+++ /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: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* Sviluppo: 2008-2010 *)
-(* *)
-(* ********************************************************************** *)
-
-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.
- (lt_w16 (w32h dw1) (w32h dw2)) ⊕
- ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (lt_w16 (w32l dw1) (w32l dw2))).
-
-(* operatore ≤ *)
-ndefinition le_w32 ≝
-λdw1,dw2:word32.
- (lt_w16 (w32h dw1) (w32h dw2)) ⊕
- ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (le_w16 (w32l dw1) (w32l dw2))).
-
-(* operatore > *)
-ndefinition gt_w32 ≝
-λdw1,dw2:word32.
- (gt_w16 (w32h dw1) (w32h dw2)) ⊕
- ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (gt_w16 (w32l dw1) (w32l dw2))).
-
-(* operatore ≥ *)
-ndefinition ge_w32 ≝
-λdw1,dw2:word32.
- (gt_w16 (w32h dw1) (w32h dw2)) ⊕
- ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (ge_w16 (w32l dw1) (w32l 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:nat) on n ≝
- match n with
- [ O ⇒ dw
- | S n' ⇒ ror_w32_n (ror_w32 dw) 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:nat) on n ≝
- match n with
- [ O ⇒ dw
- | S n' ⇒ rol_w32_n (rol_w32 dw) 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:nat) on c ≝
- let w' ≝ plus_w32_d_d divd (compl_w32 divs) in
- match c with
- [ 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〉〉)) ]
- | S c' ⇒ match le_w32 divs divd with
- [ true ⇒ div_w16_aux w' (ror_w32 divs) (ror_w16 molt) (or_w16 molt q) c'
- | false ⇒ div_w16_aux divd (ror_w32 divs) (ror_w16 molt) q 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〉 nat15) 〈〈x8,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 nat15 ]].
-
-(* 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).
-
-(* iteratore sulle word *)
-ndefinition forall_w32 ≝
- λP.
- forall_w16 (λbh.
- forall_w16 (λbl.
- P (mk_word32 bh bl ))).
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