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Arithmetic-geometric mean: Difference between revisions
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Line 22:
=={{header|11l}}==
{{trans|Python}}
<
V an = (a0 + g0) / 2.0
V gn = sqrt(a0 * g0)
Line 29:
R an
print(agm(1, 1 / sqrt(2)))</
{{out}}
<pre>0.847213</pre>
Line 35:
=={{header|360 Assembly}}==
For maximum compatibility, this program uses only the basic instruction set.
<
USING AGM,R13
SAVEAREA B STM-SAVEAREA(R15)
Line 125:
LTORG
YREGS
END AGM</
{{out}}
<pre>
Line 132:
=={{header|8th}}==
<
with: n
Line 146:
;with
bye
</syntaxhighlight>
{{out}}
<pre>
Line 155:
{{libheader|Action! Tool Kit}}
{{libheader|Action! Real Math}}
<
PROC Agm(REAL POINTER a0,g0,result)
Line 191:
Print(",") PrintR(g)
Print(")=") PrintRE(res)
RETURN</
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Arithmetic-geometric_mean.png Screenshot from Atari 8-bit computer]
Line 199:
=={{header|Ada}}==
<
procedure Arith_Geom_Mean is
Line 224:
begin
N_IO.Put(AGM(1.0, 1.0/Math.Sqrt(2.0)), Fore => 1, Aft => 17, Exp => 0);
end Arith_Geom_Mean;</
Output:<pre>0.84721308479397909</pre>
Line 232:
Printing out the difference between the means at each iteration nicely demonstrates the quadratic convergence.
<
BEGIN
PROC agm = (LONG REAL x, y) LONG REAL :
Line 239:
ELIF x + y = LONG 0.0 THEN LONG 0.0 CO Edge cases CO
ELSE
a
FI
END;
printf (($l(-35,33)l$, agm (LONG 1.0, LONG 1.0 / long sqrt (LONG 2.0))))
END
</syntaxhighlight>
Output:<pre>+1.707106781186547524400844362e +0 +2.928932188134524755991556379e -1
+2.928932188134524755991556379e -1 +1.265697533955921916929670477e -2
Line 269:
=={{header|APL}}==
<syntaxhighlight lang="apl">
agd←{(⍺-⍵)<10*¯8:⍺⋄((⍺+⍵)÷2)∇(⍺×⍵)*÷2}
1 agd ÷2*÷2
</syntaxhighlight>
Output: <pre>0.8472130848</pre>
Line 278:
By functional composition:
<
property tolerance : 1.0E-5
Line 336:
end script
end if
end mReturn</
{{Out}}
<pre>0.847213084835</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">agm: function [a,g][
delta: 1e-15
[aNew, aOld, gOld]: @[0, a, g]
while [delta < abs aOld - gOld][
aNew: 0.5 * aOld + gOld
gOld: sqrt aOld * gOld
aOld: aNew
]
return aOld
]
print agm 1.0 1.0/sqrt 2.0</lang>
{{out}}
<pre>0.8472130847939792</pre>
=={{header|AutoHotkey}}==
<
While abs(a-g) > tolerance
{
Line 351 ⟶ 371:
}
SetFormat, FloatFast, 0.15
MsgBox % agm(1, 1/sqrt(2))</
Output:
<pre>0.847213084793979</pre>
=={{header|AWK}}==
<
BEGIN {
printf "%.16g\n", agm(1.0,sqrt(0.5))
Line 372 ⟶ 392:
return (x<0 ? -x : x)
}
</syntaxhighlight>
Output
<pre>0.8472130847939792</pre>
=={{header|BASIC}}==
==={{header|ANSI BASIC}}===
{{works with|
<syntaxhighlight lang="basic">100 PROGRAM ArithmeticGeometricMean
110 FUNCTION AGM (A, G)
120 DO
130 LET TA = (A + G) / 2
140 LET G = SQR(A * G)
150 LET
160 LET
170 LET
180 LOOP UNTIL
190 LET AGM = A
200 END FUNCTION
210 REM ********************
220 PRINT AGM(1, 1 / SQR(2))
230 END</syntaxhighlight>
{{out}}
<pre> .84721308479398 </pre>
==={{header|Applesoft BASIC}}===
Same code as [[#Commodore_BASIC|Commodore BASIC]]
The [[#BASIC|BASIC]] solution works without any changes.
==={{header|BASIC256}}===
<
end
Line 410 ⟶ 434:
return a
end function</
{{out}}
<pre>0.84721308479</pre>
==={{header|BBC BASIC}}===
{{works with|BBC BASIC for Windows}}
<
@% = &1010
PRINT FNagm(1, 1/SQR(2))
Line 443 ⟶ 453:
UNTIL a = ta
= a
</syntaxhighlight>
{{out}}
<pre>0.8472130847939792</pre>
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="qbasic">10 print agm(1,1/sqr(2))
20 end
100 sub agm(a,g)
110 do
120 let ta = (a+g)/2
130 let g = sqr(a*g)
140 let x = a
150 let a = ta
160 let ta = x
170 loop until a = ta
180 agm = a
190 end sub</syntaxhighlight>
{{out}}
<pre>0.847213</pre>
==={{header|Commodore BASIC}}===
<syntaxhighlight lang="commodorebasic">10 A = 1
20 G = 1/SQR(2)
30 GOSUB 100
40 PRINT A
50 END
100 TA = A
110 A = (A+G)/2
120 G = SQR(TA*G)
130 IF A<TA THEN 100
140 RETURN</syntaxhighlight>
==={{header|Craft Basic}}===
<syntaxhighlight lang="basic">let a = 1
let g = 1 / sqrt(2)
do
let t = (a + g) / 2
let g = sqrt(a * g)
let x = a
let a = t
let t = x
loopuntil a = t
print a</syntaxhighlight>
{{out| Output}}
<pre>0.85</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">' version 16-09-2015
' compile with: fbc -s console
Function agm(a As Double, g As Double) As Double
Dim As Double t_a
Do
t_a = (a + g) / 2
g = Sqr(a * g)
Swap a, t_a
Loop Until a = t_a
Return a
End Function
' ------=< MAIN >=------
Print agm(1, 1 / Sqr(2) )
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}
<pre> 0.8472130847939792</pre>
==={{header|Gambas}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">Public Sub Main()
Print AGM(1, 1 / Sqr(2))
End
Function AGM(a As Float, g As Float) As Float
Dim t_a As Float
Do
t_a = (a + g) / 2
g = Sqr(a * g)
Swap a, t_a
Loop Until a = t_a
Return a
End Function</syntaxhighlight>
==={{header|GW-BASIC}}===
<
20 G = 1!/SQR(2!)
30 FOR I=1 TO 20 'twenty iterations is plenty
Line 457 ⟶ 564:
60 A = B
70 NEXT I
80 PRINT A</
==={{header|IS-BASIC}}===
<
110 DEF AGM(A,G)
120 DO
Line 467 ⟶ 574:
150 LOOP UNTIL A=TA
160 LET AGM=A
170 END DEF</
==={{header|Liberty BASIC}}===
{{works with|Just BASIC}}
<syntaxhighlight lang="lb">
print agm(1, 1/sqr(2))
print using("#.#################",agm(1, 1/sqr(2)))
end
function agm(a,g)
do
absdiff = abs(a-g)
an=(a+g)/2
gn=sqr(a*g)
a=an
g=gn
loop while abs(an-gn)< absdiff
agm = a
end function
</syntaxhighlight>
{{out}}
<pre>0.84721308
0.84721308479397904</pre>
==={{header|Minimal BASIC}}===
{{trans|Commodore BASIC}}
{{works with|IS-BASIC}}
<syntaxhighlight lang="qbasic">10 LET A = 1
20 LET G = 1 / SQR(2)
30 GOSUB 60
40 PRINT A
50 STOP
60 LET T = A
70 LET A = (A + G) / 2
80 LET G = SQR(T * G)
90 IF A < T THEN 60
100 RETURN
110 END</syntaxhighlight>
{{out}}
<pre> .84721308</pre>
==={{header|MSX Basic}}===
{{works with|MSX BASIC|any}}
The [[#Commodore BASIC|Commodore BASIC]] solution works without any changes.
The [[#GW-BASIC|GW-BASIC]] solution works without any changes.
==={{header|PureBasic}}===
<syntaxhighlight lang="purebasic">Procedure.d AGM(a.d, g.d, ErrLim.d=1e-15)
Protected.d ta=a+1, tg
While ta <> a
ta=a: tg=g
a=(ta+tg)*0.5
g=Sqr(ta*tg)
Wend
ProcedureReturn a
EndProcedure
If OpenConsole()
PrintN(StrD(AGM(1, 1/Sqr(2)), 16))
Input()
CloseConsole()
EndIf</syntaxhighlight>
{{out}}
<pre> 0.8472130847939792</pre>
==={{header|QuickBASIC}}===
{{works with|QBasic}}
<syntaxhighlight lang="qbasic">PRINT AGM(1, 1 / SQR(2))
END
FUNCTION AGM (a, g)
DO
ta = (a + g) / 2
g = SQR(a * g)
SWAP a, ta
LOOP UNTIL a = ta
AGM = a
END FUNCTION</syntaxhighlight>
{{out}}
<pre>.8472131</pre>
==={{header|Quite BASIC}}===
{{trans|Commodore BASIC}}
<syntaxhighlight lang="qbasic">10 LET A = 1
20 LET G = 1 / SQR(2)
30 GOSUB 100
40 PRINT A
50 END
100 LET T = A
110 LET A = (A + G) / 2
120 LET G = SQR(T * G)
130 IF A < T THEN 100
140 RETURN</syntaxhighlight>
{{out}}
<pre>0.8472130847939792</pre>
==={{header|Run BASIC}}===
<syntaxhighlight lang="runbasic">print agm(1, 1/sqr(2))
print agm(1,1/2^.5)
print using("#.############################",agm(1, 1/sqr(2)))
function agm(agm,g)
while agm
an = (agm + g)/2
gn = sqr(agm*g)
if abs(agm-g) <= abs(an-gn) then exit while
agm = an
g = gn
wend
end function</syntaxhighlight>{{out}}
<pre>0.847213085
0.847213085
0.8472130847939791165772005376</pre>
==={{header|Sinclair ZX81 BASIC}}===
{{trans|COBOL}}
Works with 1k of RAM.
The specification calls for a function. Sadly that is not available to us, so this program uses a subroutine: pass the arguments in the global variables <tt>A</tt> and <tt>G</tt>, and the result will be returned in <tt>AGM</tt>. The performance is quite acceptable. Note that the subroutine clobbers <tt>A</tt> and <tt>G</tt>, so you should save them if you want to use them again.
Better precision than this is not easily obtainable on the ZX81, unfortunately.
<syntaxhighlight lang="basic"> 10 LET A=1
20 LET G=1/SQR 2
30 GOSUB 100
40 PRINT AGM
50 STOP
100 LET A0=A
110 LET A=(A+G)/2
120 LET G=SQR (A0*G)
130 IF ABS(A-G)>.00000001 THEN GOTO 100
140 LET AGM=A
150 RETURN</syntaxhighlight>
{{out}}
<pre>0.84721309</pre>
==={{header|TI-83 BASIC}}===
<syntaxhighlight lang="ti83b">1→A:1/sqrt(2)→G
While abs(A-G)>e-15
(A+G)/2→B
sqrt(AG)→G:B→A
End
A</syntaxhighlight>
{{out}}
<pre>.8472130848</pre>
==={{header|True BASIC}}===
{{works with|QBasic}}
<
DO
LET ta = (a + g) / 2
Line 482 ⟶ 734:
LET AGM = a
END FUNCTION
PRINT AGM(1, 1 / SQR(2))
END</
{{out}}
<pre>.84721308</pre>
==={{header|VBA}}===
<syntaxhighlight lang="vb">Private Function agm(a As Double, g As Double, Optional tolerance As Double = 0.000000000000001) As Double
Do While Abs(a - g) > tolerance
tmp = a
a = (a + g) / 2
g = Sqr(tmp * g)
Debug.Print a
Loop
agm = a
End Function
Public Sub main()
Debug.Print agm(1, 1 / Sqr(2))
End Sub</syntaxhighlight>{{out}}
<pre> 0,853553390593274
0,847224902923494
0,847213084835193
0,847213084793979
0,847213084793979 </pre>
==={{header|VBScript}}===
{{trans|BBC BASIC}}
<syntaxhighlight lang="vb">Function agm(a,g)
Do Until a = tmp_a
tmp_a = a
a = (a + g)/2
g = Sqr(tmp_a * g)
Loop
agm = a
End Function
WScript.Echo agm(1,1/Sqr(2))</syntaxhighlight>
{{Out}}
<pre>0.847213084793979</pre>
==={{header|Yabasic}}===
<syntaxhighlight lang="vb">print AGM(1, 1 / sqrt(2))
end
sub AGM(a, g)
repeat
ta = (a + g) / 2
g = sqrt(a * g)
x = a
a = ta
ta = x
until a = ta
return a
end sub</syntaxhighlight>
{{out}}
<pre>0.847213</pre>
==={{header|Visual Basic .NET}}===
{{trans|C#}}
====Double, Decimal Versions====
<syntaxhighlight lang="vbnet">Imports System.Math
Imports System.Console
Module Module1
Function CalcAGM(ByVal a As Double, ByVal b As Double) As Double
Dim c As Double, d As Double = 0, ld As Double = 1
While ld <> d : c = a : a = (a + b) / 2 : b = Sqrt(c * b)
ld = d : d = a - b : End While : Return b
End Function
Function DecSqRoot(ByVal v As Decimal) As Decimal
Dim r As Decimal = CDec(Sqrt(CDbl(v))), t As Decimal = 0, d As Decimal = 0, ld As Decimal = 1
While ld <> d : t = v / r : r = (r + t) / 2
ld = d : d = t - r : End While : Return t
End Function
Function CalcAGM(ByVal a As Decimal, ByVal b As Decimal) As Decimal
Dim c As Decimal, d As Decimal = 0, ld As Decimal = 1
While ld <> d : c = a : a = (a + b) / 2 : b = DecSqRoot(c * b)
ld = d : d = a - b : End While : Return b
End Function
Sub Main(ByVal args As String())
WriteLine("Double result: {0}", CalcAGM(1.0, DecSqRoot(0.5)))
WriteLine("Decimal result: {0}", CalcAGM(1D, DecSqRoot(0.5D)))
If System.Diagnostics.Debugger.IsAttached Then ReadKey()
End Sub
End Module</syntaxhighlight>
{{out}}
<pre>Double result: 0.847213084793979
Decimal result: 0.8472130847939790866064991235</pre>
====System.Numerics====
{{trans|C#}}
{{Libheader|System.Numerics}}
<syntaxhighlight lang="vbnet">Imports System.Math
Imports System.Console
Imports BI = System.Numerics.BigInteger
Module Module1
Function BIP(ByVal leadDig As Char, ByVal numDigs As Integer) As BI
BIP = BI.Parse(leadDig & New String("0"c, numDigs))
End Function
Function IntSqRoot(ByVal v As BI, ByVal res As BI) As BI ' res is the initial guess of the square root
Dim d As BI = 0, dl As BI = 1
While dl <> d : IntSqRoot = v / res : res = (res + IntSqRoot) / 2
dl = d : d = IntSqRoot - res : End While
End Function
Function CalcByAGM(ByVal digits As Integer) As BI
Dim a As BI = BIP("1"c, digits), ' value is 1, extended to required number of digits
c as BI, ' a temporary variable for swapping a and b
diff As BI = 0, ldiff As BI = 1 ' difference of a and b, last difference
CalcByAGM = BI.Parse(String.Format("{0:0.00000000000000000}", ' initial value of square root of 0.5
Sqrt(0.5)).Substring(2) & New String("0"c, digits - 17))
CalcByAGM = IntSqRoot(BIP("5"c, (digits << 1) - 1), CalcByAGM) ' value is now the square root of 0.5
While ldiff <> diff : c = a : a = (a + CalcByAGM) >> 1 : CalcByAGM = IntSqRoot(c * CalcByAGM, a)
ldiff = diff : diff = a - CalcByAGM : End While
End Function
Sub Main(ByVal args As String())
Dim digits As Integer = 25000
If args.Length > 0 Then Integer.TryParse(args(0), digits) : _
If digits < 1 OrElse digits > 999999 Then digits = 25000
WriteLine("0.{0}", CalcByAGM(digits))
If System.Diagnostics.Debugger.IsAttached Then ReadKey()
End Sub
End Module</syntaxhighlight>
{{out}}
<pre style="height:64ex; overflow:scroll; white-space: 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3839674251648</pre>
==={{header|ZX Spectrum Basic}}===
{{trans|ERRE}}
<syntaxhighlight lang="zxbasic">10 LET a=1: LET g=1/SQR 2
20 LET ta=a
30 LET a=(a+g)/2
40 LET g=SQR (ta*g)
50 IF a<ta THEN GO TO 20
60 PRINT a
</syntaxhighlight>
{{out}}
<pre>0.84721309</pre>
=={{header|bc}}==
<
* numbers x and y.
* Result will have d digits after the decimal point.
Line 516 ⟶ 909:
scale = 20
m(1, 1 / sqrt(2), 20)</
{{Out}}
Line 522 ⟶ 915:
=={{header|BQN}}==
<
(|𝕨-𝕩) ≤ 1e¯15? 𝕨;
(0.5×𝕨+𝕩) 𝕊 √𝕨×𝕩
}
1 AGM 1÷√2</
{{out}}
<pre>0.8472130847939792</pre>
Line 533 ⟶ 926:
=={{header|C}}==
===Basic===
<
#include<stdio.h>
#include<stdlib.h>
Line 565 ⟶ 958:
return 0;
}
</syntaxhighlight>
Original output:
Line 579 ⟶ 972:
===GMP===
<
Nigel_Galloway
Line 612 ⟶ 1,005:
return 0;
}</
The first couple of iterations produces:
Line 628 ⟶ 1,021:
=={{header|C sharp|C#}}==
<
{
using System;
Line 705 ⟶ 1,098:
}
}
}</
Output:
<pre>0.847213084835193</pre>
Note that the last 5 digits are spurious, as ''maximumRelativeDifference'' was only specified to be 1e-5. Using 1e-11 instead will give the result 0.847213084793979, which is as far as ''double'' can take it.
===Using Decimal Type===
<
class Program {
Line 727 ⟶ 1,120:
if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();
}
}</
{{Out}}
<pre>0.8472130847939790866064991235</pre>
Line 734 ⟶ 1,127:
{{Libheader|System.Numerics}}
Even though the System.Numerics library directly supports only '''BigInteger''' (and not big rationals or big floating point numbers), it can be coerced into making this calculation. One just has to keep track of the decimal place and multiply by a very large constant.
<
using static System.Console;
using BI = System.Numerics.BigInteger;
Line 763 ⟶ 1,156:
WriteLine("0.{0}", CalcByAGM(digits));
if (System.Diagnostics.Debugger.IsAttached) ReadKey(); }
}</
{{out}}
<pre style="height:64ex; overflow:scroll; 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2204840459913839674251648</pre>
=={{header|C++}}==
<
#include<bits/stdc++.h>
using namespace std;
Line 797 ⟶ 1,190:
return 0;
}
</syntaxhighlight>
Line 806 ⟶ 1,199:
=={{header|Clojure}}==
<
(:gen-class))
Line 831 ⟶ 1,224:
(println (agm one isqrt2))
</syntaxhighlight>
{{Output}}
<pre>
Line 838 ⟶ 1,231:
=={{header|COBOL}}==
<
PROGRAM-ID. ARITHMETIC-GEOMETRIC-MEAN-PROG.
DATA DIVISION.
Line 870 ⟶ 1,263:
COMPUTE G = FUNCTION SQRT(G).
SUBTRACT A FROM G GIVING DIFF.
COMPUTE DIFF = FUNCTION ABS(DIFF).</
{{out}}
<pre>0.8472130847939792</pre>
=={{header|Common Lisp}}==
<
(loop for a = a0 then (* (+ a g) 5d-1)
and g = g0 then (sqrt (* a g))
until (< (abs (- a g)) tolerance)
finally (return a)))
</syntaxhighlight>
{{out}}
Line 891 ⟶ 1,284:
=={{header|D}}==
<
real agm(real a, real g, in int bitPrecision=60) pure nothrow @nogc @safe {
Line 903 ⟶ 1,296:
void main() @safe {
writefln("%0.19f", agm(1, 1 / sqrt(2.0)));
}</
{{out}}
<pre>0.8472130847939790866</pre>
Line 910 ⟶ 1,303:
{{libheader| System.SysUtils}}
{{Trans|C#}}
<syntaxhighlight lang="delphi">
program geometric_mean;
Line 954 ⟶ 1,347:
writeln(format('The arithmetic-geometric mean is %.6f', [agm(x, y)]));
readln;
end.</
{{out}}
<pre>Enter two numbers:1
2
The arithmetic-geometric mean is 1,456791</pre>
=={{header|dc}}==
<syntaxhighlight lang="dc">>>> 200 k ? sbsa [lalb +2/ lalb *vsb dsa lb - 0!=:]ds:xlap
?> 1 1 2 v /</syntaxhighlight>
{{out}}
<pre>
.8472130847939790866064991234821916364814459103269421850605793726597\
34004834134759723200293994611229942122285625233410963097962665830871\
05969971363598338425117632681428906038970676860161665004828118868
</pre>
You can change the precision (200 by default)
=={{header|EasyLang}}==
{{trans|AWK}}
<syntaxhighlight lang=easylang>
func agm a g .
repeat
a0 = a
a = (a0 + g) / 2
g = sqrt (a0 * g)
until abs (a0 - a) < abs (a) * 1e-15
.
return a
.
numfmt 16 0
print agm 1 sqrt 0.5
</syntaxhighlight>
=={{header|EchoLisp}}==
We use the '''(~= a b)''' operator which tests for |a - b| < ε = (math-precision).
<
(lib 'math)
Line 977 ⟶ 1,399:
(agm 1 (/ 1 (sqrt 2)))
→ 0.8472130847939792
</syntaxhighlight>
=={{header|Elixir}}==
<
def mean(a,g,tol) when abs(a-g) <= tol, do: a
def mean(a,g,tol) do
Line 988 ⟶ 1,410:
end
IO.puts ArithhGeom.mean(1,1/:math.sqrt(2),0.0000000001)</
{{out}}
Line 996 ⟶ 1,418:
=={{header|Erlang}}==
<
%% Author: Abhay Jain
Line 1,014 ⟶ 1,436:
A1 = (A+B) / 2,
B1 = math:pow(A*B, 0.5),
agm(A1, B1).</
Output:
<
=={{header|ERRE}}==
<syntaxhighlight lang="text">
PROGRAM AGM
Line 1,041 ⟶ 1,463:
PRINT(A)
END PROGRAM
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
{{trans|OCaml}}
<
if precision > abs(a - g) then a else
agm (0.5 * (a + g)) (sqrt (a * g)) precision
printfn "%g" (agm 1. (sqrt(0.5)) 1e-15)</
Output
<pre>0.847213</pre>
=={{header|Factor}}==
<
IN: rosetta-code.arithmetic-geometric-mean
: agm ( a g -- a' g' ) 2dup [ + 0.5 * ] 2dip * sqrt ;
1 1 2 sqrt / [ 2dup - 1e-15 > ] [ agm ] while drop .</
{{out}}
<pre>
Line 1,066 ⟶ 1,488:
=={{header|Forth}}==
<
begin
fover fover f+ 2e f/
Line 1,074 ⟶ 1,496:
fdrop ;
1e 2e -0.5e f** agm f. \ 0.847213084793979</
=={{header|Fortran}}==
A '''Fortran 77''' implementation
<
implicit none
double precision agm,a,b,eps,c
Line 1,092 ⟶ 1,514:
double precision agm
print*,agm(1.0d0,1.0d0/sqrt(2.0d0))
end</
=={{header|Futhark}}==
{{incorrect|Futhark|Futhark's syntax has changed, so this example will not compile}}
<syntaxhighlight lang="futhark">
import "futlib/math"
Line 1,139 ⟶ 1,531:
fun main(x: f64, y: f64): f64 =
agm(x,y)
</syntaxhighlight>
=={{header|Go}}==
<
import (
Line 1,160 ⟶ 1,552:
func main() {
fmt.Println(agm(1, 1/math.Sqrt2))
}</
{{out}}
<pre>
Line 1,169 ⟶ 1,561:
{{trans|Java}}
Solution:
<
double an = a, gn = g
while ((an-gn).abs() >= 10.0**-14) { (an, gn) = [(an+gn)*0.5, (an*gn)**0.5] }
an
}</
Test:
<
assert (0.8472130847939792 - agm(1, 0.5**0.5)).abs() <= 10.0**-14</
Output:
Line 1,183 ⟶ 1,575:
=={{header|Haskell}}==
<
-- The result is considered accurate when two successive approximations are
-- sufficiently close, as determined by "eq".
Line 1,202 ⟶ 1,594:
main = do
let equal = (< 0.000000001) . relDiff
print $ agm 1 (1 / sqrt 2) equal</
{{out}}
<pre>0.8472130847527654</pre>
Line 1,208 ⟶ 1,600:
=={{header|Icon}} and {{header|Unicon}}==
<syntaxhighlight lang="text">procedure main(A)
a := real(A[1]) | 1.0
g := real(A[2]) | (1 / 2^0.5)
Line 1,223 ⟶ 1,615:
}
return an
end</
Output:
Line 1,239 ⟶ 1,631:
First, the basic approach (with display precision set to 16 digits, which slightly exceeds the accuracy of 64 bit IEEE floating point arithmetic):
<
(mean , */ %:~ #)^:_] 1,%%:2
0.8472130847939792 0.8472130847939791</
This is the limit -- it stops when values are within a small epsilon of previous calculations. We can ask J for unique values (which also means -- unless we specify otherwise -- values within a small epsilon of each other, for floating point values):
<
0.8472130847939792</
Another variation would be to show intermediate values, in the limit process:
<
1 0.7071067811865475
0.8535533905932737 0.8408964152537145
0.8472249029234942 0.8472012667468915
0.8472130848351929 0.8472130847527654
0.8472130847939792 0.8472130847939791</
=== Arbitrary Precision ===
Line 1,263 ⟶ 1,655:
Borrowing routines from that page, but going with a default of approximately 100 digits of precision:
<
round=: DP&$: : (4 : 0)
Line 1,292 ⟶ 1,684:
n=. e (>i.1:) a (^%!@]) i.>.a^.e [ a=. |y-m*^.2
(2x^m) * 1++/*/\d%1+i.n
)</
We are also going to want a routine to display numbers with this precision, and we are going to need to manage epsilon manually, and we are going to need an arbitrary root routine:
<
x{.deb (x*2j1)":y
)
Line 1,302 ⟶ 1,694:
root=: ln@] exp@% [
epsilon=: 1r9^DP</
Some example uses:
<
1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572
fmt *~sqrt 2
Line 1,313 ⟶ 1,705:
0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000418
fmt 2 root 2
1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572</
Note that 2 root 2 is considerably slower than sqrt 2. The price of generality. So, while we could define geometric mean generally, a desire for good performance pushes us to use a routine specialized for two numbers:
<
geomean2=: [: sqrt */</
A quick test to make sure these can be equivalent:
<
3.872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673517
fmt geomean2 3 5
3.872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673517</
Now for our task example:
<
1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0.707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786
0.853553390593273762200422181052424519642417968844237018294169934497683119615526759712596883581910393 0.840896415253714543031125476233214895040034262356784510813226085974924754953902239814324004199292536
Line 1,337 ⟶ 1,729:
0.847213084793979086606499123482191636481445984459557704232275241670533381126169243513557113565344075 0.847213084793979086606499123482191636481445836194326665888883503648934628542100275932846717790147361
0.847213084793979086606499123482191636481445910326942185060579372659734004834134759723201915677745718 0.847213084793979086606499123482191636481445910326942185060579372659734004834134759723198672311476741
0.847213084793979086606499123482191636481445910326942185060579372659734004834134759723200293994611229 0.847213084793979086606499123482191636481445910326942185060579372659734004834134759723200293994611229</
We could of course extract out only a representative final value, but it's obvious enough, and showing how rapidly this converges is fun.
Line 1,343 ⟶ 1,735:
=={{header|Java}}==
<syntaxhighlight lang="java">/*
* Arithmetic-Geometric Mean of 1 & 1/sqrt(2)
* Brendan Shaklovitz
Line 1,365 ⟶ 1,757:
System.out.println(agm(1.0, 1.0 / Math.sqrt(2.0)));
}
}</
{{out}}
<pre>0.8472130847939792</pre>
Line 1,372 ⟶ 1,764:
===ES5===
<
var an = (a0 + g0) / 2,
gn = Math.sqrt(a0 * g0);
Line 1,381 ⟶ 1,773:
}
agm(1, 1 / Math.sqrt(2));</
===ES6===
<
'use strict';
Line 1,426 ⟶ 1,818:
return agm(1, 1 / Math.sqrt(2));
})();</
{{Out}}
<syntaxhighlight lang
=={{header|jq}}==
{{works with|jq|1.4}}
Naive version that assumes tolerance is appropriately specified:
<
def abs: if . < 0 then -. else . end;
def _agm:
Line 1,442 ⟶ 1,834:
else .
end;
[a, g] | _agm | .[0] ;</
This version avoids an infinite loop if the requested tolerance is too small:
<
def abs: if . < 0 then -. else . end;
def _agm:
Line 1,459 ⟶ 1,851:
# Example:
agm(1; 1/(2|sqrt); 1e-100)</
{{Out}}
$ jq -n -f Arithmetic-geometric_mean.jq
Line 1,466 ⟶ 1,858:
=={{header|Julia}}==
{{works with|Julia|1.2}}
<
(x ≤ 0 || y ≤ 0 || e ≤ 0) && throw(DomainError("x, y must be strictly positive"))
g, a = minmax(x, y)
Line 1,485 ⟶ 1,877:
println("# Using ", precision(BigFloat), "-bit float numbers:")
x, y = big(1.0), 1 / √big(2.0)
@show agm(x, y)</
The ε for this calculation is given as a positive integer multiple of the machine ε for <tt>x</tt>.
Line 1,498 ⟶ 1,890:
=={{header|Klingphix}}==
{{trans|Oforth}}
<
:agm [ over over + 2 / rot rot * sqrt ] [ over over tostr swap tostr # ] while drop ;
Line 1,506 ⟶ 1,898:
pstack
" " input</
{{trans|F#}}
<
:agm %a %g %p !p !g !a
Line 1,517 ⟶ 1,909:
pstack
" " input</
{{out}}
<pre>(0.847213)</pre>
=={{header|Kotlin}}==
<
fun agm(a: Double, g: Double): Double {
Line 1,540 ⟶ 1,932:
fun main(args: Array<String>) {
println(agm(1.0, 1.0 / Math.sqrt(2.0)))
}</
{{out}}
Line 1,546 ⟶ 1,938:
0.8472130847939792
</pre>
=={{header|Lambdatalk}}==
<syntaxhighlight lang="Scheme">
{def eps 1e-15}
-> eps
{def agm
{lambda {:a :g}
{if {> {abs {- :a :g}} {eps}}
then {agm {/ {+ :a :g} 2}
{sqrt {* :a :g}}}
else :a }}}
-> agm
{agm 1 {/ 1 {sqrt 2}}}
-> 0.8472130847939792
Multi-precision version using the lib_BN library
{BN.DEC 70}
-> 70 digits
{def EPS {BN./ 1 {BN.pow 10 45}}}
-> EPS
{def AGM
{lambda {:a :g}
{if {= {BN.compare {BN.abs {BN.- :a :g}} {EPS}} 1}
then {AGM {BN./ {BN.+ :a :g} 2}
{BN.sqrt {BN.* :a :g}}}
else :a }}}
-> AGM
{AGM 1 {BN./ 1 {BN.sqrt 2}}}
-> 0.8472130847939790866064991234821916364814459103269421850605793726597339
</syntaxhighlight>
=={{header|LFE}}==
<
(defun agm (a g)
(agm a g 1.0e-15))
Line 1,565 ⟶ 1,992:
(defun next-g (a g)
(math:sqrt (* a g)))
</syntaxhighlight>
Usage:
Line 1,573 ⟶ 2,000:
0.8472130847939792
</pre>
=={{header|LiveCode}}==
<
put abs(aa-g) into absdiff
put (aa+g)/2 into aan
Line 1,605 ⟶ 2,014:
end repeat
return aa
end agm</
Example
<
-- ouput
-- 0.847213</
=={{header|LLVM}}==
<
; LLVM does not provide a way to print values, so the alternative would be
; to just load the string into memory, and that would be boring.
Line 1,714 ⟶ 2,123:
attributes #2 = { nounwind readnone speculatable }
attributes #4 = { nounwind }
attributes #6 = { noreturn }</
{{out}}
<pre>The arithmetic-geometric mean is 0.8472130847939791654</pre>
=={{header|Logo}}==
<
output and [:a - :b < 1e-15] [:a - :b > -1e-15]
end
Line 1,728 ⟶ 2,137:
show agm 1 1/sqrt 2
</syntaxhighlight>
=={{header|Lua}}==
<
if not tolerance or tolerance < 1e-15 then
tolerance = 1e-15
Line 1,742 ⟶ 2,151:
end
print(string.format("%.15f", agm(1, 1 / math.sqrt(2))))</
'''Output:'''
Line 1,749 ⟶ 2,158:
=={{header|M2000 Interpreter}}==
<syntaxhighlight lang="m2000 interpreter">
Module Checkit {
Function Agm {
Line 1,764 ⟶ 2,173:
}
Checkit
</syntaxhighlight>
=={{header|Maple}}==
Maple provides this function under the name GaussAGM. To compute a floating point approximation, use evalf.
<syntaxhighlight lang="maple">
> evalf( GaussAGM( 1, 1 / sqrt( 2 ) ) ); # default precision is 10 digits
0.8472130847
Line 1,775 ⟶ 2,184:
0.847213084793979086606499123482191636481445910326942185060579372659\
7340048341347597232002939946112300
</syntaxhighlight>
Alternatively, if one or both arguments is already a float, Maple will compute a floating point approximation automatically.
<syntaxhighlight lang="maple">
> GaussAGM( 1.0, 1 / sqrt( 2 ) );
0.8472130847
</syntaxhighlight>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
To any arbitrary precision, just increase PrecisionDigits
<
AGMean[a_, b_] := FixedPoint[{ Tr@#/2, Sqrt[Times@@#] }&, N[{a,b}, PrecisionDigits]]〚1〛</
<pre>AGMean[1, 1/Sqrt[2]]
Line 1,791 ⟶ 2,200:
=={{header|MATLAB}} / {{header|Octave}}==
<
%%arithmetic_geometric_mean(a,g)
while (1)
Line 1,799 ⟶ 2,208:
if (abs(a0-a) < a*eps) break; end;
end;
end</
<pre>octave:26> agm(1,1/sqrt(2))
ans = 0.84721
Line 1,805 ⟶ 2,214:
=={{header|Maxima}}==
<
agm(1, 1/sqrt(2)), bfloat, fpprec: 85;
/* 8.472130847939790866064991234821916364814459103269421850605793726597340048341347597232b-1 */</
=={{header|МК-61/52}}==
<syntaxhighlight lang="text">П1 <-> П0 1 ВП 8 /-/ П2 ИП0 ИП1
- ИП2 - /-/ x<0 31 ИП1 П3 ИП0 ИП1
* КвКор П1 ИП0 ИП3 + 2 / П0 БП
08 ИП0 С/П</
=={{header|Modula-2}}==
{{trans|C}}
<
FROM EXCEPTIONS IMPORT AllocateSource,ExceptionSource,GetMessage,RAISE;
FROM LongConv IMPORT ValueReal;
Line 1,887 ⟶ 2,296:
WriteReal(AGM(x, y));
WriteLn
END AGM.</
{{out}}
<pre>Enter two numbers: 1.0
Line 1,898 ⟶ 2,307:
=={{header|NetRexx}}==
{{trans|Java}}
<
options replace format comments java crossref symbols nobinary
Line 1,922 ⟶ 2,331:
end
return a1 + 0
</syntaxhighlight>
'''Output:'''
<pre>
Line 1,929 ⟶ 2,338:
=={{header|NewLISP}}==
<syntaxhighlight lang="newlisp">
(define (a-next a g) (mul 0.5 (add a g)))
Line 1,951 ⟶ 2,360:
(amg 1.0 root-reciprocal-2 quadrillionth)
)
</syntaxhighlight>
=={{header|Nim}}==
<
proc agm(a, g: float,delta: float = 1.0e-15): float =
Line 1,967 ⟶ 2,376:
result = aOld
echo agm(1.0,1.0/sqrt(2.0))</
Output:<br/>
Line 1,976 ⟶ 2,385:
See first 24 iterations:
<
from strutils import parseFloat, formatFloat, ffDecimal
Line 1,995 ⟶ 2,404:
echo("Result A: " & formatFloat(t.resA, ffDecimal, 24))
echo("Result G: " & formatFloat(t.resG, ffDecimal, 24))</
=={{header|Oberon-2}}==
{{works with|oo2c}}
<
MODULE Agm;
IMPORT
Line 2,025 ⟶ 2,434:
Out.LongReal(Of(1,1 / Math.sqrt(2)),0,0);Out.Ln
END Agm.
</syntaxhighlight>
{{Out}}
<pre>
Line 2,033 ⟶ 2,442:
=={{header|Objeck}}==
{{trans|Java}}
<
class ArithmeticMean {
function : Amg(a : Float, g : Float) ~ Nil {
Line 2,050 ⟶ 2,459:
}
}
</syntaxhighlight>
Output:
Line 2,056 ⟶ 2,465:
=={{header|OCaml}}==
<
if tol > abs_float (a -. g) then a else
agm (0.5*.(a+.g)) (sqrt (a*.g)) tol
let _ = Printf.printf "%.16f\n" (agm 1.0 (sqrt 0.5) 1e-15)</
Output
<pre>0.8472130847939792</pre>
Line 2,066 ⟶ 2,475:
=={{header|Oforth}}==
<
while( 2dup <> ) [ 2dup + 2 / -rot * sqrt ] drop ;</
Usage :
<syntaxhighlight lang
{{out}}
Line 2,078 ⟶ 2,487:
=={{header|OOC}}==
<
import math // import for sqrt() function
Line 2,098 ⟶ 2,507:
"%.16f" printfln(agm(1., sqrt(0.5)))
}
</syntaxhighlight>
Output
<pre>0.8472130847939792</pre>
=={{header|ooRexx}}==
<
say agm(1, 1/rxcalcsqrt(2,16))
Line 2,120 ⟶ 2,529:
return a1+0
::requires rxmath LIBRARY</
{{out}}
<pre>0.8472130847939791968</pre>
Line 2,126 ⟶ 2,535:
=={{header|PARI/GP}}==
Built-in:
<
Iteration:
<
=={{header|Pascal}}==
Line 2,135 ⟶ 2,544:
{{libheader|GMP}}
Port of the C example:
<
uses
Line 2,169 ⟶ 2,578:
mp_printf ('%.20000Ff'+nl, @x0);
mp_printf ('%.20000Ff'+nl+nl, @y0);
end.</
Output is as long as the C example.
=={{header|Perl}}==
<
my ($a0, $g0, $a1, $g1);
Line 2,189 ⟶ 2,598:
}
print agm(1, 1/sqrt(2))."\n";</
Output:
<pre>0.847213084793979</pre>
=={{header|Phix}}==
<!--<
<span style="color: #008080;">function</span> <span style="color: #000000;">agm</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">tolerance</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1.0e-15</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">-</span><span style="color: #000000;">g</span><span style="color: #0000FF;">)></span><span style="color: #000000;">tolerance</span> <span style="color: #008080;">do</span>
Line 2,203 ⟶ 2,612:
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">agm</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- (rounds to 10 d.p.)</span>
<!--</
{{out}}
<pre>
Line 2,214 ⟶ 2,623:
=={{header|Phixmonti}}==
<
1.0e-15 var tolerance
Line 2,228 ⟶ 2,637:
enddef
1 1 2 sqrt / agm tostr ?</
=={{header|PHP}}==
<
define('PRECISION', 13);
Line 2,254 ⟶ 2,663:
bcscale(PRECISION);
echo agm(1, 1 / bcsqrt(2));
</syntaxhighlight>
{{out}}
<pre>
0.8472130848350
</pre>
=={{header|Picat}}==
<syntaxhighlight lang="picat">main =>
println(agm(1.0, 1/sqrt(2))).
agm(A,G) = A, A-G < 1.0e-10 => true.
agm(A,G) = agm((A+G)/2, sqrt(A*G)).
</syntaxhighlight>
{{out}}
<pre>
0.847213084835193
</pre>
=={{header|PicoLisp}}==
<
(de agm (A G)
Line 2,270 ⟶ 2,692:
(round
(agm 1.0 (*/ 1.0 1.0 (sqrt 2.0 1.0)))
70 )</
Output:
<pre>-> "0.8472130847939790866064991234821916364814459103269421850605793726597340"</pre>
=={{header|PL/I}}==
<syntaxhighlight lang="pl/i">
arithmetic_geometric_mean: /* 31 August 2012 */
procedure options (main);
Line 2,289 ⟶ 2,711:
put skip list ('The result is:', a);
end arithmetic_geometric_mean;
</syntaxhighlight>
Results:
<pre>
Line 2,302 ⟶ 2,724:
=={{header|Potion}}==
Input values should be floating point
<
xi = 1
7 times :
Line 2,318 ⟶ 2,740:
.
x
.</
=={{header|PowerShell}}==
<syntaxhighlight lang="powershell">
function agm ([Double]$a, [Double]$g) {
[Double]$eps = 1E-15
Line 2,336 ⟶ 2,758:
}
agm 1 (1/[Math]::Sqrt(2))
</syntaxhighlight>
<b>Output:</b>
<pre>
Line 2,345 ⟶ 2,767:
=={{header|Prolog}}==
<syntaxhighlight lang="prolog">
agm(A,G,A) :- abs(A-G) < 1.0e-15, !.
agm(A,G,Res) :- A1 is (A+G)/2.0, G1 is sqrt(A*G),!, agm(A1,G1,Res).
Line 2,351 ⟶ 2,773:
?- agm(1,1/sqrt(2),Res).
Res = 0.8472130847939792.
</syntaxhighlight>
=={{header|Python}}==
Line 2,376 ⟶ 2,779:
===Basic Version===
<
def agm(a0, g0, tolerance=1e-10):
Line 2,391 ⟶ 2,794:
return an
print agm(1, 1 / sqrt(2))</
{{out}}
<pre> 0.847213084835</pre>
===Multi-Precision Version===
<
def agm(a, g, tolerance=Decimal("1e-65")):
Line 2,404 ⟶ 2,807:
getcontext().prec = 70
print agm(Decimal(1), 1 / Decimal(2).sqrt())</
{{out}}
<pre>0.847213084793979086606499123482191636481445910326942185060579372659734</pre>
Line 2,411 ⟶ 2,814:
=={{header|Quackery}}==
<
[ temp put
Line 2,428 ⟶ 2,831:
125 point$ echo$ cr cr
swap say "Num: " echo cr
say "Den: " echo</
{{out}}
Line 2,441 ⟶ 2,844:
=={{header|R}}==
<
geometricMean <- function(a, b) { sqrt(a * b) }
Line 2,454 ⟶ 2,857:
agm <- arithmeticGeometricMean(1, 1/sqrt(2))
print(format(agm, digits=16))</
{{out}}
<pre> agm rel_error
1 0.8472130847939792 1.310441309927519e-16</pre>
This function also works on vectors a and b (following the spirit of R):
<
b <- c(1/sqrt(2), 1/sqrt(3), 1/2)
agm <- arithmeticGeometricMean(a, b)
print(format(agm, digits=16))</
{{out}}
<pre> agm rel_error
Line 2,471 ⟶ 2,874:
=={{header|Racket}}==
This version uses Racket's normal numbers:
<
#lang racket
(define (agm a g [ε 1e-15])
Line 2,479 ⟶ 2,882:
(agm 1 (/ 1 (sqrt 2)))
</syntaxhighlight>
Output:
<pre>
Line 2,486 ⟶ 2,889:
This alternative version uses arbitrary precision floats:
<
#lang racket
(require math/bigfloat)
(bf-precision 200)
(bfagm 1.bf (bf/ (bfsqrt 2.bf)))
</syntaxhighlight>
Output:
<pre>
Line 2,499 ⟶ 2,902:
=={{header|Raku}}==
(formerly Perl 6)
<syntaxhighlight lang="raku"
($a, $g) = ($a + $g)/2, sqrt $a * $g until $a ≅ $g;
return $a;
}
say agm 1, 1/sqrt 2;</
{{out}}
<pre>0.84721308479397917</pre>
It's also possible to write it recursively:
<syntaxhighlight lang="raku"
$a ≅ $g ?? $a !! agm(|@$_)
given ($a + $g)/2, sqrt $a * $g;
}
say agm 1, 1/sqrt 2;</
We can also get a bit fancy and use a converging sequence of complex numbers:
<syntaxhighlight lang=raku>sub agm {
($^z, {(.re+.im)/2 + (.re*.im).sqrt*1i} ... * ≅ *)
.tail.re
}
say agm 1 + 1i/2.sqrt</syntaxhighlight>
=={{header|Raven}}==
<
# $errlim $g $a "%d %g %d\n" print
$a 1.0 + as $t
Line 2,528 ⟶ 2,940:
16 1 2 sqrt / 1 agm "agm: %.15g\n" print</
{{out}}
<pre>t: 0.853553 a: 0.853553 g: 0.840896
Line 2,537 ⟶ 2,949:
=={{header|Relation}}==
<syntaxhighlight lang="relation">
function agm(x,y)
set a = x
Line 2,556 ⟶ 2,968:
echo sqrt(x+y)
echo agm(x,y)
</syntaxhighlight>
<pre>
Line 2,568 ⟶ 2,980:
REXX supports arbitrary precision, so the default digits can be changed if desired.
<
parse arg a b digs . /*obtain optional numbers from the C.L.*/
if digs=='' | digs=="," then digs= 120 /*No DIGS specified? Then use default.*/
Line 2,599 ⟶ 3,011:
numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2
do j=0 while h>9; m.j=h; h=h % 2 + 1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g</
{{out|output|text= when using the default input:}}
<pre>
Line 2,608 ⟶ 3,020:
=={{header|Ring}}==
<
decimals(9)
see agm(1, 1/sqrt(2)) + nl
Line 2,622 ⟶ 3,034:
end
return gn
</syntaxhighlight>
=={{header|RPL}}==
≪ 1E-10 → epsilon
≪ '''WHILE''' DUP2 - ABS epsilon > '''REPEAT'''
DUP2 + 2 / ROT ROT * √
'''END''' DROP
≫ ≫ ‘'''AGM'''’ STO
{{in}}
<pre>
1 2 / √ AGM
</pre>
{{out}}
<pre>
1: .847213084835
</pre>
=={{header|Ruby}}==
===Flt Version===
The thing to note about this implementation is that it uses the [http://flt.rubyforge.org/ Flt] library for high-precision math. This lets you adapt context (including precision and epsilon) to a ridiculous-in-real-life degree.
<
# It lets us control 'context' of numbers, individually or collectively -- including precision
# (which adjusts the context's value of epsilon accordingly).
Line 2,647 ⟶ 3,074:
end
puts agm(1, 1 / BinNum(2).sqrt)</
{{out}}
<pre>0.84721308479397908660649912348219163648144591032694218506057937265973400483413475972320029399461122994212228562523341096309796266583087105969971363598338426</pre>
Line 2,654 ⟶ 3,081:
===BigDecimal Version===
Ruby has a BigDecimal class in standard library
<
PRECISION = 100
Line 2,669 ⟶ 3,096:
a = BigDecimal(1)
g = 1 / BigDecimal(2).sqrt(PRECISION)
puts agm(a, g)</
{{out}}
<pre>
Line 2,675 ⟶ 3,102:
0.8472130847939790866064991234821916364814459103269421850605793726597340048341347597231986723114767413E0
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">// Accepts two command line arguments
// cargo run --name agm arg1 arg2
Line 2,726 ⟶ 3,134:
}
}
}</
{{out}}
Line 2,735 ⟶ 3,143:
=={{header|Scala}}==
<
def agm(a: Double, g: Double, eps: Double): Double = {
if (math.abs(a - g) < eps) (a + g) / 2
Line 2,742 ⟶ 3,150:
agm(1, math.sqrt(2)/2, 1e-15)
</syntaxhighlight>
=={{header|Scheme}}==
<
(define agm
(case-lambda
Line 2,757 ⟶ 3,165:
(display (agm 1 (/ 1 (sqrt 2)))) (newline)
</syntaxhighlight>
{{out}}
Line 2,765 ⟶ 3,173:
=={{header|Seed7}}==
<
include "float.s7i";
include "math.s7i";
Line 2,794 ⟶ 3,202:
writeln(agm(1.0, 2.0) digits 6);
writeln(agm(1.0, 1.0 / sqrt(2.0)) digits 6);
end func;</
{{out}}
Line 2,803 ⟶ 3,211:
=={{header|SequenceL}}==
<
agm(a, g) :=
Line 2,815 ⟶ 3,223:
agm(arithmeticMean, geometricMean);
main := agm(1.0, 1.0 / sqrt(2));</
{{out}}
Line 2,823 ⟶ 3,231:
=={{header|Sidef}}==
<
loop {
var (a1, g1) = ((a+g)/2, sqrt(a*g))
Line 2,831 ⟶ 3,239:
}
say agm(1, 1/sqrt(2))</
{{out}}
<pre>0.8472130847939790866064991234821916364814</pre>
=={{header|Smalltalk}}==
{{works with|Smalltalk/X}}
That is simply a copy/paste of the already existing agm method in the Number class:
<
"return the arithmetic-geometric mean agm(x, y)
of the receiver (x) and the argument, y.
Line 2,877 ⟶ 3,264:
gi := gn.
] doUntil:[ delta < epsilon ].
^ ai</
<
Transcript showCR: ( (1/2) agm:(1/6) ).
Transcript showCR: (1 agm:(1 / 2 sqrt)).</
{{out}}
<pre>13.4581714817256
Line 2,890 ⟶ 3,277:
{{works with|oracle|11.2 and higher}}
The solution uses recursive WITH clause (aka recursive CTE, recursive query, recursive factored subquery). Some, perhaps many, but not all SQL dialects support recursive WITH clause. The solution below was written and tested in Oracle SQL - Oracle has supported recursive WITH clause since version 11.2.
<
rec (rn, a, g, diff) as (
select 1, 1, 1/sqrt(2), 1 - 1/sqrt(2)
Line 2,902 ⟶ 3,289:
from rec
where diff <= 1e-38
;</
Line 2,912 ⟶ 3,299:
=={{header|Standard ML}}==
<
fun agm(a, g) = let
fun agm'(a, g, eps) =
Line 2,921 ⟶ 3,308:
in agm'(a, g, 1e~15)
end;
</syntaxhighlight>
{{out}}
<pre>
Line 2,928 ⟶ 3,315:
=={{header|Stata}}==
<
real scalar agm(real scalar a, real scalar b) {
Line 2,941 ⟶ 3,328:
agm(1,1/sqrt(2))
end</
{{out}}
<pre>.8472130848</pre>
=={{header|Swift}}==
<
enum AGRError : Error {
Line 2,976 ⟶ 3,363:
} catch {
print("agr is undefined when a * g < 0")
}</
{{out}}
<pre>0.847213084835193</pre>
Line 2,982 ⟶ 3,369:
=={{header|Tcl}}==
The tricky thing about this implementation is that despite the finite precision available to IEEE doubles (which Tcl uses in its implementation of floating point arithmetic, in common with many other languages) the sequence of values does not ''quite'' converge to a single value; it gets to within a ULP and then errors prevent it from getting closer. This means that an additional termination condition is required: once a value does not change (hence the <code>old_b</code> variable) we have got as close as we can. Note also that we are using exact equality with floating point; this is reasonable because this is a rapidly converging sequence (it only takes 4 iterations in this case).
<
set old_b [expr {$b<0?inf:-inf}]
while {$a != $b && $b != $old_b} {
Line 2,991 ⟶ 3,378:
}
puts [agm 1 [expr 1/sqrt(2)]]</
Output:
<pre>0.8472130847939792</pre>
=={{header|TI
{| class="wikitable"
|+ Texas Instruments SR-56 Program Listing for "Arithmetic-geometric mean"
|-
! Display !! Key !! Display !! Key !! Display !! Key !! Display !! Key
|-
| 00 33 || STO || 25 03 || 3 || 50 || || 75 ||
|-
| 01 02 || 2 || 26 12 || INV || 51 || || 76 ||
|-
| 02 32 || x<>t || 27 44 || EE || 52 || || 77 ||
|-
| 03 64 || × || 28 41 || R/S || 53 || || 78 ||
|-
| 04 32 || x<>t || 29 || || 54 || || 79 ||
|-
| 05 94 || = || 30 || || 55 || || 80 ||
|-
| 06 48 || *√x || 31 || || 56 || || 81 ||
|-
| 07 32 || x<>t || 32 || || 57 || || 82 ||
|-
| 08 84 || + || 33 || || 58 || || 83 ||
|-
| 09 34 || RCL || 34 || || 59 || || 84 ||
|-
| 10 02 || 2 || 35 || || 60 || || 85 ||
|-
| 11 94 || = || 36 || || 61 || || 86 ||
|-
| 12 54 || ÷ || 37 || || 62 || || 87 ||
|-
| 13 02 || 2 || 38 || || 63 || || 88 ||
|-
| 14 94 || = || 39 || || 64 || || 89 ||
|-
| 15 33 || STO || 40 || || 65 || || 90 ||
|-
| 16 02 || 2 || 41 || || 66 || || 91 ||
|-
| 17 44 || EE || 42 || || 67 || || 92 ||
|-
| 18 94 || = || 43 || || 68 || || 93 ||
|-
| 19 32 || x<>t || 44 || || 69 || || 94 ||
|-
| 20 44 || EE || 45 || || 70 || || 95 ||
|-
| 21 94 || = || 46 || || 71 || || 96 ||
|-
| 22 12 || INV || 47 || || 72 || || 97 ||
|-
| 23 37 || *x=t || 48 || || 73 || || 98 ||
|-
| 24 00 || 0 || 49 || || 74 || || 99 ||
|}
Asterisk denotes 2nd function key.
{| class="wikitable"
|+ Register allocation
|-
| 0: Unused || 1: Unused || 2: Previous Term || 3: Unused || 4: Unused
|-
| 5: Unused || 6: Unused || 7: Unused || 8: Unused || 9: Unused
|}
Annotated listing:
<syntaxhighlight lang="text">
STO 2 x<>t // x := term a, t := R2 := term g
× x<>t = √x // Calculate term g'
x<>t + RCL 2 = / 2 = STO 2 // Calculate term a'
EE = x<>t EE = // Round terms to ten digits
INV x=t 0 3 // Loop if unequal
INV EE // Exit scientific notation
R/S // End
</syntaxhighlight>
'''Usage:'''
Enter term a, press x<>t, then enter term g. Finally, press RST R/S to run the program.
{{in}}
<pre>
1 x<>t 2 √x 1/x RST R/S
</pre>
{{out}}
<pre>
.8472130848
</pre>
=={{header|UNIX Shell}}==
{{works with|ksh93}}
ksh is one of the few unix shells that can do floating point arithmetic (bash does not).
<
float a=$1 g=$2 eps=${3:-1e-11} tmp
while (( abs(a-g) > eps )); do
Line 3,019 ⟶ 3,490:
}
agm $((1/sqrt(2))) 1</
{{output}}
Line 3,030 ⟶ 3,501:
0.8472130848</pre>
You can get a more approximate convergence by changing the while condition to compare the numbers as strings: change <
=={{header|
<syntaxhighlight lang="v (vlang)">import math
const ep = 1e-14
fn agm(aa f64, gg f64) f64 {
mut a, mut g := aa, gg
for math.abs(a-g) > math.abs(a)*ep {
t := a
a, g = (a+g)*.5, math.sqrt(t*g)
}
return a
}
fn main() {
println(agm(1.0, 1.0/math.sqrt2))
}</syntaxhighlight>
Using standard math module
<syntaxhighlight lang="vlang">import math.stats
import math
fn main() {
println(stats.geometric_mean<f64>([1.0, 1.0/math.sqrt2]))
}</syntaxhighlight>
{{out}}
<pre>0.8408964152537145
</pre>
=={{header|Wren}}==
{{trans|Go}}
<
var agm = Fn.new { |a, g|
Line 3,161 ⟶ 3,544:
}
System.print(agm.call(1, 1/2.sqrt))</
{{out}}
Line 3,169 ⟶ 3,552:
=={{header|XPL0}}==
<
real A, A1, G;
[Format(0, 16);
Line 3,178 ⟶ 3,561:
RlOut(0, A); RlOut(0, G); RlOut(0, A-G); CrLf(0);
until A=G;
]</
Output:
Line 3,190 ⟶ 3,573:
=={{header|zkl}}==
{{trans|XPL0}}
<
while(not a.closeTo(g,1.0e-15)){
a1:=(a+g)/2.0; g=(a*g).sqrt(); a=a1;
println(a," ",g," ",a-g);
}</
{{out}}
<pre>
Line 3,203 ⟶ 3,586:
</pre>
Or, using tail recursion
<
if(a.closeTo(g,1.0e-15)) return(a) else return(self.fcn((a+g)/2.0, (a*g).sqrt()));
}()</
{{out}}
<pre>
Line 3,214 ⟶ 3,597:
0.847213 0.847213 1.11022e-16
</pre>
| |||