--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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: *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* Questo materiale fa parte della tesi: *)
+(* "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale" *)
+(* *)
+(* data ultima modifica 15/11/2007 *)
+(* ********************************************************************** *)
+
+include "freescale/byte8.ma".
+
+(* **** *)
+(* WORD *)
+(* **** *)
+
+nrecord word16 : Type ≝
+ {
+ w16h: byte8;
+ w16l: byte8
+ }.
+
+ndefinition word16_ind : ΠP:word16 → Prop.(Πb:byte8.Πb1:byte8.P (mk_word16 b b1)) → Πw:word16.P w ≝
+λP:word16 → Prop.λf:Πb:byte8.Πb1:byte8.P (mk_word16 b b1).λw:word16.
+ match w with [ mk_word16 (b:byte8) (b1:byte8) ⇒ f b b1 ].
+
+ndefinition word16_rec : ΠP:word16 → Set.(Πb:byte8.Πb1:byte8.P (mk_word16 b b1)) → Πw:word16.P w ≝
+λP:word16 → Set.λf:Πb:byte8.Πb1:byte8.P (mk_word16 b b1).λw:word16.
+ match w with [ mk_word16 (b:byte8) (b1:byte8) ⇒ f b b1 ].
+
+ndefinition word16_rect : ΠP:word16 → Type.(Πb:byte8.Πb1:byte8.P (mk_word16 b b1)) → Πw:word16.P w ≝
+λP:word16 → Type.λf:Πb:byte8.Πb1:byte8.P (mk_word16 b b1).λw:word16.
+ match w with [ mk_word16 (b:byte8) (b1:byte8) ⇒ f b b1 ].
+
+ndefinition w16h ≝ λw:word16.match w with [ mk_word16 x _ ⇒ x ].
+ndefinition w16l ≝ λw:word16.match w with [ mk_word16 _ x ⇒ x ].
+
+(* \langle \rangle *)
+notation "〈x:y〉" non associative with precedence 80
+ for @{ 'mk_word16 $x $y }.
+interpretation "mk_word16" 'mk_word16 x y = (mk_word16 x y).
+
+(* operatore = *)
+ndefinition eq_w16 ≝ λw1,w2.(eq_b8 (w16h w1) (w16h w2)) ⊗ (eq_b8 (w16l w1) (w16l w2)).
+
+(* operatore < *)
+ndefinition lt_w16 ≝
+λw1,w2:word16.match lt_b8 (w16h w1) (w16h w2) with
+ [ true ⇒ true
+ | false ⇒ match gt_b8 (w16h w1) (w16h w2) with
+ [ true ⇒ false
+ | false ⇒ lt_b8 (w16l w1) (w16l w2) ]].
+
+(* operatore ≤ *)
+ndefinition le_w16 ≝ λw1,w2:word16.(eq_w16 w1 w2) ⊕ (lt_w16 w1 w2).
+
+(* operatore > *)
+ndefinition gt_w16 ≝ λw1,w2:word16.⊖ (le_w16 w1 w2).
+
+(* operatore ≥ *)
+ndefinition ge_w16 ≝ λw1,w2:word16.⊖ (lt_w16 w1 w2).
+
+(* operatore and *)
+ndefinition and_w16 ≝
+λw1,w2:word16.mk_word16 (and_b8 (w16h w1) (w16h w2)) (and_b8 (w16l w1) (w16l w2)).
+
+(* operatore or *)
+ndefinition or_w16 ≝
+λw1,w2:word16.mk_word16 (or_b8 (w16h w1) (w16h w2)) (or_b8 (w16l w1) (w16l w2)).
+
+(* operatore xor *)
+ndefinition xor_w16 ≝
+λw1,w2:word16.mk_word16 (xor_b8 (w16h w1) (w16h w2)) (xor_b8 (w16l w1) (w16l w2)).
+
+(* operatore rotazione destra con carry *)
+ndefinition rcr_w16 ≝
+λw:word16.λc:bool.match rcr_b8 (w16h w) c with
+ [ pair wh' c' ⇒ match rcr_b8 (w16l w) c' with
+ [ pair wl' c'' ⇒ pair ?? (mk_word16 wh' wl') c'' ]].
+
+(* operatore shift destro *)
+ndefinition shr_w16 ≝
+λw:word16.match rcr_b8 (w16h w) false with
+ [ pair wh' c' ⇒ match rcr_b8 (w16l w) c' with
+ [ pair wl' c'' ⇒ pair ?? (mk_word16 wh' wl') c'' ]].
+
+(* operatore rotazione destra *)
+ndefinition ror_w16 ≝
+λw:word16.match rcr_b8 (w16h w) false with
+ [ pair wh' c' ⇒ match rcr_b8 (w16l w) c' with
+ [ pair wl' c'' ⇒ match c'' with
+ [ true ⇒ mk_word16 (or_b8 (mk_byte8 x8 x0) wh') wl'
+ | false ⇒ mk_word16 wh' wl' ]]].
+
+(* operatore rotazione destra n-volte *)
+nlet rec ror_w16_n (w:word16) (n:nat) on n ≝
+ match n with
+ [ O ⇒ w
+ | S n' ⇒ ror_w16_n (ror_w16 w) n' ].
+
+(* operatore rotazione sinistra con carry *)
+ndefinition rcl_w16 ≝
+λw:word16.λc:bool.match rcl_b8 (w16l w) c with
+ [ pair wl' c' ⇒ match rcl_b8 (w16h w) c' with
+ [ pair wh' c'' ⇒ pair ?? (mk_word16 wh' wl') c'' ]].
+
+(* operatore shift sinistro *)
+ndefinition shl_w16 ≝
+λw:word16.match rcl_b8 (w16l w) false with
+ [ pair wl' c' ⇒ match rcl_b8 (w16h w) c' with
+ [ pair wh' c'' ⇒ pair ?? (mk_word16 wh' wl') c'' ]].
+
+(* operatore rotazione sinistra *)
+ndefinition rol_w16 ≝
+λw:word16.match rcl_b8 (w16l w) false with
+ [ pair wl' c' ⇒ match rcl_b8 (w16h w) c' with
+ [ pair wh' c'' ⇒ match c'' with
+ [ true ⇒ mk_word16 wh' (or_b8 (mk_byte8 x0 x1) wl')
+ | false ⇒ mk_word16 wh' wl' ]]].
+
+(* operatore rotazione sinistra n-volte *)
+nlet rec rol_w16_n (w:word16) (n:nat) on n ≝
+ match n with
+ [ O ⇒ w
+ | S n' ⇒ rol_w16_n (rol_w16 w) n' ].
+
+(* operatore not/complemento a 1 *)
+ndefinition not_w16 ≝
+λw:word16.mk_word16 (not_b8 (w16h w)) (not_b8 (w16l w)).
+
+(* operatore somma con data+carry → data+carry *)
+ndefinition plus_w16_dc_dc ≝
+λw1,w2:word16.λc:bool.
+ match plus_b8_dc_dc (w16l w1) (w16l w2) c with
+ [ pair l c ⇒ match plus_b8_dc_dc (w16h w1) (w16h w2) c with
+ [ pair h c' ⇒ pair ?? 〈h:l〉 c' ]].
+
+(* operatore somma con data+carry → data *)
+ndefinition plus_w16_dc_d ≝
+λw1,w2:word16.λc:bool.
+ match plus_b8_dc_dc (w16l w1) (w16l w2) c with
+ [ pair l c ⇒ 〈plus_b8_dc_d (w16h w1) (w16h w2) c:l〉 ].
+
+(* operatore somma con data+carry → c *)
+ndefinition plus_w16_dc_c ≝
+λw1,w2:word16.λc:bool.
+ plus_b8_dc_c (w16h w1) (w16h w2) (plus_b8_dc_c (w16l w1) (w16l w2) c).
+
+(* operatore somma con data → data+carry *)
+ndefinition plus_w16_d_dc ≝
+λw1,w2:word16.
+ match plus_b8_d_dc (w16l w1) (w16l w2) with
+ [ pair l c ⇒ match plus_b8_dc_dc (w16h w1) (w16h w2) c with
+ [ pair h c' ⇒ pair ?? 〈h:l〉 c' ]].
+
+(* operatore somma con data → data *)
+ndefinition plus_w16_d_d ≝
+λw1,w2:word16.
+ match plus_b8_d_dc (w16l w1) (w16l w2) with
+ [ pair l c ⇒ 〈plus_b8_dc_d (w16h w1) (w16h w2) c:l〉 ].
+
+(* operatore somma con data → c *)
+ndefinition plus_w16_d_c ≝
+λw1,w2:word16.
+ plus_b8_dc_c (w16h w1) (w16h w2) (plus_b8_d_c (w16l w1) (w16l w2)).
+
+(* operatore Most Significant Bit *)
+ndefinition MSB_w16 ≝ λw:word16.eq_ex x8 (and_ex x8 (b8h (w16h w))).
+
+(* word → naturali *)
+ndefinition nat_of_word16 ≝ λw:word16. 256 * (nat_of_byte8 (w16h w)) + (nat_of_byte8 (w16l w)).
+
+(* operatore predecessore *)
+ndefinition pred_w16 ≝
+λw:word16.match eq_b8 (w16l w) (mk_byte8 x0 x0) with
+ [ true ⇒ mk_word16 (pred_b8 (w16h w)) (pred_b8 (w16l w))
+ | false ⇒ mk_word16 (w16h w) (pred_b8 (w16l w)) ].
+
+(* operatore successore *)
+ndefinition succ_w16 ≝
+λw:word16.match eq_b8 (w16l w) (mk_byte8 xF xF) with
+ [ true ⇒ mk_word16 (succ_b8 (w16h w)) (succ_b8 (w16l w))
+ | false ⇒ mk_word16 (w16h w) (succ_b8 (w16l w)) ].
+
+(* operatore neg/complemento a 2 *)
+ndefinition compl_w16 ≝
+λw:word16.match MSB_w16 w with
+ [ true ⇒ succ_w16 (not_w16 w)
+ | false ⇒ not_w16 (pred_w16 w) ].
+
+(*
+ operatore moltiplicazione senza segno: b*b=[0x0000,0xFE01]
+ ... in pratica (〈a,b〉*〈c,d〉) = (a*c)<<8+(a*d)<<4+(b*c)<<4+(b*d)
+*)
+ndefinition mul_b8 ≝
+λb1,b2:byte8.match b1 with
+[ mk_byte8 b1h b1l ⇒ match b2 with
+[ mk_byte8 b2h b2l ⇒ match mul_ex b1l b2l with
+[ mk_byte8 t1_h t1_l ⇒ match mul_ex b1h b2l with
+[ mk_byte8 t2_h t2_l ⇒ match mul_ex b2h b1l with
+[ mk_byte8 t3_h t3_l ⇒ match mul_ex b1h b2h with
+[ mk_byte8 t4_h t4_l ⇒
+ plus_w16_d_d
+ (plus_w16_d_d
+ (plus_w16_d_d 〈〈x0,t3_h〉:〈t3_l,x0〉〉 〈〈x0,t2_h〉:〈t2_l,x0〉〉) 〈〈t4_h,t4_l〉:〈x0,x0〉〉)〈〈x0,x0〉:〈t1_h,t1_l〉〉
+]]]]]].
+
+(* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
+nlet rec div_b8_aux (divd:word16) (divs:word16) (molt:byte8) (q:byte8) (c:nat) on c ≝
+ let w' ≝ plus_w16_d_d divd (compl_w16 divs) in
+ match c with
+ [ O ⇒ match le_w16 divs divd with
+ [ true ⇒ triple ??? (or_b8 molt q) (w16l w') (⊖ (eq_b8 (w16h w') 〈x0,x0〉))
+ | false ⇒ triple ??? q (w16l divd) (⊖ (eq_b8 (w16h divd) 〈x0,x0〉)) ]
+ | S c' ⇒ match le_w16 divs divd with
+ [ true ⇒ div_b8_aux w' (ror_w16 divs) (ror_b8 molt) (or_b8 molt q) c'
+ | false ⇒ div_b8_aux divd (ror_w16 divs) (ror_b8 molt) q c' ]].
+
+ndefinition div_b8 ≝
+λw:word16.λb:byte8.match eq_b8 b 〈x0,x0〉 with
+(*
+ la combinazione n/0 e' illegale, segnala solo overflow senza dare risultato
+*)
+ [ true ⇒ triple ??? 〈xF,xF〉 (w16l w) true
+ | false ⇒ match eq_w16 w 〈〈x0,x0〉:〈x0,x0〉〉 with
+(* 0 diviso qualsiasi cosa diverso da 0 da' q=0 r=0 o=false *)
+ [ true ⇒ triple ??? 〈x0,x0〉 〈x0,x0〉 false
+(* 1) e' una divisione sensata che produrra' overflow/risultato *)
+(* 2) parametri: dividendo, divisore, moltiplicatore, quoziente, contatore *)
+(* 3) ad ogni ciclo il divisore e il moltiplicatore vengono scalati di 1 a dx *)
+(* 4) il moltiplicatore e' la quantita' aggiunta al quoziente se il divisore *)
+(* puo' essere sottratto al dividendo *)
+ | false ⇒ div_b8_aux w (rol_w16_n 〈〈x0,x0〉:b〉 7) 〈x8,x0〉 〈x0,x0〉 7 ]].
+
+(* operatore x in [inf,sup] *)
+ndefinition in_range ≝
+λx,inf,sup:word16.(le_w16 inf sup) ⊗ (ge_w16 x inf) ⊗ (le_w16 x sup).
+
+(* iteratore sulle word *)
+ndefinition forall_word16 ≝
+ λP.
+ forall_byte8 (λbh.
+ forall_byte8 (λbl.
+ P (mk_word16 bh bl ))).
projects / helm.git / blobdiff