Bash implementation of Fast Doubling Fibonacci Series calculation. See: https://www.nayuki.io/page/fast-fibonacci-algorithms

fibonacci.sh

#!/bin/bash

export BC_LINE_LENGTH=0

function fib() {
	if [ $1 -lt 0 ]; then
		echo "ERROR: Negative numbers not implemented"
		exit 1
	fi

	read r ignore <<<$(_fib $1)
	echo $r
}

function _fib() {
	if [ $1 -eq 0 ]; then
		echo "0 1"
	else
		read a b <<< $(_fib $(($1 / 2)))
		c=$(bc <<< "$a * ($b * 2 - $a)")
		d=$(bc <<< "$a * $a + $b * $b")
		if [ $(bc <<< "$1 % 2") -eq 0 ]; then
			echo "$c $d"
		else
			echo "$d $(bc <<< "$c + $d")"
		fi
	fi
}

# Get nth number of Fibonacci series
#eval fib $1

# Calculate Fibonacci series stating in 1
let i=1; while true; do echo "Fb($i): $(fib $i)"; ((i++)); done