matrix_fibo.go

package main

import (
	"fmt"
)

var IDENTITY = [2][2]int64{{1, 0}, {0, 1}}
var DEFAULT = [2][2]int64{{1, 1}, {1, 0}}

func dotProduct(a, b [2][2]int64) (res [2][2]int64) {
	for i := 0; i <= 1; i++ {
		for j := 0; j <= 1; j++ {
			for l := 0; l <= 1; l++ {
				res[i][j] += a[i][l] * b[l][j]
			}
		}
	}
	return
}

func fiboMatrix(n int) (m [2][2]int64) {
	if n > 1 {
		m = dotProduct(fiboMatrix(n / 2), fiboMatrix(n / 2))
		if (n % 2) > 0 {
			m = dotProduct(DEFAULT, m)
		}
	} else if n == 0 { 
		m = IDENTITY
	} else {
		m = DEFAULT
	}

	return
}

func trippleFibo(n int) (res [3]int64) {
	m := fiboMatrix(n)
	res[0] = m[1][1]
	res[1] = m[0][1]
	res[2] = m[0][0]
	return
}

func main() {
	fmt.Println(trippleFibo(10))
}

Matrix exponentiation Fibonacci series computation.