Data update

Task/Average-loop-length/Ada/average-loop-length.adb

@@ -0,0 +1,53 @@
+with Ada.Text_IO; use Ada.Text_IO;
+with Ada.Numerics.Generic_Elementary_Functions;
+with Ada.Numerics.Discrete_Random;
+procedure Avglen is
+   package IIO is new Ada.Text_IO.Integer_IO (Positive); use IIO;
+   package LFIO is new Ada.Text_IO.Float_IO (Long_Float); use LFIO;
+   subtype FactN is Natural range 0..20;
+   TESTS : constant Natural := 1_000_000;
+
+   function Factorial (N : FactN) return Long_Float is
+      Result : Long_Float := 1.0;
+   begin
+      for I in 2..N loop Result := Result * Long_Float(I); end loop;
+      return Result;
+   end Factorial;
+
+   function Analytical (N : FactN) return Long_Float is
+      Sum : Long_Float := 0.0;
+   begin
+      for I in 1..N loop
+         Sum := Sum + Factorial(N) / Factorial(N - I) / Long_Float(N)**I;
+      end loop;
+      return Sum;
+   end Analytical;
+
+   function Experimental (N : FactN) return Long_Float is
+      subtype RandInt is Natural range 1..N;
+      package Random is new Ada.Numerics.Discrete_Random(RandInt);
+      seed : Random.Generator;
+      Num : RandInt;
+      count : Natural := 0;
+      bits : array(RandInt'Range) of Boolean;
+   begin
+      Random.Reset(seed);
+      for run in 1..TESTS loop
+         bits := (others  => false);
+         for I in RandInt'Range loop
+            Num := Random.Random(seed); exit when bits(Num);
+            bits(Num) := True; count := count + 1;
+         end loop;
+      end loop;
+      return Long_Float(count)/Long_Float(TESTS);
+   end Experimental;
+
+   A, E, err : Long_Float;
+begin
+   Put_Line(" N  avg    calc   %diff");
+   for I in 1..20 loop
+      A := Analytical(I);  E := Experimental(I); err := abs(E-A)/A*100.0;
+      Put(I, Width=>2); Put(E ,Aft=>4, exp=>0); Put(A, Aft=>4, exp=>0);
+      Put(err, Fore=>3, Aft=>3, exp=>0); New_line;
+   end loop;
+end Avglen;

Task/Average-loop-length/Crystal/average-loop-length.cr

@@ -0,0 +1,26 @@
+struct Int
+  def factorial
+    raise "only positive" if self < 0
+    (1_i64..self.to_i64).product
+  end
+end
+
+def rand_until_rep (n)
+  rands = {} of Int32 => Bool
+  loop do
+    r = rand(1..n)
+    return rands.size if rands[r]?
+    rands[r] = true
+  end
+end
+
+runs = 1_000_000
+
+puts " N    average    exp.        diff   ",
+     "===  ========  ========  ==========="
+(1..20).each do |n|
+  sum_of_runs = runs.times.sum(0_i64) { rand_until_rep(n) }
+  avg = sum_of_runs / runs
+  analytical = (1..n).sum(0.0) {|i| (n.factorial / (n.to_f**i) / (n-i).factorial) }
+  puts "%3d  %8.4f  %8.4f  (%8.4f%%)" % {n, avg, analytical, (avg/analytical - 1)*100}
+end

Task/Average-loop-length/EasyLang/average-loop-length.easy

@@ -3,7 +3,7 @@ fastfunc average n reps .
    len seen[] n
    for r to reps
       for i = 1 to n
-         f[i] = random n
+         f[i] = random 1 n
          seen[i] = 0
       .
       x = 1

Task/Average-loop-length/Pluto/average-loop-length.pluto

@@ -0,0 +1,39 @@
+require "table2"
+local fmt = require "fmt"
+
+local nmax <const> = 20
+
+local function avg(n)
+    local tests = 1e4
+    local sum = 0
+    for _ = 1, tests do
+        local v = table.rep(nmax, false)
+        local x = 1
+        while !v[x] do
+            v[x] = true
+            sum += 1
+            x = math.random(1, n)
+        end
+    end
+    return sum / tests
+end
+
+local function ana(n)
+    if n < 2 then return 1 end
+    local term = 1
+    local sum = 1
+    for i = n, 2, -1 do
+        term *= (i - 1) / n
+        sum += term
+    end
+    return sum
+end
+
+print(" N    average    analytical    (error)")
+print("===  =========  ============  =========")
+for n = 1, nmax do
+    local a = avg(n)
+    local b = ana(n)
+    local e = math.abs(a - b) / b * 100
+    fmt.print("%3d %9.4f  %12.4f   (%6.2f%%)", n, a, b, e)
+end

Task/Average-loop-length/PowerShell/average-loop-length-1.ps1

@@ -0,0 +1,59 @@
+function Get-AnalyticalLoopAverage ( [int]$N )
+    {
+    #  Expected loop average = sum from i = 1 to N of N! / (N-i)! / N^(N-i+1)
+    #  Equivalently, Expected loop average = sum from i = 1 to N of F(i)
+    #    where F(N) = 1, and F(i) = F(i+1)*i/N
+
+    $LoopAverage = $Fi = 1
+
+    If ( $N -eq 1 ) { return $LoopAverage }
+
+    ForEach ( $i in ($N-1)..1 )
+        {
+        $Fi *= $i / $N
+        $LoopAverage  += $Fi
+        }
+    return $LoopAverage
+    }
+
+function Get-ExperimentalLoopAverage ( [int]$N, [int]$Tests = 100000 )
+    {
+    If ( $N -eq 1 ) { return 1 }
+
+    #  Using 0 through N-1 instead of 1 through N for speed and simplicity
+    $NMO = $N - 1
+
+    #  Create array to hold mapping function
+    $F = New-Object int[] ( $N )
+
+    $Count = 0
+    $Random = New-Object System.Random
+
+    ForEach ( $Test in 1..$Tests )
+        {
+        #  Map each number to a random number
+        ForEach ( $i in 0..$NMO )
+            {
+            $F[$i] = $Random.Next( $N )
+            }
+
+        #  For each number...
+        ForEach ( $i in 0..$NMO )
+            {
+            #  Add the number to the list
+            $List = @()
+            $Count++
+            $List += $X = $i
+
+            #  If loop does not yet exist in list...
+            While ( $F[$X] -notin $List )
+                {
+                #  Go to the next mapped number and add it to the list
+                $Count++
+                $List += $X = $F[$X]
+                }
+            }
+        }
+    $LoopAvereage = $Count / $N / $Tests
+    return $LoopAvereage
+    }

Task/Average-loop-length/PowerShell/average-loop-length-2.ps1

@@ -0,0 +1,12 @@
+#  Display results for N = 1 through 20
+ForEach ( $N in 1..20 )
+    {
+    $AnalyticalAverage   = Get-AnalyticalLoopAverage   $N
+    $ExperimentalAverage = Get-ExperimentalLoopAverage $N
+    [pscustomobject] @{
+        N            = $N.ToString().PadLeft( 2, ' ' )
+        Analytical   = $AnalyticalAverage.ToString( '0.00000000' )
+        Experimental = $ExperimentalAverage.ToString( '0.00000000' )
+        'Error (%)'  = ( [math]::Abs( $AnalyticalAverage - $ExperimentalAverage ) / $AnalyticalAverage * 100 ).ToString( '0.00000000' )
+        }
+    }

Task/Average-loop-length/VBScript/average-loop-length.vbs

@@ -0,0 +1,48 @@
+Const MAX = 20
+Const ITER = 100000
+
+Function expected(n)
+  Dim sum
+  ni=n
+  For i = 1 To n
+    sum = sum + fact(n) / ni / fact(n-i)
+    ni=ni*n
+  Next
+  expected = sum
+End Function
+
+Function test(n )
+  Dim coun,x,bits
+  For i = 1 To ITER
+    x = 1
+    bits = 0
+    Do While Not bits And x
+      count = count + 1
+      bits = bits Or x
+      x =shift(Int(n * Rnd()))
+    Loop
+  Next
+  test = count / ITER
+End Function
+
+'VBScript formats numbers but does'nt align them!
+function rf(v,n,s) rf=right(string(n,s)& v,n):end function
+
+'some precalculations to speed things up...
+dim fact(20),shift(20)
+fact(0)=1:shift(0)=1
+for i=1 to 20
+  fact(i)=i*fact(i-1)
+  shift(i)=2*shift(i-1)
+next
+
+Dim n
+Wscript.echo "For " & ITER &" iterations"
+Wscript.Echo " n     avg.     exp.   (error%)"
+Wscript.Echo "==   ======   ======  =========="
+For n = 1 To MAX
+  av = test(n)
+  ex = expected(n)
+  Wscript.Echo rf(n,2," ")& "  "& rf(formatnumber(av, 4),7," ") & "   "& _
+  rf(formatnumber(ex,4),6," ")& "  ("& rf(Formatpercent(1 - av / ex,4),8," ") & ")"
+Next