ack.rb

def ack(m, n)
  if m == 0
    n + 1
  elsif n == 0
    ack(m - 1, 1)
  else 
    ack(m - 1, ack(m, n - 1))
  end
end

ack_catch.rb

def ack_catch(m, n)
  if m == 0
    throw :bottom, n + 1
  elsif n == 0
    catch :bottom do
      ack_catch(m - 1, 1)
    end
  else
    catch :bottom do
      ack_catch(m - 1, ack(m, n - 1))
    end
  end
end

ack_raise.rb

Bottom = Class.new(Exception)
def ack_raise(m, n)
  if m == 0
    raise Bottom, n + 1
  elsif n == 0
    begin 
      ack_raise(m - 1, 1)
    rescue Bottom => value
      return value.message
    end
  else
    begin
      ack_raise(m - 1, ack(m, n - 1))
    rescue Bottom => value
      return value.message
    end
  end
end

test.rb

require 'ack'
require 'ack_catch'
require 'ack_raise'
require 'benchmark'

puts "Value for 'm'?"
m = gets.chomp.to_i
puts "Value for 'n'?"
n = gets.chomp.to_i

Benchmark.bm(3) do |test|
  test.report("Recursive:") { puts "ack(#{m}, #{n}) => #{ack(m, n)}" }
  test.report("Catch:")     { puts "ack_catch(#{m}, #{n}) => #{ack_catch(m, n)}" }
  test.report("Raise:") { puts "ack_raise(#{m}, #{n}) => #{ack_raise(m, n)}" }
end