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Arithmetic-geometric mean: Difference between revisions
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(Arithmetic-geometric mean in Chipmunk Basic) |
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Line 239:
ELIF x + y = LONG 0.0 THEN LONG 0.0 CO Edge cases CO
ELSE
a
FI
END;
Line 397:
=={{header|BASIC}}==
==={{header|ANSI BASIC}}===
{{works with|
<syntaxhighlight lang="
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}}===
Line 432 ⟶ 436:
end function</syntaxhighlight>
{{out}}
<pre>0.84721308479</pre>
==={{header|BBC BASIC}}===
{{works with|BBC BASIC for Windows}}
<syntaxhighlight lang="bbcbasic"> *FLOAT 64
@% = &1010
PRINT FNagm(1, 1/SQR(2))
END
DEF FNagm(a,g)
LOCAL ta
REPEAT
ta = a
a = (a+g)/2
g = SQR(ta*g)
UNTIL a = ta
= a
</syntaxhighlight>
{{out}}
<pre>0.8472130847939792</pre>
==={{header|Chipmunk Basic}}===
Line 465 ⟶ 486:
140 RETURN</syntaxhighlight>
==={{header|
<syntaxhighlight lang="basic">let a = 1
let g = 1 / sqrt(2)
do
let t = (a + g) / 2
let g = sqrt(a *
let x = a
let a = t
let
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}}===
Line 505 ⟶ 575:
160 LET AGM=A
170 END DEF</syntaxhighlight>
==={{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}}===
Line 519 ⟶ 734:
LET AGM = a
END FUNCTION
PRINT AGM(1, 1 / SQR(2))
END</syntaxhighlight>
{{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}}==
Line 996 ⟶ 1,352:
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}}==
Line 1,130 ⟶ 1,515:
print*,agm(1.0d0,1.0d0/sqrt(2.0d0))
end</syntaxhighlight>
=={{header|Futhark}}==
Line 1,645 ⟶ 2,000:
0.8472130847939792
</pre>
=={{header|LiveCode}}==
Line 2,437 ⟶ 2,774:
Res = 0.8472130847939792.
</syntaxhighlight>
=={{header|Python}}==
Line 2,600 ⟶ 2,918:
say agm 1, 1/sqrt 2;</syntaxhighlight>
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}}==
Line 2,708 ⟶ 3,035:
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}}==
Line 2,760 ⟶ 3,102:
0.8472130847939790866064991234821916364814459103269421850605793726597340048341347597231986723114767413E0
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">// Accepts two command line arguments
// cargo run --name agm arg1 arg2
Line 2,919 ⟶ 3,242:
{{out}}
<pre>0.8472130847939790866064991234821916364814</pre>
=={{header|Smalltalk}}==
Line 3,173 ⟶ 3,475:
.8472130848
</pre>
=={{header|UNIX Shell}}==
Line 3,210 ⟶ 3,502:
You can get a more approximate convergence by changing the while condition to compare the numbers as strings: change <syntaxhighlight lang="bash">while (( abs(a-g) > eps ))</syntaxhighlight> to <syntaxhighlight lang="bash">while [[ $a != $g ]]</syntaxhighlight>
=={{header|V (Vlang)}}==
Line 3,357 ⟶ 3,533:
=={{header|Wren}}==
{{trans|Go}}
<syntaxhighlight lang="
var agm = Fn.new { |a, g|
Line 3,421 ⟶ 3,597:
0.847213 0.847213 1.11022e-16
</pre>
| |||