sidef-scripts/Math/inverse_of_fibonacci.sf

#!/usr/bin/ruby

# Find the position of a Fibonacci number in the Fibonacci sequence.

# See also:
#   https://en.wikipedia.org/wiki/Fibonacci_number#Recognizing_Fibonacci_numbers

func fibonacci_inverse (n) {

    var m = 5*n*n

    if (is_square(m - 4)) {
        m = isqrt(m - 4)
    }
    elsif (is_square(m + 4)) {
        m = isqrt(m + 4)
    }
    else {
        return -1    # not a Fibonacci number
    }

    log((n*sqrt(5) + m) / 2) / log(Num.phi)
}

say fibonacci_inverse(fibonacci(100))    #=> 100
say fibonacci_inverse(fibonacci(101))    #=> 101