bm_so_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
n = 2_500 # Integer(ARGV[0])
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 {print " "}
        j += n
    end
    puts "\t:"+j.to_s
    n -= WIDTH
end