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fibonacci.ml

 (* Copyright (c) 2008 the authors listed at the following URL, and/or
 the authors of referenced articles or incorporated external code:
 http://en.literateprograms.org/Fibonacci_numbers_(OCaml)?action=history&offset=20080216154027
 
 Permission is hereby granted, free of charge, to any person obtaining
 a copy of this software and associated documentation files (the
 "Software"), to deal in the Software without restriction, including
 without limitation the rights to use, copy, modify, merge, publish,
 distribute, sublicense, and/or sell copies of the Software, and to
 permit persons to whom the Software is furnished to do so, subject to
 the following conditions:
 
 The above copyright notice and this permission notice shall be
 included in all copies or substantial portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 
 Retrieved from: http://en.literateprograms.org/Fibonacci_numbers_(OCaml)?oldid=12494
 *)
 
 let rec fibonacci = function
 | 0 -> 0
 | 1 -> 1
 | n when n > 1 -> fibonacci (n-1) + fibonacci (n-2)
 | _ -> raise (Invalid_argument "Fibonacci numbers are only defined over the non-negative integers")
 
 let iterative_fib n =
   let rec i_fib a b = function
   | 0 -> a
   | 1 -> b
   | k when k > 1 -> i_fib b (a+b) (k-1)
   | _  -> raise (Invalid_argument "Fibonacci numbers are only defined over the non-negative integers")
   in
   i_fib 0 1 n
 
 
 #load "camlp4o.cma";; 
 #load "pa_extend.cmo";;
 
 let rec f a b = [< 'a; f b (a+b) >]
 
 let next = parser [< 'x >] -> x
 
 #load "nums.cma";; 
 open Big_int;;
 
 let bfib n =
   let rec bfib_i a b = function
   | 0 -> a
   | 1 -> b
   | n when n > 1 ->  bfib_i b (add_big_int a b) (n-1)
   | _ -> raise (Invalid_argument "Fibonacci numbers are only defined over the non-negative integers")
   in
   bfib_i zero_big_int unit_big_int n
 
 let rec big_f a b = [< 'a; big_f b (add_big_int a b) >]
 let big_fibs = big_f zero_big_int unit_big_int
 let big_next = parser [< 'x >] -> string_of_big_int x