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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Sviluppo: 2008-2010                                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "num/word16.ma".
+
+(* ***** *)
+(* DWORD *)
+(* ***** *)
+
+ndefinition word32 ≝ comp_num word16.
+ndefinition mk_word32 ≝ λw1,w2.mk_comp_num word16 w1 w2.
+ndefinition ext_word32 ≝ λw2.mk_comp_num word16 〈〈x0,x0〉:〈x0,x0〉〉 w2.
+
+(* \langle \rangle *)
+notation "〈x.y〉" non associative with precedence 80
+ for @{ mk_comp_num word16 $x $y }.
+
+(* iteratore sulle dword *)
+ndefinition forall_w32 ≝ forall_cn ? forall_w16.
+
+(* operatore = *)
+ndefinition eq_w32 ≝ eq2_cn ? eq_w16.
+
+(* operatore < *)
+ndefinition lt_w32 ≝ ltgt_cn ? eq_w16 lt_w16.
+
+(* operatore ≤ *)
+ndefinition le_w32 ≝ lege_cn ? eq_w16 lt_w16 le_w16.
+
+(* operatore > *)
+ndefinition gt_w32 ≝ ltgt_cn ? eq_w16 gt_w16.
+
+(* operatore ≥ *)
+ndefinition ge_w32 ≝ lege_cn ? eq_w16 gt_w16 ge_w16.
+
+(* operatore and *)
+ndefinition and_w32 ≝ fop2_cn ? and_w16.
+
+(* operatore or *)
+ndefinition or_w32 ≝ fop2_cn ? or_w16.
+
+(* operatore xor *)
+ndefinition xor_w32 ≝ fop2_cn ? xor_w16.
+
+(* operatore Most Significant Bit *)
+ndefinition getMSB_w32 ≝ getOPH_cn ? getMSB_w16.
+ndefinition setMSB_w32 ≝ setOPH_cn ? setMSB_w16.
+ndefinition clrMSB_w32 ≝ setOPH_cn ? clrMSB_w16.
+
+(* operatore Least Significant Bit *)
+ndefinition getLSB_w32 ≝ getOPL_cn ? getLSB_w16.
+ndefinition setLSB_w32 ≝ setOPL_cn ? setLSB_w16.
+ndefinition clrLSB_w32 ≝ setOPL_cn ? clrLSB_w16.
+
+(* operatore estensione unsigned *)
+ndefinition extu_w32 ≝ λw2.〈〈〈x0,x0〉:〈x0,x0〉〉.w2〉.
+ndefinition extu2_w32 ≝ λb2.〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈x0,x0〉:b2〉〉.
+ndefinition extu3_w32 ≝ λe2.〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈x0,x0〉:〈x0,e2〉〉〉.
+
+(* operatore estensione signed *)
+ndefinition exts_w32 ≝
+λw2.〈(match getMSB_w16 w2 with
+      [ true ⇒ 〈〈xF,xF〉:〈xF,xF〉〉 | false ⇒ 〈〈x0,x0〉:〈x0,x0〉〉 ]).w2〉.
+ndefinition exts2_w32 ≝
+λb2.(match getMSB_b8 b2 with
+      [ true ⇒ 〈〈〈xF,xF〉:〈xF,xF〉〉.〈〈xF,xF〉:b2〉〉 | false ⇒ 〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈x0,x0〉:b2〉〉 ]).
+ndefinition exts3_w32 ≝
+λe2.(match getMSB_ex e2 with
+      [ true ⇒ 〈〈〈xF,xF〉:〈xF,xF〉〉.〈〈xF,xF〉:〈xF,e2〉〉〉 | false ⇒ 〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈x0,x0〉:〈x0,e2〉〉〉 ]).
+
+(* operatore rotazione destra con carry *)
+ndefinition rcr_w32 ≝ opcr_cn ? rcr_w16.
+
+(* operatore shift destro *)
+ndefinition shr_w32 ≝ opcr_cn ? rcr_w16 false.
+
+(* operatore rotazione destra *)
+ndefinition ror_w32 ≝
+λw.match shr_w32 w with
+ [ pair c w' ⇒ match c with
+  [ true ⇒ setMSB_w32 w' | false ⇒ w' ]].
+
+(* operatore rotazione sinistra con carry *)
+ndefinition rcl_w32 ≝ opcl_cn ? rcl_w16.
+
+(* operatore shift sinistro *)
+ndefinition shl_w32 ≝ opcl_cn ? rcl_w16 false.
+
+(* operatore rotazione sinistra *)
+ndefinition rol_w32 ≝
+λw.match shl_w32 w with
+ [ pair c w' ⇒ match c with
+  [ true ⇒ setLSB_w32 w' | false ⇒ w' ]].
+
+(* operatore not/complemento a 1 *)
+ndefinition not_w32 ≝ fop_cn ? not_w16.
+
+(* operatore somma con data+carry → data+carry *)
+ndefinition plus_w32_dc_dc ≝ opcl2_cn ? plus_w16_dc_dc.
+
+(* operatore somma con data+carry → data *)
+ndefinition plus_w32_dc_d ≝ λc,w1,w2.snd … (plus_w32_dc_dc c w1 w2).
+
+(* operatore somma con data+carry → c *)
+ndefinition plus_w32_dc_c ≝ λc,w1,w2.fst … (plus_w32_dc_dc c w1 w2).
+
+(* operatore somma con data → data+carry *)
+ndefinition plus_w32_d_dc ≝ opcl2_cn ? plus_w16_dc_dc false.
+
+(* operatore somma con data → data *)
+ndefinition plus_w32_d_d ≝ λw1,w2.snd … (plus_w32_d_dc w1 w2).
+
+(* operatore somma con data → c *)
+ndefinition plus_w32_d_c ≝ λw1,w2.fst … (plus_w32_d_dc w1 w2).
+
+(* operatore predecessore *)
+ndefinition pred_w32 ≝ predsucc_cn ? (eq_w16 〈〈x0,x0〉:〈x0,x0〉〉) pred_w16.
+
+(* operatore successore *)
+ndefinition succ_w32 ≝ predsucc_cn ? (eq_w16 〈〈xF,xF〉:〈xF,xF〉〉) succ_w16.
+
+(* operatore neg/complemento a 2 *)
+ndefinition compl_w32 ≝
+λw:word32.match getMSB_w32 w with
+ [ true ⇒ succ_w32 (not_w32 w)
+ | false ⇒ not_w32 (pred_w32 w) ].
+
+(* operatore abs *)
+ndefinition abs_w32 ≝
+λw:word32.match getMSB_w32 w with
+ [ true ⇒ compl_w32 w | false ⇒ w ].
+
+(* operatore x in [inf,sup] o in sup],[inf *)
+ndefinition inrange_w32 ≝
+λx,inf,sup:word32.
+ match le_w32 inf sup with
+  [ true ⇒ and_bool | false ⇒ or_bool ]
+ (le_w32 inf x) (le_w32 x sup).
+
+(* operatore moltiplicazione senza segno *)
+(* 〈a1,a2〉 * 〈b1,b2〉 = (a1*b1) x0 x0 + x0 (a1*b2) x0 + x0 (a2*b1) x0 + x0 x0 (a2*b2) *)
+ndefinition mulu_w16_aux ≝
+λw.nat_it ? rol_w32 w nat8.
+
+ndefinition mulu_w16 ≝
+λw1,w2:word16.
+ plus_w32_d_d 〈(mulu_b8 (cnH ? w1) (cnH ? w2)).〈〈x0,x0〉:〈x0,x0〉〉〉
+ (plus_w32_d_d (mulu_w16_aux (extu_w32 (mulu_b8 (cnH ? w1) (cnL ? w2))))
+  (plus_w32_d_d (mulu_w16_aux (extu_w32 (mulu_b8 (cnL ? w1) (cnH ? w2))))
+                (extu_w32 (mulu_b8 (cnL ? w1) (cnL ? w2))))).
+
+(* operatore moltiplicazione con segno *)
+(* x * y = sgn(x) * sgn(y) * |x| * |y| *)
+ndefinition muls_w16 ≝
+λw1,w2:word16.
+(* ++/-- → +, +-/-+ → - *)
+ match (getMSB_w16 w1) ⊙ (getMSB_w16 w2) with
+  (* +- -+ → - *)
+  [ true ⇒ compl_w32
+  (* ++/-- → + *)
+  | false ⇒ λx.x ] (mulu_w16 (abs_w16 w1) (abs_w16 w2)).
+
+nlemma pippo : ∃b.b=(muls_w16 〈〈xC,x3〉:〈x0,x4〉〉 〈〈x7,xE〉:〈xF,x9〉〉). nnormalize;
+