source: Deliverables/D3.1/C-semantics/Floats.ma @ 535

Last change on this file since 535 was 487, checked in by campbell, 9 years ago

Port Clight semantics to the new-new matita syntax.

File size: 2.6 KB
RevLine 
[3]1(* *********************************************************************)
2(*                                                                     *)
3(*              The Compcert verified compiler                         *)
4(*                                                                     *)
5(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
6(*                                                                     *)
7(*  Copyright Institut National de Recherche en Informatique et en     *)
8(*  Automatique.  All rights reserved.  This file is distributed       *)
9(*  under the terms of the GNU General Public License as published by  *)
10(*  the Free Software Foundation, either version 2 of the License, or  *)
11(*  (at your option) any later version.  This file is also distributed *)
12(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
13(*                                                                     *)
14(* *********************************************************************)
15
16(* * Axiomatization of floating-point numbers. *)
17
18(* * In contrast with what we do with machine integers, we do not bother
19  to formalize precisely IEEE floating-point arithmetic.  Instead, we
20  simply axiomatize a type [float] for IEEE double-precision floats
21  and the associated operations.  *)
22
23include "Coqlib.ma".
24include "Integers.ma".
25
[487]26axiom float: Type[0].
[3]27
28(*Module Float.*)
29
[487]30axiom Fzero: float.
31axiom Fone: float.
[3]32
[487]33axiom Fneg: float → float.
34axiom Fabs: float → float.
35axiom singleoffloat: float → float.
36axiom intoffloat: float → int.
37axiom intuoffloat: float → int.
38axiom floatofint: int → float.
39axiom floatofintu: int → float.
[3]40
[487]41axiom Fadd: float → float → float.
42axiom Fsub: float → float → float.
43axiom Fmul: float → float → float.
44axiom Fdiv: float → float → float.
[3]45
[487]46axiom Fcmp: comparison → float → float → bool.
[3]47
[487]48axiom eq_dec: ∀f1,f2: float. (f1 = f2) + (f1 ≠ f2).
[3]49
50(* * Below are the only properties of floating-point arithmetic that we
51  rely on in the compiler proof. *)
52
[487]53axiom addf_commut: ∀f1,f2. Fadd f1 f2 = Fadd f2 f1.
[3]54
[487]55axiom subf_addf_opp: ∀f1,f2. Fsub f1 f2 = Fadd f1 (Fneg f2).
[3]56
[487]57axiom singleoffloat_idem:
[3]58  ∀f. singleoffloat (singleoffloat f) = singleoffloat f.
59
[487]60axiom Fcmp_ne_eq:
[3]61  ∀ f1,f2. Fcmp Cne f1 f2 = ¬(Fcmp Ceq f1 f2).
[487]62axiom Fcmp_le_lt_eq:
[3]63  ∀ f1,f2. Fcmp Cle f1 f2 = (Fcmp Clt f1 f2 ∨ Fcmp Ceq f1 f2).
[487]64axiom Fcmp_ge_gt_eq:
[3]65  ∀f1,f2. Fcmp Cge f1 f2 = (Fcmp Cgt f1 f2 ∨ Fcmp Ceq f1 f2).
66
[487]67axiom Feq_zero_true: Fcmp Ceq Fzero Fzero = true.
68axiom Feq_zero_false: ∀f. f ≠ Fzero → Fcmp Ceq f Fzero = false.
[3]69
70(*End Float.*)
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