1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* ********************************************************************** *)
16 (* Progetto FreeScale *)
18 (* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
19 (* Ultima modifica: 05/08/2009 *)
21 (* ********************************************************************** *)
23 include "num/word16.ma".
29 nrecord word32 : Type ≝
36 notation "〈x.y〉" non associative with precedence 80
37 for @{ 'mk_word32 $x $y }.
38 interpretation "mk_word32" 'mk_word32 x y = (mk_word32 x y).
41 ndefinition eq_w32 ≝ λdw1,dw2.(eq_w16 (w32h dw1) (w32h dw2)) ⊗ (eq_w16 (w32l dw1) (w32l dw2)).
46 (lt_w16 (w32h dw1) (w32h dw2)) ⊕
47 ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (lt_w16 (w32l dw1) (w32l dw2))).
52 (lt_w16 (w32h dw1) (w32h dw2)) ⊕
53 ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (le_w16 (w32l dw1) (w32l dw2))).
58 (gt_w16 (w32h dw1) (w32h dw2)) ⊕
59 ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (gt_w16 (w32l dw1) (w32l dw2))).
64 (gt_w16 (w32h dw1) (w32h dw2)) ⊕
65 ((eq_w16 (w32h dw1) (w32h dw2)) ⊗ (ge_w16 (w32l dw1) (w32l dw2))).
69 λdw1,dw2:word32.mk_word32 (and_w16 (w32h dw1) (w32h dw2)) (and_w16 (w32l dw1) (w32l dw2)).
73 λdw1,dw2:word32.mk_word32 (or_w16 (w32h dw1) (w32h dw2)) (or_w16 (w32l dw1) (w32l dw2)).
77 λdw1,dw2:word32.mk_word32 (xor_w16 (w32h dw1) (w32h dw2)) (xor_w16 (w32l dw1) (w32l dw2)).
79 (* operatore rotazione destra con carry *)
81 λdw:word32.λc:bool.match rcr_w16 (w32h dw) c with
82 [ pair wh' c' ⇒ match rcr_w16 (w32l dw) c' with
83 [ pair wl' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
85 (* operatore shift destro *)
87 λdw:word32.match rcr_w16 (w32h dw) false with
88 [ pair wh' c' ⇒ match rcr_w16 (w32l dw) c' with
89 [ pair wl' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
91 (* operatore rotazione destra *)
93 λdw:word32.match rcr_w16 (w32h dw) false with
94 [ pair wh' c' ⇒ match rcr_w16 (w32l dw) c' with
95 [ pair wl' c'' ⇒ match c'' with
96 [ true ⇒ mk_word32 (or_w16 (mk_word16 (mk_byte8 x8 x0) (mk_byte8 x0 x0)) wh') wl'
97 | false ⇒ mk_word32 wh' wl' ]]].
99 (* operatore rotazione destra n-volte *)
100 nlet rec ror_w32_n (dw:word32) (n:nat) on n ≝
103 | S n' ⇒ ror_w32_n (ror_w32 dw) n' ].
105 (* operatore rotazione sinistra con carry *)
106 ndefinition rcl_w32 ≝
107 λdw:word32.λc:bool.match rcl_w16 (w32l dw) c with
108 [ pair wl' c' ⇒ match rcl_w16 (w32h dw) c' with
109 [ pair wh' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
111 (* operatore shift sinistro *)
112 ndefinition shl_w32 ≝
113 λdw:word32.match rcl_w16 (w32l dw) false with
114 [ pair wl' c' ⇒ match rcl_w16 (w32h dw) c' with
115 [ pair wh' c'' ⇒ pair … (mk_word32 wh' wl') c'' ]].
117 (* operatore rotazione sinistra *)
118 ndefinition rol_w32 ≝
119 λdw:word32.match rcl_w16 (w32l dw) false with
120 [ pair wl' c' ⇒ match rcl_w16 (w32h dw) c' with
121 [ pair wh' c'' ⇒ match c'' with
122 [ true ⇒ mk_word32 wh' (or_w16 (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x1)) wl')
123 | false ⇒ mk_word32 wh' wl' ]]].
125 (* operatore rotazione sinistra n-volte *)
126 nlet rec rol_w32_n (dw:word32) (n:nat) on n ≝
129 | S n' ⇒ rol_w32_n (rol_w32 dw) n' ].
131 (* operatore not/complemento a 1 *)
132 ndefinition not_w32 ≝
133 λdw:word32.mk_word32 (not_w16 (w32h dw)) (not_w16 (w32l dw)).
135 (* operatore somma con data+carry → data+carry *)
136 ndefinition plus_w32_dc_dc ≝
137 λdw1,dw2:word32.λc:bool.
138 match plus_w16_dc_dc (w32l dw1) (w32l dw2) c with
139 [ pair l c ⇒ match plus_w16_dc_dc (w32h dw1) (w32h dw2) c with
140 [ pair h c' ⇒ pair … 〈h.l〉 c' ]].
142 (* operatore somma con data+carry → data *)
143 ndefinition plus_w32_dc_d ≝
144 λdw1,dw2:word32.λc:bool.
145 match plus_w16_dc_dc (w32l dw1) (w32l dw2) c with
146 [ pair l c ⇒ 〈plus_w16_dc_d (w32h dw1) (w32h dw2) c.l〉 ].
148 (* operatore somma con data+carry → c *)
149 ndefinition plus_w32_dc_c ≝
150 λdw1,dw2:word32.λc:bool.
151 plus_w16_dc_c (w32h dw1) (w32h dw2) (plus_w16_dc_c (w32l dw1) (w32l dw2) c).
153 (* operatore somma con data → data+carry *)
154 ndefinition plus_w32_d_dc ≝
156 match plus_w16_d_dc (w32l dw1) (w32l dw2) with
157 [ pair l c ⇒ match plus_w16_dc_dc (w32h dw1) (w32h dw2) c with
158 [ pair h c' ⇒ pair … 〈h.l〉 c' ]].
160 (* operatore somma con data → data *)
161 ndefinition plus_w32_d_d ≝
163 match plus_w16_d_dc (w32l dw1) (w32l dw2) with
164 [ pair l c ⇒ 〈plus_w16_dc_d (w32h dw1) (w32h dw2) c.l〉 ].
166 (* operatore somma con data → c *)
167 ndefinition plus_w32_d_c ≝
169 plus_w16_dc_c (w32h dw1) (w32h dw2) (plus_w16_d_c (w32l dw1) (w32l dw2)).
171 (* operatore Most Significant Bit *)
172 ndefinition MSB_w32 ≝ λdw:word32.eq_ex x8 (and_ex x8 (b8h (w16h (w32h dw)))).
174 (* operatore predecessore *)
175 ndefinition pred_w32 ≝
176 λdw:word32.match eq_w16 (w32l dw) (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x0)) with
177 [ true ⇒ mk_word32 (pred_w16 (w32h dw)) (pred_w16 (w32l dw))
178 | false ⇒ mk_word32 (w32h dw) (pred_w16 (w32l dw)) ].
180 (* operatore successore *)
181 ndefinition succ_w32 ≝
182 λdw:word32.match eq_w16 (w32l dw) (mk_word16 (mk_byte8 xF xF) (mk_byte8 xF xF)) with
183 [ true ⇒ mk_word32 (succ_w16 (w32h dw)) (succ_w16 (w32l dw))
184 | false ⇒ mk_word32 (w32h dw) (succ_w16 (w32l dw)) ].
186 (* operatore neg/complemento a 2 *)
187 ndefinition compl_w32 ≝
188 λdw:word32.match MSB_w32 dw with
189 [ true ⇒ succ_w32 (not_w32 dw)
190 | false ⇒ not_w32 (pred_w32 dw) ].
193 operatore moltiplicazione senza segno: b*b=[0x00000000,0xFFFE0001]
194 ... in pratica (〈a:b〉*〈c:d〉) = (a*c)<<16+(a*d)<<8+(b*c)<<8+(b*d)
196 ndefinition mul_w16 ≝
197 λw1,w2:word16.match w1 with
198 [ mk_word16 b1h b1l ⇒ match w2 with
199 [ mk_word16 b2h b2l ⇒ match mul_b8 b1l b2l with
200 [ mk_word16 t1_h t1_l ⇒ match mul_b8 b1h b2l with
201 [ mk_word16 t2_h t2_l ⇒ match mul_b8 b2h b1l with
202 [ mk_word16 t3_h t3_l ⇒ match mul_b8 b1h b2h with
203 [ mk_word16 t4_h t4_l ⇒
206 (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〉〉
209 (* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
210 nlet rec div_w16_aux (divd:word32) (divs:word32) (molt:word16) (q:word16) (c:nat) on c ≝
211 let w' ≝ plus_w32_d_d divd (compl_w32 divs) in
213 [ O ⇒ match le_w32 divs divd with
214 [ true ⇒ triple … (or_w16 molt q) (w32l w') (⊖ (eq_w16 (w32h w') 〈〈x0,x0〉:〈x0,x0〉〉))
215 | false ⇒ triple … q (w32l divd) (⊖ (eq_w16 (w32h divd) 〈〈x0,x0〉:〈x0,x0〉〉)) ]
216 | S c' ⇒ match le_w32 divs divd with
217 [ true ⇒ div_w16_aux w' (ror_w32 divs) (ror_w16 molt) (or_w16 molt q) c'
218 | false ⇒ div_w16_aux divd (ror_w32 divs) (ror_w16 molt) q c' ]].
220 ndefinition div_w16 ≝
221 λw:word32.λb:word16.match eq_w16 b 〈〈x0,x0〉:〈x0,x0〉〉 with
223 la combinazione n/0 e' illegale, segnala solo overflow senza dare risultato
225 [ true ⇒ triple … 〈〈xF,xF〉:〈xF,xF〉〉 (w32l w) true
226 | false ⇒ match eq_w32 w 〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈x0,x0〉:〈x0,x0〉〉〉 with
227 (* 0 diviso qualsiasi cosa diverso da 0 da' q=0 r=0 o=false *)
228 [ true ⇒ triple … 〈〈x0,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 false
229 (* 1) e' una divisione sensata che produrra' overflow/risultato *)
230 (* 2) parametri: dividendo, divisore, moltiplicatore, quoziente, contatore *)
231 (* 3) ad ogni ciclo il divisore e il moltiplicatore vengono scalati di 1 a dx *)
232 (* 4) il moltiplicatore e' la quantita' aggiunta al quoziente se il divisore *)
233 (* puo' essere sottratto al dividendo *)
234 | false ⇒ div_w16_aux w (rol_w32_n 〈〈〈x0,x0〉:〈x0,x0〉〉.b〉 nat15) 〈〈x8,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 nat15 ]].
236 (* operatore x in [inf,sup] *)
237 ndefinition inrange_w32 ≝
238 λx,inf,sup:word32.(le_w32 inf x) ⊗ (le_w32 x sup).
240 (* iteratore sulle word *)
241 ndefinition forall_w32 ≝
245 P (mk_word32 bh bl ))).