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|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
module type ZArith = sig
type t
val zero : t
val one : t
val two : t
val add : t -> t -> t
val sub : t -> t -> t
val mul : t -> t -> t
val div : t -> t -> t
val neg : t -> t
val sign : t -> int
val equal : t -> t -> bool
val compare : t -> t -> int
val power_int : t -> int -> t
val quomod : t -> t -> t * t
val ppcm : t -> t -> t
val gcd : t -> t -> t
val lcm : t -> t -> t
val to_string : t -> string
end
module Z = struct
type t = Big_int.big_int
open Big_int
let zero = zero_big_int
let one = unit_big_int
let two = big_int_of_int 2
let add = Big_int.add_big_int
let sub = Big_int.sub_big_int
let mul = Big_int.mult_big_int
let div = Big_int.div_big_int
let neg = Big_int.minus_big_int
let sign = Big_int.sign_big_int
let equal = eq_big_int
let compare = compare_big_int
let power_int = power_big_int_positive_int
let quomod = quomod_big_int
let ppcm x y =
let g = gcd_big_int x y in
let x' = div_big_int x g in
let y' = div_big_int y g in
mult_big_int g (mult_big_int x' y')
let gcd = gcd_big_int
let lcm x y =
if eq_big_int x zero && eq_big_int y zero then zero
else abs_big_int (div_big_int (mult_big_int x y) (gcd x y))
let to_string = string_of_big_int
end
module type QArith = sig
module Z : ZArith
type t
val of_int : int -> t
val zero : t
val one : t
val two : t
val ten : t
val neg_one : t
module Notations : sig
val ( // ) : t -> t -> t
val ( +/ ) : t -> t -> t
val ( -/ ) : t -> t -> t
val ( */ ) : t -> t -> t
val ( =/ ) : t -> t -> bool
val ( <>/ ) : t -> t -> bool
val ( >/ ) : t -> t -> bool
val ( >=/ ) : t -> t -> bool
val ( </ ) : t -> t -> bool
val ( <=/ ) : t -> t -> bool
end
val compare : t -> t -> int
val make : Z.t -> Z.t -> t
val den : t -> Z.t
val num : t -> Z.t
val of_bigint : Z.t -> t
val to_bigint : t -> Z.t
val neg : t -> t
(* val inv : t -> t *)
val max : t -> t -> t
val min : t -> t -> t
val sign : t -> int
val abs : t -> t
val mod_ : t -> t -> t
val floor : t -> t
(* val floorZ : t -> Z.t *)
val ceiling : t -> t
val round : t -> t
val pow2 : int -> t
val pow10 : int -> t
val power : int -> t -> t
val to_string : t -> string
val of_string : string -> t
val to_float : t -> float
end
module Q : QArith with module Z = Z = struct
module Z = Z
type t = Num.num
open Num
let of_int x = Int x
let zero = Int 0
let one = Int 1
let two = Int 2
let ten = Int 10
let neg_one = Int (-1)
module Notations = struct
let ( // ) = div_num
let ( +/ ) = add_num
let ( -/ ) = sub_num
let ( */ ) = mult_num
let ( =/ ) = eq_num
let ( <>/ ) = ( <>/ )
let ( >/ ) = ( >/ )
let ( >=/ ) = ( >=/ )
let ( </ ) = ( </ )
let ( <=/ ) = ( <=/ )
end
let compare = compare_num
let make x y = Big_int x // Big_int y
let numdom r =
let r' = Ratio.normalize_ratio (ratio_of_num r) in
(Ratio.numerator_ratio r', Ratio.denominator_ratio r')
let num x = numdom x |> fst
let den x = numdom x |> snd
let of_bigint x = Big_int x
let to_bigint = big_int_of_num
let neg = minus_num
(* let inv = *)
let max = max_num
let min = min_num
let sign = sign_num
let abs = abs_num
let mod_ = mod_num
let floor = floor_num
let ceiling = ceiling_num
let round = round_num
let pow2 n = power_num two (Int n)
let pow10 n = power_num ten (Int n)
let power x = power_num (Int x)
let to_string = string_of_num
let of_string = num_of_string
let to_float = float_of_num
end
|
