(* WORD *)
(* **** *)
-nrecord word16 : Type ≝
- {
- w16h: byte8;
- w16l: byte8
- }.
+ndefinition word16 ≝ comp_num byte8.
+ndefinition mk_word16 ≝ λb1,b2.mk_comp_num byte8 b1 b2.
(* \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).
+ for @{ mk_comp_num byte8 $x $y }.
+
+(* iteratore sulle word *)
+ndefinition forall_w16 ≝ forall_cn ? forall_b8.
(* operatore = *)
-ndefinition eq_w16 ≝ λw1,w2.(eq_b8 (w16h w1) (w16h w2)) ⊗ (eq_b8 (w16l w1) (w16l w2)).
+ndefinition eq_w16 ≝ eq2_cn ? eq_b8.
(* operatore < *)
-ndefinition lt_w16 ≝
-λw1,w2:word16.
- (lt_b8 (w16h w1) (w16h w2)) ⊕
- ((eq_b8 (w16h w1) (w16h w2)) ⊗ (lt_b8 (w16l w1) (w16l w2))).
+ndefinition lt_w16 ≝ ltgt_cn ? eq_b8 lt_b8.
(* operatore ≤ *)
-ndefinition le_w16 ≝
-λw1,w2:word16.
- (lt_b8 (w16h w1) (w16h w2)) ⊕
- ((eq_b8 (w16h w1) (w16h w2)) ⊗ (le_b8 (w16l w1) (w16l w2))).
+ndefinition le_w16 ≝ lege_cn ? eq_b8 lt_b8 le_b8.
(* operatore > *)
-ndefinition gt_w16 ≝
-λw1,w2:word16.
- (gt_b8 (w16h w1) (w16h w2)) ⊕
- ((eq_b8 (w16h w1) (w16h w2)) ⊗ (gt_b8 (w16l w1) (w16l w2))).
+ndefinition gt_w16 ≝ ltgt_cn ? eq_b8 gt_b8.
(* operatore ≥ *)
-ndefinition ge_w16 ≝
-λw1,w2:word16.
- (gt_b8 (w16h w1) (w16h w2)) ⊕
- ((eq_b8 (w16h w1) (w16h w2)) ⊗ (ge_b8 (w16l w1) (w16l w2))).
+ndefinition ge_w16 ≝ lege_cn ? eq_b8 gt_b8 ge_b8.
(* operatore and *)
-ndefinition and_w16 ≝
-λw1,w2:word16.mk_word16 (and_b8 (w16h w1) (w16h w2)) (and_b8 (w16l w1) (w16l w2)).
+ndefinition and_w16 ≝ fop2_cn ? and_b8.
(* operatore or *)
-ndefinition or_w16 ≝
-λw1,w2:word16.mk_word16 (or_b8 (w16h w1) (w16h w2)) (or_b8 (w16l w1) (w16l w2)).
+ndefinition or_w16 ≝ fop2_cn ? or_b8.
(* operatore xor *)
-ndefinition xor_w16 ≝
-λw1,w2:word16.mk_word16 (xor_b8 (w16h w1) (w16h w2)) (xor_b8 (w16l w1) (w16l w2)).
+ndefinition xor_w16 ≝ fop2_cn ? xor_b8.
+
+(* operatore Most Significant Bit *)
+ndefinition getMSB_w16 ≝ getOPH_cn ? getMSB_b8.
+ndefinition setMSB_w16 ≝ setOPH_cn ? setMSB_b8.
+
+(* operatore Least Significant Bit *)
+ndefinition getLSB_w16 ≝ getOPL_cn ? getLSB_b8.
+ndefinition setLSB_w16 ≝ setOPL_cn ? setLSB_b8.
(* 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'' ]].
+ndefinition rcr_w16 ≝ opcr_cn ? rcr_b8.
(* operatore shift destro *)
-ndefinition shr_w16 ≝
-λw:word16.match shr_b8 (w16h w) with
- [ pair wh' c' ⇒ match rcr_b8 (w16l w) c' with
- [ pair wl' c'' ⇒ pair … (mk_word16 wh' wl') c'' ]].
+ndefinition shr_w16 ≝ opcr_cn ? rcr_b8 false.
(* operatore rotazione destra *)
ndefinition ror_w16 ≝
-λw:word16.match shr_b8 (w16h w) 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) (e:exadecim) (re:rec_exadecim e) on re ≝
- match re with
- [ ex_O ⇒ w
- | ex_S e' n' ⇒ ror_w16_n (ror_w16 w) e' n' ].
+λw.match shr_w16 w with
+ [ pair c w' ⇒ match c with
+ [ true ⇒ setMSB_w16 w' | false ⇒ w' ]].
(* 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'' ]].
+ndefinition rcl_w16 ≝ opcl_cn ? rcl_b8.
(* operatore shift sinistro *)
-ndefinition shl_w16 ≝
-λw:word16.match shl_b8 (w16l w) with
- [ pair wl' c' ⇒ match rcl_b8 (w16h w) c' with
- [ pair wh' c'' ⇒ pair … (mk_word16 wh' wl') c'' ]].
+ndefinition shl_w16 ≝ opcl_cn ? rcl_b8 false.
(* operatore rotazione sinistra *)
ndefinition rol_w16 ≝
-λw:word16.match shl_b8 (w16l w) 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) (e:exadecim) (re:rec_exadecim e) on re ≝
- match re with
- [ ex_O ⇒ w
- | ex_S e' n' ⇒ rol_w16_n (rol_w16 w) e' n' ].
+λw.match shl_w16 w with
+ [ pair c w' ⇒ match c with
+ [ true ⇒ setLSB_w16 w' | false ⇒ w' ]].
(* operatore not/complemento a 1 *)
-ndefinition not_w16 ≝
-λw:word16.mk_word16 (not_b8 (w16h w)) (not_b8 (w16l w)).
+ndefinition not_w16 ≝ fop_cn ? not_b8.
(* 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'' ]].
+ndefinition plus_w16_dc_dc ≝ opcl2_cn ? plus_b8_dc_dc.
(* 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〉 ].
+ndefinition plus_w16_dc_d ≝ λc,w1,w2.snd … (plus_w16_dc_dc c w1 w2).
(* 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).
+ndefinition plus_w16_dc_c ≝ λc,w1,w2.fst … (plus_w16_dc_dc c w1 w2).
(* 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' ]].
+ndefinition plus_w16_d_dc ≝ opcl2_cn ? plus_b8_dc_dc false.
(* 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〉 ].
+ndefinition plus_w16_d_d ≝ λw1,w2.snd … (plus_w16_d_dc w1 w2).
(* 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))).
+ndefinition plus_w16_d_c ≝ λw1,w2.fst … (plus_w16_d_dc w1 w2).
(* 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)) ].
+ndefinition pred_w16 ≝ predsucc_cn ? (eq_b8 〈x0,x0〉) pred_b8.
(* 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)) ].
+ndefinition succ_w16 ≝ predsucc_cn ? (eq_b8 〈xF,xF〉) succ_b8.
(* operatore neg/complemento a 2 *)
ndefinition compl_w16 ≝
-λw:word16.match MSB_w16 w with
+λw:word16.match getMSB_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_w16_b8_aux (divd:word16) (divs:word16) (molt:byte8) (q:byte8) (o:oct) (ro:rec_oct o) on ro ≝
- let w' ≝ plus_w16_d_d divd (compl_w16 divs) in
- match ro with
- [ oc_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〉)) ]
- | oc_S o' ro' ⇒ match le_w16 divs divd with
- [ true ⇒ div_w16_b8_aux w' (ror_w16 divs) (ror_b8 molt) (or_b8 molt q) o' ro'
- | false ⇒ div_w16_b8_aux divd (ror_w16 divs) (ror_b8 molt) q o' ro' ]].
-
-ndefinition div_w16_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_w16_b8_aux w (rol_w16_n 〈〈x0,x0〉:b〉 ? (ex_to_recex x7)) 〈x8,x0〉 〈x0,x0〉 ? (oct_to_recoct o7) ]].
-
(* operatore x in [inf,sup] o in sup],[inf *)
ndefinition inrange_w16 ≝
λx,inf,sup:word16.
[ true ⇒ and_bool | false ⇒ or_bool ]
(le_w16 inf x) (le_w16 x sup).
-(* iteratore sulle word *)
-ndefinition forall_w16 ≝
- λP.
- forall_b8 (λbh.
- forall_b8 (λbl.
- P (mk_word16 bh bl ))).
-
(* word16 ricorsive *)
ninductive rec_word16 : word16 → Type ≝
w16_O : rec_word16 〈〈x0,x0〉:〈x0,x0〉〉
ndefinition w16_to_recw16 : Πw.rec_word16 w ≝
λw.
- match w with [ mk_word16 h l ⇒
- match l with [ mk_byte8 lh ll ⇒
+ match w with [ mk_comp_num h l ⇒
+ match l with [ mk_comp_num lh ll ⇒
w16_to_recw16_aux4 h lh ll (w16_to_recw16_aux3 h lh (w16_to_recw16_aux2 h (b8_to_recb8 h))) ]].
projects / helm.git / blobdiff