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+(***********************************************************************)
+(* *)
+(* Objective Caml *)
+(* *)
+(* Valerie Menissier-Morain, projet Cristal, INRIA Rocquencourt *)
+(* *)
+(* Copyright 1996 Institut National de Recherche en Informatique et *)
+(* en Automatique. All rights reserved. This file is distributed *)
+(* under the terms of the GNU Library General Public License, with *)
+(* the special exception on linking described in file ../../LICENSE. *)
+(* *)
+(***********************************************************************)
+
+(* $Id$ *)
+
+(* Module [Ratio]: operations on rational numbers *)
+
+open Nat
+open Big_int
+
+(* Rationals (type [ratio]) are arbitrary-precision rational numbers,
+ plus the special elements [1/0] (infinity) and [0/0] (undefined).
+ In constrast with numbers (type [num]), the special cases of
+ small integers and big integers are not optimized specially. *)
+
+type ratio
+
+val null_denominator : ratio -> bool
+val numerator_ratio : ratio -> big_int
+val denominator_ratio : ratio -> big_int
+val sign_ratio : ratio -> int
+val normalize_ratio : ratio -> ratio
+val cautious_normalize_ratio : ratio -> ratio
+val cautious_normalize_ratio_when_printing : ratio -> ratio
+val create_ratio : big_int -> big_int -> ratio
+val create_normalized_ratio : big_int -> big_int -> ratio
+val is_normalized_ratio : ratio -> bool
+val report_sign_ratio : ratio -> big_int -> big_int
+val abs_ratio : ratio -> ratio
+val is_integer_ratio : ratio -> bool
+val add_ratio : ratio -> ratio -> ratio
+val minus_ratio : ratio -> ratio
+val add_int_ratio : int -> ratio -> ratio
+val add_big_int_ratio : big_int -> ratio -> ratio
+val sub_ratio : ratio -> ratio -> ratio
+val mult_ratio : ratio -> ratio -> ratio
+val mult_int_ratio : int -> ratio -> ratio
+val mult_big_int_ratio : big_int -> ratio -> ratio
+val square_ratio : ratio -> ratio
+val inverse_ratio : ratio -> ratio
+val div_ratio : ratio -> ratio -> ratio
+val integer_ratio : ratio -> big_int
+val floor_ratio : ratio -> big_int
+val round_ratio : ratio -> big_int
+val ceiling_ratio : ratio -> big_int
+val eq_ratio : ratio -> ratio -> bool
+val compare_ratio : ratio -> ratio -> int
+val lt_ratio : ratio -> ratio -> bool
+val le_ratio : ratio -> ratio -> bool
+val gt_ratio : ratio -> ratio -> bool
+val ge_ratio : ratio -> ratio -> bool
+val max_ratio : ratio -> ratio -> ratio
+val min_ratio : ratio -> ratio -> ratio
+val eq_big_int_ratio : big_int -> ratio -> bool
+val compare_big_int_ratio : big_int -> ratio -> int
+val lt_big_int_ratio : big_int -> ratio -> bool
+val le_big_int_ratio : big_int -> ratio -> bool
+val gt_big_int_ratio : big_int -> ratio -> bool
+val ge_big_int_ratio : big_int -> ratio -> bool
+val int_of_ratio : ratio -> int
+val ratio_of_int : int -> ratio
+val ratio_of_nat : nat -> ratio
+val nat_of_ratio : ratio -> nat
+val ratio_of_big_int : big_int -> ratio
+val big_int_of_ratio : ratio -> big_int
+val div_int_ratio : int -> ratio -> ratio
+val div_ratio_int : ratio -> int -> ratio
+val div_big_int_ratio : big_int -> ratio -> ratio
+val div_ratio_big_int : ratio -> big_int -> ratio
+val approx_ratio_fix : int -> ratio -> string
+val approx_ratio_exp : int -> ratio -> string
+val float_of_rational_string : ratio -> string
+val string_of_ratio : ratio -> string
+val ratio_of_string : string -> ratio
+val float_of_ratio : ratio -> float
+val power_ratio_positive_int : ratio -> int -> ratio
+val power_ratio_positive_big_int : ratio -> big_int -> ratio