pidigits.rb

# The Great Computer Language Shootout
# http://shootout.alioth.debian.org/
#
# contributed by Gabriele Renzi

class PiDigitSpigot

    def initialize()
        @z = Transformation.new 1,0,0,1
        @x = Transformation.new 0,0,0,0
        @inverse = Transformation.new 0,0,0,0
    end

    def next!
        @y = @z.extract(3)
        if safe? @y
            @z = produce(@y)
            @y
        else
            @z = consume @x.next!()
            next!()
        end
    end

    def safe?(digit)
        digit == @z.extract(4)
    end

    def produce(i)
        @inverse.qrst(10,-10*i,0,1).compose(@z)
    end

    def consume(a)
        @z.compose(a)
    end
end


class Transformation
    attr_reader :q, :r, :s, :t
    def initialize (q, r, s, t)
        @q,@r,@s,@t,@k = q,r,s,t,0
    end

    def next!()
        @q = @k = @k + 1
        @r = 4 * @k + 2
        @s = 0
        @t = 2 * @k + 1
        self
    end

    def extract(j)
        (@q * j + @r) / (@s * j + @t)
    end

    def compose(a)
        self.class.new( @q * a.q,
                        @q * a.r + r * a.t,
                        @s * a.q + t * a.s,
                        @s * a.r + t * a.t
                    )
    end

    def qrst *args
        initialize *args
        self
    end


end

WIDTH = 10

def compute_pidigits(count)
  n = count
  j = 0
  
  digits = PiDigitSpigot.new
  
  while n > 0
      if n >= WIDTH
          WIDTH.times { print digits.next! }
          j += WIDTH
      else
          n.times {print digits.next!}
          (WIDTH-n).times { " "}
          j += n
      end
      n -= WIDTH
  end
  puts
end