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Task/Average-loop-length/Nim/average-loop-length.nim

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+import math, strfmt
+randomize()
+
+const
+  maxN = 20
+  times = 1_000_000
+
+proc factorial(n): float =
+  result = 1
+  for i in 1 .. n:
+    result *= i.float
+
+proc expected(n): float =
+  for i in 1 .. n:
+    result += factorial(n) / pow(n.float, i.float) / factorial(n - i)
+
+proc test(n, times): int =
+  for i in 1 .. times:
+    var
+      x = 1
+      bits = 0
+    while (bits and x) == 0:
+      inc result
+      bits = bits or x
+      x = 1 shl random(n)
+
+echo " n\tavg\texp.\tdiff"
+echo "-------------------------------"
+for n in 1 .. maxN:
+  let cnt = test(n, times)
+  let avg = cnt.float / times
+  let theory = expected(n)
+  let diff = (avg / theory - 1) * 100
+  printlnfmt "{:2} {:8.4f} {:8.4f} {:6.3f}%", n, avg, theory, diff