_DEFINE F AS _UNSIGNED _INTEGER64
CLS
PRINT
PRINT "Enter 40 to more easily see the difference in calculation speeds."
PRINT
INPUT "Enter n for Fibonacci(n): ", n
PRINT
PRINT " Analytic Method (Fastest): F("; LTRIM$(STR$(n)); ") ="; fA(n)
PRINT "Iterative Method    (Fast): F("; LTRIM$(STR$(n)); ") ="; fI(n)
PRINT "Recursive Method    (Slow): F("; LTRIM$(STR$(n)); ") ="; fR(n)
END

' === Analytic Fibonacci Function (Fastest)
FUNCTION fA (n)
  fA = INT(0.5 + (((SQR(5) + 1) / 2) ^ n) / SQR(5))
END FUNCTION

' === Iterative Fibonacci Function (Fast)
FUNCTION fI (n)
  FOR i = 1 TO n
    IF i < 3 THEN a = 1: b = 1
    t = fI + b: fI = b: b = t
  NEXT
END FUNCTION

' === Recursive Fibonacci function (Slow)
FUNCTION fR (n)
  IF n <= 1 THEN
    fR = n
  ELSE
    fR = fR(n - 1) + fR(n - 2)
  END IF
END FUNCTION