--- /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 *)
+(* Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* *)
+(* ********************************************************************** *)
+
+include "num/word16.ma".
+
+(* ***** *)
+(* DWORD *)
+(* ***** *)
+
+nrecord word32 : Type ≝
+ {
+ w32h: word16;
+ w32l: word16
+ }.
+
+(* \langle \rangle *)
+notation "〈x.y〉" non associative with precedence 80
+ for @{ 'mk_word32 $x $y }.
+interpretation "mk_word32" 'mk_word32 x y = (mk_word32 x y).
+
+(* operatore = *)
+ndefinition eq_w32 ≝ λdw1,dw2.(eq_w16 (w32h dw1) (w32h dw2)) ⊗ (eq_w16 (w32l dw1) (w32l dw2)).
+
+(* operatore < *)
+ndefinition lt_w32 ≝
+λdw1,dw2:word32.match lt_w16 (w32h dw1) (w32h dw2) with
+ [ true ⇒ true
+ | false ⇒ match gt_w16 (w32h dw1) (w32h dw2) with
+ [ true ⇒ false
+ | false ⇒ lt_w16 (w32l dw1) (w32l dw2) ]].
+
+(* operatore ≤ *)
+ndefinition le_w32 ≝ λdw1,dw2:word32.(eq_w32 dw1 dw2) ⊕ (lt_w32 dw1 dw2).
+
+(* operatore > *)
+ndefinition gt_w32 ≝ λdw1,dw2:word32.⊖ (le_w32 dw1 dw2).
+
+(* operatore ≥ *)
+ndefinition ge_w32 ≝ λdw1,dw2:word32.⊖ (lt_w32 dw1 dw2).
+
+(* operatore and *)
+ndefinition and_w32 ≝
+λdw1,dw2:word32.mk_word32 (and_w16 (w32h dw1) (w32h dw2)) (and_w16 (w32l dw1) (w32l dw2)).
+
+(* operatore or *)
+ndefinition or_w32 ≝
+λdw1,dw2:word32.mk_word32 (or_w16 (w32h dw1) (w32h dw2)) (or_w16 (w32l dw1) (w32l dw2)).
+
+(* operatore xor *)
+ndefinition xor_w32 ≝
+λdw1,dw2:word32.mk_word32 (xor_w16 (w32h dw1) (w32h dw2)) (xor_w16 (w32l dw1) (w32l dw2)).
+
+(* operatore rotazione destra con carry *)
+ndefinition rcr_w32 ≝
+λdw:word32.λc:bool.match rcr_w16 (w32h dw) c with
+ [ pair wh' c' ⇒ match rcr_w16 (w32l dw) c' with
+ [ pair wl' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
+
+(* operatore shift destro *)
+ndefinition shr_w32 ≝
+λdw:word32.match rcr_w16 (w32h dw) false with
+ [ pair wh' c' ⇒ match rcr_w16 (w32l dw) c' with
+ [ pair wl' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
+
+(* operatore rotazione destra *)
+ndefinition ror_w32 ≝
+λdw:word32.match rcr_w16 (w32h dw) false with
+ [ pair wh' c' ⇒ match rcr_w16 (w32l dw) c' with
+ [ pair wl' c'' ⇒ match c'' with
+ [ true ⇒ mk_word32 (or_w16 (mk_word16 (mk_byte8 x8 x0) (mk_byte8 x0 x0)) wh') wl'
+ | false ⇒ mk_word32 wh' wl' ]]].
+
+(* operatore rotazione destra n-volte *)
+nlet rec ror_w32_n (dw:word32) (n:bitrigesim) (r:rec_bitrigesim n) on r ≝
+ match r with
+ [ bi_O ⇒ dw
+ | bi_S t n' ⇒ ror_w32_n (ror_w32 dw) t n' ].
+
+(* operatore rotazione sinistra con carry *)
+ndefinition rcl_w32 ≝
+λdw:word32.λc:bool.match rcl_w16 (w32l dw) c with
+ [ pair wl' c' ⇒ match rcl_w16 (w32h dw) c' with
+ [ pair wh' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
+
+(* operatore shift sinistro *)
+ndefinition shl_w32 ≝
+λdw:word32.match rcl_w16 (w32l dw) false with
+ [ pair wl' c' ⇒ match rcl_w16 (w32h dw) c' with
+ [ pair wh' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
+
+(* operatore rotazione sinistra *)
+ndefinition rol_w32 ≝
+λdw:word32.match rcl_w16 (w32l dw) false with
+ [ pair wl' c' ⇒ match rcl_w16 (w32h dw) c' with
+ [ pair wh' c'' ⇒ match c'' with
+ [ true ⇒ mk_word32 wh' (or_w16 (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x1)) wl')
+ | false ⇒ mk_word32 wh' wl' ]]].
+
+(* operatore rotazione sinistra n-volte *)
+nlet rec rol_w32_n (dw:word32) (n:bitrigesim) (r:rec_bitrigesim n) on r ≝
+ match r with
+ [ bi_O ⇒ dw
+ | bi_S t n' ⇒ rol_w32_n (rol_w32 dw) t n' ].
+
+(* operatore not/complemento a 1 *)
+ndefinition not_w32 ≝
+λdw:word32.mk_word32 (not_w16 (w32h dw)) (not_w16 (w32l dw)).
+
+(* operatore somma con data+carry → data+carry *)
+ndefinition plus_w32_dc_dc ≝
+λdw1,dw2:word32.λc:bool.
+ match plus_w16_dc_dc (w32l dw1) (w32l dw2) c with
+ [ pair l c ⇒ match plus_w16_dc_dc (w32h dw1) (w32h dw2) c with
+ [ pair h c' ⇒ pair … 〈h.l〉 c' ]].
+
+(* operatore somma con data+carry → data *)
+ndefinition plus_w32_dc_d ≝
+λdw1,dw2:word32.λc:bool.
+ match plus_w16_dc_dc (w32l dw1) (w32l dw2) c with
+ [ pair l c ⇒ 〈plus_w16_dc_d (w32h dw1) (w32h dw2) c.l〉 ].
+
+(* operatore somma con data+carry → c *)
+ndefinition plus_w32_dc_c ≝
+λdw1,dw2:word32.λc:bool.
+ plus_w16_dc_c (w32h dw1) (w32h dw2) (plus_w16_dc_c (w32l dw1) (w32l dw2) c).
+
+(* operatore somma con data → data+carry *)
+ndefinition plus_w32_d_dc ≝
+λdw1,dw2:word32.
+ match plus_w16_d_dc (w32l dw1) (w32l dw2) with
+ [ pair l c ⇒ match plus_w16_dc_dc (w32h dw1) (w32h dw2) c with
+ [ pair h c' ⇒ pair … 〈h.l〉 c' ]].
+
+(* operatore somma con data → data *)
+ndefinition plus_w32_d_d ≝
+λdw1,dw2:word32.
+ match plus_w16_d_dc (w32l dw1) (w32l dw2) with
+ [ pair l c ⇒ 〈plus_w16_dc_d (w32h dw1) (w32h dw2) c.l〉 ].
+
+(* operatore somma con data → c *)
+ndefinition plus_w32_d_c ≝
+λdw1,dw2:word32.
+ plus_w16_dc_c (w32h dw1) (w32h dw2) (plus_w16_d_c (w32l dw1) (w32l dw2)).
+
+(* operatore Most Significant Bit *)
+ndefinition MSB_w32 ≝ λdw:word32.eq_ex x8 (and_ex x8 (b8h (w16h (w32h dw)))).
+
+(* operatore predecessore *)
+ndefinition pred_w32 ≝
+λdw:word32.match eq_w16 (w32l dw) (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x0)) with
+ [ true ⇒ mk_word32 (pred_w16 (w32h dw)) (pred_w16 (w32l dw))
+ | false ⇒ mk_word32 (w32h dw) (pred_w16 (w32l dw)) ].
+
+(* operatore successore *)
+ndefinition succ_w32 ≝
+λdw:word32.match eq_w16 (w32l dw) (mk_word16 (mk_byte8 xF xF) (mk_byte8 xF xF)) with
+ [ true ⇒ mk_word32 (succ_w16 (w32h dw)) (succ_w16 (w32l dw))
+ | false ⇒ mk_word32 (w32h dw) (succ_w16 (w32l dw)) ].
+
+(* operatore neg/complemento a 2 *)
+ndefinition compl_w32 ≝
+λdw:word32.match MSB_w32 dw with
+ [ true ⇒ succ_w32 (not_w32 dw)
+ | false ⇒ not_w32 (pred_w32 dw) ].
+
+(*
+ operatore moltiplicazione senza segno: b*b=[0x00000000,0xFFFE0001]
+ ... in pratica (〈a:b〉*〈c:d〉) = (a*c)<<16+(a*d)<<8+(b*c)<<8+(b*d)
+*)
+ndefinition mul_w16 ≝
+λw1,w2:word16.match w1 with
+[ mk_word16 b1h b1l ⇒ match w2 with
+[ mk_word16 b2h b2l ⇒ match mul_b8 b1l b2l with
+[ mk_word16 t1_h t1_l ⇒ match mul_b8 b1h b2l with
+[ mk_word16 t2_h t2_l ⇒ match mul_b8 b2h b1l with
+[ mk_word16 t3_h t3_l ⇒ match mul_b8 b1h b2h with
+[ mk_word16 t4_h t4_l ⇒
+ plus_w32_d_d
+ (plus_w32_d_d
+ (plus_w32_d_d 〈〈〈x0,x0〉:t3_h〉.〈t3_l:〈x0,x0〉〉〉 〈〈〈x0,x0〉:t2_h〉.〈t2_l:〈x0,x0〉〉〉) 〈〈t4_h:t4_l〉.〈〈x0,x0〉:〈x0,x0〉〉〉)〈〈〈x0,x0〉:〈x0,x0〉〉.〈t1_h:t1_l〉〉
+]]]]]].
+
+(* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
+nlet rec div_w16_aux (divd:word32) (divs:word32) (molt:word16) (q:word16) (c:exadecim) (rc:rec_exadecim c) on rc ≝
+ let w' ≝ plus_w32_d_d divd (compl_w32 divs) in
+ match rc with
+ [ ex_O ⇒ match le_w32 divs divd with
+ [ true ⇒ triple … (or_w16 molt q) (w32l w') (⊖ (eq_w16 (w32h w') 〈〈x0,x0〉:〈x0,x0〉〉))
+ | false ⇒ triple … q (w32l divd) (⊖ (eq_w16 (w32h divd) 〈〈x0,x0〉:〈x0,x0〉〉)) ]
+ | ex_S t c' ⇒ match le_w32 divs divd with
+ [ true ⇒ div_w16_aux w' (ror_w32 divs) (ror_w16 molt) (or_w16 molt q) t c'
+ | false ⇒ div_w16_aux divd (ror_w32 divs) (ror_w16 molt) q t c' ]].
+
+ndefinition div_w16 ≝
+λw:word32.λb:word16.match eq_w16 b 〈〈x0,x0〉:〈x0,x0〉〉 with
+(*
+ la combinazione n/0 e' illegale, segnala solo overflow senza dare risultato
+*)
+ [ true ⇒ triple … 〈〈xF,xF〉:〈xF,xF〉〉 (w32l w) true
+ | false ⇒ match eq_w32 w 〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈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〉〉 〈〈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_w16_aux w (rol_w32_n 〈〈〈x0,x0〉:〈x0,x0〉〉.b〉 ? (bit_to_recbit t0F)) 〈〈x8,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 ? (ex_to_recex xF) ]].
+
+(* operatore x in [inf,sup] *)
+ndefinition inrange_w32 ≝
+λx,inf,sup:word32.(le_w32 inf sup) ⊗ (ge_w32 x inf) ⊗ (le_w32 x sup).
+
+(* iteratore sulle word *)
+ndefinition forall_w32 ≝
+ λP.
+ forall_w16 (λbh.
+ forall_w16 (λbl.
+ P (mk_word32 bh bl ))).
projects / helm.git / blobdiff