Arithmetic-geometric mean: Difference between revisions

=={{header|11l}}==

{{trans|Python}}

V an = (a0 + g0) / 2.0

V gn = sqrt(a0 * g0)

R an

{{out}}

<pre>0.847213</pre>

=={{header|360 Assembly}}==

For maximum compatibility, this program uses only the basic instruction set.

USING AGM,R13

SAVEAREA B STM-SAVEAREA(R15)

LTORG

YREGS

{{out}}

<pre>

=={{header|8th}}==

with: n

;with

bye

{{out}}

<pre>

{{libheader|Action! Tool Kit}}

{{libheader|Action! Real Math}}

PROC Agm(REAL POINTER a0,g0,result)

Print(",") PrintR(g)

Print(")=") PrintRE(res)

{{out}}

[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Arithmetic-geometric_mean.png Screenshot from Atari 8-bit computer]

=={{header|Ada}}==

procedure Arith_Geom_Mean is

begin

N_IO.Put(AGM(1.0, 1.0/Math.Sqrt(2.0)), Fore => 1, Aft => 17, Exp => 0);

Output:<pre>0.84721308479397909</pre>

Printing out the difference between the means at each iteration nicely demonstrates the quadratic convergence.

BEGIN

PROC agm = (LONG REAL x, y) LONG REAL :

printf (($l(-35,33)l$, agm (LONG 1.0, LONG 1.0 / long sqrt (LONG 2.0))))

END

Output:<pre>+1.707106781186547524400844362e +0 +2.928932188134524755991556379e -1

+2.928932188134524755991556379e -1 +1.265697533955921916929670477e -2

=={{header|APL}}==

agd←{(⍺-⍵)<10*¯8:⍺⋄((⍺+⍵)÷2)∇(⍺×⍵)*÷2}

1 agd ÷2*÷2

Output: <pre>0.8472130848</pre>

By functional composition:

property tolerance : 1.0E-5

end script

end if

{{Out}}

<pre>0.847213084835</pre>

=={{header|AutoHotkey}}==

While abs(a-g) > tolerance

{

}

SetFormat, FloatFast, 0.15

Output:

<pre>0.847213084793979</pre>

=={{header|AWK}}==

BEGIN {

printf "%.16g\n", agm(1.0,sqrt(0.5))

return (x<0 ? -x : x)

}

Output

<pre>0.8472130847939792</pre>

==={{header|BASIC}}===

{{works with|QBasic}}

END

AGM = a

{{out}}

<pre>

==={{header|BASIC256}}===

end

return a

{{out}}

<pre>

==={{header|Commodore BASIC}}===

20 G = 1/SQR(2)

30 GOSUB 100

120 G = SQR(TA*G)

130 IF A<TA THEN 100

==={{header|BBC BASIC}}===

{{works with|BBC BASIC for Windows}}

@% = &1010

PRINT FNagm(1, 1/SQR(2))

UNTIL a = ta

= a

Produces this output:

<pre>

==={{header|GW-BASIC}}===

20 G = 1!/SQR(2!)

30 FOR I=1 TO 20 'twenty iterations is plenty

60 A = B

70 NEXT I

==={{header|IS-BASIC}}===

110 DEF AGM(A,G)

120 DO

150 LOOP UNTIL A=TA

160 LET AGM=A

==={{header|True BASIC}}===

{{works with|QBasic}}

DO

LET ta = (a + g) / 2

PRINT AGM(1, 1 / SQR(2))

{{out}}

<pre>

=={{header|bc}}==

* numbers x and y.

* Result will have d digits after the decimal point.

scale = 20

{{Out}}

=={{header|BQN}}==

(|𝕨-𝕩) ≤ 1e¯15? 𝕨;

(0.5×𝕨+𝕩) 𝕊 √𝕨×𝕩

}

{{out}}

<pre>0.8472130847939792</pre>

=={{header|C}}==

===Basic===

#include<stdio.h>

#include<stdlib.h>

return 0;

}

Original output:

===GMP===

Nigel_Galloway

return 0;

The first couple of iterations produces:

=={{header|C sharp|C#}}==

{

using System;

}

}

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 {

if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();

}

{{Out}}

<pre>0.8472130847939790866064991235</pre>

{{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;

WriteLine("0.{0}", CalcByAGM(digits));

if (System.Diagnostics.Debugger.IsAttached) ReadKey(); }

{{out}}

<pre style="height:64ex; overflow:scroll; white-space:pre-wrap;">0.8472130847939790866064991234821916364814459103269421850605793726597340048341347597232002939946112299421222856252334109630979626658308710596997136359833842511763268142890603897067686016166500482811887218977133094117674620199443929629021672891944995072316778973468639476066710579805578521731403493983042004221192160398395535950981936412937163406460295999679705994343516020318426487569502421748638554059819545816017424178878541927588041627190120855876856483268341404312184008040358092045594943138778151209265222545743971242868207663409547336745996217926655353486256861185433086262872872875630108355631935706687147856390889821151088363521476969796126218329432284178681137684451700181460219136940270209459966835135963278808042743454817445873632200251539529362658066141983656164916262596074347237066169023530800173753128478525584306319074542749341526857906552694060031475910203327467196861247963255105546489028208552974396512499400966255286606758044873538921857014011677169765350140849524768489932573213370289846689391946658618737529663875622660459147770442046810892565844083803204091061900315370673411959410100747433105990550582052432600995169279241747821697678106168369771411073927334392155014302200708736736596227214925877619285105238036702689046390962190766364423553808590294523406519001334234510583834171218051425500392370111132541114461262890625413355052664365359582455215629339751825147065013464104705697935568130660632937334503871097709729487591717901581732028157828848714993134081549334236779704471278593761859508514667736455467920161593422399714298407078888227903265675159652843581779572728480835648996350440414073422611018338354697596266333042208499985230074270393027724347497971797326455254654301983169496846109869074390506801376611925291977093844129970701588949316666116199459226501131118396635250253056164643158720845452298877547517727274765672164898291823923889520720764283971088470596035692199292183190154814128076659269829446445714923966632997307581390495762243896242317520950731901842446244237098642728114951118082282605386248461767518014098312749725765198375649235690280021617490553142720815343954059556357637112728165705973733744297003905604015638866307222570038923015911237696012158008177907786335124086243107357158376592650454665278733787444483440631024475703968125545398226643035341641303561380163416557526558975294452116687345122019122746673319157124076375382110696814107692639007483317574339675231966033086497357138387419609898383220288269488219130281936694995442224069727616862136951165783888501219909616065545461154325314816424933269479700415949147632311292059351651899794335004597628821729262591808940550843146639378254833513955019065337087206206402407705607584879649984365159272826453442863661541914258577710675618501727803328717519518930503180550524542602233552290077141812879865435118791800635627959362476826778641224946033812608262825409889531252767753465624327921451122955551603181843313369296172304178385515712556740498341666592696958000895372457305769454227537216020968719147039887846636724326270619112707171659082464004167994112040565710364083000241929439855307399465653967781049270105541035951333943219992506667620207839469555376055179640100974921885631130101781388857879381317209594806253920130098365028791769582798590527994772194179799702494306215841946888532811549772157996019440962347768614408507573928429882375939682322367058033413477462311289762585932437663177897491107726190970448952220450963072551559009382490402136480779203476721504856844602255440999282616317431264228578762898338065072202301037175314926350463106018857377256700661838129058063895450812703131137104371613583348806583395543121790134839883321641305763524471251153947206667033010134871651632411382881763983962952612114126321979596509865678675525076076042409590751752302194610453256433324961490125353332922372386894812788502013596630537605584935892839163046940388785496002747148719780145765957904958580226006609952496736432496683346176010660815670697514238186650361083885220976165500251607311499216129477579019972924868963822060380876027628167237016681910663358577515465038133423672234764202655856558846416010210540489855618711473588497637840648642679818650448631907747038228671143515112300360708657429886477146674733750114345818852797006056211724692174847180694866251199472893444270378304620707354938052872720621560630718828685805645211106967080285699069825769177220998671959968507790681443494932804976811543680463259938693076235070999518295129581121235707245383354826190752395158273098248180549665897909168867984071707793705959045775840910473413109604194111357756620727337797833203797301137672658535747710279781409721309612142393854737462769615041307952837372882050658719152259765084027796991761175393006725492491229845082362975568722711065849435533850494532638736489804606655979954360169503092790092450057856477235876198848986034412195340795369002996411974549060741600978859537660722905160772428590070901156639138364299041220826769629797867649032356499981990765997439870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2204840459913839674251648</pre>

=={{header|C++}}==

#include<bits/stdc++.h>

using namespace std;

return 0;

}

=={{header|Clojure}}==

(:gen-class))

(println (agm one isqrt2))

{{Output}}

<pre>

=={{header|COBOL}}==

PROGRAM-ID. ARITHMETIC-GEOMETRIC-MEAN-PROG.

DATA DIVISION.

COMPUTE G = FUNCTION SQRT(G).

SUBTRACT A FROM G GIVING 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)))

{{out}}

=={{header|D}}==

real agm(real a, real g, in int bitPrecision=60) pure nothrow @nogc @safe {

void main() @safe {

writefln("%0.19f", agm(1, 1 / sqrt(2.0)));

{{out}}

<pre>0.8472130847939790866</pre>

{{libheader| System.SysUtils}}

{{Trans|C#}}

program geometric_mean;

writeln(format('The arithmetic-geometric mean is %.6f', [agm(x, y)]));

readln;

{{out}}

<pre>Enter two numbers:1

=={{header|EchoLisp}}==

We use the '''(~= a b)''' operator which tests for |a - b| < ε = (math-precision).

(lib 'math)

(agm 1 (/ 1 (sqrt 2)))

→ 0.8472130847939792

=={{header|Elixir}}==

def mean(a,g,tol) when abs(a-g) <= tol, do: a

def mean(a,g,tol) do

end

{{out}}

=={{header|Erlang}}==

%% Author: Abhay Jain

A1 = (A+B) / 2,

B1 = math:pow(A*B, 0.5),

Output:

=={{header|ERRE}}==

PRINT(A)

END PROGRAM

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

{{trans|OCaml}}

if precision > abs(a - g) then a else

agm (0.5 * (a + g)) (sqrt (a * g)) precision

Output

<pre>0.847213</pre>

=={{header|Factor}}==

IN: rosetta-code.arithmetic-geometric-mean

: agm ( a g -- a' g' ) 2dup [ + 0.5 * ] 2dip * sqrt ;

{{out}}

<pre>

=={{header|Forth}}==

begin

fover fover f+ 2e f/

fdrop ;

=={{header|Fortran}}==

A '''Fortran 77''' implementation

implicit none

double precision agm,a,b,eps,c

double precision agm

print*,agm(1.0d0,1.0d0/sqrt(2.0d0))

=={{header|FreeBASIC}}==

' compile with: fbc -s console

Print : Print "hit any key to end program"

Sleep

{{out}}

<pre> 0.8472130847939792</pre>

{{incorrect|Futhark|Futhark's syntax has changed, so this example will not compile}}

import "futlib/math"

fun main(x: f64, y: f64): f64 =

agm(x,y)

=={{header|Go}}==

import (

func main() {

fmt.Println(agm(1, 1/math.Sqrt2))

{{out}}

<pre>

{{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:

Output:

=={{header|Haskell}}==

-- The result is considered accurate when two successive approximations are

-- sufficiently close, as determined by "eq".

main = do

let equal = (< 0.000000001) . relDiff

{{out}}

<pre>0.8472130847527654</pre>

}

return an

Output:

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

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):

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

=== Arbitrary Precision ===

Borrowing routines from that page, but going with a default of approximately 100 digits of precision:

round=: DP&$: : (4 : 0)

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

)

root=: ln@] exp@% [

Some example uses:

1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572

fmt *~sqrt 2

0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000418

fmt 2 root 2

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:

A quick test to make sure these can be equivalent:

3.872983346207416885179265399782399610832921705291590826587573766113483091936979033519287376858673517

fmt geomean2 3 5

Now for our task example:

1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0.707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786

0.853553390593273762200422181052424519642417968844237018294169934497683119615526759712596883581910393 0.840896415253714543031125476233214895040034262356784510813226085974924754953902239814324004199292536

0.847213084793979086606499123482191636481445984459557704232275241670533381126169243513557113565344075 0.847213084793979086606499123482191636481445836194326665888883503648934628542100275932846717790147361

0.847213084793979086606499123482191636481445910326942185060579372659734004834134759723201915677745718 0.847213084793979086606499123482191636481445910326942185060579372659734004834134759723198672311476741

We could of course extract out only a representative final value, but it's obvious enough, and showing how rapidly this converges is fun.

=={{header|Java}}==

* Arithmetic-Geometric Mean of 1 & 1/sqrt(2)

* Brendan Shaklovitz

System.out.println(agm(1.0, 1.0 / Math.sqrt(2.0)));

}

{{out}}

<pre>0.8472130847939792</pre>

===ES5===

var an = (a0 + g0) / 2,

gn = Math.sqrt(a0 * g0);

}

===ES6===

'use strict';

return agm(1, 1 / Math.sqrt(2));

{{Out}}

=={{header|jq}}==

{{works with|jq|1.4}}

Naive version that assumes tolerance is appropriately specified:

def abs: if . < 0 then -. else . end;

def _agm:

else .

end;

This version avoids an infinite loop if the requested tolerance is too small:

def abs: if . < 0 then -. else . end;

def _agm:

# Example:

{{Out}}

$ jq -n -f Arithmetic-geometric_mean.jq

=={{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)

println("# Using ", precision(BigFloat), "-bit float numbers:")

x, y = big(1.0), 1 / √big(2.0)

The &epsilon; for this calculation is given as a positive integer multiple of the machine &epsilon; for <tt>x</tt>.

=={{header|Klingphix}}==

{{trans|Oforth}}

:agm [ over over + 2 / rot rot * sqrt ] [ over over tostr swap tostr # ] while drop ;

pstack

{{trans|F#}}

:agm %a %g %p !p !g !a

pstack

{{out}}

<pre>(0.847213)</pre>

=={{header|Kotlin}}==

fun agm(a: Double, g: Double): Double {

fun main(args: Array<String>) {

println(agm(1.0, 1.0 / Math.sqrt(2.0)))

{{out}}

=={{header|LFE}}==

(defun agm (a g)

(agm a g 1.0e-15))

(defun next-g (a g)

(math:sqrt (* a g)))

Usage:

=={{header|Liberty BASIC}}==

print agm(1, 1/sqr(2))

print using("#.#################",agm(1, 1/sqr(2)))

end function

=={{header|LiveCode}}==

put abs(aa-g) into absdiff

put (aa+g)/2 into aan

end repeat

return aa

Example

-- ouput

=={{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.

attributes #2 = { nounwind readnone speculatable }

attributes #4 = { nounwind }

{{out}}

<pre>The arithmetic-geometric mean is 0.8472130847939791654</pre>

=={{header|Logo}}==

output and [:a - :b < 1e-15] [:a - :b > -1e-15]

end

show agm 1 1/sqrt 2

=={{header|Lua}}==

if not tolerance or tolerance < 1e-15 then

tolerance = 1e-15

end

'''Output:'''

=={{header|M2000 Interpreter}}==

Module Checkit {

Function Agm {

}

Checkit

=={{header|Maple}}==

Maple provides this function under the name GaussAGM. To compute a floating point approximation, use evalf.

> evalf( GaussAGM( 1, 1 / sqrt( 2 ) ) ); # default precision is 10 digits

0.8472130847

0.847213084793979086606499123482191636481445910326942185060579372659\

7340048341347597232002939946112300

Alternatively, if one or both arguments is already a float, Maple will compute a floating point approximation automatically.

> GaussAGM( 1.0, 1 / sqrt( 2 ) );

0.8472130847

=={{header|Mathematica}}/{{header|Wolfram Language}}==

To any arbitrary precision, just increase PrecisionDigits

<pre>AGMean[1, 1/Sqrt[2]]

=={{header|MATLAB}} / {{header|Octave}}==

%%arithmetic_geometric_mean(a,g)

while (1)

if (abs(a0-a) < a*eps) break; end;

end;

<pre>octave:26> agm(1,1/sqrt(2))

ans = 0.84721

=={{header|Maxima}}==

agm(1, 1/sqrt(2)), bfloat, fpprec: 85;

=={{header|МК-61/52}}==

- ИП2 - /-/ x<0 31 ИП1 П3 ИП0 ИП1

* КвКор П1 ИП0 ИП3 + 2 / П0 БП

=={{header|Modula-2}}==

{{trans|C}}

FROM EXCEPTIONS IMPORT AllocateSource,ExceptionSource,GetMessage,RAISE;

FROM LongConv IMPORT ValueReal;

WriteReal(AGM(x, y));

WriteLn

{{out}}

<pre>Enter two numbers: 1.0

=={{header|NetRexx}}==

{{trans|Java}}

options replace format comments java crossref symbols nobinary

end

return a1 + 0

'''Output:'''

<pre>

=={{header|NewLISP}}==

(define (a-next a g) (mul 0.5 (add a g)))

(amg 1.0 root-reciprocal-2 quadrillionth)

)

=={{header|Nim}}==

proc agm(a, g: float,delta: float = 1.0e-15): float =

result = aOld

Output:<br/>

See first 24 iterations:

from strutils import parseFloat, formatFloat, ffDecimal

echo("Result A: " & formatFloat(t.resA, ffDecimal, 24))

=={{header|Oberon-2}}==

{{works with|oo2c}}

MODULE Agm;

IMPORT

Out.LongReal(Of(1,1 / Math.sqrt(2)),0,0);Out.Ln

END Agm.

{{Out}}

<pre>

=={{header|Objeck}}==

{{trans|Java}}

class ArithmeticMean {

function : Amg(a : Float, g : Float) ~ Nil {

}

}

Output:

=={{header|OCaml}}==

if tol > abs_float (a -. g) then a else

agm (0.5*.(a+.g)) (sqrt (a*.g)) tol

Output

<pre>0.8472130847939792</pre>

=={{header|Oforth}}==

Usage :

{{out}}

=={{header|OOC}}==

import math // import for sqrt() function

"%.16f" printfln(agm(1., sqrt(0.5)))

}

Output

<pre>0.8472130847939792</pre>

=={{header|ooRexx}}==

say agm(1, 1/rxcalcsqrt(2,16))

return a1+0

{{out}}

<pre>0.8472130847939791968</pre>

=={{header|PARI/GP}}==

Built-in:

Iteration:

=={{header|Pascal}}==

{{libheader|GMP}}

Port of the C example:

uses

mp_printf ('%.20000Ff'+nl, @x0);

mp_printf ('%.20000Ff'+nl+nl, @y0);

Output is as long as the C example.

=={{header|Perl}}==

my ($a0, $g0, $a1, $g1);

}

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>

<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>

=={{header|Phixmonti}}==

1.0e-15 var tolerance

enddef

=={{header|PHP}}==

define('PRECISION', 13);

bcscale(PRECISION);

echo agm(1, 1 / bcsqrt(2));

{{out}}

<pre>

=={{header|Picat}}==

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)).

{{out}}

=={{header|PicoLisp}}==

(de agm (A G)

(round

(agm 1.0 (*/ 1.0 1.0 (sqrt 2.0 1.0)))

Output:

<pre>-> "0.8472130847939790866064991234821916364814459103269421850605793726597340"</pre>

=={{header|PL/I}}==

arithmetic_geometric_mean: /* 31 August 2012 */

procedure options (main);

put skip list ('The result is:', a);

end arithmetic_geometric_mean;

Results:

<pre>

=={{header|Potion}}==

Input values should be floating point

xi = 1

7 times :

.

x

=={{header|PowerShell}}==

function agm ([Double]$a, [Double]$g) {

[Double]$eps = 1E-15

}

agm 1 (1/[Math]::Sqrt(2))

<b>Output:</b>

<pre>

=={{header|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).

?- agm(1,1/sqrt(2),Res).

Res = 0.8472130847939792.

=={{header|PureBasic}}==

Protected.d ta=a+1, tg

While ta <> a

Input()

CloseConsole()

0.8472130847939792

===Basic Version===

def agm(a0, g0, tolerance=1e-10):

return an

{{out}}

<pre> 0.847213084835</pre>

===Multi-Precision Version===

def agm(a, g, tolerance=Decimal("1e-65")):

getcontext().prec = 70

{{out}}

<pre>0.847213084793979086606499123482191636481445910326942185060579372659734</pre>

=={{header|Quackery}}==

[ temp put

125 point$ echo$ cr cr

swap say "Num: " echo cr

{{out}}

=={{header|R}}==

geometricMean <- function(a, b) { sqrt(a * b) }

agm <- arithmeticGeometricMean(1, 1/sqrt(2))

{{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)

{{out}}

<pre> agm rel_error

=={{header|Racket}}==

This version uses Racket's normal numbers:

#lang racket

(define (agm a g [ε 1e-15])

(agm 1 (/ 1 (sqrt 2)))

Output:

<pre>

This alternative version uses arbitrary precision floats:

#lang racket

(require math/bigfloat)

(bf-precision 200)

(bfagm 1.bf (bf/ (bfsqrt 2.bf)))

Output:

<pre>

=={{header|Raku}}==

(formerly Perl 6)

($a, $g) = ($a + $g)/2, sqrt $a * $g until $a ≅ $g;

return $a;

}