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(* (a, b, c) means a * 10^-b. c is the original string *)
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type t = Num.num * int * string 
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let pp fmt (c, e, s) =
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    Format.fprintf fmt "%s%s"
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      s
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      (if String.get s (-1 + String.length s) = '.' then "0" else "")
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let pp_ada fmt (c, e, s) =
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  Format.fprintf fmt "%s.0*1.0e-%i" (Num.string_of_num c) e
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let create m e s = Num.num_of_string m, e, s
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let create_num n s = n, 0, s
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let to_num (c, e, s) =
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  let num_10 = Num.num_of_int 10 in
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  Num.(c // (num_10 **/ (num_of_int e)))
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let rec to_q (c, e, s) =
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  if e = 0 then
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        Q.of_string (Num.string_of_num c)
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  else
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    if e > 0 then Q.div (to_q (c,e-1,s)) (Q.of_int 10)
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    else (* if exp<0 then *)
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      Q.mul
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        (to_q (c,e+1,s))
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        (Q.of_int 10)
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let to_string (_, _, s) = s
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let eq r1 r2 =
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  Num.eq_num (to_num r1) (to_num r2)
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let num_binop op r1 r2 =
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  let n1 = to_num r1 and n2 = to_num r2 in
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  op n1 n2
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let arith_binop op r1 r2 =
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  let r = num_binop op r1 r2 in
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  create_num r (Num.string_of_num r)
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let add   = arith_binop (Num.(+/))
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let minus = arith_binop (Num.(-/))
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let times = arith_binop (Num.( */))
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let div   = arith_binop (Num.(//)) 
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let uminus (c, e, s) = Num.minus_num c, e, "-" ^ s
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let lt = num_binop (Num.(</))
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let le = num_binop (Num.(<=/))
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let gt = num_binop (Num.(>/))
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let ge = num_binop (Num.(>=/))
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let diseq = num_binop (Num.(<>/))
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let eq = num_binop (Num.(=/))
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let zero = Num.num_of_int 0, 0, "0.0"
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let is_zero r = Num.eq_num (to_num r) (Num.num_of_int 0)
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let is_one r = Num.eq_num (to_num r) (Num.num_of_int 1)
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