fib.asm

global fib
global _fib
fib:
_fib:
  cmp rdi, 1    ; set flags according to value of rdi minus one, i.e., relationship of rdi to 1
  jle return_one; if the relationship is "less than or equal", goto return_one
  dec rdi       ; rdi = rdi - 1
  push rdi      ;  ^ this guy is going to decrement it again, save "n-1" on the stack
  call fib      ; do call
  pop rdi       ; restore "n-1" to rdi
  push rax      ; save result of fib(rdi-1) onto stack
  dec rdi       ; rdi = rdi - 1 ( = n-2 )
  call fib      ; do call - we don't care about n-2 anymore after this anyway
                ; now rax contains fib(n-2) and fib(n-1) is on the stack
  pop rdx       ; now rdx contains fib(n-1)
  add rax, rdx  ; now rax contains fib(n-2)+fib(n-1)
  ret           ; that's the value we want to return, already in rax!

return_one:
  mov rax, 1
  ret