1 | include "RTLabs/syntax.ma". |
---|
2 | include "RTL/RTL.ma". |
---|
3 | include "common/AssocList.ma". |
---|
4 | include "common/Graphs.ma". |
---|
5 | include "common/FrontEndOps.ma". |
---|
6 | |
---|
7 | definition add_graph ≝ |
---|
8 | λl: label. |
---|
9 | λstmt. |
---|
10 | λp. |
---|
11 | let rtl_if_luniverse' ≝ rtl_if_luniverse p in |
---|
12 | let rtl_if_runiverse' ≝ rtl_if_runiverse p in |
---|
13 | let rtl_if_sig' ≝ rtl_if_sig p in |
---|
14 | let rtl_if_result' ≝ rtl_if_result p in |
---|
15 | let rtl_if_params' ≝ rtl_if_params p in |
---|
16 | let rtl_if_locals' ≝ rtl_if_locals p in |
---|
17 | let rtl_if_stacksize' ≝ rtl_if_stacksize p in |
---|
18 | let rtl_if_graph' ≝ add ? ? (rtl_if_graph p) l stmt in |
---|
19 | let rtl_if_entry' ≝ rtl_if_entry p in |
---|
20 | let rtl_if_exit' ≝ rtl_if_exit p in |
---|
21 | mk_rtl_internal_function rtl_if_luniverse' rtl_if_runiverse' rtl_if_sig' |
---|
22 | rtl_if_params' rtl_if_params' rtl_if_locals' |
---|
23 | rtl_if_stacksize' rtl_if_graph' rtl_if_entry' |
---|
24 | rtl_if_exit'. |
---|
25 | |
---|
26 | definition fresh_label: rtl_internal_function → rtl_internal_function × label ≝ |
---|
27 | λdef. |
---|
28 | let 〈lbl, new_univ〉 ≝ fresh LabelTag (rtl_if_luniverse def) in |
---|
29 | let locals ≝ rtl_if_locals def in |
---|
30 | let rtl_if_luniverse' ≝ new_univ in |
---|
31 | let rtl_if_runiverse' ≝ rtl_if_runiverse def in |
---|
32 | let rtl_if_sig' ≝ rtl_if_sig def in |
---|
33 | let rtl_if_result' ≝ rtl_if_result def in |
---|
34 | let rtl_if_params' ≝ rtl_if_params def in |
---|
35 | let rtl_if_locals' ≝ rtl_if_locals def in |
---|
36 | let rtl_if_stacksize' ≝ rtl_if_stacksize def in |
---|
37 | let rtl_if_graph' ≝ rtl_if_graph def in |
---|
38 | let rtl_if_entry' ≝ rtl_if_entry def in |
---|
39 | let rtl_if_exit' ≝ rtl_if_exit def in |
---|
40 | 〈mk_rtl_internal_function |
---|
41 | rtl_if_luniverse' rtl_if_runiverse' rtl_if_sig' rtl_if_result' |
---|
42 | rtl_if_params' rtl_if_locals' rtl_if_stacksize' rtl_if_graph' |
---|
43 | rtl_if_entry' rtl_if_exit', lbl〉. |
---|
44 | |
---|
45 | axiom register_fresh: universe RegisterTag → register. |
---|
46 | |
---|
47 | definition fresh_reg: rtl_internal_function → rtl_internal_function × register ≝ |
---|
48 | λdef. |
---|
49 | let r ≝ register_fresh (rtl_if_runiverse def) in |
---|
50 | let locals ≝ r :: rtl_if_locals def in |
---|
51 | let rtl_if_luniverse' ≝ rtl_if_luniverse def in |
---|
52 | let rtl_if_runiverse' ≝ rtl_if_runiverse def in |
---|
53 | let rtl_if_sig' ≝ rtl_if_sig def in |
---|
54 | let rtl_if_result' ≝ rtl_if_result def in |
---|
55 | let rtl_if_params' ≝ rtl_if_params def in |
---|
56 | let rtl_if_locals' ≝ locals in |
---|
57 | let rtl_if_stacksize' ≝ rtl_if_stacksize def in |
---|
58 | let rtl_if_graph' ≝ rtl_if_graph def in |
---|
59 | let rtl_if_entry' ≝ rtl_if_entry def in |
---|
60 | let rtl_if_exit' ≝ rtl_if_exit def in |
---|
61 | 〈mk_rtl_internal_function |
---|
62 | rtl_if_luniverse' rtl_if_runiverse' rtl_if_sig' rtl_if_result' |
---|
63 | rtl_if_params' rtl_if_locals' rtl_if_stacksize' rtl_if_graph' |
---|
64 | rtl_if_entry' rtl_if_exit', r〉. |
---|
65 | |
---|
66 | let rec fresh_regs (def: rtl_internal_function) (n: nat) on n ≝ |
---|
67 | match n with |
---|
68 | [ O ⇒ 〈def, [ ]〉 |
---|
69 | | S n ⇒ |
---|
70 | let 〈def, res〉 ≝ fresh_regs def n in |
---|
71 | let 〈def, r〉 ≝ fresh_reg def in |
---|
72 | 〈def, r :: res〉 |
---|
73 | ]. |
---|
74 | |
---|
75 | axiom fresh_regs_length: |
---|
76 | ∀def: rtl_internal_function. |
---|
77 | ∀n: nat. |
---|
78 | |(\snd (fresh_regs def n))| = n. |
---|
79 | |
---|
80 | definition addr_regs ≝ |
---|
81 | λregs. |
---|
82 | match regs with |
---|
83 | [ cons hd tl ⇒ |
---|
84 | match tl with |
---|
85 | [ cons hd' tl' ⇒ Some (register × register) 〈hd, hd'〉 |
---|
86 | | nil ⇒ None (register × register) |
---|
87 | ] |
---|
88 | | nil ⇒ None (register × register) (* registers are not an address *) |
---|
89 | ]. |
---|
90 | |
---|
91 | let rec register_freshes (runiverse: universe RegisterTag) (n: nat) on n ≝ |
---|
92 | match n with |
---|
93 | [ O ⇒ [ ] |
---|
94 | | S n' ⇒ register_fresh runiverse :: (register_freshes runiverse n') |
---|
95 | ]. |
---|
96 | |
---|
97 | definition choose_rest ≝ |
---|
98 | λA: Type[0]. |
---|
99 | λleft, right: list A. |
---|
100 | λprfl: 0 < |left|. |
---|
101 | λprfr: 0 < |right|. |
---|
102 | match left return λx. 0 < |x| → list A with |
---|
103 | [ nil ⇒ λnil_prf. |
---|
104 | match right return λx. 0 < |x| → list A with |
---|
105 | [ nil ⇒ λnil_nil_absrd. ? |
---|
106 | | _ ⇒ λnil_cons_prf. right |
---|
107 | ] prfr |
---|
108 | | _ ⇒ λcons_prf. right |
---|
109 | ] prfl. |
---|
110 | normalize in nil_prf; |
---|
111 | cases(not_le_Sn_O 0) |
---|
112 | #HYP |
---|
113 | cases(HYP nil_prf) |
---|
114 | qed. |
---|
115 | |
---|
116 | definition complete_regs ≝ |
---|
117 | λdef. |
---|
118 | λsrcrs1. |
---|
119 | λsrcrs2. |
---|
120 | let nb_added ≝ abs ((length ? srcrs1) - (length ? srcrs2)) in |
---|
121 | let 〈def, added_regs〉 ≝ fresh_regs def nb_added in |
---|
122 | if gtb nb_added 0 then |
---|
123 | 〈〈srcrs1, srcrs2 @ added_regs〉, added_regs〉 |
---|
124 | else |
---|
125 | 〈〈srcrs1 @ added_regs, srcrs2〉, added_regs〉. |
---|
126 | |
---|
127 | (* obvious, but proof doesn't look easy! *) |
---|
128 | axiom complete_regs_length: |
---|
129 | ∀def. |
---|
130 | ∀left. |
---|
131 | ∀right. |
---|
132 | |\fst (\fst (complete_regs def left right))| = |\snd (\fst (complete_regs def left right))|. |
---|
133 | |
---|
134 | definition size_of_sig_type ≝ |
---|
135 | λsig. |
---|
136 | match sig with |
---|
137 | [ ASTint isize sign ⇒ |
---|
138 | let isize' ≝ match isize with [ I8 ⇒ 8 | I16 ⇒ 16 | I32 ⇒ 32 ] in |
---|
139 | isize' ÷ (nat_of_bitvector ? int_size) |
---|
140 | | ASTfloat _ ⇒ ? (* dpm: not implemented *) |
---|
141 | | ASTptr rgn ⇒ nat_of_bitvector ? ptr_size |
---|
142 | ]. |
---|
143 | cases not_implemented; |
---|
144 | qed. |
---|
145 | |
---|
146 | inductive register_type: Type[0] ≝ |
---|
147 | | register_int: register → register_type |
---|
148 | | register_ptr: register → register → register_type. |
---|
149 | |
---|
150 | definition local_env ≝ BitVectorTrie (list register). |
---|
151 | |
---|
152 | definition mem_local_env ≝ |
---|
153 | λr: register. |
---|
154 | match r with |
---|
155 | [ an_identifier w ⇒ member (list register) 16 w |
---|
156 | ]. |
---|
157 | |
---|
158 | definition add_local_env ≝ |
---|
159 | λr: register. |
---|
160 | match r with |
---|
161 | [ an_identifier w ⇒ insert (list register) 16 w |
---|
162 | ]. |
---|
163 | |
---|
164 | definition find_local_env ≝ |
---|
165 | λr: register. |
---|
166 | λbvt. |
---|
167 | match r with |
---|
168 | [ an_identifier w ⇒ lookup (list register) 16 w bvt [ ] |
---|
169 | ]. |
---|
170 | |
---|
171 | definition initialize_local_env_internal ≝ |
---|
172 | λruniverse. |
---|
173 | λlenv. |
---|
174 | λr_sig. |
---|
175 | let 〈r, sig〉 ≝ r_sig in |
---|
176 | let size ≝ size_of_sig_type sig in |
---|
177 | let rs ≝ register_freshes runiverse size in |
---|
178 | add_local_env r rs lenv. |
---|
179 | |
---|
180 | definition initialize_local_env ≝ |
---|
181 | λruniverse. |
---|
182 | λregisters. |
---|
183 | λresult. |
---|
184 | let registers ≝ registers @ |
---|
185 | match result with |
---|
186 | [ None ⇒ [ ] |
---|
187 | | Some rt ⇒ [ rt ] |
---|
188 | ] |
---|
189 | in |
---|
190 | foldl ? ? (initialize_local_env_internal runiverse) (Stub …) registers. |
---|
191 | |
---|
192 | definition map_list_local_env_internal ≝ |
---|
193 | λlenv. |
---|
194 | λres. |
---|
195 | λr. |
---|
196 | res @ (find_local_env r lenv). |
---|
197 | |
---|
198 | definition map_list_local_env ≝ |
---|
199 | λlenv. |
---|
200 | λregs. |
---|
201 | foldl ? ? (map_list_local_env_internal lenv) [ ] regs. |
---|
202 | |
---|
203 | definition make_addr ≝ |
---|
204 | λA. |
---|
205 | λlst: list A. |
---|
206 | λprf: 2 ≤ length A lst. |
---|
207 | match lst return λx. 2 ≤ |x| → A × A with |
---|
208 | [ nil ⇒ λlst_nil_prf. ? |
---|
209 | | cons hd tl ⇒ λprf. |
---|
210 | match tl return λx. 1 ≤ |x| → A × A with |
---|
211 | [ nil ⇒ λtl_nil_prf. ? |
---|
212 | | cons hd' tl' ⇒ λtl_cons_prf. 〈hd, hd'〉 |
---|
213 | ] ? |
---|
214 | ] prf. |
---|
215 | [1: normalize in lst_nil_prf; |
---|
216 | cases(not_le_Sn_O 1); |
---|
217 | #HYP cases(HYP lst_nil_prf) |
---|
218 | |2: normalize in prf; |
---|
219 | @le_S_S_to_le |
---|
220 | assumption |
---|
221 | |3: normalize in tl_nil_prf; |
---|
222 | cases(not_le_Sn_O 0) |
---|
223 | #HYP cases(HYP tl_nil_prf) |
---|
224 | ] |
---|
225 | qed. |
---|
226 | |
---|
227 | definition find_and_addr ≝ |
---|
228 | λr. |
---|
229 | λlenv. |
---|
230 | make_addr ? (find_local_env r lenv). |
---|
231 | |
---|
232 | definition rtl_args ≝ |
---|
233 | λregs_list. |
---|
234 | λlenv. |
---|
235 | flatten ? (map ? ? ( |
---|
236 | λr. find_local_env r lenv) regs_list). |
---|
237 | |
---|
238 | definition change_label ≝ |
---|
239 | λlbl. |
---|
240 | λstmt: rtl_statement. |
---|
241 | match stmt with |
---|
242 | [ rtl_st_skip _ ⇒ rtl_st_skip lbl |
---|
243 | | rtl_st_cost cost_lbl _ ⇒ rtl_st_cost cost_lbl lbl |
---|
244 | | rtl_st_addr r1 r2 id _ ⇒ rtl_st_addr r1 r2 id lbl |
---|
245 | | rtl_st_stack_addr r1 r2 _ ⇒ rtl_st_stack_addr r1 r2 lbl |
---|
246 | | rtl_st_int r i _ ⇒ rtl_st_int r i lbl |
---|
247 | | rtl_st_move r1 r2 _ ⇒ rtl_st_move r1 r2 lbl |
---|
248 | | rtl_st_opaccs opaccs d s1 s2 s3 _ ⇒ rtl_st_opaccs opaccs d s1 s2 s3 lbl |
---|
249 | | rtl_st_op1 op1 d s _ ⇒ rtl_st_op1 op1 d s lbl |
---|
250 | | rtl_st_op2 op2 d s1 s2 _ ⇒ rtl_st_op2 op2 d s1 s2 lbl |
---|
251 | | rtl_st_load d a1 a2 _ ⇒ rtl_st_load d a1 a2 lbl |
---|
252 | | rtl_st_store a1 a2 s _ ⇒ rtl_st_store a1 a2 s lbl |
---|
253 | | rtl_st_call_id f a r _ ⇒ rtl_st_call_id f a r lbl |
---|
254 | | rtl_st_call_ptr f1 f2 a r _ ⇒ rtl_st_call_ptr f1 f2 a r lbl |
---|
255 | | rtl_st_tailcall_id f a ⇒ rtl_st_tailcall_id f a |
---|
256 | | rtl_st_tailcall_ptr f1 f2 a ⇒ rtl_st_tailcall_ptr f1 f2 a |
---|
257 | | rtl_st_cond r l1 l2 ⇒ rtl_st_cond r l1 l2 |
---|
258 | | rtl_st_clear_carry l ⇒ rtl_st_clear_carry lbl |
---|
259 | | rtl_st_set_carry l ⇒ rtl_st_set_carry lbl |
---|
260 | | rtl_st_return r ⇒ rtl_st_return r |
---|
261 | ]. |
---|
262 | |
---|
263 | (* Ack! Should generating a fresh label ever fail? This seems to be a side-effect |
---|
264 | of implementing everything as a bitvector, which is bounded. If we implemented |
---|
265 | labels as unbounded nats then this function will never fail. |
---|
266 | *) |
---|
267 | (* Fixed with changes to label generation. |
---|
268 | *) |
---|
269 | let rec adds_graph (stmt_list: ?) (start_lbl: label) (dest_lbl: label) (def: rtl_internal_function) ≝ |
---|
270 | match stmt_list with |
---|
271 | [ nil ⇒ def |
---|
272 | | cons hd tl ⇒ |
---|
273 | match tl with |
---|
274 | [ nil ⇒ add_graph start_lbl (change_label dest_lbl hd) def |
---|
275 | | cons hd' tl' ⇒ |
---|
276 | let 〈new_def, tmp_lbl〉 ≝ fresh_label def in |
---|
277 | let stmt ≝ change_label tmp_lbl hd in |
---|
278 | let def ≝ add_graph start_lbl stmt new_def in |
---|
279 | adds_graph tl tmp_lbl dest_lbl new_def |
---|
280 | ] |
---|
281 | ]. |
---|
282 | |
---|
283 | let rec add_translates (translate_list: ?) (start_lbl: label) (dest_lbl: label) |
---|
284 | (def: ?) on translate_list ≝ |
---|
285 | match translate_list with |
---|
286 | [ nil ⇒ def |
---|
287 | | cons hd tl ⇒ |
---|
288 | match tl with |
---|
289 | [ nil ⇒ hd start_lbl dest_lbl def |
---|
290 | | cons hd' tl' ⇒ |
---|
291 | let 〈new_def, tmp_lbl〉 ≝ fresh_label def in |
---|
292 | let applied ≝ hd start_lbl tmp_lbl new_def in |
---|
293 | add_translates tl tmp_lbl dest_lbl applied |
---|
294 | ] |
---|
295 | ]. |
---|
296 | |
---|
297 | definition translate_cst_int_internal ≝ |
---|
298 | λdest_lbl. |
---|
299 | λr. |
---|
300 | λi. |
---|
301 | rtl_st_int r i dest_lbl. |
---|
302 | |
---|
303 | axiom translate_cst: |
---|
304 | ∀cst: constant. |
---|
305 | ∀destrs: list register. |
---|
306 | ∀start_lbl: label. |
---|
307 | ∀dest_lbl: label. |
---|
308 | ∀def: rtl_internal_function. |
---|
309 | rtl_internal_function. |
---|
310 | |
---|
311 | definition translate_move_internal ≝ |
---|
312 | λstart_lbl: label. |
---|
313 | λdestr: register. |
---|
314 | λsrcr: register. |
---|
315 | rtl_st_move destr srcr start_lbl. |
---|
316 | |
---|
317 | definition translate_move ≝ |
---|
318 | λdestrs: list register. |
---|
319 | λsrcrs: list register. |
---|
320 | λstart_lbl: label. |
---|
321 | match reduce_strong register destrs srcrs with |
---|
322 | [ dp crl_crr len_proof ⇒ |
---|
323 | let commonl ≝ \fst (\fst crl_crr) in |
---|
324 | let commonr ≝ \fst (\snd crl_crr) in |
---|
325 | let restl ≝ \snd (\fst crl_crr) in |
---|
326 | let restr ≝ \snd (\snd crl_crr) in |
---|
327 | let f_common ≝ translate_move_internal start_lbl in |
---|
328 | let translate1 ≝ adds_graph (map2 … f_common commonl commonr ?) in |
---|
329 | let translate2 ≝ translate_cst (Ointconst ? (repr I8 0)) restl in (* should this be 8? *) |
---|
330 | add_translates [ translate1 ; translate2 ] start_lbl |
---|
331 | ]. |
---|
332 | @len_proof |
---|
333 | qed. |
---|
334 | |
---|
335 | let rec make |
---|
336 | (A: Type[0]) (elt: A) (n: nat) on n ≝ |
---|
337 | match n with |
---|
338 | [ O ⇒ [ ] |
---|
339 | | S n' ⇒ elt :: make A elt n' |
---|
340 | ]. |
---|
341 | |
---|
342 | lemma make_length: |
---|
343 | ∀A: Type[0]. |
---|
344 | ∀elt: A. |
---|
345 | ∀n: nat. |
---|
346 | n = length ? (make A elt n). |
---|
347 | #A #ELT #N |
---|
348 | elim N |
---|
349 | [ normalize % |
---|
350 | | #N #IH |
---|
351 | normalize <IH % |
---|
352 | ] |
---|
353 | qed. |
---|
354 | |
---|
355 | definition translate_cast_unsigned ≝ |
---|
356 | λdestrs. |
---|
357 | λstart_lbl. |
---|
358 | λdest_lbl. |
---|
359 | λdef. |
---|
360 | let 〈def, tmp_zero〉 ≝ fresh_reg def in |
---|
361 | let zeros ≝ make ? tmp_zero (length ? destrs) in |
---|
362 | add_translates [ |
---|
363 | adds_graph [ |
---|
364 | rtl_st_int tmp_zero (bitvector_of_nat ? 0) start_lbl |
---|
365 | ]; |
---|
366 | translate_move destrs zeros |
---|
367 | ] start_lbl dest_lbl def. |
---|
368 | |
---|
369 | definition translate_cast_signed ≝ |
---|
370 | λdestrs. |
---|
371 | λsrcr. |
---|
372 | λstart_lbl. |
---|
373 | λdest_lbl. |
---|
374 | λdef. |
---|
375 | let 〈def, tmp_128〉 ≝ fresh_reg def in |
---|
376 | let 〈def, tmp_255〉 ≝ fresh_reg def in |
---|
377 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
378 | let 〈def, dummy〉 ≝ fresh_reg def in |
---|
379 | let insts ≝ [ |
---|
380 | rtl_st_int tmp_128 (bitvector_of_nat ? 128) start_lbl; |
---|
381 | rtl_st_op2 And tmpr tmp_128 srcr start_lbl; |
---|
382 | rtl_st_opaccs DivuModu tmpr dummy tmpr tmp_128 start_lbl; |
---|
383 | rtl_st_int tmp_255 (bitvector_of_nat ? 255) start_lbl; |
---|
384 | rtl_st_opaccs Mul tmpr dummy tmpr tmp_255 start_lbl |
---|
385 | ] in |
---|
386 | let srcrs ≝ make ? tmpr (length ? destrs) in |
---|
387 | add_translates [ |
---|
388 | adds_graph insts; |
---|
389 | translate_move destrs srcrs |
---|
390 | ] start_lbl dest_lbl def. |
---|
391 | |
---|
392 | definition translate_cast ≝ |
---|
393 | λsrc_size. |
---|
394 | λsrc_sign. |
---|
395 | λdest_size. |
---|
396 | λdestrs. |
---|
397 | λsrcrs. |
---|
398 | match |srcrs| return λx. |srcrs| = x → ? with |
---|
399 | [ O ⇒ λzero_prf. adds_graph [ ] |
---|
400 | | S n' ⇒ λsucc_prf. |
---|
401 | if ltb dest_size src_size then |
---|
402 | translate_move destrs srcrs |
---|
403 | else |
---|
404 | match reduce_strong ? destrs srcrs with |
---|
405 | [ dp crl len_proof ⇒ |
---|
406 | let commonl ≝ \fst (\fst crl) in |
---|
407 | let commonr ≝ \fst (\snd crl) in |
---|
408 | let restl ≝ \snd (\fst crl) in |
---|
409 | let restr ≝ \snd (\snd crl) in |
---|
410 | let insts_common ≝ translate_move commonl commonr in |
---|
411 | let sign_reg ≝ last_safe ? srcrs ? in |
---|
412 | let insts_sign ≝ |
---|
413 | match src_sign with |
---|
414 | [ Unsigned ⇒ translate_cast_unsigned restl |
---|
415 | | Signed ⇒ translate_cast_signed restl sign_reg |
---|
416 | ] |
---|
417 | in |
---|
418 | add_translates [ insts_common; insts_sign ] |
---|
419 | ] |
---|
420 | ] (refl ? (|srcrs|)). |
---|
421 | >succ_prf // |
---|
422 | qed. |
---|
423 | |
---|
424 | definition translate_negint ≝ |
---|
425 | λdestrs. |
---|
426 | λsrcrs. |
---|
427 | λstart_lbl. |
---|
428 | λdest_lbl. |
---|
429 | λdef. |
---|
430 | λprf: | destrs | = | srcrs |. (* assert in caml code *) |
---|
431 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
432 | let f_cmpl ≝ λdestr. λsrcr. rtl_st_op1 Cmpl destr srcr start_lbl in |
---|
433 | let insts_cmpl ≝ map2 ? ? ? f_cmpl destrs srcrs prf in |
---|
434 | let insts_init ≝ [ |
---|
435 | rtl_st_set_carry start_lbl; |
---|
436 | rtl_st_int tmpr (zero ?) start_lbl |
---|
437 | ] in |
---|
438 | let f_add ≝ λdestr. rtl_st_op2 Addc destr destr tmpr start_lbl in |
---|
439 | let insts_add ≝ map … f_add destrs in |
---|
440 | adds_graph (insts_cmpl @ insts_init @ insts_add) start_lbl dest_lbl def. |
---|
441 | |
---|
442 | definition translate_notbool ≝ |
---|
443 | λdestrs. |
---|
444 | λsrcrs. |
---|
445 | λstart_lbl. |
---|
446 | λdest_lbl. |
---|
447 | λdef. |
---|
448 | match destrs with |
---|
449 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
450 | | cons destr destrs ⇒ |
---|
451 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
452 | let 〈def, tmp_srcrs〉 ≝ fresh_regs def (length ? srcrs) in |
---|
453 | let save_srcrs ≝ translate_move tmp_srcrs srcrs in |
---|
454 | let init_destr ≝ rtl_st_int destr (bitvector_of_nat ? 1) start_lbl in |
---|
455 | let f ≝ λtmp_srcr. [ |
---|
456 | rtl_st_clear_carry start_lbl; |
---|
457 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
458 | rtl_st_op2 Sub tmpr tmpr tmp_srcr start_lbl; |
---|
459 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
460 | rtl_st_op2 Addc tmpr tmpr tmpr start_lbl; |
---|
461 | rtl_st_op2 Xor destr destr tmpr start_lbl |
---|
462 | ] in |
---|
463 | let insts ≝ init_destr :: (flatten ? (map … f tmp_srcrs)) in |
---|
464 | let epilogue ≝ translate_cst (Ointconst I8 (bitvector_of_nat ? 0)) destrs in |
---|
465 | add_translates [ |
---|
466 | save_srcrs; adds_graph insts; epilogue |
---|
467 | ] start_lbl dest_lbl def |
---|
468 | ]. |
---|
469 | |
---|
470 | (* TODO: examine this properly. This is a change from the O'caml code due |
---|
471 | to us dropping the explicit use of a cast destination size field. We |
---|
472 | instead infer the size of the cast's destination from the context. Is |
---|
473 | this correct? |
---|
474 | *) |
---|
475 | definition translate_op1 ≝ |
---|
476 | λop1: unary_operation. |
---|
477 | λdestrs: list register. |
---|
478 | λsrcrs: list register. |
---|
479 | λprf: |destrs| = |srcrs|. |
---|
480 | λstart_lbl: label. |
---|
481 | λdest_lbl: label. |
---|
482 | λdef: rtl_internal_function. |
---|
483 | match op1 with |
---|
484 | [ Ocastint src_sign src_size ⇒ |
---|
485 | let dest_size ≝ |destrs| * 8 in |
---|
486 | let src_size ≝ bitsize_of_intsize src_size in |
---|
487 | translate_cast src_size src_sign dest_size destrs srcrs start_lbl dest_lbl def |
---|
488 | | Onegint ⇒ |
---|
489 | translate_negint destrs srcrs start_lbl dest_lbl def prf |
---|
490 | | Onotbool ⇒ |
---|
491 | translate_notbool destrs srcrs start_lbl dest_lbl def |
---|
492 | | Onotint ⇒ |
---|
493 | let f ≝ λdestr. λsrcr. rtl_st_op1 Cmpl destr srcr start_lbl in |
---|
494 | let l ≝ map2 … f destrs srcrs prf in |
---|
495 | adds_graph l start_lbl dest_lbl def |
---|
496 | | Optrofint r ⇒ |
---|
497 | translate_move destrs srcrs start_lbl dest_lbl def |
---|
498 | | Ointofptr r ⇒ |
---|
499 | translate_move destrs srcrs start_lbl dest_lbl def |
---|
500 | | Oid ⇒ |
---|
501 | translate_move destrs srcrs start_lbl dest_lbl def |
---|
502 | | _ ⇒ ? (* float operations implemented in runtime *) |
---|
503 | ]. |
---|
504 | cases not_implemented |
---|
505 | qed. |
---|
506 | |
---|
507 | definition translate_op ≝ |
---|
508 | λop. |
---|
509 | λdestrs. |
---|
510 | λsrcrs1. |
---|
511 | λsrcrs2. |
---|
512 | λstart_lbl. |
---|
513 | λdest_lbl. |
---|
514 | λdef. |
---|
515 | match reduce_strong ? srcrs1 srcrs2 with |
---|
516 | [ dp reduced first_reduced_proof ⇒ |
---|
517 | let srcrsl_common ≝ \fst (\fst reduced) in |
---|
518 | let srcrsr_common ≝ \fst (\snd reduced) in |
---|
519 | let srcrsl_rest ≝ \snd (\fst reduced) in |
---|
520 | let srcrsr_rest ≝ \snd (\snd reduced) in |
---|
521 | let srcrs_rest ≝ choose_rest ? srcrsl_rest srcrsr_rest ? ? in |
---|
522 | match reduce_strong ? destrs srcrsl_common with |
---|
523 | [ dp reduced second_reduced_proof ⇒ |
---|
524 | let destrs_common ≝ \fst (\fst reduced) in |
---|
525 | let destrs_rest ≝ \snd (\fst reduced) in |
---|
526 | match reduce_strong ? destrs_rest srcrs_rest with |
---|
527 | [ dp reduced third_reduced_proof ⇒ |
---|
528 | let destrs_cted ≝ \fst (\fst reduced) in |
---|
529 | let destrs_rest ≝ \snd (\fst reduced) in |
---|
530 | let srcrs_cted ≝ \fst (\snd reduced) in |
---|
531 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
532 | let insts_init ≝ [ |
---|
533 | rtl_st_clear_carry start_lbl; |
---|
534 | rtl_st_int tmpr (zero ?) start_lbl |
---|
535 | ] in |
---|
536 | let f_add ≝ λdestr. λsrcr1. λsrcr2. rtl_st_op2 op destr srcr1 srcr2 start_lbl in |
---|
537 | let insts_add ≝ map3 … f_add destrs_common srcrsl_common srcrsr_common ? ? in |
---|
538 | let f_add_cted ≝ λdestr. λsrcr. rtl_st_op2 op destr srcr tmpr start_lbl in |
---|
539 | let insts_add_cted ≝ map2 ? ? ? f_add_cted destrs_cted srcrs_cted ? in |
---|
540 | let f_rest ≝ λdestr. rtl_st_op2 op destr tmpr tmpr start_lbl in |
---|
541 | let insts_rest ≝ map … f_rest destrs_rest in |
---|
542 | adds_graph (insts_init @ insts_add @ insts_add_cted @ insts_rest) start_lbl dest_lbl def |
---|
543 | ] |
---|
544 | ] |
---|
545 | ]. |
---|
546 | [1: @third_reduced_proof |
---|
547 | |3: @first_reduced_proof |
---|
548 | |*: cases daemon (* TODO *) |
---|
549 | ] |
---|
550 | qed. |
---|
551 | |
---|
552 | let rec translate_mul1 |
---|
553 | (dummy: register) (tmpr: register) (destrs: list register) |
---|
554 | (srcrs1: list register) (srcr2: register) (start_lbl: label) |
---|
555 | on srcrs1 ≝ |
---|
556 | match destrs with |
---|
557 | [ nil ⇒ adds_graph [ rtl_st_skip start_lbl ] start_lbl |
---|
558 | | cons destr tl ⇒ |
---|
559 | match tl with |
---|
560 | [ nil ⇒ |
---|
561 | match srcrs1 with |
---|
562 | [ nil ⇒ |
---|
563 | adds_graph [ |
---|
564 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
565 | rtl_st_op2 Addc destr destr tmpr start_lbl |
---|
566 | ] start_lbl |
---|
567 | | cons srcr1 tl' ⇒ |
---|
568 | adds_graph [ |
---|
569 | rtl_st_opaccs Mul tmpr dummy srcr2 srcr1 start_lbl; |
---|
570 | rtl_st_op2 Addc destr destr tmpr start_lbl |
---|
571 | ] start_lbl |
---|
572 | ] |
---|
573 | | cons destr2 destrs ⇒ |
---|
574 | match srcrs1 with |
---|
575 | [ nil ⇒ |
---|
576 | add_translates [ |
---|
577 | adds_graph [ |
---|
578 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
579 | rtl_st_op2 Addc destr destr tmpr start_lbl; |
---|
580 | rtl_st_op2 Addc destr2 tmpr tmpr start_lbl |
---|
581 | ]; |
---|
582 | translate_cst (Ointconst I8 (zero ?)) destrs |
---|
583 | ] start_lbl |
---|
584 | | cons srcr1 srcrs1 ⇒ |
---|
585 | match destrs with |
---|
586 | [ nil ⇒ |
---|
587 | add_translates [ |
---|
588 | adds_graph [ |
---|
589 | rtl_st_int tmpr (zero ?) start_lbl; |
---|
590 | rtl_st_op2 Addc destr destr tmpr start_lbl; |
---|
591 | rtl_st_op2 Addc destr2 tmpr tmpr start_lbl |
---|
592 | ]; |
---|
593 | translate_cst (Ointconst I8 (zero ?)) destrs |
---|
594 | ] start_lbl |
---|
595 | | cons destr2 destrs ⇒ |
---|
596 | add_translates [ |
---|
597 | adds_graph [ |
---|
598 | rtl_st_opaccs Mul tmpr destr2 srcr2 srcr1 start_lbl; |
---|
599 | rtl_st_op2 Addc destr destr tmpr start_lbl |
---|
600 | ]; |
---|
601 | translate_mul1 dummy tmpr (destr2 :: destrs) srcrs1 srcr2 |
---|
602 | ] start_lbl |
---|
603 | ] |
---|
604 | ] |
---|
605 | ] |
---|
606 | ]. |
---|
607 | |
---|
608 | definition translate_muli ≝ |
---|
609 | λdummy: register. |
---|
610 | λtmpr: register. |
---|
611 | λdestrs: list register. |
---|
612 | λtmp_destrs: list register. |
---|
613 | λsrcrs1: list register. |
---|
614 | λdummy_lbl: label. |
---|
615 | λi: nat. |
---|
616 | λi_prf. |
---|
617 | λtranslates: list ?. |
---|
618 | λsrcr2i: register. |
---|
619 | let 〈tmp_destrs1, tmp_destrs2〉 ≝ split ? tmp_destrs i i_prf in |
---|
620 | let tmp_destrs2' ≝ |
---|
621 | match tmp_destrs2 with |
---|
622 | [ nil ⇒ [ ] |
---|
623 | | cons tmp_destr2 tmp_destrs2 ⇒ [ |
---|
624 | adds_graph [ |
---|
625 | rtl_st_clear_carry dummy_lbl; |
---|
626 | rtl_st_int tmp_destr2 (zero ?) dummy_lbl |
---|
627 | ]; |
---|
628 | translate_mul1 dummy tmpr tmp_destrs2 srcrs1 srcr2i; |
---|
629 | translate_cst (Ointconst I8 (zero ?)) tmp_destrs1; |
---|
630 | adds_graph [ |
---|
631 | rtl_st_clear_carry dummy_lbl |
---|
632 | ]; |
---|
633 | translate_op Addc destrs destrs tmp_destrs |
---|
634 | ] |
---|
635 | ] |
---|
636 | in |
---|
637 | translates @ tmp_destrs2'. |
---|
638 | |
---|
639 | axiom translate_mul: |
---|
640 | ∀destrs: list register. |
---|
641 | ∀srcrs1: list register. |
---|
642 | ∀srcrs2: list register. |
---|
643 | ∀start_lbl: label. |
---|
644 | ∀dest_lbl: label. |
---|
645 | ∀def: rtl_internal_function. |
---|
646 | rtl_internal_function. |
---|
647 | |
---|
648 | (* |
---|
649 | definition translate_mul ≝ |
---|
650 | λdestrs: list register. |
---|
651 | λsrcrs1: list register. |
---|
652 | λsrcrs2: list register. |
---|
653 | λstart_lbl: label. |
---|
654 | λdest_lbl: label. |
---|
655 | λdef: rtl_internal_function. |
---|
656 | let 〈def, dummy〉 ≝ fresh_reg def in |
---|
657 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
658 | let 〈def, tmp_destrs〉 ≝ fresh_regs def (|destrs|) in |
---|
659 | let 〈def, fresh_srcrs1〉 ≝ fresh_regs def (|srcrs1|) in |
---|
660 | let 〈def, fresh_srcrs2〉 ≝ fresh_regs def (|srcrs2|) in |
---|
661 | let insts_init ≝ [ |
---|
662 | translate_move fresh_srcrs1 srcrs1; |
---|
663 | translate_move fresh_srcrs2 srcrs2; |
---|
664 | translate_cst (Ointconst I8 (zero ?)) destrs |
---|
665 | ] |
---|
666 | in |
---|
667 | let f ≝ λi. translate_muli dummy tmpr destrs tmp_destrs ? fresh_srcrs1 start_lbl i ? in |
---|
668 | let insts_mul ≝ foldi ? ? [ ] srcrs2 in ?. [5: check insts_init. |
---|
669 | add_translates (insts_init @ insts_mul) start_lbl dest_lbl def. |
---|
670 | *) |
---|
671 | |
---|
672 | definition translate_divumodu8 ≝ |
---|
673 | λorder: bool. |
---|
674 | λdestrs: list register. |
---|
675 | λsrcr1: register. |
---|
676 | λsrcr2: register. |
---|
677 | λstart_lbl: label. |
---|
678 | λdest_lbl: label. |
---|
679 | λdef: rtl_internal_function. |
---|
680 | match destrs with |
---|
681 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
682 | | cons destr destrs ⇒ |
---|
683 | let 〈def, dummy〉 ≝ fresh_reg def in |
---|
684 | let 〈destr1, destr2〉 ≝ match order with [ true ⇒ 〈destr, dummy〉 | _ ⇒ 〈dummy, destr〉 ] in |
---|
685 | let inst_div ≝ adds_graph [ |
---|
686 | rtl_st_opaccs DivuModu destr1 destr2 srcr1 srcr2 start_lbl |
---|
687 | ] |
---|
688 | in |
---|
689 | let insts_rest ≝ translate_cst (Ointconst I8 (zero ?)) destrs in |
---|
690 | add_translates [ inst_div; insts_rest ] start_lbl dest_lbl def |
---|
691 | ]. |
---|
692 | |
---|
693 | definition translate_ne: ? → ? → ? → ? → ? → ? → rtl_internal_function ≝ |
---|
694 | λdestrs: list register. |
---|
695 | λsrcrs1: list register. |
---|
696 | λsrcrs2: list register. |
---|
697 | λstart_lbl: label. |
---|
698 | λdest_lbl: label. |
---|
699 | λdef: rtl_internal_function. |
---|
700 | match destrs with |
---|
701 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
702 | | cons destr destrs ⇒ |
---|
703 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
704 | let 〈def, tmp_zero〉 ≝ fresh_reg def in |
---|
705 | let 〈def, tmp_srcrs1〉 ≝ fresh_regs def (|srcrs1|) in |
---|
706 | let save_srcrs1 ≝ translate_move tmp_srcrs1 srcrs1 in |
---|
707 | let 〈def, tmp_srcrs2〉 ≝ fresh_regs def (|srcrs2|) in |
---|
708 | let save_srcrs2 ≝ translate_move tmp_srcrs2 srcrs2 in |
---|
709 | match reduce_strong ? tmp_srcrs1 tmp_srcrs2 with |
---|
710 | [ dp crl their_proof ⇒ |
---|
711 | let commonl ≝ \fst (\fst crl) in |
---|
712 | let commonr ≝ \fst (\snd crl) in |
---|
713 | let restl ≝ \snd (\snd crl) in |
---|
714 | let restr ≝ \snd (\snd crl) in |
---|
715 | let rest ≝ choose_rest ? restl restr ? ? in |
---|
716 | let inits ≝ [ |
---|
717 | rtl_st_int destr (zero ?) start_lbl; |
---|
718 | rtl_st_int tmp_zero (zero ?) start_lbl |
---|
719 | ] |
---|
720 | in |
---|
721 | let f_common ≝ λtmp_srcr1. λtmp_srcr2. [ |
---|
722 | rtl_st_clear_carry start_lbl; |
---|
723 | rtl_st_op2 Sub tmpr tmp_srcr1 tmp_srcr2 start_lbl; |
---|
724 | rtl_st_op2 Or destr destr tmpr start_lbl |
---|
725 | ] |
---|
726 | in |
---|
727 | let insts_common ≝ flatten ? (map2 … f_common commonl commonr ?) in |
---|
728 | let f_rest ≝ λtmp_srcr. [ |
---|
729 | rtl_st_clear_carry start_lbl; |
---|
730 | rtl_st_op2 Sub tmpr tmp_zero tmp_srcr start_lbl; |
---|
731 | rtl_st_op2 Or destr destr tmpr start_lbl |
---|
732 | ] |
---|
733 | in |
---|
734 | let insts_rest ≝ flatten ? (map ? ? f_rest rest) in |
---|
735 | let insts ≝ inits @ insts_common @ insts_rest in |
---|
736 | let epilogue ≝ translate_cst (Ointconst I8 (zero ?)) destrs in |
---|
737 | add_translates [ |
---|
738 | save_srcrs1; save_srcrs2; adds_graph insts; epilogue |
---|
739 | ] start_lbl dest_lbl def |
---|
740 | ] |
---|
741 | ]. |
---|
742 | [1: @their_proof |
---|
743 | |*: cases not_implemented (* choose rest requires non-emptiness proofs but |
---|
744 | these appear impossible to obtain, similar proof |
---|
745 | to above *) |
---|
746 | ] |
---|
747 | qed. |
---|
748 | |
---|
749 | definition translate_eq_reg ≝ |
---|
750 | λtmp_zero: register. |
---|
751 | λtmp_one: register. |
---|
752 | λtmpr1: register. |
---|
753 | λtmpr2: register. |
---|
754 | λdestr: register. |
---|
755 | λdummy_lbl: label. |
---|
756 | λsrcr12: register × register. |
---|
757 | let 〈srcr1, srcr2〉 ≝ srcr12 in |
---|
758 | [ rtl_st_clear_carry dummy_lbl; |
---|
759 | rtl_st_op2 Sub tmpr1 srcr1 srcr2 dummy_lbl; |
---|
760 | rtl_st_op2 Addc tmpr1 tmp_zero tmp_zero dummy_lbl; |
---|
761 | rtl_st_op2 Sub tmpr2 srcr2 srcr1 dummy_lbl; |
---|
762 | rtl_st_op2 Addc tmpr2 tmp_zero tmp_zero dummy_lbl; |
---|
763 | rtl_st_op2 Or tmpr1 tmpr1 tmpr2 dummy_lbl; |
---|
764 | rtl_st_op2 Xor tmpr1 tmpr1 tmp_one dummy_lbl; |
---|
765 | rtl_st_op2 And destr destr tmpr1 dummy_lbl ]. |
---|
766 | |
---|
767 | definition translate_eq_list ≝ |
---|
768 | λtmp_zero: register. |
---|
769 | λtmp_one: register. |
---|
770 | λtmpr1: register. |
---|
771 | λtmpr2: register. |
---|
772 | λdestr: register. |
---|
773 | λleq: list (register × register). |
---|
774 | λdummy_lbl: label. |
---|
775 | let f ≝ translate_eq_reg tmp_zero tmp_one tmpr1 tmpr2 destr dummy_lbl in |
---|
776 | (rtl_st_int destr (bitvector_of_nat ? 1) dummy_lbl) :: |
---|
777 | flatten ? (map ? ? f leq). |
---|
778 | |
---|
779 | definition translate_atom ≝ |
---|
780 | λtmp_zero: register. |
---|
781 | λtmp_one: register. |
---|
782 | λtmpr1: register. |
---|
783 | λtmpr2: register. |
---|
784 | λtmpr3: register. |
---|
785 | λdestr: register. |
---|
786 | λdummy_lbl: label. |
---|
787 | λleq: list (register × register). |
---|
788 | λsrcr1: register. |
---|
789 | λsrcr2: register. |
---|
790 | translate_eq_list tmp_zero tmp_one tmpr1 tmpr2 tmpr3 leq dummy_lbl @ |
---|
791 | [ rtl_st_clear_carry dummy_lbl; |
---|
792 | rtl_st_op2 Sub tmpr1 srcr1 srcr2 dummy_lbl; |
---|
793 | rtl_st_op2 Addc tmpr1 tmp_zero tmp_zero dummy_lbl; |
---|
794 | rtl_st_op2 And tmpr3 tmpr3 tmpr1 dummy_lbl; |
---|
795 | rtl_st_op2 Or destr destr tmpr3 dummy_lbl ]. |
---|
796 | |
---|
797 | definition translate_lt_main ≝ |
---|
798 | λtmp_zero: register. |
---|
799 | λtmp_one: register. |
---|
800 | λtmpr1: register. |
---|
801 | λtmpr2: register. |
---|
802 | λtmpr3: register. |
---|
803 | λdestr: register. |
---|
804 | λdummy_lbl: label. |
---|
805 | λsrcrs1: list register. |
---|
806 | λsrcrs2: list register. |
---|
807 | λproof: |srcrs1| = |srcrs2|. |
---|
808 | let f ≝ λinsts_leq. λsrcr1. λsrcr2. |
---|
809 | let 〈insts, leq〉 ≝ insts_leq in |
---|
810 | let added_insts ≝ translate_atom tmp_zero tmp_one tmpr1 tmpr2 tmpr3 destr dummy_lbl leq srcr1 srcr2 in |
---|
811 | 〈insts @ added_insts, leq @ [〈srcr1, srcr2〉]〉 |
---|
812 | in |
---|
813 | \fst (fold_left2 ? ? ? f 〈[ ], [ ]〉 srcrs1 srcrs2 proof). |
---|
814 | |
---|
815 | definition fresh_regs_strong: |
---|
816 | rtl_internal_function → ∀n: nat. Σfresh: rtl_internal_function × (list register). |\snd fresh| = n ≝ |
---|
817 | λdef. |
---|
818 | λn. |
---|
819 | fresh_regs def n. |
---|
820 | @fresh_regs_length |
---|
821 | qed. |
---|
822 | |
---|
823 | definition complete_regs_strong: |
---|
824 | rtl_internal_function → list register → list register → Σcomplete: (list register) × (list register) × (list register). |\fst (\fst complete)| = |\snd (\fst complete)| ≝ |
---|
825 | λdef. |
---|
826 | λleft. |
---|
827 | λright. |
---|
828 | complete_regs def left right. |
---|
829 | @complete_regs_length |
---|
830 | qed. |
---|
831 | |
---|
832 | definition translate_lt ≝ |
---|
833 | λdestrs: list register. |
---|
834 | λprf_destrs: lt 0 (|destrs|). |
---|
835 | λsrcrs1: list register. |
---|
836 | λsrcrs2: list register. |
---|
837 | λstart_lbl: label. |
---|
838 | λdest_lbl: label. |
---|
839 | λdef: rtl_internal_function. |
---|
840 | match destrs with |
---|
841 | [ nil ⇒ add_graph start_lbl (rtl_st_skip dest_lbl) def |
---|
842 | | _ ⇒ |
---|
843 | match fresh_regs_strong def (|destrs|) with |
---|
844 | [ dp def_tmp_destrs tmp_destrs_proof ⇒ |
---|
845 | let def ≝ \fst def_tmp_destrs in |
---|
846 | let tmp_destrs ≝ \snd def_tmp_destrs in |
---|
847 | let tmp_destr ≝ hd_safe ? tmp_destrs ? in |
---|
848 | let 〈def, tmp_zero〉 ≝ fresh_reg def in |
---|
849 | let 〈def, tmp_one〉 ≝ fresh_reg def in |
---|
850 | let 〈def, tmpr1〉 ≝ fresh_reg def in |
---|
851 | let 〈def, tmpr2〉 ≝ fresh_reg def in |
---|
852 | let 〈def, tmpr3〉 ≝ fresh_reg def in |
---|
853 | match complete_regs_strong def srcrs1 srcrs2 with |
---|
854 | [ dp srcrs12_added srcrs12_proof ⇒ |
---|
855 | let srcrs1 ≝ \fst (\fst srcrs12_added) in |
---|
856 | let srcrs2 ≝ \snd (\fst srcrs12_added) in |
---|
857 | let added ≝ \snd srcrs12_added in |
---|
858 | let srcrs1' ≝ rev ? srcrs1 in |
---|
859 | let srcrs2' ≝ rev ? srcrs2 in |
---|
860 | let insts_init ≝ [ |
---|
861 | translate_cst (Ointconst I8 (zero ?)) tmp_destrs; |
---|
862 | translate_cst (Ointconst I8 (zero ?)) added; |
---|
863 | adds_graph [ |
---|
864 | rtl_st_int tmp_zero (zero ?) start_lbl; |
---|
865 | rtl_st_int tmp_one (bitvector_of_nat ? 1) start_lbl |
---|
866 | ] |
---|
867 | ] |
---|
868 | in |
---|
869 | let insts_main ≝ |
---|
870 | translate_lt_main tmp_zero tmp_one tmpr1 tmpr2 tmpr3 tmp_destr start_lbl srcrs1' srcrs2' ? in |
---|
871 | let insts_main ≝ [ adds_graph insts_main ] in |
---|
872 | let insts_exit ≝ [ translate_move destrs tmp_destrs ] in |
---|
873 | add_translates (insts_init @ insts_main @ insts_exit) start_lbl dest_lbl def |
---|
874 | ] |
---|
875 | ] |
---|
876 | ]. |
---|
877 | [2: >tmp_destrs_proof @prf_destrs |
---|
878 | |1: normalize nodelta |
---|
879 | generalize in match srcrs12_proof |
---|
880 | #HYP >rev_length >rev_length @HYP |
---|
881 | ] |
---|
882 | qed. |
---|
883 | |
---|
884 | definition add_128_to_last ≝ |
---|
885 | λtmp_128: register. |
---|
886 | λrs. |
---|
887 | λprf: 0 < |rs|. |
---|
888 | λstart_lbl: label. |
---|
889 | match rs with |
---|
890 | [ nil ⇒ adds_graph [ ] start_lbl |
---|
891 | | _ ⇒ |
---|
892 | let r ≝ last_safe ? rs prf in |
---|
893 | adds_graph [ |
---|
894 | rtl_st_op2 Add r r tmp_128 start_lbl |
---|
895 | ] start_lbl |
---|
896 | ]. |
---|
897 | |
---|
898 | definition translate_lts ≝ |
---|
899 | λdestrs: list register. |
---|
900 | λdestrs_prf: lt 0 (|destrs|). |
---|
901 | λsrcrs1: list register. |
---|
902 | λsrcrs2: list register. |
---|
903 | λsrcrs1_lt_prf: 0 < |srcrs1|. |
---|
904 | λsrcrs2_lt_prf: 0 < |srcrs2|. |
---|
905 | λstart_lbl: label. |
---|
906 | λdest_lbl: label. |
---|
907 | λdef: rtl_internal_function. |
---|
908 | match fresh_regs_strong def (|srcrs1|) with |
---|
909 | [ dp def_tmp_srcrs1 srcrs1_prf ⇒ |
---|
910 | let def ≝ \fst def_tmp_srcrs1 in |
---|
911 | let tmp_srcrs1 ≝ \snd def_tmp_srcrs1 in |
---|
912 | match fresh_regs_strong def (|srcrs2|) with |
---|
913 | [ dp def_tmp_srcrs2 srcrs2_prf ⇒ |
---|
914 | let def ≝ \fst def_tmp_srcrs2 in |
---|
915 | let tmp_srcrs2 ≝ \snd def_tmp_srcrs2 in |
---|
916 | let 〈def, tmp_128〉 ≝ fresh_reg def in |
---|
917 | add_translates [ |
---|
918 | translate_move tmp_srcrs1 srcrs1; |
---|
919 | translate_move tmp_srcrs2 srcrs2; |
---|
920 | adds_graph [ |
---|
921 | rtl_st_int tmp_128 (bitvector_of_nat ? 128) start_lbl |
---|
922 | ]; |
---|
923 | add_128_to_last tmp_128 tmp_srcrs1 ?; |
---|
924 | add_128_to_last tmp_128 tmp_srcrs2 ?; |
---|
925 | translate_lt destrs destrs_prf tmp_srcrs1 tmp_srcrs2 |
---|
926 | ] start_lbl dest_lbl def |
---|
927 | ] |
---|
928 | ]. |
---|
929 | [1: >srcrs1_prf @srcrs1_lt_prf |
---|
930 | |2: >srcrs2_prf @srcrs2_lt_prf |
---|
931 | ] |
---|
932 | qed. |
---|
933 | |
---|
934 | definition translate_op2 ≝ |
---|
935 | λop2. |
---|
936 | λdestrs: list register. |
---|
937 | λdestrs_prf: lt 0 (|destrs|). |
---|
938 | λsrcrs1: list register. |
---|
939 | λsrcrs2: list register. |
---|
940 | λsrcrs1_prf: lt 0 (|srcrs1|). (* can this be relaxed? i think it can |
---|
941 | but we need more dep. typ. in modu/divu |
---|
942 | cases *) |
---|
943 | λsrcrs2_prf: lt 0 (|srcrs2|). |
---|
944 | λstart_lbl: label. |
---|
945 | λdest_lbl: label. |
---|
946 | λdef: rtl_internal_function. |
---|
947 | match op2 with |
---|
948 | [ Oadd ⇒ |
---|
949 | translate_op Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
950 | | Oaddp ⇒ |
---|
951 | translate_op Addc destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
952 | | Osub ⇒ |
---|
953 | translate_op Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
954 | | Osubpi ⇒ |
---|
955 | translate_op Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
956 | | Osubpp sz ⇒ |
---|
957 | translate_op Sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
958 | | Omul ⇒ |
---|
959 | translate_mul destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
960 | | Odivu ⇒ |
---|
961 | match srcrs1 return λx. 0 < |x| → rtl_internal_function with |
---|
962 | [ cons hd tl ⇒ λcons_prf. |
---|
963 | match tl with |
---|
964 | [ nil ⇒ translate_divumodu8 true destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
965 | | _ ⇒ ? (* not implemented *) |
---|
966 | ] |
---|
967 | | nil ⇒ λnil_absrd. ? |
---|
968 | ] srcrs1_prf |
---|
969 | | Omodu ⇒ |
---|
970 | match srcrs1 return λx. 0 < |x| → rtl_internal_function with |
---|
971 | [ cons hd tl ⇒ λcons_prf. |
---|
972 | match tl with |
---|
973 | [ nil ⇒ translate_divumodu8 false destrs hd (hd_safe register srcrs2 ?) start_lbl dest_lbl def |
---|
974 | | _ ⇒ ? (* not implemented *) |
---|
975 | ] |
---|
976 | | nil ⇒ λnil_absrd. ? |
---|
977 | ] srcrs1_prf |
---|
978 | | Oand ⇒ |
---|
979 | translate_op And destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
980 | | Oor ⇒ |
---|
981 | translate_op Or destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
982 | | Oxor ⇒ |
---|
983 | translate_op Xor destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
984 | | Ocmp c ⇒ |
---|
985 | match c with |
---|
986 | [ Ceq ⇒ |
---|
987 | add_translates [ |
---|
988 | translate_ne destrs srcrs1 srcrs2; |
---|
989 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
990 | ] start_lbl dest_lbl def |
---|
991 | | Cne ⇒ translate_ne destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
992 | | Clt ⇒ translate_lts destrs destrs_prf srcrs1 srcrs2 ? ? start_lbl dest_lbl def |
---|
993 | | Cgt ⇒ translate_lts destrs destrs_prf srcrs2 srcrs1 ? ? start_lbl dest_lbl def |
---|
994 | | Cle ⇒ |
---|
995 | add_translates [ |
---|
996 | translate_lts destrs destrs_prf srcrs2 srcrs1 ? ?; |
---|
997 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
998 | ] start_lbl dest_lbl def |
---|
999 | | Cge ⇒ |
---|
1000 | add_translates [ |
---|
1001 | translate_lts destrs destrs_prf srcrs1 srcrs2 ? ?; |
---|
1002 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1003 | ] start_lbl dest_lbl def |
---|
1004 | ] |
---|
1005 | | Ocmpu c ⇒ |
---|
1006 | match c with |
---|
1007 | [ Ceq ⇒ |
---|
1008 | add_translates [ |
---|
1009 | translate_ne destrs srcrs1 srcrs2; |
---|
1010 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1011 | ] start_lbl dest_lbl def |
---|
1012 | | Cne ⇒ translate_ne destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1013 | | Clt ⇒ translate_lt destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1014 | | Cgt ⇒ translate_lt destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
1015 | | Cle ⇒ |
---|
1016 | add_translates [ |
---|
1017 | translate_lt destrs destrs_prf srcrs2 srcrs1; |
---|
1018 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1019 | ] start_lbl dest_lbl def |
---|
1020 | | Cge ⇒ |
---|
1021 | add_translates [ |
---|
1022 | translate_lt destrs destrs_prf srcrs1 srcrs2; |
---|
1023 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1024 | ] start_lbl dest_lbl def |
---|
1025 | ] |
---|
1026 | | Ocmpp c ⇒ |
---|
1027 | match c with |
---|
1028 | [ Ceq ⇒ |
---|
1029 | add_translates [ |
---|
1030 | translate_ne destrs srcrs1 srcrs2; |
---|
1031 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1032 | ] start_lbl dest_lbl def |
---|
1033 | | Cne ⇒ translate_ne destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1034 | | Clt ⇒ translate_lt destrs destrs_prf srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1035 | | Cgt ⇒ translate_lt destrs destrs_prf srcrs2 srcrs1 start_lbl dest_lbl def |
---|
1036 | | Cle ⇒ |
---|
1037 | add_translates [ |
---|
1038 | translate_lt destrs destrs_prf srcrs2 srcrs1; |
---|
1039 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1040 | ] start_lbl dest_lbl def |
---|
1041 | | Cge ⇒ |
---|
1042 | add_translates [ |
---|
1043 | translate_lt destrs destrs_prf srcrs1 srcrs2; |
---|
1044 | translate_op1 Onotbool destrs destrs (refl ? (|destrs|)) |
---|
1045 | ] start_lbl dest_lbl def |
---|
1046 | ] |
---|
1047 | | _ ⇒ ? (* assert false, implemented in run time or float op *) |
---|
1048 | ]. |
---|
1049 | [ 2,6: normalize in nil_absrd; |
---|
1050 | cases(not_le_Sn_O 0) |
---|
1051 | #HYP cases(HYP nil_absrd) |
---|
1052 | | 3,7,12,17,13,15,18,19,20,21,14,16: |
---|
1053 | assumption |
---|
1054 | | *: cases not_implemented (* yes, really *) |
---|
1055 | ] |
---|
1056 | qed. |
---|
1057 | |
---|
1058 | definition translate_cond ≝ |
---|
1059 | λsrcrs: list register. |
---|
1060 | λstart_lbl: label. |
---|
1061 | λlbl_true: label. |
---|
1062 | λlbl_false: label. |
---|
1063 | λdef: rtl_internal_function. |
---|
1064 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
1065 | let 〈def, tmp_lbl〉 ≝ fresh_label def in |
---|
1066 | let init ≝ rtl_st_int tmpr (zero ?) start_lbl in |
---|
1067 | let f ≝ λsrcr. rtl_st_op2 Or tmpr tmpr srcr start_lbl in |
---|
1068 | let def ≝ adds_graph (init :: (map … f srcrs)) start_lbl tmp_lbl def in |
---|
1069 | add_graph tmp_lbl (rtl_st_cond tmpr lbl_true lbl_false) def. |
---|
1070 | |
---|
1071 | definition translate_load ≝ |
---|
1072 | λaddr. |
---|
1073 | λaddr_prf: 2 ≤ |addr|. |
---|
1074 | λdestrs: list register. |
---|
1075 | λstart_lbl: label. |
---|
1076 | λdest_lbl: label. |
---|
1077 | λdef: rtl_internal_function. |
---|
1078 | match fresh_regs_strong def (|addr|) with |
---|
1079 | [ dp def_save_addr save_addr_prf ⇒ |
---|
1080 | let def ≝ \fst def_save_addr in |
---|
1081 | let save_addr ≝ \snd def_save_addr in |
---|
1082 | match fresh_regs_strong def (|addr|) with |
---|
1083 | [ dp def_tmp_addr tmp_addr_prf ⇒ |
---|
1084 | let def ≝ \fst def_tmp_addr in |
---|
1085 | let tmp_addr ≝ \snd def_tmp_addr in |
---|
1086 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr ? tmp_addr ? in |
---|
1087 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
1088 | let insts_save_addr ≝ translate_move save_addr addr in |
---|
1089 | let f ≝ λtranslates_off. λr. |
---|
1090 | let 〈translates, off〉 ≝ translates_off in |
---|
1091 | let translates ≝ translates @ [ |
---|
1092 | adds_graph [ |
---|
1093 | rtl_st_int tmpr off start_lbl |
---|
1094 | ]; |
---|
1095 | translate_op2 Oaddp tmp_addr ? save_addr [tmpr] ? ?; |
---|
1096 | adds_graph [ |
---|
1097 | rtl_st_load r tmp_addr1 tmp_addr2 dest_lbl |
---|
1098 | ] |
---|
1099 | ] |
---|
1100 | in |
---|
1101 | let 〈carry, result〉 ≝ half_add ? off int_size in |
---|
1102 | 〈translates, result〉 |
---|
1103 | in |
---|
1104 | let 〈translates, ignore〉 ≝ foldl ? ? f 〈[ ], (zero ?)〉 destrs in |
---|
1105 | add_translates (insts_save_addr :: translates) start_lbl dest_lbl def |
---|
1106 | ] |
---|
1107 | ]. |
---|
1108 | [1: normalize // |
---|
1109 | |2: >save_addr_prf normalize |
---|
1110 | @(transitive_le 1 2 (|addr|)) // |
---|
1111 | |3: >tmp_addr_prf normalize |
---|
1112 | @(transitive_le 1 2 (|addr|)) // |
---|
1113 | |*: >tmp_addr_prf assumption |
---|
1114 | ] |
---|
1115 | qed. |
---|
1116 | |
---|
1117 | definition translate_store ≝ |
---|
1118 | λaddr. |
---|
1119 | λaddr_prf: 2 ≤ |addr|. |
---|
1120 | λsrcrs: list register. |
---|
1121 | λstart_lbl: label. |
---|
1122 | λdest_lbl: label. |
---|
1123 | λdef: rtl_internal_function. |
---|
1124 | match fresh_regs_strong def (|addr|) with |
---|
1125 | [ dp def_tmp_addr tmp_addr_prf ⇒ |
---|
1126 | let def ≝ \fst def_tmp_addr in |
---|
1127 | let tmp_addr ≝ \snd def_tmp_addr in |
---|
1128 | let 〈tmp_addr1, tmp_addr2〉 ≝ make_addr ? tmp_addr ? in |
---|
1129 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
1130 | let f ≝ λtranslate_off. λsrcr. |
---|
1131 | let 〈translates, off〉 ≝ translate_off in |
---|
1132 | let translates ≝ translates @ [ |
---|
1133 | adds_graph [ |
---|
1134 | rtl_st_int tmpr off start_lbl |
---|
1135 | ]; |
---|
1136 | translate_op2 Oaddp tmp_addr ? addr [tmpr] ? ?; |
---|
1137 | adds_graph [ |
---|
1138 | rtl_st_store tmp_addr1 tmp_addr2 srcr dest_lbl |
---|
1139 | ] |
---|
1140 | ] |
---|
1141 | in |
---|
1142 | let 〈carry, result〉 ≝ half_add ? off int_size in |
---|
1143 | 〈translates, result〉 |
---|
1144 | in |
---|
1145 | let 〈translates, ignore〉 ≝ foldl ? ? f 〈[ ], zero ?〉 srcrs in |
---|
1146 | add_translates translates start_lbl dest_lbl def |
---|
1147 | ]. |
---|
1148 | [1: normalize // |
---|
1149 | |2: >tmp_addr_prf normalize |
---|
1150 | @(transitive_le 1 2 (|addr|)) // |
---|
1151 | |3: >tmp_addr_prf normalize |
---|
1152 | @(transitive_le 1 2 (|addr|)) // |
---|
1153 | |*: >tmp_addr_prf assumption |
---|
1154 | ] |
---|
1155 | qed. |
---|
1156 | |
---|
1157 | definition translate_stmt ≝ |
---|
1158 | λlenv. |
---|
1159 | λlbl: label. |
---|
1160 | λstmt. |
---|
1161 | λdef: rtl_internal_function. |
---|
1162 | match stmt with |
---|
1163 | [ St_skip lbl' ⇒ add_graph lbl (rtl_st_skip lbl') def |
---|
1164 | | St_cost cost_lbl lbl' ⇒ add_graph lbl (rtl_st_cost cost_lbl lbl') def |
---|
1165 | | St_const destr cst lbl' ⇒ |
---|
1166 | translate_cst cst (find_local_env destr lenv) lbl lbl' def |
---|
1167 | | St_op1 op1 destr srcr lbl' ⇒ |
---|
1168 | translate_op1 op1 (find_local_env destr lenv) (find_local_env srcr lenv) ? lbl lbl' def |
---|
1169 | | St_op2 op2 destr srcr1 srcr2 lbl' ⇒ |
---|
1170 | translate_op2 op2 (find_local_env destr lenv) ? (find_local_env srcr1 lenv) (find_local_env srcr2 lenv) ? ? lbl lbl' def |
---|
1171 | | St_load ignore addr destr lbl' ⇒ |
---|
1172 | translate_load (find_local_env addr lenv) ? (find_local_env destr lenv) lbl lbl' def |
---|
1173 | | St_store ignore addr srcr lbl' ⇒ |
---|
1174 | translate_store (find_local_env addr lenv) ? (find_local_env srcr lenv) lbl lbl' def |
---|
1175 | | St_call_id f args retr lbl' ⇒ |
---|
1176 | match retr with |
---|
1177 | [ Some retr ⇒ |
---|
1178 | add_graph lbl (rtl_st_call_id f (rtl_args args lenv) (find_local_env retr lenv) lbl') def |
---|
1179 | | None ⇒ add_graph lbl (rtl_st_call_id f (rtl_args args lenv) [ ] lbl') def |
---|
1180 | ] |
---|
1181 | | St_call_ptr f args retr lbl' ⇒ |
---|
1182 | match retr with |
---|
1183 | [ None ⇒ |
---|
1184 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
---|
1185 | add_graph lbl (rtl_st_call_ptr f1 f2 (rtl_args args lenv) [ ] lbl') def |
---|
1186 | | Some retr ⇒ |
---|
1187 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
---|
1188 | add_graph lbl (rtl_st_call_ptr f1 f2 (rtl_args args lenv) (find_local_env retr lenv) lbl') def |
---|
1189 | ] |
---|
1190 | | St_tailcall_id f args ⇒ |
---|
1191 | add_graph lbl (rtl_st_tailcall_id f (rtl_args args lenv)) def |
---|
1192 | | St_tailcall_ptr f args ⇒ |
---|
1193 | let 〈f1, f2〉 ≝ find_and_addr f lenv ? in |
---|
1194 | add_graph lbl (rtl_st_tailcall_ptr f1 f2 (rtl_args args lenv)) def |
---|
1195 | | St_cond r lbl_true lbl_false ⇒ |
---|
1196 | translate_cond (find_local_env r lenv) lbl lbl_true lbl_false def |
---|
1197 | | St_jumptable r l ⇒ ? (* assert false: not implemented yet *) |
---|
1198 | | St_return r ⇒ |
---|
1199 | match r with |
---|
1200 | [ None ⇒ add_graph lbl (rtl_st_return [ ]) def |
---|
1201 | | Some r ⇒ add_graph lbl (rtl_st_return (find_local_env r lenv)) def |
---|
1202 | ] |
---|
1203 | | _ ⇒ ? |
---|
1204 | ]. |
---|
1205 | |
---|
1206 | let translate_stmt lenv lbl stmt def = match stmt with |
---|
1207 | |
---|
1208 | | RTLabs.St_skip lbl' -> |
---|
1209 | add_graph lbl (RTL.St_skip lbl') def |
---|
1210 | |
---|
1211 | | RTLabs.St_cost (cost_lbl, lbl') -> |
---|
1212 | add_graph lbl (RTL.St_cost (cost_lbl, lbl')) def |
---|
1213 | |
---|
1214 | | RTLabs.St_cst (destr, cst, lbl') -> |
---|
1215 | translate_cst cst (find_local_env destr lenv) lbl lbl' def |
---|
1216 | |
---|
1217 | | RTLabs.St_op1 (op1, destr, srcr, lbl') -> |
---|
1218 | translate_op1 op1 (find_local_env destr lenv) (find_local_env srcr lenv) |
---|
1219 | lbl lbl' def |
---|
1220 | |
---|
1221 | | RTLabs.St_op2 (op2, destr, srcr1, srcr2, lbl') -> |
---|
1222 | translate_op2 op2 (find_local_env destr lenv) |
---|
1223 | (find_local_env srcr1 lenv) (find_local_env srcr2 lenv) lbl lbl' def |
---|
1224 | |
---|
1225 | | RTLabs.St_load (_, addr, destr, lbl') -> |
---|
1226 | translate_load (find_local_env addr lenv) (find_local_env destr lenv) |
---|
1227 | lbl lbl' def |
---|
1228 | |
---|
1229 | | RTLabs.St_store (_, addr, srcr, lbl') -> |
---|
1230 | translate_store (find_local_env addr lenv) (find_local_env srcr lenv) |
---|
1231 | lbl lbl' def |
---|
1232 | |
---|
1233 | | RTLabs.St_call_id (f, args, None, _, lbl') -> |
---|
1234 | add_graph lbl (RTL.St_call_id (f, rtl_args args lenv, [], lbl')) def |
---|
1235 | |
---|
1236 | | RTLabs.St_call_id (f, args, Some retr, _, lbl') -> |
---|
1237 | add_graph lbl (RTL.St_call_id (f, rtl_args args lenv, |
---|
1238 | find_local_env retr lenv, lbl')) def |
---|
1239 | |
---|
1240 | | RTLabs.St_call_ptr (f, args, None, _, lbl') -> |
---|
1241 | let (f1, f2) = find_and_addr f lenv in |
---|
1242 | add_graph lbl (RTL.St_call_ptr (f1, f2, rtl_args args lenv, [], lbl')) def |
---|
1243 | |
---|
1244 | | RTLabs.St_call_ptr (f, args, Some retr, _, lbl') -> |
---|
1245 | let (f1, f2) = find_and_addr f lenv in |
---|
1246 | add_graph lbl |
---|
1247 | (RTL.St_call_ptr |
---|
1248 | (f1, f2, rtl_args args lenv, find_local_env retr lenv, lbl')) def |
---|
1249 | |
---|
1250 | | RTLabs.St_tailcall_id (f, args, _) -> |
---|
1251 | add_graph lbl (RTL.St_tailcall_id (f, rtl_args args lenv)) def |
---|
1252 | |
---|
1253 | | RTLabs.St_tailcall_ptr (f, args, _) -> |
---|
1254 | let (f1, f2) = find_and_addr f lenv in |
---|
1255 | add_graph lbl (RTL.St_tailcall_ptr (f1, f2, rtl_args args lenv)) def |
---|
1256 | |
---|
1257 | | RTLabs.St_cond (r, lbl_true, lbl_false) -> |
---|
1258 | translate_cond (find_local_env r lenv) lbl lbl_true lbl_false def |
---|
1259 | |
---|
1260 | | RTLabs.St_jumptable _ -> |
---|
1261 | error "Jump tables not supported yet." |
---|
1262 | |
---|
1263 | | RTLabs.St_return None -> |
---|
1264 | add_graph lbl (RTL.St_return []) def |
---|
1265 | |
---|
1266 | | RTLabs.St_return (Some r) -> |
---|
1267 | add_graph lbl (RTL.St_return (find_local_env r lenv)) def |
---|
1268 | |
---|
1269 | definition filter_and_to_list_local_env_internal ≝ |
---|
1270 | λlenv. |
---|
1271 | λl. |
---|
1272 | λr. |
---|
1273 | match assoc_list_lookup ? ? r (eq_identifier RegisterTag) lenv with |
---|
1274 | [ Some entry ⇒ |
---|
1275 | match entry with |
---|
1276 | [ register_ptr r1 r2 ⇒ (l @ [ r1; r2 ]) |
---|
1277 | | register_int r ⇒ (l @ [ r ]) |
---|
1278 | ] |
---|
1279 | | None ⇒ [ ] (* dpm: should this be none? *) |
---|
1280 | ]. |
---|
1281 | |
---|
1282 | definition filter_and_to_list_local_env ≝ |
---|
1283 | λlenv. |
---|
1284 | λregisters. |
---|
1285 | foldl ? ? (filter_and_to_list_local_env_internal lenv) [ ] registers. |
---|
1286 | |
---|
1287 | definition list_of_register_type ≝ |
---|
1288 | λrt. |
---|
1289 | match rt with |
---|
1290 | [ register_ptr r1 r2 ⇒ [ r1; r2 ] |
---|
1291 | | register_int r ⇒ [ r ] |
---|
1292 | ]. |
---|
1293 | |
---|
1294 | definition find_and_list ≝ |
---|
1295 | λr. |
---|
1296 | λlenv. |
---|
1297 | match assoc_list_lookup ? ? r (eq_identifier RegisterTag) lenv with |
---|
1298 | [ None ⇒ [ ] (* dpm: should this be none? *) |
---|
1299 | | Some lkup ⇒ list_of_register_type lkup |
---|
1300 | ]. |
---|
1301 | |
---|
1302 | definition find_and_list_args ≝ |
---|
1303 | λargs. |
---|
1304 | λlenv. |
---|
1305 | map ? ? (λr. find_and_list r lenv) args. |
---|
1306 | |
---|
1307 | (* dpm: horrendous, use dependent types. |
---|
1308 | length destr = length srcrs *) |
---|
1309 | let rec translate_move (destrs: ?) (srcrs: ?) (start_lbl: label) |
---|
1310 | (dest_lbl: label) (def: ?) ≝ |
---|
1311 | match destrs with |
---|
1312 | [ nil ⇒ |
---|
1313 | match srcrs with |
---|
1314 | [ nil ⇒ Some ? def |
---|
1315 | | cons hd tl ⇒ None ? |
---|
1316 | ] |
---|
1317 | | cons hd tl ⇒ |
---|
1318 | match srcrs with |
---|
1319 | [ nil ⇒ None ? |
---|
1320 | | cons hd' tl' ⇒ |
---|
1321 | match tl with |
---|
1322 | [ nil ⇒ |
---|
1323 | match tl' with |
---|
1324 | (* one element lists *) |
---|
1325 | [ nil ⇒ Some ? (add_graph start_lbl (rtl_st_move hd hd' dest_lbl) def) |
---|
1326 | | cons hd'' tl'' ⇒ None ? |
---|
1327 | ] |
---|
1328 | | cons hd'' tl'' ⇒ |
---|
1329 | match tl' with |
---|
1330 | [ nil ⇒ None ? |
---|
1331 | (* multielement lists *) |
---|
1332 | | cons hd''' tl''' ⇒ |
---|
1333 | let tmp_lbl ≝ fresh_label def in |
---|
1334 | match tmp_lbl with |
---|
1335 | [ None ⇒ None ? |
---|
1336 | | Some tmp_lbl ⇒ |
---|
1337 | let def ≝ add_graph start_lbl (rtl_st_move hd hd' tmp_lbl) def in |
---|
1338 | translate_move tl tl' tmp_lbl dest_lbl def |
---|
1339 | ] |
---|
1340 | ] |
---|
1341 | ] |
---|
1342 | ] |
---|
1343 | ]. |
---|
1344 | |
---|
1345 | definition extract_singleton ≝ |
---|
1346 | λA: Type[0]. |
---|
1347 | λl: list A. |
---|
1348 | match l with |
---|
1349 | [ nil ⇒ None ? |
---|
1350 | | cons hd tl ⇒ |
---|
1351 | match tl with |
---|
1352 | [ nil ⇒ Some ? hd |
---|
1353 | | cons hd tl ⇒ None ? |
---|
1354 | ] |
---|
1355 | ]. |
---|
1356 | |
---|
1357 | definition extract_pair ≝ |
---|
1358 | λA: Type[0]. |
---|
1359 | λl: list A. |
---|
1360 | match l with |
---|
1361 | [ nil ⇒ None ? |
---|
1362 | | cons hd tl ⇒ |
---|
1363 | match tl with |
---|
1364 | [ nil ⇒ None ? |
---|
1365 | | cons hd' tl' ⇒ |
---|
1366 | match tl' with |
---|
1367 | [ nil ⇒ Some ? 〈hd, hd'〉 |
---|
1368 | | cons hd'' tl'' ⇒ None ? |
---|
1369 | ] |
---|
1370 | ] |
---|
1371 | ]. |
---|
1372 | |
---|
1373 | definition translate_op1 ≝ |
---|
1374 | λop1. |
---|
1375 | λdestrs. |
---|
1376 | λsrcrs. |
---|
1377 | λstart_lbl. |
---|
1378 | λdest_lbl. |
---|
1379 | λdef. |
---|
1380 | match op1 with |
---|
1381 | [ op_cast8_unsigned ⇒ translate_move destrs srcrs start_lbl dest_lbl def |
---|
1382 | | op_cast8_signed ⇒ translate_move destrs srcrs start_lbl dest_lbl def |
---|
1383 | | op_cast16_unsigned ⇒ translate_move destrs srcrs start_lbl dest_lbl def |
---|
1384 | | op_cast16_signed ⇒ translate_move destrs srcrs start_lbl dest_lbl def |
---|
1385 | | op_neg_int ⇒ |
---|
1386 | let dstr ≝ extract_singleton ? destrs in |
---|
1387 | let srcr ≝ extract_singleton ? srcrs in |
---|
1388 | match dstr with |
---|
1389 | [ None ⇒ None ? |
---|
1390 | | Some dstr ⇒ |
---|
1391 | match srcr with |
---|
1392 | [ None ⇒ None ? |
---|
1393 | | Some srcr ⇒ |
---|
1394 | adds_graph [ |
---|
1395 | rtl_st_op1 Cmpl dstr srcr start_lbl; |
---|
1396 | rtl_st_op1 Inc dstr dstr start_lbl |
---|
1397 | ] start_lbl dest_lbl def |
---|
1398 | ] |
---|
1399 | ] |
---|
1400 | | op_not_int ⇒ |
---|
1401 | let dstr ≝ extract_singleton ? destrs in |
---|
1402 | let srcr ≝ extract_singleton ? srcrs in |
---|
1403 | match dstr with |
---|
1404 | [ None ⇒ None ? |
---|
1405 | | Some dstr ⇒ |
---|
1406 | match srcr with |
---|
1407 | [ None ⇒ None ? |
---|
1408 | | Some srcr ⇒ |
---|
1409 | adds_graph [ |
---|
1410 | rtl_st_op1 Cmpl dstr srcr start_lbl |
---|
1411 | ] start_lbl dest_lbl def |
---|
1412 | ] |
---|
1413 | ] |
---|
1414 | | op_id ⇒ translate_move destrs srcrs start_lbl dest_lbl def |
---|
1415 | | op_ptr_of_int ⇒ |
---|
1416 | let destr12 ≝ extract_pair ? destrs in |
---|
1417 | let srcr ≝ extract_singleton ? srcrs in |
---|
1418 | match destr12 with |
---|
1419 | [ None ⇒ None ? |
---|
1420 | | Some destr12 ⇒ |
---|
1421 | let 〈destr1, destr2〉 ≝ destr12 in |
---|
1422 | match srcr with |
---|
1423 | [ None ⇒ None ? |
---|
1424 | | Some srcr ⇒ |
---|
1425 | adds_graph [ |
---|
1426 | rtl_st_move destr1 srcr dest_lbl; |
---|
1427 | rtl_st_int destr2 (bitvector_of_nat ? 0) start_lbl |
---|
1428 | ] start_lbl dest_lbl def |
---|
1429 | ] |
---|
1430 | ] |
---|
1431 | | op_int_of_ptr ⇒ |
---|
1432 | let destr ≝ extract_singleton ? destrs in |
---|
1433 | match destr with |
---|
1434 | [ None ⇒ None ? |
---|
1435 | | Some destr ⇒ |
---|
1436 | match srcrs with |
---|
1437 | [ nil ⇒ None ? |
---|
1438 | | cons srcr tl ⇒ |
---|
1439 | Some ? (add_graph start_lbl (rtl_st_move destr srcr dest_lbl) def) |
---|
1440 | ] |
---|
1441 | ] |
---|
1442 | | op_not_bool ⇒ |
---|
1443 | let destr ≝ extract_singleton ? destrs in |
---|
1444 | let srcrs ≝ extract_singleton ? srcrs in |
---|
1445 | match destr with |
---|
1446 | [ None ⇒ None ? |
---|
1447 | | Some destr ⇒ |
---|
1448 | match srcrs with |
---|
1449 | [ None ⇒ None ? |
---|
1450 | | Some srcr ⇒ |
---|
1451 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
1452 | adds_graph [ |
---|
1453 | rtl_st_int tmpr (bitvector_of_nat ? 0) start_lbl; |
---|
1454 | rtl_st_clear_carry start_lbl; |
---|
1455 | rtl_st_op2 Sub destr tmpr srcr start_lbl; |
---|
1456 | rtl_st_int destr (bitvector_of_nat ? 0) dest_lbl; |
---|
1457 | rtl_st_op2 Addc destr destr destr start_lbl; |
---|
1458 | rtl_st_int tmpr (bitvector_of_nat ? 1) dest_lbl; |
---|
1459 | rtl_st_op2 Xor destr destr tmpr start_lbl |
---|
1460 | ] start_lbl dest_lbl def |
---|
1461 | ] |
---|
1462 | ] |
---|
1463 | | _ ⇒ None ? (* error float *) |
---|
1464 | ]. |
---|
1465 | |
---|
1466 | definition translate_condptr ≝ |
---|
1467 | λr1. |
---|
1468 | λr2. |
---|
1469 | λstart_lbl: label. |
---|
1470 | λlbl_true: label. |
---|
1471 | λlbl_false: label. |
---|
1472 | λdef. |
---|
1473 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
1474 | adds_graph [ |
---|
1475 | rtl_st_op2 Or tmpr r1 r2 start_lbl; |
---|
1476 | rtl_st_cond_acc tmpr lbl_true lbl_false |
---|
1477 | ] start_lbl start_lbl def. |
---|
1478 | |
---|
1479 | |
---|
1480 | |
---|
1481 | (* |
---|
1482 | let rec translate_op2 (op2: ?) (destrs: ?) (srcrs1: ?) (srcrs2: ?) |
---|
1483 | (start_lbl: label) (dest_lbl: label) (def: ?) on op2 ≝ |
---|
1484 | match op2 with |
---|
1485 | [ op_add ⇒ |
---|
1486 | let destr ≝ extract_singleton ? destrs in |
---|
1487 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1488 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1489 | match destr with |
---|
1490 | [ None ⇒ None ? |
---|
1491 | | Some destr ⇒ |
---|
1492 | match srcr1 with |
---|
1493 | [ None ⇒ None ? |
---|
1494 | | Some srcr1 ⇒ |
---|
1495 | match srcr2 with |
---|
1496 | [ None ⇒ None ? |
---|
1497 | | Some srcr2 ⇒ |
---|
1498 | adds_graph [ |
---|
1499 | rtl_st_op2 Add destr srcr1 srcr2 start_lbl |
---|
1500 | ] start_lbl dest_lbl def |
---|
1501 | ] |
---|
1502 | ] |
---|
1503 | ] |
---|
1504 | | op_sub ⇒ |
---|
1505 | let destr ≝ extract_singleton ? destrs in |
---|
1506 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1507 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1508 | match destr with |
---|
1509 | [ None ⇒ None ? |
---|
1510 | | Some destr ⇒ |
---|
1511 | match srcr1 with |
---|
1512 | [ None ⇒ None ? |
---|
1513 | | Some srcr1 ⇒ |
---|
1514 | match srcr2 with |
---|
1515 | [ None ⇒ None ? |
---|
1516 | | Some srcr2 ⇒ |
---|
1517 | adds_graph [ |
---|
1518 | rtl_st_clear_carry start_lbl; |
---|
1519 | rtl_st_op2 Sub destr srcr1 srcr2 start_lbl |
---|
1520 | ] start_lbl dest_lbl def |
---|
1521 | ] |
---|
1522 | ] |
---|
1523 | ] |
---|
1524 | | op_mul ⇒ |
---|
1525 | let destr ≝ extract_singleton ? destrs in |
---|
1526 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1527 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1528 | match destr with |
---|
1529 | [ None ⇒ None ? |
---|
1530 | | Some destr ⇒ |
---|
1531 | match srcr1 with |
---|
1532 | [ None ⇒ None ? |
---|
1533 | | Some srcr1 ⇒ |
---|
1534 | match srcr2 with |
---|
1535 | [ None ⇒ None ? |
---|
1536 | | Some srcr2 ⇒ |
---|
1537 | adds_graph [ |
---|
1538 | rtl_st_opaccs Mul destr srcr1 srcr2 start_lbl |
---|
1539 | ] start_lbl dest_lbl def |
---|
1540 | ] |
---|
1541 | ] |
---|
1542 | ] |
---|
1543 | | op_div ⇒ None ? (* signed div not supported *) |
---|
1544 | | op_divu ⇒ |
---|
1545 | let destr ≝ extract_singleton ? destrs in |
---|
1546 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1547 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1548 | match destr with |
---|
1549 | [ None ⇒ None ? |
---|
1550 | | Some destr ⇒ |
---|
1551 | match srcr1 with |
---|
1552 | [ None ⇒ None ? |
---|
1553 | | Some srcr1 ⇒ |
---|
1554 | match srcr2 with |
---|
1555 | [ None ⇒ None ? |
---|
1556 | | Some srcr2 ⇒ |
---|
1557 | adds_graph [ |
---|
1558 | rtl_st_opaccs Divu destr srcr1 srcr2 start_lbl |
---|
1559 | ] start_lbl dest_lbl def |
---|
1560 | ] |
---|
1561 | ] |
---|
1562 | ] |
---|
1563 | | op_modu ⇒ |
---|
1564 | let destr ≝ extract_singleton ? destrs in |
---|
1565 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1566 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1567 | match destr with |
---|
1568 | [ None ⇒ None ? |
---|
1569 | | Some destr ⇒ |
---|
1570 | match srcr1 with |
---|
1571 | [ None ⇒ None ? |
---|
1572 | | Some srcr1 ⇒ |
---|
1573 | match srcr2 with |
---|
1574 | [ None ⇒ None ? |
---|
1575 | | Some srcr2 ⇒ |
---|
1576 | adds_graph [ |
---|
1577 | rtl_st_opaccs Modu destr srcr1 srcr2 start_lbl |
---|
1578 | ] start_lbl dest_lbl def |
---|
1579 | ] |
---|
1580 | ] |
---|
1581 | ] |
---|
1582 | | op_mod ⇒ None ? (* signed mod not supported *) |
---|
1583 | | op_and ⇒ |
---|
1584 | let destr ≝ extract_singleton ? destrs in |
---|
1585 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1586 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1587 | match destr with |
---|
1588 | [ None ⇒ None ? |
---|
1589 | | Some destr ⇒ |
---|
1590 | match srcr1 with |
---|
1591 | [ None ⇒ None ? |
---|
1592 | | Some srcr1 ⇒ |
---|
1593 | match srcr2 with |
---|
1594 | [ None ⇒ None ? |
---|
1595 | | Some srcr2 ⇒ |
---|
1596 | adds_graph [ |
---|
1597 | rtl_st_op2 And destr srcr1 srcr2 start_lbl |
---|
1598 | ] start_lbl dest_lbl def |
---|
1599 | ] |
---|
1600 | ] |
---|
1601 | ] |
---|
1602 | | op_or ⇒ |
---|
1603 | let destr ≝ extract_singleton ? destrs in |
---|
1604 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1605 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1606 | match destr with |
---|
1607 | [ None ⇒ None ? |
---|
1608 | | Some destr ⇒ |
---|
1609 | match srcr1 with |
---|
1610 | [ None ⇒ None ? |
---|
1611 | | Some srcr1 ⇒ |
---|
1612 | match srcr2 with |
---|
1613 | [ None ⇒ None ? |
---|
1614 | | Some srcr2 ⇒ |
---|
1615 | adds_graph [ |
---|
1616 | rtl_st_op2 Or destr srcr1 srcr2 start_lbl |
---|
1617 | ] start_lbl dest_lbl def |
---|
1618 | ] |
---|
1619 | ] |
---|
1620 | ] |
---|
1621 | | op_xor ⇒ |
---|
1622 | let destr ≝ extract_singleton ? destrs in |
---|
1623 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1624 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1625 | match destr with |
---|
1626 | [ None ⇒ None ? |
---|
1627 | | Some destr ⇒ |
---|
1628 | match srcr1 with |
---|
1629 | [ None ⇒ None ? |
---|
1630 | | Some srcr1 ⇒ |
---|
1631 | match srcr2 with |
---|
1632 | [ None ⇒ None ? |
---|
1633 | | Some srcr2 ⇒ |
---|
1634 | adds_graph [ |
---|
1635 | rtl_st_op2 Xor destr srcr1 srcr2 start_lbl |
---|
1636 | ] start_lbl dest_lbl def |
---|
1637 | ] |
---|
1638 | ] |
---|
1639 | ] |
---|
1640 | | op_shru ⇒ None ? (* shifts not supported *) |
---|
1641 | | op_shr ⇒ None ? |
---|
1642 | | op_shl ⇒ None ? |
---|
1643 | | op_addf ⇒ None ? (* floats not supported *) |
---|
1644 | | op_subf ⇒ None ? |
---|
1645 | | op_mulf ⇒ None ? |
---|
1646 | | op_divf ⇒ None ? |
---|
1647 | | op_cmpf _ ⇒ None ? |
---|
1648 | | op_addp ⇒ |
---|
1649 | let destr12 ≝ extract_pair ? destrs in |
---|
1650 | match destr12 with |
---|
1651 | [ None ⇒ None ? |
---|
1652 | | Some destr12 ⇒ |
---|
1653 | let 〈destr1, destr2〉 ≝ destr12 in |
---|
1654 | let srcr12 ≝ extract_pair ? srcrs1 in |
---|
1655 | match srcr12 with |
---|
1656 | [ None ⇒ |
---|
1657 | let srcr2 ≝ extract_singleton ? srcrs1 in |
---|
1658 | match srcr2 with |
---|
1659 | [ None ⇒ None ? |
---|
1660 | | Some srcr2 ⇒ |
---|
1661 | let srcr12 ≝ extract_pair ? srcrs2 in |
---|
1662 | match srcr12 with |
---|
1663 | [ None ⇒ None ? |
---|
1664 | | Some srcr12 ⇒ |
---|
1665 | let 〈srcr11, srcr12〉 ≝ srcr12 in |
---|
1666 | let 〈def, tmpr1〉 ≝ fresh_reg def in |
---|
1667 | let 〈def, tmpr2〉 ≝ fresh_reg def in |
---|
1668 | adds_graph [ |
---|
1669 | rtl_st_op2 Add tmpr1 srcr11 srcr2 start_lbl; |
---|
1670 | rtl_st_int tmpr2 (bitvector_of_nat ? 0) start_lbl; |
---|
1671 | rtl_st_op2 Addc destr2 tmpr2 srcr12 start_lbl; |
---|
1672 | rtl_st_move destr1 tmpr1 start_lbl |
---|
1673 | ] start_lbl dest_lbl def |
---|
1674 | ] |
---|
1675 | ] |
---|
1676 | | Some srcr12 ⇒ |
---|
1677 | let 〈srcr11, srcr12〉 ≝ srcr12 in |
---|
1678 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1679 | match srcr2 with |
---|
1680 | [ None ⇒ None ? |
---|
1681 | | Some srcr2 ⇒ |
---|
1682 | let 〈def, tmpr1〉 ≝ fresh_reg def in |
---|
1683 | let 〈def, tmpr2〉 ≝ fresh_reg def in |
---|
1684 | adds_graph [ |
---|
1685 | rtl_st_op2 Add tmpr1 srcr11 srcr2 start_lbl; |
---|
1686 | rtl_st_int tmpr2 (bitvector_of_nat ? 0) start_lbl; |
---|
1687 | rtl_st_op2 Addc destr2 tmpr2 srcr12 start_lbl; |
---|
1688 | rtl_st_move destr1 tmpr1 start_lbl |
---|
1689 | ] start_lbl dest_lbl def |
---|
1690 | ] |
---|
1691 | ] |
---|
1692 | ] |
---|
1693 | | op_subp ⇒ |
---|
1694 | let destr ≝ extract_singleton ? destrs in |
---|
1695 | match destr with |
---|
1696 | [ None ⇒ |
---|
1697 | let destr12 ≝ extract_pair ? destrs in |
---|
1698 | match destr12 with |
---|
1699 | [ None ⇒ None ? |
---|
1700 | | Some destr12 ⇒ |
---|
1701 | let 〈destr1, destr2〉 ≝ destr12 in |
---|
1702 | let srcr12 ≝ extract_pair ? srcrs1 in |
---|
1703 | match srcr12 with |
---|
1704 | [ None ⇒ None ? |
---|
1705 | | Some srcr12 ⇒ |
---|
1706 | let 〈srcr11, srcr12〉 ≝ srcr12 in |
---|
1707 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
1708 | match srcr2 with |
---|
1709 | [ None ⇒ None ? |
---|
1710 | | Some srcr2 ⇒ |
---|
1711 | adds_graph [ |
---|
1712 | rtl_st_clear_carry start_lbl; |
---|
1713 | rtl_st_op2 Sub destr1 srcr11 srcr2 start_lbl; |
---|
1714 | rtl_st_int destr2 (bitvector_of_nat ? 0) start_lbl; |
---|
1715 | rtl_st_op2 Sub destr2 srcr12 destr2 start_lbl |
---|
1716 | ] start_lbl dest_lbl def |
---|
1717 | ] |
---|
1718 | ] |
---|
1719 | ] |
---|
1720 | | Some destr ⇒ |
---|
1721 | match srcrs1 with |
---|
1722 | [ nil ⇒ None ? |
---|
1723 | | cons srcr1 tl ⇒ |
---|
1724 | match srcrs2 with |
---|
1725 | [ nil ⇒ None ? |
---|
1726 | | cons srcr2 tl' ⇒ |
---|
1727 | let 〈def, tmpr1〉 ≝ fresh_reg def in |
---|
1728 | let 〈def, tmpr2〉 ≝ fresh_reg def in |
---|
1729 | adds_graph [ |
---|
1730 | rtl_st_op1 Cmpl tmpr1 srcr2 start_lbl; |
---|
1731 | rtl_st_int tmpr2 (bitvector_of_nat ? 1) start_lbl; |
---|
1732 | rtl_st_op2 Add tmpr1 tmpr1 tmpr2 start_lbl; |
---|
1733 | rtl_st_op2 Add destr srcr1 tmpr1 start_lbl |
---|
1734 | ] start_lbl dest_lbl def |
---|
1735 | ] |
---|
1736 | ] |
---|
1737 | ] |
---|
1738 | | op_cmp cmp ⇒ |
---|
1739 | match cmp with |
---|
1740 | [ Compare_Equal ⇒ |
---|
1741 | add_translates [ |
---|
1742 | translate_op2 op_sub destrs srcrs1 srcrs2; |
---|
1743 | translate_op1 op_not_bool destrs destrs |
---|
1744 | ] start_lbl dest_lbl def |
---|
1745 | | Compare_NotEqual ⇒ |
---|
1746 | translate_op2 op_sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1747 | | _ ⇒ None ? |
---|
1748 | ] |
---|
1749 | | op_cmpu cmp ⇒ |
---|
1750 | match cmp with |
---|
1751 | [ Compare_Equal ⇒ |
---|
1752 | add_translates [ |
---|
1753 | translate_op2 op_sub destrs srcrs1 srcrs2; |
---|
1754 | translate_op1 op_not_bool destrs destrs |
---|
1755 | ] start_lbl dest_lbl def |
---|
1756 | | Compare_NotEqual ⇒ |
---|
1757 | translate_op2 op_sub destrs srcrs1 srcrs2 start_lbl dest_lbl def |
---|
1758 | | Compare |
---|
1759 | | _ ⇒ None ? |
---|
1760 | ] |
---|
1761 | | _ ⇒ ? |
---|
1762 | ]. |
---|
1763 | |
---|
1764 | | AST.Op_cmpu AST.Cmp_lt, [destr], [srcr1], [srcr2] -> |
---|
1765 | let (def, tmpr) = fresh_reg def in |
---|
1766 | adds_graph |
---|
1767 | [RTL.St_clear_carry start_lbl ; |
---|
1768 | RTL.St_op2 (I8051.Sub, destr, srcr1, srcr2, start_lbl) ; |
---|
1769 | RTL.St_int (destr, 0, start_lbl) ; |
---|
1770 | RTL.St_op2 (I8051.Addc, destr, destr, destr, start_lbl)] |
---|
1771 | start_lbl dest_lbl def |
---|
1772 | |
---|
1773 | | AST.Op_cmpu AST.Cmp_gt, _, _, _ -> |
---|
1774 | translate_op2 (AST.Op_cmpu AST.Cmp_lt) |
---|
1775 | destrs srcrs2 srcrs1 start_lbl dest_lbl def |
---|
1776 | |
---|
1777 | | AST.Op_cmpu AST.Cmp_le, _, _, _ -> |
---|
1778 | add_translates |
---|
1779 | [translate_op2 (AST.Op_cmpu AST.Cmp_gt) destrs srcrs1 srcrs2 ; |
---|
1780 | translate_op1 AST.Op_notbool destrs destrs] |
---|
1781 | start_lbl dest_lbl def |
---|
1782 | |
---|
1783 | | AST.Op_cmpu AST.Cmp_ge, _, _, _ -> |
---|
1784 | add_translates |
---|
1785 | [translate_op2 (AST.Op_cmpu AST.Cmp_lt) destrs srcrs1 srcrs2 ; |
---|
1786 | translate_op1 AST.Op_notbool destrs destrs] |
---|
1787 | start_lbl dest_lbl def |
---|
1788 | |
---|
1789 | | AST.Op_cmp cmp, _, _, _ -> |
---|
1790 | let (def, tmprs1) = fresh_regs def (List.length srcrs1) in |
---|
1791 | let (def, tmprs2) = fresh_regs def (List.length srcrs2) in |
---|
1792 | add_translates |
---|
1793 | [translate_cst (AST.Cst_int 128) tmprs1 ; |
---|
1794 | translate_cst (AST.Cst_int 128) tmprs2 ; |
---|
1795 | translate_op2 AST.Op_add tmprs1 srcrs1 tmprs1 ; |
---|
1796 | translate_op2 AST.Op_add tmprs2 srcrs2 tmprs2 ; |
---|
1797 | translate_op2 (AST.Op_cmpu cmp) destrs tmprs1 tmprs2] |
---|
1798 | start_lbl dest_lbl def |
---|
1799 | |
---|
1800 | | AST.Op_cmpp AST.Cmp_eq, [destr], [srcr11 ; srcr12], [srcr21 ; srcr22] -> |
---|
1801 | let (def, tmpr) = fresh_reg def in |
---|
1802 | add_translates |
---|
1803 | [translate_op2 (AST.Op_cmpu AST.Cmp_ne) [tmpr] [srcr11] [srcr21] ; |
---|
1804 | translate_op2 (AST.Op_cmpu AST.Cmp_ne) [destr] [srcr21] [srcr22] ; |
---|
1805 | translate_op2 AST.Op_or [destr] [destr] [tmpr] ; |
---|
1806 | adds_graph [RTL.St_int (tmpr, 1, start_lbl)] ; |
---|
1807 | translate_op2 AST.Op_xor [destr] [destr] [tmpr]] |
---|
1808 | start_lbl dest_lbl def |
---|
1809 | |
---|
1810 | | AST.Op_cmpp AST.Cmp_lt, [destr], [srcr11 ; srcr12], [srcr21 ; srcr22] -> |
---|
1811 | let (def, tmpr1) = fresh_reg def in |
---|
1812 | let (def, tmpr2) = fresh_reg def in |
---|
1813 | add_translates |
---|
1814 | [translate_op2 (AST.Op_cmpu AST.Cmp_lt) [tmpr1] [srcr12] [srcr22] ; |
---|
1815 | translate_op2 (AST.Op_cmpu AST.Cmp_eq) [tmpr2] [srcr12] [srcr22] ; |
---|
1816 | translate_op2 (AST.Op_cmpu AST.Cmp_lt) [destr] [srcr11] [srcr21] ; |
---|
1817 | translate_op2 AST.Op_and [tmpr2] [tmpr2] [destr] ; |
---|
1818 | translate_op2 AST.Op_or [destr] [tmpr1] [tmpr2]] |
---|
1819 | start_lbl dest_lbl def |
---|
1820 | |
---|
1821 | | AST.Op_cmpp AST.Cmp_gt, _, _, _ -> |
---|
1822 | translate_op2 (AST.Op_cmpp AST.Cmp_lt) |
---|
1823 | destrs srcrs2 srcrs1 start_lbl dest_lbl def |
---|
1824 | |
---|
1825 | | AST.Op_cmpp AST.Cmp_le, _, _, _ -> |
---|
1826 | add_translates |
---|
1827 | [translate_op2 (AST.Op_cmpp AST.Cmp_gt) destrs srcrs1 srcrs2 ; |
---|
1828 | translate_op1 AST.Op_notbool destrs destrs] |
---|
1829 | start_lbl dest_lbl def |
---|
1830 | |
---|
1831 | | AST.Op_cmpp AST.Cmp_ge, _, _, _ -> |
---|
1832 | add_translates |
---|
1833 | [translate_op2 (AST.Op_cmpp AST.Cmp_lt) destrs srcrs1 srcrs2 ; |
---|
1834 | translate_op1 AST.Op_notbool destrs destrs] |
---|
1835 | start_lbl dest_lbl def |
---|
1836 | |
---|
1837 | | _ -> assert false (* wrong number of arguments *) |
---|
1838 | *) |
---|
1839 | |
---|
1840 | definition translate_condcst ≝ |
---|
1841 | λcst. |
---|
1842 | λstart_lbl: label. |
---|
1843 | λlbl_true: label. |
---|
1844 | λlbl_false: label. |
---|
1845 | λdef. |
---|
1846 | match cst with |
---|
1847 | [ cast_int i ⇒ |
---|
1848 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
1849 | adds_graph [ |
---|
1850 | rtl_st_int tmpr i start_lbl; |
---|
1851 | rtl_st_cond_acc tmpr lbl_true lbl_false |
---|
1852 | ] start_lbl start_lbl def |
---|
1853 | | cast_addr_symbol x ⇒ |
---|
1854 | let 〈def, r1〉 ≝ fresh_reg def in |
---|
1855 | let 〈def, r2〉 ≝ fresh_reg def in |
---|
1856 | let lbl ≝ fresh_label def in |
---|
1857 | match lbl with |
---|
1858 | [ None ⇒ None ? |
---|
1859 | | Some lbl ⇒ |
---|
1860 | let def ≝ add_graph start_lbl (rtl_st_addr r1 r2 x lbl) def in |
---|
1861 | translate_condptr r1 r2 lbl lbl_true lbl_false def |
---|
1862 | ] |
---|
1863 | | cast_stack_offset off ⇒ |
---|
1864 | let 〈def, r1〉 ≝ fresh_reg def in |
---|
1865 | let 〈def, r2〉 ≝ fresh_reg def in |
---|
1866 | let tmp_lbl ≝ fresh_label def in |
---|
1867 | match tmp_lbl with |
---|
1868 | [ None ⇒ None ? |
---|
1869 | | Some tmp_lbl ⇒ |
---|
1870 | let def ≝ translate_cst (cast_stack_offset off) [r1; r2] start_lbl tmp_lbl def in |
---|
1871 | match def with |
---|
1872 | [ None ⇒ None ? |
---|
1873 | | Some def ⇒ translate_condptr r1 r2 tmp_lbl lbl_true lbl_false def |
---|
1874 | ] |
---|
1875 | ] |
---|
1876 | | cast_float f ⇒ None ? (* error_float *) |
---|
1877 | ]. |
---|
1878 | |
---|
1879 | definition size_of_op1_ret ≝ |
---|
1880 | λop. |
---|
1881 | match op with |
---|
1882 | [ op_cast8_unsigned ⇒ Some ? 1 |
---|
1883 | | op_cast8_signed ⇒ Some ? 1 |
---|
1884 | | op_cast16_unsigned ⇒ Some ? 1 |
---|
1885 | | op_cast16_signed ⇒ Some ? 1 |
---|
1886 | | op_neg_int ⇒ Some ? 1 |
---|
1887 | | op_not_int ⇒ Some ? 1 |
---|
1888 | | op_int_of_ptr ⇒ Some ? 1 |
---|
1889 | | op_ptr_of_int ⇒ Some ? 2 |
---|
1890 | | op_id ⇒ None ? (* invalid_argument *) |
---|
1891 | | _ ⇒ None ? (* error_float *) |
---|
1892 | ]. |
---|
1893 | |
---|
1894 | definition translate_cond1 ≝ |
---|
1895 | λop1. |
---|
1896 | λsrcrs: list register. |
---|
1897 | λstart_lbl: label. |
---|
1898 | λlbl_true: label. |
---|
1899 | λlbl_false: label. |
---|
1900 | λdef. |
---|
1901 | match op1 with |
---|
1902 | [ op_id ⇒ |
---|
1903 | let srcr ≝ extract_singleton ? srcrs in |
---|
1904 | match srcr with |
---|
1905 | [ None ⇒ |
---|
1906 | let srcr12 ≝ extract_pair ? srcrs in |
---|
1907 | match srcr12 with |
---|
1908 | [ None ⇒ None ? |
---|
1909 | | Some srcr12 ⇒ |
---|
1910 | let 〈srcr1, srcr2〉 ≝ srcr12 in |
---|
1911 | translate_condptr srcr1 srcr2 start_lbl lbl_true lbl_false def |
---|
1912 | ] |
---|
1913 | | Some srcr ⇒ |
---|
1914 | adds_graph [ |
---|
1915 | rtl_st_cond_acc srcr lbl_true lbl_false |
---|
1916 | ] start_lbl start_lbl def |
---|
1917 | ] |
---|
1918 | | _ ⇒ |
---|
1919 | let size ≝ size_of_op1_ret op1 in |
---|
1920 | match size with |
---|
1921 | [ None ⇒ None ? |
---|
1922 | | Some size ⇒ |
---|
1923 | let 〈def, destrs〉 ≝ fresh_regs def size in |
---|
1924 | let lbl ≝ fresh_label def in |
---|
1925 | match lbl with |
---|
1926 | [ None ⇒ None ? |
---|
1927 | | Some lbl ⇒ |
---|
1928 | let def ≝ translate_op1 op1 destrs srcrs start_lbl lbl def in |
---|
1929 | match def with |
---|
1930 | [ None ⇒ None ? |
---|
1931 | | Some def ⇒ |
---|
1932 | let destr ≝ extract_singleton ? destrs in |
---|
1933 | match destr with |
---|
1934 | [ None ⇒ |
---|
1935 | let destr12 ≝ extract_pair ? destrs in |
---|
1936 | match destr12 with |
---|
1937 | [ None ⇒ None ? |
---|
1938 | | Some destr12 ⇒ |
---|
1939 | let 〈destr1, destr2〉 ≝ destr12 in |
---|
1940 | translate_condptr destr1 destr2 start_lbl lbl_true lbl_false def |
---|
1941 | ] |
---|
1942 | | Some destr ⇒ |
---|
1943 | adds_graph [ |
---|
1944 | rtl_st_cond_acc destr lbl_true lbl_false |
---|
1945 | ] start_lbl start_lbl def |
---|
1946 | ] |
---|
1947 | ] |
---|
1948 | ] |
---|
1949 | ] |
---|
1950 | ]. |
---|
1951 | |
---|
1952 | definition size_of_op2_ret ≝ |
---|
1953 | λn: nat. |
---|
1954 | λop2. |
---|
1955 | match op2 with |
---|
1956 | [ op_add ⇒ Some ? 1 |
---|
1957 | | op_sub ⇒ Some ? 1 |
---|
1958 | | op_mul ⇒ Some ? 1 |
---|
1959 | | op_div ⇒ Some ? 1 |
---|
1960 | | op_divu ⇒ Some ? 1 |
---|
1961 | | op_mod ⇒ Some ? 1 |
---|
1962 | | op_modu ⇒ Some ? 1 |
---|
1963 | | op_and ⇒ Some ? 1 |
---|
1964 | | op_or ⇒ Some ? 1 |
---|
1965 | | op_xor ⇒ Some ? 1 |
---|
1966 | | op_shl ⇒ Some ? 1 |
---|
1967 | | op_shr ⇒ Some ? 1 |
---|
1968 | | op_shru ⇒ Some ? 1 |
---|
1969 | | op_cmp _ ⇒ Some ? 1 |
---|
1970 | | op_cmpu _ ⇒ Some ? 1 |
---|
1971 | | op_cmpp _ ⇒ Some ? 1 |
---|
1972 | | op_addp ⇒ Some ? 2 |
---|
1973 | | op_subp ⇒ |
---|
1974 | if eq_nat n 4 then |
---|
1975 | Some ? 1 |
---|
1976 | else |
---|
1977 | Some ? 2 |
---|
1978 | | _ ⇒ None ? (* error_float *) |
---|
1979 | ]. |
---|
1980 | |
---|
1981 | axiom translate_op2: |
---|
1982 | op2 → list register → list register → list register → label → label → rtl_internal_function → option rtl_internal_function. |
---|
1983 | |
---|
1984 | definition translate_cond2 ≝ |
---|
1985 | λop2. |
---|
1986 | λsrcrs1: list register. |
---|
1987 | λsrcrs2: list register. |
---|
1988 | λstart_lbl: label. |
---|
1989 | λlbl_true: label. |
---|
1990 | λlbl_false: label. |
---|
1991 | λdef. |
---|
1992 | match op2 with |
---|
1993 | [ op_cmp cmp ⇒ |
---|
1994 | match cmp with |
---|
1995 | [ Compare_Equal ⇒ |
---|
1996 | let srcr1 ≝ extract_singleton ? srcrs1 in |
---|
1997 | match srcr1 with |
---|
1998 | [ None ⇒ None ? |
---|
1999 | | Some srcr1 ⇒ |
---|
2000 | let srcr2 ≝ extract_singleton ? srcrs2 in |
---|
2001 | match srcr2 with |
---|
2002 | [ None ⇒ None ? |
---|
2003 | | Some srcr2 ⇒ |
---|
2004 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2005 | adds_graph [ |
---|
2006 | rtl_st_clear_carry start_lbl; |
---|
2007 | rtl_st_op2 Sub tmpr srcr1 srcr2 start_lbl; |
---|
2008 | rtl_st_cond_acc tmpr lbl_false lbl_true |
---|
2009 | ] start_lbl start_lbl def |
---|
2010 | ] |
---|
2011 | ] |
---|
2012 | | _ ⇒ |
---|
2013 | let n ≝ length ? srcrs1 + length ? srcrs2 in |
---|
2014 | match size_of_op2_ret n op2 with |
---|
2015 | [ None ⇒ None ? |
---|
2016 | | Some size ⇒ |
---|
2017 | let 〈def, destrs〉 ≝ fresh_regs def size in |
---|
2018 | let lbl ≝ fresh_label def in |
---|
2019 | match lbl with |
---|
2020 | [ None ⇒ None ? |
---|
2021 | | Some lbl ⇒ |
---|
2022 | match translate_op2 op2 destrs srcrs1 srcrs2 start_lbl lbl def with |
---|
2023 | [ None ⇒ None ? |
---|
2024 | | Some def ⇒ translate_cond1 op_id destrs lbl lbl_true lbl_false def |
---|
2025 | ] |
---|
2026 | ] |
---|
2027 | ] |
---|
2028 | ] |
---|
2029 | | _ ⇒ |
---|
2030 | let n ≝ length ? srcrs1 + length ? srcrs2 in |
---|
2031 | match size_of_op2_ret n op2 with |
---|
2032 | [ None ⇒ None ? |
---|
2033 | | Some size ⇒ |
---|
2034 | let 〈def, destrs〉 ≝ fresh_regs def size in |
---|
2035 | let lbl ≝ fresh_label def in |
---|
2036 | match lbl with |
---|
2037 | [ None ⇒ None ? |
---|
2038 | | Some lbl ⇒ |
---|
2039 | match translate_op2 op2 destrs srcrs1 srcrs2 start_lbl lbl def with |
---|
2040 | [ None ⇒ None ? |
---|
2041 | | Some def ⇒ translate_cond1 op_id destrs lbl lbl_true lbl_false def |
---|
2042 | ] |
---|
2043 | ] |
---|
2044 | ] |
---|
2045 | ]. |
---|
2046 | |
---|
2047 | let rec addressing_pointer (mode: ?) (args: ?) (destr1: ?) |
---|
2048 | (destr2: ?) (start_lbl: label) |
---|
2049 | (dest_lbl: label) (def: rtl_internal_function) ≝ |
---|
2050 | let destrs ≝ [ destr1; destr2 ] in |
---|
2051 | match mode with |
---|
2052 | [ Aindexed off ⇒ |
---|
2053 | let srcr12 ≝ extract_singleton ? args in |
---|
2054 | match srcr12 with |
---|
2055 | [ None ⇒ None ? |
---|
2056 | | Some srcr12 ⇒ |
---|
2057 | let srcr12 ≝ extract_pair ? srcr12 in |
---|
2058 | match srcr12 with |
---|
2059 | [ None ⇒ None ? |
---|
2060 | | Some srcr12 ⇒ |
---|
2061 | let 〈srcr1, srcr2〉 ≝ srcr12 in |
---|
2062 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2063 | add_translates [ |
---|
2064 | adds_graph [ |
---|
2065 | rtl_st_int tmpr off start_lbl |
---|
2066 | ]; |
---|
2067 | translate_op2 op_addp destrs [ srcr1 ; srcr2 ] [tmpr] |
---|
2068 | ] start_lbl dest_lbl def |
---|
2069 | ] |
---|
2070 | ] |
---|
2071 | | Aindexed2 ⇒ |
---|
2072 | let args_pair ≝ extract_pair ? args in |
---|
2073 | match args_pair with |
---|
2074 | [ None ⇒ None ? |
---|
2075 | | Some args_pair ⇒ |
---|
2076 | let 〈lft, rgt〉 ≝ args_pair in |
---|
2077 | let srcr1112 ≝ extract_pair ? lft in |
---|
2078 | let srcr2 ≝ extract_singleton ? rgt in |
---|
2079 | match srcr1112 with |
---|
2080 | [ None ⇒ |
---|
2081 | let srcr2 ≝ extract_singleton ? rgt in |
---|
2082 | let srcr1112 ≝ extract_pair ? lft in |
---|
2083 | match srcr2 with |
---|
2084 | [ None ⇒ None ? |
---|
2085 | | Some srcr2 ⇒ |
---|
2086 | match srcr1112 with |
---|
2087 | [ None ⇒ None ? |
---|
2088 | | Some srcr1112 ⇒ |
---|
2089 | let 〈srcr11, srcr12〉 ≝ srcr1112 in |
---|
2090 | translate_op2 op_addp destrs [ srcr11; srcr12 ] [ srcr2 ] start_lbl dest_lbl def |
---|
2091 | ] |
---|
2092 | ] |
---|
2093 | | Some srcr1112 ⇒ |
---|
2094 | let 〈srcr11, srcr12〉 ≝ srcr1112 in |
---|
2095 | match srcr2 with |
---|
2096 | [ None ⇒ None ? |
---|
2097 | | Some srcr2 ⇒ |
---|
2098 | translate_op2 op_addp destrs [ srcr11; srcr12 ] [ srcr2 ] start_lbl dest_lbl def |
---|
2099 | ] |
---|
2100 | ] |
---|
2101 | ] |
---|
2102 | | Aglobal x off ⇒ |
---|
2103 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2104 | add_translates [ |
---|
2105 | adds_graph [ |
---|
2106 | rtl_st_int tmpr off start_lbl; |
---|
2107 | rtl_st_addr destr1 destr2 x start_lbl |
---|
2108 | ]; |
---|
2109 | translate_op2 op_addp destrs destrs [ tmpr ] |
---|
2110 | ] start_lbl dest_lbl def |
---|
2111 | | Abased x off ⇒ |
---|
2112 | let srcrs ≝ extract_singleton ? args in |
---|
2113 | match srcrs with |
---|
2114 | [ None ⇒ None ? |
---|
2115 | | Some srcrs ⇒ |
---|
2116 | let 〈def, tmpr1〉 ≝ fresh_reg def in |
---|
2117 | let 〈def, tmpr2〉 ≝ fresh_reg def in |
---|
2118 | (* mode, args, destr1, destr2, start_lbl, dest_lbl, def *) |
---|
2119 | (* addressing_pointer (Aglobal x off) [ ] tmpr1 tmpr2; *) |
---|
2120 | let address_unfold ≝ |
---|
2121 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2122 | add_translates [ |
---|
2123 | adds_graph [ |
---|
2124 | rtl_st_int tmpr off start_lbl; |
---|
2125 | rtl_st_addr tmpr1 tmpr2 x start_lbl |
---|
2126 | ]; |
---|
2127 | translate_op2 op_addp destrs destrs [ tmpr ] |
---|
2128 | ] |
---|
2129 | in |
---|
2130 | add_translates [ |
---|
2131 | address_unfold; |
---|
2132 | translate_op2 op_addp destrs [ tmpr1; tmpr2 ] srcrs |
---|
2133 | ] start_lbl dest_lbl def |
---|
2134 | ] |
---|
2135 | | Ainstack off ⇒ |
---|
2136 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2137 | add_translates [ |
---|
2138 | adds_graph [ |
---|
2139 | rtl_st_int tmpr off start_lbl; |
---|
2140 | rtl_st_stack_addr destr1 destr2 start_lbl |
---|
2141 | ]; |
---|
2142 | translate_op2 op_addp destrs destrs [ tmpr ] |
---|
2143 | ] start_lbl dest_lbl def |
---|
2144 | | _ ⇒ None ? (* wrong number of arguments *) |
---|
2145 | ]. |
---|
2146 | |
---|
2147 | definition translate_load ≝ |
---|
2148 | λq. |
---|
2149 | λmode. |
---|
2150 | λargs. |
---|
2151 | λdestrs. |
---|
2152 | λstart_lbl: label. |
---|
2153 | λdest_lbl: label. |
---|
2154 | λdef. |
---|
2155 | match q with |
---|
2156 | [ q_int b ⇒ |
---|
2157 | if eq_bv ? b (bitvector_of_nat ? 1) then |
---|
2158 | match extract_singleton ? destrs with |
---|
2159 | [ None ⇒ None ? (* error: size error in load *) |
---|
2160 | | Some destr ⇒ |
---|
2161 | let 〈def, addr1〉 ≝ fresh_reg def in |
---|
2162 | let 〈def, addr2〉 ≝ fresh_reg def in |
---|
2163 | Some ? (add_translates [ |
---|
2164 | addressing_pointer mode args addr1 addr2; |
---|
2165 | adds_graph [ |
---|
2166 | rtl_st_load destr addr1 addr2 start_lbl |
---|
2167 | ] |
---|
2168 | ] start_lbl dest_lbl def) |
---|
2169 | ] |
---|
2170 | else |
---|
2171 | None ? (* error: size error in load *) |
---|
2172 | | q_ptr ⇒ |
---|
2173 | match extract_pair ? destrs with |
---|
2174 | [ None ⇒ None ? (* error: size error in load *) |
---|
2175 | | Some destr12 ⇒ |
---|
2176 | let 〈destr1, destr2〉 ≝ destr12 in |
---|
2177 | let 〈def, addr1〉 ≝ fresh_reg def in |
---|
2178 | let 〈def, addr2〉 ≝ fresh_reg def in |
---|
2179 | let addr ≝ [ addr1; addr2 ] in |
---|
2180 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2181 | Some ? ( |
---|
2182 | add_translates [ |
---|
2183 | addressing_pointer mode args addr1 addr2; |
---|
2184 | adds_graph [ |
---|
2185 | rtl_st_load destr1 addr1 addr2 start_lbl; |
---|
2186 | rtl_st_int tmpr (bitvector_of_nat ? 1) start_lbl |
---|
2187 | ]; |
---|
2188 | translate_op2 op_addp addr addr [ tmpr ]; |
---|
2189 | adds_graph [ |
---|
2190 | rtl_st_load destr2 addr1 addr2 start_lbl |
---|
2191 | ] |
---|
2192 | ] start_lbl dest_lbl def |
---|
2193 | ) |
---|
2194 | ] |
---|
2195 | | _ ⇒ None ? (* error: size error in load *) |
---|
2196 | ]. |
---|
2197 | |
---|
2198 | definition make_addr ≝ |
---|
2199 | λA: Type[0]. |
---|
2200 | λlst: list A. |
---|
2201 | match lst with |
---|
2202 | [ cons hd tl ⇒ |
---|
2203 | match tl with |
---|
2204 | [ cons hd' tl' ⇒ Some ? 〈hd, hd'〉 |
---|
2205 | | _ ⇒ None ? (* do not use on these arguments *) |
---|
2206 | ] |
---|
2207 | | _ ⇒ None ? (* do not use on these arguments *) |
---|
2208 | ]. |
---|
2209 | |
---|
2210 | definition translate_store_internal ≝ |
---|
2211 | λaddr. |
---|
2212 | λtmp_addr. |
---|
2213 | λtmpr. |
---|
2214 | λstart_lbl. |
---|
2215 | λdest_lbl. |
---|
2216 | λtmp_addr1. |
---|
2217 | λtmp_addr2. |
---|
2218 | λtranslates_off. |
---|
2219 | λsrcr. |
---|
2220 | let 〈translates, off〉 ≝ translates_off in |
---|
2221 | let translates ≝ translates @ |
---|
2222 | [ adds_graph [ |
---|
2223 | rtl_st_int tmpr off start_lbl |
---|
2224 | ]; |
---|
2225 | translate_op2 op_addp tmp_addr addr [ tmpr ]; |
---|
2226 | adds_graph [ |
---|
2227 | rtl_st_store tmp_addr1 tmp_addr2 srcr dest_lbl |
---|
2228 | ] |
---|
2229 | ] |
---|
2230 | in |
---|
2231 | let 〈ignore, result〉 ≝ half_add ? off int_size in |
---|
2232 | 〈translates, result〉. |
---|
2233 | |
---|
2234 | definition translate_store ≝ |
---|
2235 | λaddr. |
---|
2236 | λsrcrs. |
---|
2237 | λstart_lbl. |
---|
2238 | λdest_lbl. |
---|
2239 | λdef. |
---|
2240 | let 〈def, tmp_addr〉 ≝ fresh_regs def (length ? addr) in |
---|
2241 | match make_addr ? tmp_addr with |
---|
2242 | [ None ⇒ None ? |
---|
2243 | | Some tmp_addr12 ⇒ |
---|
2244 | let 〈tmp_addr1, tmp_addr2〉 ≝ tmp_addr12 in |
---|
2245 | let 〈def, tmpr〉 ≝ fresh_reg def in |
---|
2246 | let f ≝ translate_store_internal addr tmp_addr tmpr start_lbl dest_lbl tmp_addr1 tmp_addr2 in |
---|
2247 | let 〈translates, ignore〉 ≝ foldl ? ? f 〈[], zero ?〉 srcrs in |
---|
2248 | add_translates translates start_lbl dest_lbl def |
---|
2249 | ]. |
---|
2250 | |
---|
2251 | definition translate_stmt ≝ |
---|
2252 | λlenv. |
---|
2253 | λlbl. |
---|
2254 | λstmt. |
---|
2255 | λdef. |
---|
2256 | match stmt with |
---|
2257 | [ St_skip lbl' ⇒ add_graph lbl (rtl_st_skip lbl') def |
---|
2258 | | St_cost cost_lbl lbl' ⇒ add_graph lbl (rtl_st_cost cost_lbl lbl') def |
---|
2259 | | St_cast destr cst lbl' ⇒ |
---|
2260 | translate_cst cst (find_local_env destr lenv) lbl lbl' def |
---|
2261 | | _ ⇒ ? |
---|
2262 | ]. |
---|
2263 | |
---|
2264 | let translate_stmt lenv lbl stmt def = match stmt with |
---|
2265 | |
---|
2266 | | RTLabs.St_skip lbl' -> |
---|
2267 | add_graph lbl (RTL.St_skip lbl') def |
---|
2268 | |
---|
2269 | | RTLabs.St_cost (cost_lbl, lbl') -> |
---|
2270 | add_graph lbl (RTL.St_cost (cost_lbl, lbl')) def |
---|
2271 | |
---|
2272 | | RTLabs.St_cst (destr, cst, lbl') -> |
---|
2273 | translate_cst cst (find_local_env destr lenv) lbl lbl' def |
---|
2274 | |
---|
2275 | | RTLabs.St_op1 (op1, destr, srcr, lbl') -> |
---|
2276 | translate_op1 op1 (find_local_env destr lenv) (find_local_env srcr lenv) |
---|
2277 | lbl lbl' def |
---|
2278 | |
---|
2279 | | RTLabs.St_op2 (op2, destr, srcr1, srcr2, lbl') -> |
---|
2280 | translate_op2 op2 (find_local_env destr lenv) |
---|
2281 | (find_local_env srcr1 lenv) (find_local_env srcr2 lenv) lbl lbl' def |
---|
2282 | |
---|
2283 | | RTLabs.St_load (_, addr, destr, lbl') -> |
---|
2284 | translate_load (find_local_env addr lenv) (find_local_env destr lenv) |
---|
2285 | lbl lbl' def |
---|
2286 | |
---|
2287 | | RTLabs.St_store (_, addr, srcr, lbl') -> |
---|
2288 | translate_store (find_local_env addr lenv) (find_local_env srcr lenv) |
---|
2289 | lbl lbl' def |
---|
2290 | |
---|
2291 | | RTLabs.St_call_id (f, args, None, _, lbl') -> |
---|
2292 | add_graph lbl (RTL.St_call_id (f, rtl_args args lenv, [], lbl')) def |
---|
2293 | |
---|
2294 | | RTLabs.St_call_id (f, args, Some retr, _, lbl') -> |
---|
2295 | add_graph lbl (RTL.St_call_id (f, rtl_args args lenv, |
---|
2296 | find_local_env retr lenv, lbl')) def |
---|
2297 | |
---|
2298 | | RTLabs.St_call_ptr (f, args, None, _, lbl') -> |
---|
2299 | let (f1, f2) = find_and_addr f lenv in |
---|
2300 | add_graph lbl (RTL.St_call_ptr (f1, f2, rtl_args args lenv, [], lbl')) def |
---|
2301 | |
---|
2302 | | RTLabs.St_call_ptr (f, args, Some retr, _, lbl') -> |
---|
2303 | let (f1, f2) = find_and_addr f lenv in |
---|
2304 | add_graph lbl |
---|
2305 | (RTL.St_call_ptr |
---|
2306 | (f1, f2, rtl_args args lenv, find_local_env retr lenv, lbl')) def |
---|
2307 | |
---|
2308 | | RTLabs.St_tailcall_id (f, args, _) -> |
---|
2309 | add_graph lbl (RTL.St_tailcall_id (f, rtl_args args lenv)) def |
---|
2310 | |
---|
2311 | | RTLabs.St_tailcall_ptr (f, args, _) -> |
---|
2312 | let (f1, f2) = find_and_addr f lenv in |
---|
2313 | add_graph lbl (RTL.St_tailcall_ptr (f1, f2, rtl_args args lenv)) def |
---|
2314 | |
---|
2315 | | RTLabs.St_cond (r, lbl_true, lbl_false) -> |
---|
2316 | translate_cond (find_local_env r lenv) lbl lbl_true lbl_false def |
---|
2317 | |
---|
2318 | | RTLabs.St_jumptable _ -> |
---|
2319 | error "Jump tables not supported yet." |
---|
2320 | |
---|
2321 | | RTLabs.St_return None -> |
---|
2322 | add_graph lbl (RTL.St_return []) def |
---|
2323 | |
---|
2324 | | RTLabs.St_return (Some r) -> |
---|
2325 | add_graph lbl (RTL.St_return (find_local_env r lenv)) def |
---|