I do have 64-bit ints, but that shouldn't stop you from doing fib(100). It just rolls over to using floats (with loss of accuracy obviously). You should be able to go all the way to 1476:

     1 :                    1
     2 :                    1
     3 :                    2
     4 :                    3
     5 :                    5
     6 :                    8
     7 :                   13
 
    98 : 135301852344706760000
    99 : 218922995834555200000
   100 : 354224848179262000000
...
  1476 : 1306989223763398700000000000000000000000000000000000000000000
+000000000000000000000000000000000000000000000000000000000000000000000
+000000000000000000000000000000000000000000000000000000000000000000000
+000000000000000000000000000000000000000000000000000000000000000000000
+00000000000000000000000000000000000000000
  1477 :                    1
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