gistfile1.rb

#!/usr/bin/env ruby                                                                                                           

dev_size = 2048 * 1024 * 1024   # 1T                                                                                          
block_size = 2048 * 1
nr_blocks = dev_size / block_size
io_size = 128

#----------------------------------------------------------------                                                             

def calc_cows(n, nr_blocks)
  alpha = (nr_blocks - 1).fdiv(nr_blocks)
  num = 1.0 - (alpha ** n)
  den = 1.0 - alpha
  num / den
end

# find the 50% mark                                                                                                           
step = 1024
n_low = 0
n_high = 1000000

half = nr_blocks.fdiv(2)

fifty_percent = catch :done do
  loop do
    if n_high - n_low == 1
      throw :done, n_high
    end

    mid = (n_high + n_low) / 2
    c = calc_cows(mid, nr_blocks)

    if c < half
      n_low = mid
    elsif c > half
      n_high = mid
    else
      throw :done, n_high
    end
  end
end

one_t = 2048 * 1024 * 1024
userland_io = fifty_percent * io_size
puts "fifty percent cows takes #{fifty_percent} ios, #{userland_io / 2048}m sectors of userland io, throughput fraction #{use\
rland_io.fdiv(userland_io + one_t) * 100.0}%"