1(**************************************************************************)
2(*                                                                        *)
3(*                                 OCaml                                  *)
4(*                                                                        *)
5(*     Valerie Menissier-Morain, projet Cristal, INRIA Rocquencourt       *)
6(*                                                                        *)
7(*   Copyright 1996 Institut National de Recherche en Informatique et     *)
8(*     en Automatique.                                                    *)
9(*                                                                        *)
10(*   All rights reserved.  This file is distributed under the terms of    *)
11(*   the GNU Lesser General Public License version 2.1, with the          *)
12(*   special exception on linking described in the file LICENSE.          *)
13(*                                                                        *)
14(**************************************************************************)
15
16(** Operation on rational numbers.
17
18    This module is used to support the implementation of {!Num} and
19    should not be called directly. *)
20
21open Nat
22open Big_int
23
24(* Rationals (type [ratio]) are arbitrary-precision rational numbers,
25   plus the special elements [1/0] (infinity) and [0/0] (undefined).
26   In constrast with numbers (type [num]), the special cases of
27   small integers and big integers are not optimized specially. *)
28
29type ratio
30
31(**/**)
32
33val null_denominator : ratio -> bool
34val numerator_ratio : ratio -> big_int
35val denominator_ratio : ratio -> big_int
36val sign_ratio : ratio -> int
37val normalize_ratio : ratio -> ratio
38val cautious_normalize_ratio : ratio -> ratio
39val cautious_normalize_ratio_when_printing : ratio -> ratio
40val create_ratio : big_int -> big_int -> ratio (* assumes nothing *)
41val create_normalized_ratio : big_int -> big_int -> ratio
42                              (* assumes normalized argument *)
43val is_normalized_ratio : ratio -> bool
44val report_sign_ratio : ratio -> big_int -> big_int
45val abs_ratio : ratio -> ratio
46val is_integer_ratio : ratio -> bool
47val add_ratio : ratio -> ratio -> ratio
48val minus_ratio : ratio -> ratio
49val add_int_ratio : int -> ratio -> ratio
50val add_big_int_ratio : big_int -> ratio -> ratio
51val sub_ratio : ratio -> ratio -> ratio
52val mult_ratio : ratio -> ratio -> ratio
53val mult_int_ratio : int -> ratio -> ratio
54val mult_big_int_ratio : big_int -> ratio -> ratio
55val square_ratio : ratio -> ratio
56val inverse_ratio : ratio -> ratio
57val div_ratio : ratio -> ratio -> ratio
58val integer_ratio : ratio -> big_int
59val floor_ratio : ratio -> big_int
60val round_ratio : ratio -> big_int
61val ceiling_ratio : ratio -> big_int
62val eq_ratio : ratio -> ratio -> bool
63val compare_ratio : ratio -> ratio -> int
64val lt_ratio : ratio -> ratio -> bool
65val le_ratio : ratio -> ratio -> bool
66val gt_ratio : ratio -> ratio -> bool
67val ge_ratio : ratio -> ratio -> bool
68val max_ratio : ratio -> ratio -> ratio
69val min_ratio : ratio -> ratio -> ratio
70val eq_big_int_ratio : big_int -> ratio -> bool
71val compare_big_int_ratio : big_int -> ratio -> int
72val lt_big_int_ratio : big_int -> ratio -> bool
73val le_big_int_ratio : big_int -> ratio -> bool
74val gt_big_int_ratio : big_int -> ratio -> bool
75val ge_big_int_ratio : big_int -> ratio -> bool
76val int_of_ratio : ratio -> int
77val ratio_of_int : int -> ratio
78val ratio_of_nat : nat -> ratio
79val nat_of_ratio : ratio -> nat
80val ratio_of_big_int : big_int -> ratio
81val big_int_of_ratio : ratio -> big_int
82val div_int_ratio : int -> ratio -> ratio
83val div_ratio_int : ratio -> int -> ratio
84val div_big_int_ratio : big_int -> ratio -> ratio
85val div_ratio_big_int : ratio -> big_int -> ratio
86val approx_ratio_fix : int -> ratio -> string
87val approx_ratio_exp : int -> ratio -> string
88val float_of_rational_string : ratio -> string
89val string_of_ratio : ratio -> string
90val ratio_of_string : string -> ratio
91val float_of_ratio : ratio -> float
92val power_ratio_positive_int : ratio -> int -> ratio
93val power_ratio_positive_big_int : ratio -> big_int -> ratio
94