langs a-z

Task/Monte-Carlo-methods/OCaml/monte-carlo-methods.ocaml

@@ -0,0 +1,12 @@
+let get_pi throws =
+  let rec helper i count =
+    if i = throws then count
+    else
+      let rand_x = Random.float 2.0 -. 1.0
+      and rand_y = Random.float 2.0 -. 1.0 in
+      let dist = sqrt (rand_x *. rand_x +. rand_y *. rand_y) in
+      if dist < 1.0 then
+        helper (i+1) (count+1)
+      else
+        helper (i+1) count
+  in float (4 * helper 0 0) /. float throws

Task/Monte-Carlo-methods/Octave/monte-carlo-methods-1.octave

@@ -0,0 +1,16 @@
+function p = montepi(samples)
+  in_circle = 0;
+  for samp = 1:samples
+    v = [ unifrnd(-1,1), unifrnd(-1,1) ];
+    if ( v*v.' <= 1.0 )
+      in_circle++;
+    endif
+  endfor
+  p = 4*in_circle/samples;
+endfunction
+
+l = 1e4;
+while (l < 1e7)
+  disp(montepi(l));
+  l *= 10;
+endwhile

Task/Monte-Carlo-methods/Octave/monte-carlo-methods-2.octave

@@ -0,0 +1,3 @@
+function result = montepi(n)
+  result = sum(rand(1,n).^2+rand(1,n).^2<1)/n*4;
+endfunction

Task/Monte-Carlo-methods/PARI-GP/monte-carlo-methods.pari

@@ -0,0 +1 @@
+MonteCarloPi(tests)=4.*sum(i=1,tests,norml2([random(1.),random(1.)])<1)/tests;

Task/Monte-Carlo-methods/Pascal/monte-carlo-methods.pascal

@@ -0,0 +1,29 @@
+Program MonteCarlo(output);
+
+uses
+  Math;
+
+function MC_Pi(expo: integer): real;
+  var
+    x, y: real;
+    i, hits, samples: longint;
+  begin
+    samples := 10**expo;
+    hits := 0;
+    randomize;
+    for i := 1 to samples do
+    begin
+      x := random;
+      y := random;
+      if sqrt(x*x + y*y) < 1.0 then
+        inc(hits);
+    end;
+    MC_Pi := 4.0 * hits / samples;
+  end;
+
+var
+  i: integer;
+begin
+  for i := 4 to 8 do
+    writeln (10**i, ' samples give ', MC_Pi(i):7:5, ' as pi.');
+end.

Task/Monte-Carlo-methods/Perl-6/monte-carlo-methods-1.pl6

@@ -0,0 +1,10 @@
+sub approximate_pi (Int $sample_size) {
+    my Int $in = 0;
+    (rand - 1/2)**2 + (rand - 1/2)**2 < 1/4 and ++$in
+        for ^$sample_size;
+    return 4 * $in / $sample_size;
+}
+
+say 'n =    100: ', approximate_pi    100;
+say 'n =  1,000: ', approximate_pi  1_000;
+say 'n = 10,000: ', approximate_pi 10_000;

Task/Monte-Carlo-methods/Perl-6/monte-carlo-methods-2.pl6

@@ -0,0 +1,6 @@
+sub approximate_pi (Int $sample_size) {
+    $sample_size R/ [+]
+        4 xx grep 0 ..^ 1/4,
+                (rand - 1/2)**2 + (rand - 1/2)**2 xx
+                    $sample_size;
+}

Task/Monte-Carlo-methods/PowerShell/monte-carlo-methods.psh

@@ -0,0 +1,17 @@
+function Get-Pi ($Iterations = 10000) {
+    $InCircle = 0
+    for ($i = 0; $i -lt $Iterations; $i++) {
+        $x = Get-Random 1.0
+        $y = Get-Random 1.0
+        if ([Math]::Sqrt($x * $x + $y * $y) -le 1) {
+            $InCircle++
+        }
+    }
+    $Pi = [decimal] $InCircle / $Iterations * 4
+    $RealPi = [decimal] "3.141592653589793238462643383280"
+    $Diff = [Math]::Abs(($Pi - $RealPi) / $RealPi * 100)
+    New-Object PSObject `
+        | Add-Member -PassThru NoteProperty Iterations $Iterations `
+        | Add-Member -PassThru NoteProperty Pi $Pi `
+        | Add-Member -PassThru NoteProperty "% Difference" $Diff
+}

Task/Monte-Carlo-methods/PureBasic/monte-carlo-methods.purebasic

@@ -0,0 +1,24 @@
+OpenConsole()
+
+Procedure.d MonteCarloPi(throws.d)
+	inCircle.d = 0
+		For i = 1 To throws.d
+			randX.d = (Random(2147483647)/2147483647)*2-1
+			randY.d = (Random(2147483647)/2147483647)*2-1
+			dist.d  = Sqr(randX.d*randX.d + randY.d*randY.d)
+			If dist.d < 1
+				inCircle = inCircle + 1
+			EndIf
+		Next i
+	pi.d = (4 * inCircle / throws.d)	
+	ProcedureReturn pi.d
+	
+EndProcedure
+
+PrintN ("'built-in' #Pi         = " + StrD(#PI,20))
+PrintN ("MonteCarloPi(10000)    = " + StrD(MonteCarloPi(10000),20))
+PrintN ("MonteCarloPi(100000)   = " + StrD(MonteCarloPi(100000),20))
+PrintN ("MonteCarloPi(1000000)  = " + StrD(MonteCarloPi(1000000),20))
+PrintN ("MonteCarloPi(10000000) = " + StrD(MonteCarloPi(10000000),20))
+
+PrintN("Press any key"): Repeat: Until Inkey() <> ""

Task/Monte-Carlo-methods/Seed7/monte-carlo-methods.seed7

@@ -0,0 +1,26 @@
+$ include "seed7_05.s7i";
+  include "float.s7i";
+
+const func float: pi (in integer: throws) is func
+  result
+    var float: pi is 0.0;
+  local
+    var integer: throw is 0;
+    var integer: inside is 0;
+  begin
+    for throw range 1 to throws do
+      if rand(0.0, 1.0) ** 2 + rand(0.0, 1.0) ** 2 <= 1.0 then
+        incr(inside);
+      end if;
+    end for;
+    pi := flt(4 * inside) / flt(throws);
+  end func;
+
+const proc: main is func
+  begin
+    writeln("    10000: " <& pi(    10000) digits 5);
+    writeln("   100000: " <& pi(   100000) digits 5);
+    writeln("  1000000: " <& pi(  1000000) digits 5);
+    writeln(" 10000000: " <& pi( 10000000) digits 5);
+    writeln("100000000: " <& pi(100000000) digits 5);
+  end func;

Task/Monte-Carlo-methods/Ursala/monte-carlo-methods-1.ursala

@@ -0,0 +1,4 @@
+#import std
+#import flo
+
+mcp "n" = times/4. div\float"n" (rep"n" (fleq/.5+ sqrt+ plus+ ~~ sqr+ minus/.5+ rand)?/~& plus/1.) 0.

Task/Monte-Carlo-methods/Ursala/monte-carlo-methods-2.ursala

@@ -0,0 +1,3 @@
+#cast %eL
+
+pis = mcp* <10,100,1000,10000,100000,1000000>

Task/Monte-Carlo-methods/XPL0/monte-carlo-methods.xpl0

@@ -0,0 +1,21 @@
+code Ran=1, CrLf=9;
+code real RlOut=48;
+
+func real MontePi(N);   \Calculate pi using Monte Carlo method
+int  N;                 \number of randomly selected points
+int  I, X, Y, C;
+def  R = 10000;         \radius of circle
+[C:= 0;                 \initialize count of points in circle
+for I:= 0 to N-1 do
+        [X:= Ran(R);
+         Y:= Ran(R);
+        if X*X + Y*Y <= R*R then C:= C+1;
+        ];
+return float(C)*4.0 / float(N);   \Acir/Asqr = pi*R^2/4*R^2 = pi/4
+];
+
+[RlOut(0, MontePi(        100));  CrLf(0);
+ RlOut(0, MontePi(     10_000));  CrLf(0);
+ RlOut(0, MontePi(  1_000_000));  CrLf(0);
+ RlOut(0, MontePi(100_000_000));  CrLf(0);
+]