Integer#isqrt - sqrt in Integer precision

integer_isqrt.rb

class Integer
  def isqrt
    return 0.0/0 if self < 0
    return self if self < 2
    return 1 if self < 4
    # === Newton's Method (in Integer precision) ===
    n = self.div 2  # self / 2
    while n * n > self
      on = n
      n = (n * n + self).div(2 * n)
      break if n == on
    end
    n
  end
end
### v- to Enable the Following for Efficiency
# class Fixnum
#   def isqrt
#     return Math.sqrt(self).floor if 0 <= self && self < 2**53
#     super
#   end
# end