Problem Statement

The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively:

Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow and are mostly used as an exercise in recursion). The sequence is sometimes extended into negative numbers by using a straightforward inverse of the positive definition: support for negative     n     in the solution is optional.

Let's start with the solution:

[               # todo: n(<2) -- 1 and break 2 levels
  d -           # 0
  1 +           # 1
  q
] s1

[               # todo: n(>-1) -- F(n)
  d 0=1         # n(!=0)
  d 1=1         # n(!in {0,1})
  2 - d 1 +     # (n-2) (n-1)
  lF x          # (n-2) F(n-1)
  r             # F(n-1) (n-2)
  lF x          # F(n-1)+F(n-2)
  +
] sF

33 lF x f