 2001 digits of the square root of 2: 141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
{{trans|C++}}
<syntaxhighlight lang="Delphi">
function IntRoot(Base: int64; N: cardinal): int64;
var N1: cardinal;
var N2,N3,C: int64;
var D,E: int64;
begin
if Base < 2 then Result:=Base
else if N = 0 then Result:=1
else
begin
N1:=N - 1;
N2:=N;
N3:=N1;
C:=1;
d:=round((N3 + Base) / N2);
e:=round((N3 * D + Base / Power(D, N1)) / N2);
while (C<>D) and (C<>E) do
begin
C:=D;
D:=E;
E:=Round((N3*E + Base / Power(E, N1)) / N2);
end;
if D < E then Result:=D
else Result:=E;
end;
end;
procedure ShowIntegerRoots(Memo: TMemo);
var Base: int64;
begin
Memo.Lines.Add('3rd integer root of 8 = '+IntToStr(IntRoot(8, 3)));
Memo.Lines.Add('3rd integer root of 9 = '+IntToStr(IntRoot(9, 3)));
Base:=2000000000000000000;
Memo.Lines.Add('sqaure root of 2 = '+IntToStr(IntRoot(Base, 2)));
end;
</syntaxhighlight>
{{out}}
<pre>
3rd integer root of 8 = 2
3rd integer root of 9 = 2
sqaure root of 2 = 1414213562
Elapsed Time: 2.747 ms.
</pre>
=={{header|EasyLang}}==
{{trans|C}}
<syntaxhighlight>
func root base n .
if base < 2
return base
.
if n = 0
return 1
.
n1 = n - 1
n2 = n
n3 = n1
c = 1
d = (n3 + base) div n2
e = (n3 * d + base div pow d n1) div n2
while c <> d and c <> e
c = d
d = e
e = (n3 * e + base div pow e n1) div n2
.
if (d < e)
return d
.
return e
.
print "3rd root of 8 = " & root 8 3
print "3rd root of 9 = " & root 9 3
b = 2e18
print "2nd root of " & b & " = " & root b 2
</syntaxhighlight>
{{out}}
<pre>
3rd root of 8 = 2
3rd root of 9 = 2
2nd root of 2e+18 = 1414213562
</pre>
=={{header|Elixir}}==
Line 1,010 ⟶ 1,162:
10**($n.chars div $p),
{ ( $d * $^x + $n div ($x ** $d) ) div $p } ...
).tail(2).min;
}
Line 1,166 ⟶ 1,318:
3
</pre>
=={{header|RPL}}==
{{trans|Python}}
« DUP 1 -
→ x n n1
« '''IF''' x 2 < '''THEN''' x
'''ELSE'''
« n1 OVER * x 3 PICK n1 ^ / IP + n / IP »
→ func
« 1 func EVAL func EVAL
'''WHILE''' ROT DUP2 ≠ SWAP 4 PICK ≠ AND
'''REPEAT''' func EVAL '''END'''
MIN
»
'''END'''
» » '<span style="color:blue">IROOT</span>' STO <span style="color:grey"> @ ''( x n → root ) with root^n ≤ x</span>''
=={{header|Ruby}}==
Line 1,405 ⟶ 1,573:
=={{header|Wren}}==
<syntaxhighlight lang="wren">import "./big" for BigInt
// only use for integers less than 2^53
var intRoot = Fn.new { |x, n|
if (!(x is Num && x.isInteger && x >= 0)) {
Fiber.abort("First argument must be a non-negative integer.")
Line 1,421 ⟶ 1,591:
var n = e[1]
System.print("%(x) ^ (1/%(n)) = %(intRoot.call(x, n))")
}
System.print("\nFirst 2001 digits of the square root of 2:")
System.print((BigInt.two * BigInt.new(100).pow(2000)).isqrt)</syntaxhighlight>
{{out}}
Line 1,428 ⟶ 1,601:
9 ^ (1/3) = 2
2e+18 ^ (1/2) = 1414213562
First 2001 digits of the square root of 2:
141421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988939443709265918003113882464681570826301005948587040031864803421948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698683684507257993647290607629969413804756548237289971803268024744206292691248590521810044598421505911202494413417285314781058036033710773091828693147101711116839165817268894197587165821521282295184884720896946338628915628827659526351405422676532396946175112916024087155101351504553812875600526314680171274026539694702403005174953188629256313851881634780015693691768818523786840522878376293892143006558695686859645951555016447245098368960368873231143894155766510408839142923381132060524336294853170499157717562285497414389991880217624309652065642118273167262575395947172559346372386322614827426222086711558395999265211762526989175409881593486400834570851814722318142040704265090565323333984364578657967965192672923998753666172159825788602633636178274959942194037777536814262177387991945513972312740668983299898953867288228563786977496625199665835257761989393228453447356947949629521688914854925389047558288345260965240965428893945386466257449275563819644103169798330618520193793849400571563337205480685405758679996701213722394758214263065851322174088323829472876173936474678374319600015921888073478576172522118674904249773669292073110963697216089337086611567345853348332952546758516447107578486024636008
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang "XPL0">func real IRoot(X, N);
real X, N;
return Floor(Pow(X, 1./N));
[Format(1, 0);
RlOut(0, IRoot(8., 3.)); CrLf(0);
RlOut(0, IRoot(9., 3.)); CrLf(0);
RlOut(0, IRoot(2e18, 2.)); CrLf(0);
]</syntaxhighlight>
{{out}}
<pre>
2
2
1414213562
</pre>
=={{header|Yabasic}}==
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