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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 Library General Public License, with *)
(* the special exception on linking described in file ../../LICENSE. *)
(* *)
(***********************************************************************)
(* $Id$ *)
(** 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 *)
(** {6 Coercions between numerical types} *)
val int_of_num : num -> int
val num_of_int : int -> num
val nat_of_num : num -> nat
val num_of_nat : nat -> num
val num_of_big_int : big_int -> num
val big_int_of_num : num -> big_int
val ratio_of_num : num -> ratio
val num_of_ratio : ratio -> num
val float_of_num : num -> float
|