_nmax = 20
_times = 1000000

local fn Average( n as long, times as long ) as double
  long   i, x
  double b, c = 0

  for i = 0 to times
    x = 1 : b = 0
    while ( b and x ) == 0
      c++
      b = b || x
      x = 1 << ( rnd(n) - 1 )
    wend
  next
end fn = c / times

local fn Analyltic( n as long ) as double
  double nn = (double)n
  double term = 1.0
  double sum = 1.0
  long   i

  for i = nn - 1 to i >= 1 step -1
    term = term * i / nn
    sum = sum + term
  next
end fn = sum

local fn DoIt
  long   n
  double average, theory, difference

  window 1
  printf @"\nSamples tested: %ld\n", _times
  print " N    Average    Analytical    (error)"
  print "===  =========  ============  ========="
  for n = 1 to _nmax
    average    = fn Average( n, _times )
    theory     = fn Analyltic( n )
    difference = ( average / theory - 1) * 100
    printf @"%3d  %9.4f  %9.4f  %10.4f%%", n, average, theory, difference
  next
end fn

randomize
fn DoIt

HandleEvents