fib_blog_5.go

//(a+b√5)(c+d√5) = (ac+5bd)+(ad+bc)√5
func fibMul(t1, t2 fibNum) (r fibNum) {
	//(ac+5bd)
	var r1, r2 *big.Rat
	tmp1 := new(big.Rat).Mul(t1.num, t2.num)
	tmp2 := new(big.Rat).Mul(
		new(big.Rat).Mul(t1.numMultipliedBySR, t2.numMultipliedBySR),
		big.NewRat(5, 1),
	)
	r1 = new(big.Rat).Add(tmp1, tmp2)

	//(ad+bc)√5
	tmp3 := new(big.Rat).Mul(t1.num, t2.numMultipliedBySR)
	tmp4 := new(big.Rat).Mul(t1.numMultipliedBySR, t2.num)
	r2 = new(big.Rat).Add(tmp3, tmp4)

	//(ac+5bd)+(ad+bc)√5
	//new(big.Rat).Add(r3, rr3)

	r.num = r1
	r.numMultipliedBySR = r2
	return
}