# 浮動小数点の誤差は考慮していない
def f(u, v)
	return [0] if u <= 0
	seq = []
	loop do
		n = v.to_i
		return seq + [u.ceil] if n >= u.ceil
		seq << n
		u, v = 1 / (v - n), 1 / (u - n)
	end
end
 
def g(x, y)
	a = x.to_f.abs
	seq = f(a - y, a + y)
	z = seq.pop.quo(1)
	z = seq.pop + 1.quo(z) while !seq.empty?
	z *= x < 0 ? -1 : 1
	puts "x=#{x}, y=#{y}  ->  #{z} = #{z.to_f}"
end
 
g(0.02, 0.03)
g(0.3, 0.1)
g(0.5, 0.2)
g(-0.3, 0.1)
g(0.07, 0.02)
g(0.0000000123, 0.0000000003)
g(3.14159265358979, 0.00000000000001)

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