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