X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_assembly%2Fnum%2Fbyte8.ma;h=b2ad856f0e1f0fc09b8918a19dd2273b969fff96;hb=6ee4fa0ba5f4b6601b62afd482d4f30bd2de2f91;hp=4d621bb29168702bcf9405615975fa1c715a900c;hpb=bf0cc84dcef9ae3d2145e79754bb39feb3985574;p=helm.git

diff --git a/helm/software/matita/contribs/ng_assembly/num/byte8.ma b/helm/software/matita/contribs/ng_assembly/num/byte8.ma
index 4d621bb29..b2ad856f0 100755
--- a/helm/software/matita/contribs/ng_assembly/num/byte8.ma
+++ b/helm/software/matita/contribs/ng_assembly/num/byte8.ma
@@ -16,180 +16,125 @@
 (*                          Progetto FreeScale                            *)
 (*                                                                        *)
 (*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
-(*   Ultima modifica: 05/08/2009                                          *)
+(*   Sviluppo: 2008-2010                                                  *)
 (*                                                                        *)
 (* ********************************************************************** *)
 
 include "num/exadecim.ma".
+include "num/comp_num.ma".
 include "num/bitrigesim.ma".
+include "common/nat.ma".
 
 (* **** *)
 (* BYTE *)
 (* **** *)
 
-nrecord byte8 : Type ≝
- {
- b8h: exadecim;
- b8l: exadecim
- }.
+ndefinition byte8 ≝ comp_num exadecim.
+ndefinition mk_byte8 ≝ λe1,e2.mk_comp_num exadecim e1 e2.
 
 (* \langle \rangle *)
 notation "〈x,y〉" non associative with precedence 80
- for @{ 'mk_byte8 $x $y }.
-interpretation "mk_byte8" 'mk_byte8 x y = (mk_byte8 x y).
+ for @{ mk_comp_num exadecim $x $y }.
+
+(* iteratore sui byte *)
+ndefinition forall_b8 ≝ forall_cn ? forall_ex.
 
 (* operatore = *)
-ndefinition eq_b8 ≝ λb1,b2:byte8.(eq_ex (b8h b1) (b8h b2)) ⊗ (eq_ex (b8l b1) (b8l b2)).
+ndefinition eq_b8 ≝ eq2_cn ? eq_ex.
 
 (* operatore < *)
-ndefinition lt_b8 ≝
-λb1,b2:byte8.
- (lt_ex (b8h b1) (b8h b2)) ⊕
- ((eq_ex (b8h b1) (b8h b2)) ⊗ (lt_ex (b8l b1) (b8l b2))).
+ndefinition lt_b8 ≝ ltgt_cn ? eq_ex lt_ex.
 
 (* operatore ≤ *)
-ndefinition le_b8 ≝
-λb1,b2:byte8.
- (lt_ex (b8h b1) (b8h b2)) ⊕
- ((eq_ex (b8h b1) (b8h b2)) ⊗ (le_ex (b8l b1) (b8l b2))).
+ndefinition le_b8 ≝ lege_cn ? eq_ex lt_ex le_ex.
 
 (* operatore > *)
-ndefinition gt_b8 ≝
-λb1,b2:byte8.
- (gt_ex (b8h b1) (b8h b2)) ⊕
- ((eq_ex (b8h b1) (b8h b2)) ⊗ (gt_ex (b8l b1) (b8l b2))).
+ndefinition gt_b8 ≝ ltgt_cn ? eq_ex gt_ex.
 
 (* operatore ≥ *)
-ndefinition ge_b8 ≝
-λb1,b2:byte8.
- (gt_ex (b8h b1) (b8h b2)) ⊕
- ((eq_ex (b8h b1) (b8h b2)) ⊗ (ge_ex (b8l b1) (b8l b2))).
+ndefinition ge_b8 ≝ lege_cn ? eq_ex gt_ex ge_ex.
 
 (* operatore and *)
-ndefinition and_b8 ≝
-λb1,b2:byte8.mk_byte8 (and_ex (b8h b1) (b8h b2)) (and_ex (b8l b1) (b8l b2)).
+ndefinition and_b8 ≝ fop2_cn ? and_ex.
 
 (* operatore or *)
-ndefinition or_b8 ≝
-λb1,b2:byte8.mk_byte8 (or_ex (b8h b1) (b8h b2)) (or_ex (b8l b1) (b8l b2)).
+ndefinition or_b8 ≝ fop2_cn ? or_ex.
 
 (* operatore xor *)
-ndefinition xor_b8 ≝
-λb1,b2:byte8.mk_byte8 (xor_ex (b8h b1) (b8h b2)) (xor_ex (b8l b1) (b8l b2)).
+ndefinition xor_b8 ≝ fop2_cn ? xor_ex.
+
+(* operatore Most Significant Bit *)
+ndefinition getMSB_b8 ≝ getOPH_cn ? getMSB_ex.
+ndefinition setMSB_b8 ≝ setOPH_cn ? setMSB_ex.
+
+(* operatore Least Significant Bit *)
+ndefinition getLSB_b8 ≝ getOPL_cn ? getLSB_ex.
+ndefinition setLSB_b8 ≝ setOPL_cn ? setLSB_ex.
 
 (* operatore rotazione destra con carry *)
-ndefinition rcr_b8 ≝
-λb:byte8.λc:bool.match rcr_ex (b8h b) c with
- [ pair bh' c' ⇒ match rcr_ex (b8l b) c' with
-  [ pair bl' c'' ⇒ pair … (mk_byte8 bh' bl') c'' ]]. 
+ndefinition rcr_b8 ≝ opcr_cn ? rcr_ex.
 
 (* operatore shift destro *)
-ndefinition shr_b8 ≝
-λb:byte8.match rcr_ex (b8h b) false with
- [ pair bh' c' ⇒ match rcr_ex (b8l b) c' with
-  [ pair bl' c'' ⇒ pair … (mk_byte8 bh' bl') c'' ]].
+ndefinition shr_b8 ≝ opcr_cn ? rcr_ex false.
 
 (* operatore rotazione destra *)
 ndefinition ror_b8 ≝
-λb:byte8.match rcr_ex (b8h b) false with
- [ pair bh' c' ⇒ match rcr_ex (b8l b) c' with
-  [ pair bl' c'' ⇒ match c'' with
-   [ true ⇒ mk_byte8 (or_ex x8 bh') bl'
-   | false ⇒ mk_byte8 bh' bl' ]]].
-
-(* operatore rotazione destra n-volte *)
-nlet rec ror_b8_n (b:byte8) (n:nat) on n ≝
- match n with
-  [ O ⇒ b
-  | S n' ⇒ ror_b8_n (ror_b8 b) n' ].
+λb.match shr_b8 b with
+ [ pair c b' ⇒ match c with
+  [ true ⇒ setMSB_b8 b' | false ⇒ b' ]].
 
 (* operatore rotazione sinistra con carry *)
-ndefinition rcl_b8 ≝
-λb:byte8.λc:bool.match rcl_ex (b8l b) c with
- [ pair bl' c' ⇒ match rcl_ex (b8h b) c' with
-  [ pair bh' c'' ⇒ pair … (mk_byte8 bh' bl') c'' ]]. 
+ndefinition rcl_b8 ≝ opcl_cn ? rcl_ex.
 
 (* operatore shift sinistro *)
-ndefinition shl_b8 ≝
-λb:byte8.match rcl_ex (b8l b) false with
- [ pair bl' c' ⇒ match rcl_ex (b8h b) c' with
-  [ pair bh' c'' ⇒ pair … (mk_byte8 bh' bl') c'' ]].
+ndefinition shl_b8 ≝ opcl_cn ? rcl_ex false.
 
 (* operatore rotazione sinistra *)
 ndefinition rol_b8 ≝
-λb:byte8.match rcl_ex (b8l b) false with
- [ pair bl' c' ⇒ match rcl_ex (b8h b) c' with
-  [ pair bh' c'' ⇒ match c'' with
-   [ true ⇒ mk_byte8 bh' (or_ex x1 bl')
-   | false ⇒ mk_byte8 bh' bl' ]]].
-
-(* operatore rotazione sinistra n-volte *)
-nlet rec rol_b8_n (b:byte8) (n:nat) on n ≝
- match n with
-  [ O ⇒ b
-  | S n' ⇒ rol_b8_n (rol_b8 b) n' ].
+λb.match shl_b8 b with
+ [ pair c b' ⇒ match c with
+  [ true ⇒ setLSB_b8 b' | false ⇒ b' ]].
 
 (* operatore not/complemento a 1 *)
-ndefinition not_b8 ≝
-λb:byte8.mk_byte8 (not_ex (b8h b)) (not_ex (b8l b)).
+ndefinition not_b8 ≝ fop_cn ? not_ex.
 
 (* operatore somma con data+carry → data+carry *)
-ndefinition plus_b8_dc_dc ≝
-λb1,b2:byte8.λc:bool.
- match plus_ex_dc_dc (b8l b1) (b8l b2) c with
-  [ pair l c ⇒ match plus_ex_dc_dc (b8h b1) (b8h b2) c with
-   [ pair h c' ⇒ pair … 〈h,l〉 c' ]].
+ndefinition plus_b8_dc_dc ≝ opcl2_cn ? plus_ex_dc_dc.
 
 (* operatore somma con data+carry → data *)
-ndefinition plus_b8_dc_d ≝
-λb1,b2:byte8.λc:bool.
- match plus_ex_dc_dc (b8l b1) (b8l b2) c with
-  [ pair l c ⇒ 〈plus_ex_dc_d (b8h b1) (b8h b2) c,l〉 ].
+ndefinition plus_b8_dc_d ≝ λc,b1,b2.snd … (plus_b8_dc_dc c b1 b2).
 
 (* operatore somma con data+carry → c *)
-ndefinition plus_b8_dc_c ≝
-λb1,b2:byte8.λc:bool.
- plus_ex_dc_c (b8h b1) (b8h b2) (plus_ex_dc_c (b8l b1) (b8l b2) c).
+ndefinition plus_b8_dc_c ≝ λc,b1,b2.fst … (plus_b8_dc_dc c b1 b2).
 
 (* operatore somma con data → data+carry *)
-ndefinition plus_b8_d_dc ≝
-λb1,b2:byte8.
- match plus_ex_d_dc (b8l b1) (b8l b2) with
-  [ pair l c ⇒ match plus_ex_dc_dc (b8h b1) (b8h b2) c with
-   [ pair h c' ⇒ pair … 〈h,l〉 c' ]].
+ndefinition plus_b8_d_dc ≝ opcl2_cn ? plus_ex_dc_dc false.
 
 (* operatore somma con data → data *)
-ndefinition plus_b8_d_d ≝
-λb1,b2:byte8.
- match plus_ex_d_dc (b8l b1) (b8l b2) with
-  [ pair l c ⇒ 〈plus_ex_dc_d (b8h b1) (b8h b2) c,l〉 ].
+ndefinition plus_b8_d_d ≝ λb1,b2.snd … (plus_b8_d_dc b1 b2).
 
 (* operatore somma con data → c *)
-ndefinition plus_b8_d_c ≝
-λb1,b2:byte8.
- plus_ex_dc_c (b8h b1) (b8h b2) (plus_ex_d_c (b8l b1) (b8l b2)).
-
-(* operatore Most Significant Bit *)
-ndefinition MSB_b8 ≝ λb:byte8.eq_ex x8 (and_ex x8 (b8h b)).
+ndefinition plus_b8_d_c ≝ λb1,b2.fst … (plus_b8_d_dc b1 b2).
 
 (* operatore predecessore *)
-ndefinition pred_b8 ≝
-λb:byte8.match eq_ex (b8l b) x0 with
- [ true ⇒ mk_byte8 (pred_ex (b8h b)) (pred_ex (b8l b))
- | false ⇒ mk_byte8 (b8h b) (pred_ex (b8l b)) ]. 
+ndefinition pred_b8 ≝ predsucc_cn ? (eq_ex x0) pred_ex.
 
 (* operatore successore *)
-ndefinition succ_b8 ≝
-λb:byte8.match eq_ex (b8l b) xF with
- [ true ⇒ mk_byte8 (succ_ex (b8h b)) (succ_ex (b8l b))
- | false ⇒ mk_byte8 (b8h b) (succ_ex (b8l b)) ]. 
+ndefinition succ_b8 ≝ predsucc_cn ? (eq_ex xF) succ_ex.
 
 (* operatore neg/complemento a 2 *)
 ndefinition compl_b8 ≝
-λb:byte8.match MSB_b8 b with
+λb:byte8.match getMSB_b8 b with
  [ true ⇒ succ_b8 (not_b8 b)
  | false ⇒ not_b8 (pred_b8 b) ].
 
+(* operatore x in [inf,sup] o in sup],[inf *)
+ndefinition inrange_b8 ≝
+λx,inf,sup:byte8.
+ match le_b8 inf sup with
+  [ true ⇒ and_bool | false ⇒ or_bool ]
+ (le_b8 inf x) (le_b8 x sup).
+
 (* operatore moltiplicazione senza segno: e*e=[0x00,0xE1] *)
 ndefinition mul_ex ≝
 λe1,e2:exadecim.match e1 with
@@ -286,7 +231,7 @@ ndefinition daa_b8 ≝
   (* X' = [(b16l X):0x0-0x9] X + [h=1 ? 0x06 : 0x00] + [c=1 ? 0x60 : 0x00]
           [(b16l X):0xA-0xF] X + 0x06 + [c=1 ? 0x60 : 0x00] *)
   [ true ⇒
-   let X' ≝ match (lt_ex (b8l X) xA) ⊗ (⊖h) with
+   let X' ≝ match (lt_ex (cnL ? X) xA) ⊗ (⊖h) with
     [ true ⇒ X
     | false ⇒ plus_b8_d_d X 〈x0,x6〉 ] in
    let X'' ≝ match c with
@@ -299,23 +244,37 @@ ndefinition daa_b8 ≝
           [(b16l X):0x0-0x9] X + [h=1 ? 0x06 : 0x00] + 0x60
           [(b16l X):0xA-0xF] X + 0x6 + 0x60 *) 
   | false ⇒
-   let X' ≝ match (lt_ex (b8l X) xA) ⊗ (⊖h) with
+   let X' ≝ match (lt_ex (cnL ? X) xA) ⊗ (⊖h) with
     [ true ⇒ X
     | false ⇒ plus_b8_d_d X 〈x0,x6〉 ] in
    let X'' ≝ plus_b8_d_d X' 〈x6,x0〉 in
    pair … X'' true
   ].
 
-(* operatore x in [inf,sup] *)
-ndefinition inrange_b8 ≝
-λx,inf,sup:byte8.(le_b8 inf x) ⊗ (le_b8 x sup).
-
-(* iteratore sui byte *)
-ndefinition forall_b8 ≝
- λP.
-  forall_ex (λbh.
-  forall_ex (λbl.
-   P (mk_byte8 bh bl))).
+(* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
+nlet rec div_b8_ex_aux (divd:byte8) (divs:byte8) (molt:exadecim) (q:exadecim) (n:nat) on n ≝
+ let w' ≝ plus_b8_d_d divd (compl_b8 divs) in
+  match n with
+  [ O ⇒ match le_b8 divs divd with
+   [ true ⇒ triple … (or_ex molt q) (cnL ? w') (⊖ (eq_ex (cnH ? w') x0))
+   | false ⇒ triple … q (cnL ? divd) (⊖ (eq_ex (cnH ? divd) x0)) ]
+  | S n' ⇒ match le_b8 divs divd with
+   [ true ⇒ div_b8_ex_aux w' (ror_b8 divs) (ror_ex molt) (or_ex molt q) n'
+   | false ⇒ div_b8_ex_aux divd (ror_b8 divs) (ror_ex molt) q n' ]].
+
+ndefinition div_b8_ex ≝
+λb:byte8.λe:exadecim.match eq_ex e x0 with
+(* la combinazione n/0 e' illegale, segnala solo overflow senza dare risultato *)
+ [ true ⇒ triple … xF (cnL ? b) true
+ | false ⇒ match eq_b8 b 〈x0,x0〉 with
+(* 0 diviso qualsiasi cosa diverso da 0 da' q=0 r=0 o=false *)
+  [ true ⇒ triple … 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_ex_aux b (nat_it ? rol_b8 〈x0,e〉 nat3) x8 x0 nat3 ]].
 
 (* byte ricorsivi *)
 ninductive rec_byte8 : byte8 → Type ≝
@@ -389,7 +348,8 @@ nqed.
 *)
 
 ndefinition b8_to_recb8 : Πb.rec_byte8 b ≝
-λb.match b with [ mk_byte8 h l ⇒ b8_to_recb8_aux3 h l (b8_to_recb8_aux2 h (ex_to_recex h)) ].
+λb.match b with
+ [ mk_comp_num h l ⇒ b8_to_recb8_aux3 h l (b8_to_recb8_aux2 h (ex_to_recex h)) ].
 
 (* ottali → esadecimali *)
 ndefinition b8_of_bit ≝