Add tasks for all the new languages

Task/Average-loop-length/EchoLisp/average-loop-length.echolisp

@@ -0,0 +1,29 @@
+(lib 'math) ;; Σ aka (sigma f(n)  nfrom nto)
+
+(define (f-count  N (times 100000))
+    (define count 0)
+    (for ((i times))
+
+    ;; new  random f mapping from  0..N-1 to 0..N-1
+    ;; (f n) is NOT (random N)
+    ;; because each call (f n) must return the same value
+
+    (define f (build-vector N  (lambda(i) (random N))))
+
+    (define hits (make-vector N))
+        (define n 0)
+        (while (zero? [hits n])
+            (++ count)
+            (vector+= hits n 1)
+            (set! n [f n])))
+    (// count times))
+
+(define (f-anal N)
+    (Σ  (lambda(i) (// (! N) (! (- N i)) (^  N i))) 1 N))
+
+(decimals 5)
+(define (f-print (maxN 21))
+	(for ((N (in-range 1 maxN)))
+	(define fc (f-count N))
+	(define fa (f-anal N))
+	(printf  "%3d %10d %10d  %10.2d %%" N fc fa (// (abs (- fa fc)) fc 0.01))))

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

@@ -0,0 +1,34 @@
+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

Task/Average-loop-length/Phix/average-loop-length.phix

@@ -0,0 +1,33 @@
+constant MAX = 20,
+         ITER = 1000000
+
+function expected(integer n)
+atom sum = 0
+    for i=1 to n do
+        sum += factorial(n) / power(n,i) / factorial(n-i)
+    end for
+    return sum
+end function
+
+function test(integer n)
+integer count = 0, x, bits
+    for i=1 to ITER do
+        x = 1
+        bits = 0
+        while not and_bits(bits,x) do
+            count += 1
+            bits = or_bits(bits,x)
+            x = power(2,rand(n)-1)
+        end while
+    end for
+    return count/ITER
+end function
+
+atom av, ex
+    puts(1," n     avg.     exp.  (error%)\n");
+    puts(1,"==   ======   ======  ========\n");
+    for n=1 to MAX do
+        av = test(n)
+        ex = expected(n)
+        printf(1,"%2d %8.4f %8.4f  (%5.3f%%)\n", {n,av,ex,abs(1-av/ex)*100})
+    end for