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(**************************************************************************)
(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
(*     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 Lesser General Public License version 2.1, with the          *)
(*   special exception on linking described in the file LICENSE.          *)
(*                                                                        *)
(**************************************************************************)

(** Operation on arbitrary-precision numbers.

   Numbers (type [num]) are arbitrary-precision rational numbers,
   plus the special elements [1/0] (infinity) and [0/0] (undefined).
*)

open Nat
open Big_int
open Ratio

(** The type of numbers. *)
type num =
    Int of int
  | Big_int of big_int
  | Ratio of ratio


(** {6 Arithmetic operations} *)


val ( +/ ) : num -> num -> num
(** Same as {!Num.add_num}.*)

val add_num : num -> num -> num
(** Addition *)

val minus_num : num -> num
(** Unary negation. *)

val ( -/ ) : num -> num -> num
(** Same as {!Num.sub_num}.*)

val sub_num : num -> num -> num
(** Subtraction *)

val ( */ ) : num -> num -> num
(** Same as {!Num.mult_num}.*)

val mult_num : num -> num -> num
(** Multiplication *)

val square_num : num -> num
(** Squaring *)

val ( // ) : num -> num -> num
(** Same as {!Num.div_num}.*)

val div_num : num -> num -> num
(** Division *)

val quo_num : num -> num -> num
(** Euclidean division: quotient. *)

val mod_num : num -> num -> num
(** Euclidean division: remainder. *)

val ( **/ ) : num -> num -> num
(** Same as {!Num.power_num}. *)

val power_num : num -> num -> num
(** Exponentiation *)

val abs_num : num -> num
(** Absolute value. *)

val succ_num : num -> num
(** [succ n] is [n+1] *)

val pred_num : num -> num
(** [pred n] is [n-1] *)

val incr_num : num ref -> unit
(** [incr r] is [r:=!r+1], where [r] is a reference to a number. *)

val decr_num : num ref -> unit
(** [decr r] is [r:=!r-1], where [r] is a reference to a number. *)

val is_integer_num : num -> bool
(** Test if a number is an integer *)

(** The four following functions approximate a number by an integer : *)

val integer_num : num -> num
(** [integer_num n] returns the integer closest to [n]. In case of ties,
   rounds towards zero. *)

val floor_num : num -> num
(** [floor_num n] returns the largest integer smaller or equal to [n]. *)

val round_num : num -> num
(** [round_num n] returns the integer closest to [n]. In case of ties,
   rounds off zero. *)

val ceiling_num : num -> num
(** [ceiling_num n] returns the smallest integer bigger or equal to [n]. *)


val sign_num : num -> int
(** Return [-1], [0] or [1] according to the sign of the argument. *)

(** {7 Comparisons between numbers} *)

val ( =/ ) : num -> num -> bool
val ( </ ) : num -> num -> bool
val ( >/ ) : num -> num -> bool
val ( <=/ ) : num -> num -> bool
val ( >=/ ) : num -> num -> bool
val ( <>/ ) : num -> num -> bool
val eq_num : num -> num -> bool
val lt_num : num -> num -> bool
val le_num : num -> num -> bool
val gt_num : num -> num -> bool
val ge_num : num -> num -> bool

val compare_num : num -> num -> int
(** Return [-1], [0] or [1] if the first argument is less than,
   equal to, or greater than the second argument. *)

val max_num : num -> num -> num
(** Return the greater of the two arguments. *)

val min_num : num -> num -> num
(** Return the smaller of the two arguments. *)


(** {6 Coercions with strings} *)

val string_of_num : num -> string
(** Convert a number to a string, using fractional notation. *)

val approx_num_fix : int -> num -> string
(** See {!Num.approx_num_exp}.*)

val approx_num_exp : int -> num -> string
(** Approximate a number by a decimal. The first argument is the
   required precision. The second argument is the number to
   approximate. {!Num.approx_num_fix} uses decimal notation; the first
   argument is the number of digits after the decimal point.
   [approx_num_exp] uses scientific (exponential) notation; the
   first argument is the number of digits in the mantissa. *)

val num_of_string : string -> num
(** Convert a string to a number.
   Raise [Failure "num_of_string"] if the given string is not
   a valid representation of an integer *)

val num_of_string_opt: string -> num option
(** Convert a string to a number.
    Return [None] if the given string is not
    a valid representation of an integer.

    @since 4.05
*)

(** {6 Coercions between numerical types} *)

(* TODO: document the functions below (truncating behavior and error conditions). *)

val int_of_num : num -> int
val int_of_num_opt: num -> int option
(** @since 4.05.0 *)

val num_of_int : int -> num
val nat_of_num : num -> nat
val nat_of_num_opt: num -> nat option
(** @since 4.05.0 *)

val num_of_nat : nat -> num
val num_of_big_int : big_int -> num
val big_int_of_num : num -> big_int
val big_int_of_num_opt: num -> big_int option
(** @since 4.05.0 *)

val ratio_of_num : num -> ratio
val num_of_ratio : ratio -> num
val float_of_num : num -> float