March 2014 update

Task/Average-loop-length/D/average-loop-length.d

@@ -1,17 +1,14 @@
 import std.stdio, std.random, std.math, std.algorithm, std.range;
 
-real analytical(in int n) pure nothrow {
-    real total = 0.0;
-    foreach (immutable k; 1 .. n + 1) {
-        immutable x = reduce!q{a * b}(1.0L, iota(n - k + 1, n + 1))
-                      * k ^^ 2;
-        total += x / ((cast(real)n) ^^ (k + 1));
-    }
-    return total;
+real analytical(in int n) /*pure nothrow*/ {
+    enum aux = (int k)=> reduce!q{a * b}(1.0L, iota(n - k + 1, n + 1));
+    return iota(1, n + 1)
+           .map!(k => (aux(k) * k ^^ 2) / (real(n) ^^ (k + 1)))
+           .sum;
 }
 
 size_t loopLength(size_t maxN)(in int size, ref Xorshift rng) {
-    __gshared bool[maxN + 1] seen;
+    __gshared static bool[maxN + 1] seen;
     seen[0 .. size + 1] = false;
     int current = 1;
     size_t steps = 0;
@@ -34,8 +31,8 @@ void main() {
         long total = 0;
         foreach (immutable _; 0 .. nTrials)
             total += loopLength!maxN(n, rng);
-        immutable average = total / cast(real)nTrials;
-        immutable an = analytical(n);
+        immutable average = total / real(nTrials);
+        immutable an = n.analytical;
         immutable percentError = abs(an - average) / an * 100;
         immutable errorS = format("%2.4f", percentError);
         writefln("%3d  %9.5f  %12.5f  (%7s%%)",

Task/Average-loop-length/PARI-GP/average-loop-length.pari

@@ -0,0 +1,14 @@
+expected(n)=sum(i=1,n,n!/(n-i)!/n^i,0.);
+test(n, times)={
+  my(ct);
+  for(i=1,times,
+    my(x=1,bits);
+    while(!bitand(bits,x),ct++; bits=bitor(bits,x); x = 1<<random(n))
+  );
+  ct
+};
+TIMES=1000000;
+{for(n=1,20,
+ my(cnt=test(n, TIMES),avg=cnt/TIMES,ex=expected(n),diff=(avg/ex-1)*100.);
+ print(n"\t"avg*1."\t"ex*1."\t"diff);
+)}

Task/Average-loop-length/Ruby/average-loop-length.rb

@@ -6,7 +6,8 @@ end
 
 def rand_until_rep(n)
   rands = {}
-  loop do r = rand(1..n)
+  loop do
+    r = rand(1..n)
     return rands.size if rands[r]
     rands[r] = true
   end
@@ -14,10 +15,11 @@ end
 
 runs = 1_000_000
 
-puts " n\tavg\texp.\tdiff\n_____________________________"
+puts " N    average    exp.        diff   ",
+     "===  ========  ========  ==========="
 (1..20).each do |n|
   sum_of_runs = runs.times.inject(0){|sum, _| sum += rand_until_rep(n)}
   avg = sum_of_runs / runs.to_f
   analytical = (1..n).inject(0){|sum, i| sum += (n.factorial / (n**i).to_f / (n-i).factorial)}
-  puts "%2d %8.4f %8.4f %8.4f" % [n, avg, analytical, (avg/analytical - 1)*100]
+  puts "%3d  %8.4f  %8.4f  (%8.4f%%)" % [n, avg, analytical, (avg/analytical - 1)*100]
 end