M:= <<0,1>|<1,1>>:
fib4:= n -> mpow(n-1)[2,2]:
F[0]:= 0:
F[1]:= 1:
F[-1]:= 1:
mpow := proc(n)
 option remember;
 if type(n, posint) 
 then if type(n,even) 
      then mpow(n/2)^2
      else mpow((n-1)/2)^2 . M
      end if
 elif type(n, negint)
 then mpow(-n)^(-1)
 elif type(n,`+`) 
 then mpow(op(1,n)) . mpow(n-op(1,n))
 elif type(n,`*`) 
 then mpow(n/op(1,n))^op(1,n)
 else <<F[n-1],F[n]>|<F[n],F[n]+F[n-1]>>
 end if
end proc: 
phi:= 1/2 + sqrt(5)/2:
fibapp:= n -> phi^n/sqrt(5):
invfib := proc(x::posint)
  local q, n;
  q:= evalf((ln(x+1/2) + ln(5)/2)/ln(phi));
  n:= floor(q);
  if fib4(n) <= x then
    while fib4(n+1) <= x do
      n := n+1
    end do
  else
    while fib4(n) > x do
      n := n-1
    end do
  end if;
  n
end: