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 (* ********************************************************************** *)
18 (* Cosimo Oliboni, oliboni@cs.unibo.it *)
20 (* ********************************************************************** *)
22 include "freescale/word16.ma".
24 (* *********************** *)
25 (* DEFINIZIONE DELLE DWORD *)
26 (* *********************** *)
28 record word32 : Type ≝
35 notation "〈x.y〉" non associative with precedence 80
36 for @{ 'mk_word32 $x $y }.
37 interpretation "mk_word32" 'mk_word32 x y = (mk_word32 x y).
40 definition eq_w32 ≝ λw1,w2.(eq_w16 (w32h w1) (w32h w2)) ⊗ (eq_w16 (w32l w1) (w32l w2)).
44 λw1,w2:word32.match lt_w16 (w32h w1) (w32h w2) with
46 | false ⇒ match gt_w16 (w32h w1) (w32h w2) with
48 | false ⇒ lt_w16 (w32l w1) (w32l w2) ]].
51 definition le_w32 ≝ λw1,w2:word32.(eq_w32 w1 w2) ⊕ (lt_w32 w1 w2).
54 definition gt_w32 ≝ λw1,w2:word32.⊖ (le_w32 w1 w2).
57 definition ge_w32 ≝ λw1,w2:word32.⊖ (lt_w32 w1 w2).
61 λw1,w2:word32.mk_word32 (and_w16 (w32h w1) (w32h w2)) (and_w16 (w32l w1) (w32l w2)).
65 λw1,w2:word32.mk_word32 (or_w16 (w32h w1) (w32h w2)) (or_w16 (w32l w1) (w32l w2)).
69 λw1,w2:word32.mk_word32 (xor_w16 (w32h w1) (w32h w2)) (xor_w16 (w32l w1) (w32l w2)).
71 (* operatore rotazione destra con carry *)
73 λw:word32.λc:bool.match rcr_w16 (w32h w) c with
74 [ pair wh' c' ⇒ match rcr_w16 (w32l w) c' with
75 [ pair wl' c'' ⇒ pair ?? (mk_word32 wh' wl') c'' ]].
77 (* operatore shift destro *)
79 λw:word32.match rcr_w16 (w32h w) false with
80 [ pair wh' c' ⇒ match rcr_w16 (w32l w) c' with
81 [ pair wl' c'' ⇒ pair ?? (mk_word32 wh' wl') c'' ]].
83 (* operatore rotazione destra *)
85 λw:word32.match rcr_w16 (w32h w) false with
86 [ pair wh' c' ⇒ match rcr_w16 (w32l w) c' with
87 [ pair wl' c'' ⇒ match c'' with
88 [ true ⇒ mk_word32 (or_w16 (mk_word16 (mk_byte8 x8 x0) (mk_byte8 x0 x0)) wh') wl'
89 | false ⇒ mk_word32 wh' wl' ]]].
91 (* operatore rotazione destra n-volte *)
92 let rec ror_w32_n (w:word32) (n:nat) on n ≝
95 | S n' ⇒ ror_w32_n (ror_w32 w) n' ].
97 (* operatore rotazione sinistra con carry *)
99 λw:word32.λc:bool.match rcl_w16 (w32l w) c with
100 [ pair wl' c' ⇒ match rcl_w16 (w32h w) c' with
101 [ pair wh' c'' ⇒ pair ?? (mk_word32 wh' wl') c'' ]].
103 (* operatore shift sinistro *)
105 λw:word32.match rcl_w16 (w32l w) false with
106 [ pair wl' c' ⇒ match rcl_w16 (w32h w) c' with
107 [ pair wh' c'' ⇒ pair ?? (mk_word32 wh' wl') c'' ]].
109 (* operatore rotazione sinistra *)
111 λw:word32.match rcl_w16 (w32l w) false with
112 [ pair wl' c' ⇒ match rcl_w16 (w32h w) c' with
113 [ pair wh' c'' ⇒ match c'' with
114 [ true ⇒ mk_word32 wh' (or_w16 (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x1)) wl')
115 | false ⇒ mk_word32 wh' wl' ]]].
117 (* operatore rotazione sinistra n-volte *)
118 let rec rol_w32_n (w:word32) (n:nat) on n ≝
121 | S n' ⇒ rol_w32_n (rol_w32 w) n' ].
123 (* operatore not/complemento a 1 *)
125 λw:word32.mk_word32 (not_w16 (w32h w)) (not_w16 (w32l w)).
127 (* operatore somma con carry *)
128 definition plus_w32 ≝
129 λw1,w2:word32.λc:bool.
130 match plus_w16 (w32l w1) (w32l w2) c with
131 [ pair l c' ⇒ match plus_w16 (w32h w1) (w32h w2) c' with
132 [ pair h c'' ⇒ pair ?? (mk_word32 h l) c'' ]].
134 (* operatore somma senza carry *)
135 definition plus_w32nc ≝
136 λw1,w2:word32.fst ?? (plus_w32 w1 w2 false).
138 (* operatore carry della somma *)
139 definition plus_w32c ≝
140 λw1,w2:word32.snd ?? (plus_w32 w1 w2 false).
142 (* operatore Most Significant Bit *)
143 definition MSB_w32 ≝ λw:word32.eq_ex x8 (and_ex x8 (b8h (w16h (w32h w)))).
145 (* word → naturali *)
146 definition nat_of_word32 ≝ λw:word32. (256 * 256 * (w32h w)) + (nat_of_word16 (w32l w)).
148 coercion nat_of_word32.
150 (* naturali → word *)
151 definition word32_of_nat ≝
152 λn.mk_word32 (word16_of_nat (n / (256*256))) (word16_of_nat n).
154 (* operatore predecessore *)
155 definition pred_w32 ≝
156 λw:word32.match eq_w16 (w32l w) (mk_word16 (mk_byte8 x0 x0) (mk_byte8 x0 x0)) with
157 [ true ⇒ mk_word32 (pred_w16 (w32h w)) (pred_w16 (w32l w))
158 | false ⇒ mk_word32 (w32h w) (pred_w16 (w32l w)) ].
160 (* operatore successore *)
161 definition succ_w32 ≝
162 λw:word32.match eq_w16 (w32l w) (mk_word16 (mk_byte8 xF xF) (mk_byte8 xF xF)) with
163 [ true ⇒ mk_word32 (succ_w16 (w32h w)) (succ_w16 (w32l w))
164 | false ⇒ mk_word32 (w32h w) (succ_w16 (w32l w)) ].
166 (* operatore neg/complemento a 2 *)
167 definition compl_w32 ≝
168 λw:word32.match MSB_w32 w with
169 [ true ⇒ succ_w32 (not_w32 w)
170 | false ⇒ not_w32 (pred_w32 w) ].
173 operatore moltiplicazione senza segno: b*b=[0x00000000,0xFFFE0001]
174 ... in pratica (〈a:b〉*〈c:d〉) = (a*c)<<16+(a*d)<<8+(b*c)<<8+(b*d)
177 λb1,b2:word16.match b1 with
178 [ mk_word16 b1h b1l ⇒ match b2 with
179 [ mk_word16 b2h b2l ⇒ match mul_b8 b1l b2l with
180 [ mk_word16 t1_h t1_l ⇒ match mul_b8 b1h b2l with
181 [ mk_word16 t2_h t2_l ⇒ match mul_b8 b2h b1l with
182 [ mk_word16 t3_h t3_l ⇒ match mul_b8 b1h b2h with
183 [ mk_word16 t4_h t4_l ⇒
186 (plus_w32nc 〈〈t4_h:t4_l〉.〈〈x0,x0〉:〈x0,x0〉〉〉 〈〈〈x0,x0〉:t3_h〉.〈t3_l:〈x0,x0〉〉〉) 〈〈〈x0,x0〉:t2_h〉.〈t2_l:〈x0,x0〉〉〉)〈〈〈x0,x0〉:〈x0,x0〉〉.〈t1_h:t1_l〉〉
189 (* divisione senza segno (secondo la logica delle ALU): (quoziente resto) overflow *)
191 λw:word32.λb:word16.match eq_w16 b 〈〈x0,x0〉:〈x0,x0〉〉 with
193 la combinazione n/0 e' illegale, segnala solo overflow senza dare risultato
195 [ true ⇒ tripleT ??? 〈〈xF,xF〉:〈xF,xF〉〉 (w32l w) true
196 | false ⇒ match eq_w32 w 〈〈〈x0,x0〉:〈x0,x0〉〉.〈〈x0,x0〉:〈x0,x0〉〉〉 with
197 (* 0 diviso qualsiasi cosa diverso da 0 da' q=0 r=0 o=false *)
198 [ true ⇒ tripleT ??? 〈〈x0,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 false
199 (* 1) e' una divisione sensata che produrra' overflow/risultato *)
200 (* 2) parametri: dividendo, divisore, moltiplicatore, quoziente, contatore *)
201 (* 3) ad ogni ciclo il divisore e il moltiplicatore vengono scalati di 1 a dx *)
202 (* 4) il moltiplicatore e' la quantita' aggiunta al quoziente se il divisore *)
203 (* puo' essere sottratto al dividendo *)
204 | false ⇒ let rec aux (divd:word32) (divs:word32) (molt:word16) (q:word16) (c:nat) on c ≝
205 let w' ≝ plus_w32nc divd (compl_w32 divs) in
207 [ O ⇒ match le_w32 divs divd with
208 [ true ⇒ tripleT ??? (or_w16 molt q) (w32l w') (⊖ (eq_w16 (w32h w') 〈〈x0,x0〉:〈x0,x0〉〉))
209 | false ⇒ tripleT ??? q (w32l divd) (⊖ (eq_w16 (w32h divd) 〈〈x0,x0〉:〈x0,x0〉〉)) ]
210 | S c' ⇒ match le_w32 divs divd with
211 [ true ⇒ aux w' (ror_w32 divs) (ror_w16 molt) (or_w16 molt q) c'
212 | false ⇒ aux divd (ror_w32 divs) (ror_w16 molt) q c' ]]
213 in aux w (rol_w32_n 〈〈〈x0,x0〉:〈x0,x0〉〉.b〉 15) 〈〈x8,x0〉:〈x0,x0〉〉 〈〈x0,x0〉:〈x0,x0〉〉 15 ]].
215 (* operatore x in [inf,sup] *)
216 definition in_range ≝
217 λx,inf,sup:word32.(le_w32 inf sup) ⊗ (ge_w32 x inf) ⊗ (le_w32 x sup).
219 (* iteratore sulle word *)
220 definition forall_word32 ≝
224 P (mk_word32 bh bl ))).