Fast Factorial Approximations

Choose and factorial algorithms

  # choose and factorial were stolen from: 
  # http://bluebones.net/2007/09/combinatorics-in-ruby/
  def choose(m)
    self.factorial / (m.factorial * (self - m).factorial)
  end
  def factorial
    (2..self).inject(1) { |f, n| f * n }
  end

  def fastchoose(m)
    self.gosper / (m.to_f.gosper * (self - m).gosper)
  end

  # quick, accurate approximation to factorial
  # gleaned from http://mathworld.wolfram.com/StirlingsApproximation.html
  def gosper
    Math.sqrt( ((2*self) + (1.0/3))*Math::PI ) * ((self/Math::E)**self).round
  end

  def stirling
    Math::E ** (self*Math.log(self) - self)
  end