Tail recursion

Many recursive algorithms can be expressed using iteration. For instance, the greatest common denominator function can be written recursively:

def gdc (x, y)
  return x if y == 0
  return gdc(y, x%y)
end

or iteratively:

def gdc_iter (x, y)
  while y != 0 do
    x, y = y, x%y
  end

  return x
end

The two algorithms are equivalent in theory, but the recursive version risks a SystemStackError. However, since the recursive method ends with a call to itself, it could be optimized to avoid a stack overflow. Another way to put it: the recursive algorithm can result in the same machine code as the iterative if the compiler knows to look for the recursive method call at the end of the method. Ruby doesn’t do tail call optimization by default, but you can turn it on with:

RubyVM::InstructionSequence.compile_option = {
  tailcall_optimization: true,
  trace_instruction: false
}

In addition to turning on tail-call optimization, you also need to turn off instruction tracing. Unfortunately, these options only apply at compile time, so you either need to require the recursive method from another file or eval the method definition:

RubyVM::InstructionSequence.new(<<-EOF).eval
  def me_myself_and_i
    me_myself_and_i
  end
EOF
me_myself_and_i # Infinite loop, not stack overflow

Finally, the final return call must return the method and only the method. That means you’ll need to re-write the standard factorial function:

def fact(x)
  return 1 if x <= 1
  return x*fact(x-1)
end

To something like:

def fact(x, acc=1)
  return acc if x <= 1
  return fact(x-1, x*acc)
end

This version passes the accumulated sum via a second (optional) argument that defaults to 1.

Further reading: Tail Call Optimization in Ruby and Tailin’ Ruby.