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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
(* Beware this only works fine in ZArith >= 1.10 due to
https://github.com/ocaml/Zarith/issues/58 *)
include Z
(* Constants *)
let two = Z.of_int 2
let ten = Z.of_int 10
let power_int = Big_int_Z.power_big_int_positive_int
let quomod = Big_int_Z.quomod_big_int
(* zarith fails with division by zero if x == 0 && y == 0 *)
let lcm x y = if Z.equal x zero && Z.equal y zero then zero else Z.lcm x y
let ppcm x y =
let g = gcd x y in
let x' = Z.div x g in
let y' = Z.div y g in
Z.mul g (Z.mul x' y')
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 minus_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
let pow_check_exp x y =
let z_res =
if y = 0 then Z.one
else if y > 0 then Z.pow x y
else (* s < 0 *)
Z.pow x (abs y)
in
let z_res = Q.of_bigint z_res in
if 0 <= y then z_res else Q.inv z_res
include Q
let two = Q.(of_int 2)
let ten = Q.(of_int 10)
module Notations = struct
let ( // ) = Q.div
let ( +/ ) = Q.add
let ( -/ ) = Q.sub
let ( */ ) = Q.mul
let ( =/ ) = Q.equal
let ( <>/ ) x y = not (Q.equal x y)
let ( >/ ) = Q.gt
let ( >=/ ) = Q.geq
let ( </ ) = Q.lt
let ( <=/ ) = Q.leq
end
(* XXX: review / improve *)
let floorZ q : Z.t = Z.fdiv (num q) (den q)
let floor q : t = floorZ q |> Q.of_bigint
let ceiling q : t = Z.cdiv (Q.num q) (Q.den q) |> Q.of_bigint
let half = Q.make Z.one Z.two
(* We imitate Num's round which is to the nearest *)
let round q = floor (Q.add half q)
(* XXX: review / improve *)
let quo x y =
let s = sign y in
let res = floor (x / abs y) in
if Int.equal s (-1) then neg res else res
let mod_ x y = x - (y * quo x y)
(* XXX: review / improve *)
(* Note that Z.pow doesn't support negative exponents *)
let pow2 y = pow_check_exp Z.two y
let pow10 y = pow_check_exp Z.ten y
let power (x : int) (y : t) : t =
let y =
try Q.to_int y
with Z.Overflow ->
(* XXX: make doesn't link Pp / CErrors for csdpcert, that could be fixed *)
raise (Invalid_argument "[micromega] overflow in exponentiation")
(* CErrors.user_err (Pp.str "[micromega] overflow in exponentiation") *)
in
pow_check_exp (Z.of_int x) y
end
|
