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c8a2ab6d SP |
1 | /* Chains of recurrences. |
2 | Copyright (C) 2003, 2004 Free Software Foundation, Inc. | |
3 | Contributed by Sebastian Pop <s.pop@laposte.net> | |
4 | ||
5 | This file is part of GCC. | |
6 | ||
7 | GCC is free software; you can redistribute it and/or modify it under | |
8 | the terms of the GNU General Public License as published by the Free | |
9 | Software Foundation; either version 2, or (at your option) any later | |
10 | version. | |
11 | ||
12 | GCC is distributed in the hope that it will be useful, but WITHOUT ANY | |
13 | WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 | FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 | for more details. | |
16 | ||
17 | You should have received a copy of the GNU General Public License | |
18 | along with GCC; see the file COPYING. If not, write to the Free | |
19 | Software Foundation, 59 Temple Place - Suite 330, Boston, MA | |
20 | 02111-1307, USA. */ | |
21 | ||
22 | /* This file implements operations on chains of recurrences. Chains | |
23 | of recurrences are used for modeling evolution functions of scalar | |
24 | variables. | |
25 | */ | |
26 | ||
27 | #include "config.h" | |
28 | #include "system.h" | |
29 | #include "coretypes.h" | |
30 | #include "tm.h" | |
31 | #include "errors.h" | |
32 | #include "ggc.h" | |
33 | #include "tree.h" | |
34 | #include "diagnostic.h" | |
35 | #include "varray.h" | |
36 | #include "tree-chrec.h" | |
37 | #include "tree-pass.h" | |
38 | ||
39 | \f | |
40 | /* This part will be removed once the merging is finished. */ | |
41 | ||
42 | ||
43 | ||
44 | /* The following trees are unique elements. Thus the comparison of | |
45 | another element to these elements should be done on the pointer to | |
46 | these trees, and not on their value. */ | |
47 | ||
48 | /* The SSA_NAMEs that are not yet analyzed are qualified with NULL_TREE. */ | |
49 | tree chrec_not_analyzed_yet; | |
50 | ||
51 | /* Reserved to the cases where the analyzer has detected an | |
52 | undecidable property at compile time. */ | |
53 | tree chrec_dont_know; | |
54 | ||
55 | /* When the analyzer has detected that a property will never | |
56 | happen, then it qualifies it with chrec_known. */ | |
57 | tree chrec_known; | |
58 | ||
59 | /* Empty hook. Will be replaced by the main function from | |
60 | tree-scalar-evolution.c. */ | |
61 | ||
62 | tree | |
63 | count_ev_in_wider_type (tree foo ATTRIBUTE_UNUSED, | |
64 | tree bar ATTRIBUTE_UNUSED) | |
65 | { | |
66 | return NULL_TREE; | |
67 | } | |
68 | ||
69 | /* Empty hook. Will be replaced by the main function from | |
70 | tree-scalar-evolution.c. */ | |
71 | ||
72 | bool | |
73 | chrec_contains_symbols_defined_in_loop (tree chrec ATTRIBUTE_UNUSED, | |
74 | unsigned loop_nb ATTRIBUTE_UNUSED) | |
75 | { | |
76 | return true; | |
77 | } | |
78 | ||
79 | ||
80 | \f | |
81 | ||
82 | /* Extended folder for chrecs. */ | |
83 | ||
84 | /* Determines whether CST is not a constant evolution. */ | |
85 | ||
86 | static inline bool | |
87 | is_not_constant_evolution (tree cst) | |
88 | { | |
89 | return (TREE_CODE (cst) == POLYNOMIAL_CHREC); | |
90 | } | |
91 | ||
92 | /* Fold CODE for a polynomial function and a constant. */ | |
93 | ||
94 | static inline tree | |
95 | chrec_fold_poly_cst (enum tree_code code, | |
96 | tree type, | |
97 | tree poly, | |
98 | tree cst) | |
99 | { | |
100 | #if defined ENABLE_CHECKING | |
101 | if (poly == NULL_TREE | |
102 | || cst == NULL_TREE | |
103 | || TREE_CODE (poly) != POLYNOMIAL_CHREC | |
104 | || is_not_constant_evolution (cst)) | |
105 | abort (); | |
106 | #endif | |
107 | ||
108 | switch (code) | |
109 | { | |
110 | case PLUS_EXPR: | |
111 | return build_polynomial_chrec | |
112 | (CHREC_VARIABLE (poly), | |
113 | chrec_fold_plus (type, CHREC_LEFT (poly), cst), | |
114 | CHREC_RIGHT (poly)); | |
115 | ||
116 | case MINUS_EXPR: | |
117 | return build_polynomial_chrec | |
118 | (CHREC_VARIABLE (poly), | |
119 | chrec_fold_minus (type, CHREC_LEFT (poly), cst), | |
120 | CHREC_RIGHT (poly)); | |
121 | ||
122 | case MULT_EXPR: | |
123 | return build_polynomial_chrec | |
124 | (CHREC_VARIABLE (poly), | |
125 | chrec_fold_multiply (type, CHREC_LEFT (poly), cst), | |
126 | chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); | |
127 | ||
128 | default: | |
129 | return chrec_dont_know; | |
130 | } | |
131 | } | |
132 | ||
133 | /* Fold the addition of two polynomial functions. */ | |
134 | ||
135 | static inline tree | |
136 | chrec_fold_plus_poly_poly (enum tree_code code, | |
137 | tree type, | |
138 | tree poly0, | |
139 | tree poly1) | |
140 | { | |
141 | tree left, right; | |
142 | ||
143 | #if defined ENABLE_CHECKING | |
144 | if (poly0 == NULL_TREE | |
145 | || poly1 == NULL_TREE | |
146 | || TREE_CODE (poly0) != POLYNOMIAL_CHREC | |
147 | || TREE_CODE (poly1) != POLYNOMIAL_CHREC) | |
148 | abort (); | |
149 | #endif | |
150 | ||
151 | /* | |
152 | {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2, | |
153 | {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2, | |
154 | {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */ | |
155 | if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) | |
156 | { | |
157 | if (code == PLUS_EXPR) | |
158 | return build_polynomial_chrec | |
159 | (CHREC_VARIABLE (poly1), | |
160 | chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)), | |
161 | CHREC_RIGHT (poly1)); | |
162 | else | |
163 | return build_polynomial_chrec | |
164 | (CHREC_VARIABLE (poly1), | |
165 | chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)), | |
166 | chrec_fold_multiply (type, CHREC_RIGHT (poly1), | |
167 | convert (type, integer_minus_one_node))); | |
168 | } | |
169 | ||
170 | if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1)) | |
171 | { | |
172 | if (code == PLUS_EXPR) | |
173 | return build_polynomial_chrec | |
174 | (CHREC_VARIABLE (poly0), | |
175 | chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), | |
176 | CHREC_RIGHT (poly0)); | |
177 | else | |
178 | return build_polynomial_chrec | |
179 | (CHREC_VARIABLE (poly0), | |
180 | chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), | |
181 | CHREC_RIGHT (poly0)); | |
182 | } | |
183 | ||
184 | if (code == PLUS_EXPR) | |
185 | { | |
186 | left = chrec_fold_plus | |
187 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
188 | right = chrec_fold_plus | |
189 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
190 | } | |
191 | else | |
192 | { | |
193 | left = chrec_fold_minus | |
194 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
195 | right = chrec_fold_minus | |
196 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
197 | } | |
198 | ||
199 | if (chrec_zerop (right)) | |
200 | return left; | |
201 | else | |
202 | return build_polynomial_chrec | |
203 | (CHREC_VARIABLE (poly0), left, right); | |
204 | } | |
205 | ||
206 | \f | |
207 | ||
208 | /* Fold the multiplication of two polynomial functions. */ | |
209 | ||
210 | static inline tree | |
211 | chrec_fold_multiply_poly_poly (tree type, | |
212 | tree poly0, | |
213 | tree poly1) | |
214 | { | |
215 | #if defined ENABLE_CHECKING | |
216 | if (poly0 == NULL_TREE | |
217 | || poly1 == NULL_TREE | |
218 | || TREE_CODE (poly0) != POLYNOMIAL_CHREC | |
219 | || TREE_CODE (poly1) != POLYNOMIAL_CHREC) | |
220 | abort (); | |
221 | #endif | |
222 | ||
223 | /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, | |
224 | {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, | |
225 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
226 | if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) | |
227 | /* poly0 is a constant wrt. poly1. */ | |
228 | return build_polynomial_chrec | |
229 | (CHREC_VARIABLE (poly1), | |
230 | chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), | |
231 | CHREC_RIGHT (poly1)); | |
232 | ||
233 | if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0)) | |
234 | /* poly1 is a constant wrt. poly0. */ | |
235 | return build_polynomial_chrec | |
236 | (CHREC_VARIABLE (poly0), | |
237 | chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), | |
238 | CHREC_RIGHT (poly0)); | |
239 | ||
240 | /* poly0 and poly1 are two polynomials in the same variable, | |
241 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
242 | return | |
243 | build_polynomial_chrec | |
244 | (CHREC_VARIABLE (poly0), | |
245 | build_polynomial_chrec | |
246 | (CHREC_VARIABLE (poly0), | |
247 | ||
248 | /* "a*c". */ | |
249 | chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)), | |
250 | ||
251 | /* "a*d + b*c + b*d". */ | |
252 | chrec_fold_plus | |
253 | (type, chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)), | |
254 | ||
255 | chrec_fold_plus | |
256 | (type, | |
257 | chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_LEFT (poly1)), | |
258 | chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1))))), | |
259 | ||
260 | /* "2*b*d". */ | |
261 | chrec_fold_multiply | |
262 | (type, build_int_2 (2, 0), | |
263 | chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)))); | |
264 | } | |
265 | ||
266 | /* When the operands are automatically_generated_chrec_p, the fold has | |
267 | to respect the semantics of the operands. */ | |
268 | ||
269 | static inline tree | |
270 | chrec_fold_automatically_generated_operands (tree op0, | |
271 | tree op1) | |
272 | { | |
273 | if (op0 == chrec_dont_know | |
274 | || op1 == chrec_dont_know) | |
275 | return chrec_dont_know; | |
276 | ||
277 | if (op0 == chrec_known | |
278 | || op1 == chrec_known) | |
279 | return chrec_known; | |
280 | ||
281 | if (op0 == chrec_not_analyzed_yet | |
282 | || op1 == chrec_not_analyzed_yet) | |
283 | return chrec_not_analyzed_yet; | |
284 | ||
285 | /* The default case produces a safe result. */ | |
286 | return chrec_dont_know; | |
287 | } | |
288 | ||
289 | /* Fold the addition of two chrecs. */ | |
290 | ||
291 | static tree | |
292 | chrec_fold_plus_1 (enum tree_code code, | |
293 | tree type, | |
294 | tree op0, | |
295 | tree op1) | |
296 | { | |
297 | if (automatically_generated_chrec_p (op0) | |
298 | || automatically_generated_chrec_p (op1)) | |
299 | return chrec_fold_automatically_generated_operands (op0, op1); | |
300 | ||
301 | switch (TREE_CODE (op0)) | |
302 | { | |
303 | case POLYNOMIAL_CHREC: | |
304 | switch (TREE_CODE (op1)) | |
305 | { | |
306 | case POLYNOMIAL_CHREC: | |
307 | return chrec_fold_plus_poly_poly (code, type, op0, op1); | |
308 | ||
309 | default: | |
310 | if (code == PLUS_EXPR) | |
311 | return build_polynomial_chrec | |
312 | (CHREC_VARIABLE (op0), | |
313 | chrec_fold_plus (type, CHREC_LEFT (op0), op1), | |
314 | CHREC_RIGHT (op0)); | |
315 | else | |
316 | return build_polynomial_chrec | |
317 | (CHREC_VARIABLE (op0), | |
318 | chrec_fold_minus (type, CHREC_LEFT (op0), op1), | |
319 | CHREC_RIGHT (op0)); | |
320 | } | |
321 | ||
322 | default: | |
323 | switch (TREE_CODE (op1)) | |
324 | { | |
325 | case POLYNOMIAL_CHREC: | |
326 | if (code == PLUS_EXPR) | |
327 | return build_polynomial_chrec | |
328 | (CHREC_VARIABLE (op1), | |
329 | chrec_fold_plus (type, op0, CHREC_LEFT (op1)), | |
330 | CHREC_RIGHT (op1)); | |
331 | else | |
332 | return build_polynomial_chrec | |
333 | (CHREC_VARIABLE (op1), | |
334 | chrec_fold_minus (type, op0, CHREC_LEFT (op1)), | |
335 | chrec_fold_multiply (type, CHREC_RIGHT (op1), | |
336 | convert (type, | |
337 | integer_minus_one_node))); | |
338 | ||
339 | default: | |
340 | if (tree_contains_chrecs (op0) | |
341 | || tree_contains_chrecs (op1)) | |
342 | return build (code, type, op0, op1); | |
343 | else | |
344 | return fold (build (code, type, op0, op1)); | |
345 | } | |
346 | } | |
347 | } | |
348 | ||
349 | /* Fold the addition of two chrecs. */ | |
350 | ||
351 | tree | |
352 | chrec_fold_plus (tree type, | |
353 | tree op0, | |
354 | tree op1) | |
355 | { | |
356 | if (integer_zerop (op0)) | |
357 | return op1; | |
358 | if (integer_zerop (op1)) | |
359 | return op0; | |
360 | ||
361 | return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1); | |
362 | } | |
363 | ||
364 | /* Fold the subtraction of two chrecs. */ | |
365 | ||
366 | tree | |
367 | chrec_fold_minus (tree type, | |
368 | tree op0, | |
369 | tree op1) | |
370 | { | |
371 | if (integer_zerop (op1)) | |
372 | return op0; | |
373 | ||
374 | return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); | |
375 | } | |
376 | ||
377 | /* Fold the multiplication of two chrecs. */ | |
378 | ||
379 | tree | |
380 | chrec_fold_multiply (tree type, | |
381 | tree op0, | |
382 | tree op1) | |
383 | { | |
384 | if (automatically_generated_chrec_p (op0) | |
385 | || automatically_generated_chrec_p (op1)) | |
386 | return chrec_fold_automatically_generated_operands (op0, op1); | |
387 | ||
388 | switch (TREE_CODE (op0)) | |
389 | { | |
390 | case POLYNOMIAL_CHREC: | |
391 | switch (TREE_CODE (op1)) | |
392 | { | |
393 | case POLYNOMIAL_CHREC: | |
394 | return chrec_fold_multiply_poly_poly (type, op0, op1); | |
395 | ||
396 | default: | |
397 | if (integer_onep (op1)) | |
398 | return op0; | |
399 | if (integer_zerop (op1)) | |
400 | return convert (type, integer_zero_node); | |
401 | ||
402 | return build_polynomial_chrec | |
403 | (CHREC_VARIABLE (op0), | |
404 | chrec_fold_multiply (type, CHREC_LEFT (op0), op1), | |
405 | chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); | |
406 | } | |
407 | ||
408 | default: | |
409 | if (integer_onep (op0)) | |
410 | return op1; | |
411 | ||
412 | if (integer_zerop (op0)) | |
413 | return convert (type, integer_zero_node); | |
414 | ||
415 | switch (TREE_CODE (op1)) | |
416 | { | |
417 | case POLYNOMIAL_CHREC: | |
418 | return build_polynomial_chrec | |
419 | (CHREC_VARIABLE (op1), | |
420 | chrec_fold_multiply (type, CHREC_LEFT (op1), op0), | |
421 | chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); | |
422 | ||
423 | default: | |
424 | if (integer_onep (op1)) | |
425 | return op0; | |
426 | if (integer_zerop (op1)) | |
427 | return convert (type, integer_zero_node); | |
428 | return fold (build (MULT_EXPR, type, op0, op1)); | |
429 | } | |
430 | } | |
431 | } | |
432 | ||
433 | \f | |
434 | ||
435 | /* Operations. */ | |
436 | ||
437 | /* The factorial. */ | |
438 | ||
439 | static tree | |
440 | tree_fold_factorial (tree f) | |
441 | { | |
442 | if (tree_int_cst_sgn (f) <= 0) | |
443 | return integer_one_node; | |
444 | else | |
445 | return fold | |
446 | (build (MULT_EXPR, integer_type_node, f, | |
447 | tree_fold_factorial (fold (build (MINUS_EXPR, integer_type_node, | |
448 | f, integer_one_node))))); | |
449 | } | |
450 | ||
451 | /* The binomial coefficient. */ | |
452 | ||
453 | static tree | |
454 | tree_fold_binomial (tree n, | |
455 | tree k) | |
456 | { | |
457 | return fold | |
458 | (build (EXACT_DIV_EXPR, integer_type_node, tree_fold_factorial (n), | |
459 | fold (build (MULT_EXPR, integer_type_node, | |
460 | tree_fold_factorial (k), | |
461 | tree_fold_factorial | |
462 | (fold (build (MINUS_EXPR, integer_type_node, | |
463 | n, k))))))); | |
464 | } | |
465 | ||
466 | /* Helper function. Use the Newton's interpolating formula for | |
467 | evaluating the value of the evolution function. */ | |
468 | ||
469 | static tree | |
470 | chrec_evaluate (unsigned var, | |
471 | tree chrec, | |
472 | tree n, | |
473 | tree k) | |
474 | { | |
475 | tree type = chrec_type (chrec); | |
476 | tree binomial_n_k = tree_fold_binomial (n, k); | |
477 | ||
478 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
479 | { | |
480 | if (CHREC_VARIABLE (chrec) > var) | |
481 | return chrec_evaluate (var, CHREC_LEFT (chrec), n, k); | |
482 | ||
483 | if (CHREC_VARIABLE (chrec) == var) | |
484 | return chrec_fold_plus | |
485 | (type, | |
486 | fold (build (MULT_EXPR, type, binomial_n_k, CHREC_LEFT (chrec))), | |
487 | chrec_evaluate (var, CHREC_RIGHT (chrec), n, | |
488 | fold (build (PLUS_EXPR, type, k, integer_one_node)))); | |
489 | ||
490 | return fold (build (MULT_EXPR, type, binomial_n_k, chrec)); | |
491 | } | |
492 | else | |
493 | return fold (build (MULT_EXPR, type, binomial_n_k, chrec)); | |
494 | } | |
495 | ||
496 | /* Evaluates "CHREC (X)" when the varying variable is VAR. | |
497 | Example: Given the following parameters, | |
498 | ||
499 | var = 1 | |
500 | chrec = {3, +, 4}_1 | |
501 | x = 10 | |
502 | ||
503 | The result is given by the Newton's interpolating formula: | |
504 | 3 * \binom{10}{0} + 4 * \binom{10}{1}. | |
505 | */ | |
506 | ||
507 | tree | |
508 | chrec_apply (unsigned var, | |
509 | tree chrec, | |
510 | tree x) | |
511 | { | |
512 | tree type = chrec_type (chrec); | |
513 | tree res = chrec_dont_know; | |
514 | ||
515 | if (automatically_generated_chrec_p (chrec) | |
516 | || automatically_generated_chrec_p (x) | |
517 | ||
518 | /* When the symbols are defined in an outer loop, it is possible | |
519 | to symbolically compute the apply, since the symbols are | |
520 | constants with respect to the varying loop. */ | |
521 | || chrec_contains_symbols_defined_in_loop (chrec, var) | |
522 | || chrec_contains_symbols (x)) | |
523 | return chrec_dont_know; | |
524 | ||
525 | if (dump_file && (dump_flags & TDF_DETAILS)) | |
526 | fprintf (dump_file, "(chrec_apply \n"); | |
527 | ||
528 | if (evolution_function_is_affine_p (chrec)) | |
529 | { | |
530 | /* "{a, +, b} (x)" -> "a + b*x". */ | |
531 | if (TREE_CODE (CHREC_LEFT (chrec)) == INTEGER_CST | |
532 | && integer_zerop (CHREC_LEFT (chrec))) | |
533 | res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x); | |
534 | ||
535 | else | |
536 | res = chrec_fold_plus (type, CHREC_LEFT (chrec), | |
537 | chrec_fold_multiply (type, | |
538 | CHREC_RIGHT (chrec), x)); | |
539 | } | |
540 | ||
541 | else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
542 | res = chrec; | |
543 | ||
544 | else if (TREE_CODE (x) == INTEGER_CST | |
545 | && tree_int_cst_sgn (x) == 1) | |
546 | /* testsuite/.../ssa-chrec-38.c. */ | |
547 | res = chrec_evaluate (var, chrec, x, integer_zero_node); | |
548 | ||
549 | else | |
550 | res = chrec_dont_know; | |
551 | ||
552 | if (dump_file && (dump_flags & TDF_DETAILS)) | |
553 | { | |
554 | fprintf (dump_file, " (varying_loop = %d\n", var); | |
555 | fprintf (dump_file, ")\n (chrec = "); | |
556 | print_generic_expr (dump_file, chrec, 0); | |
557 | fprintf (dump_file, ")\n (x = "); | |
558 | print_generic_expr (dump_file, x, 0); | |
559 | fprintf (dump_file, ")\n (res = "); | |
560 | print_generic_expr (dump_file, res, 0); | |
561 | fprintf (dump_file, "))\n"); | |
562 | } | |
563 | ||
564 | return res; | |
565 | } | |
566 | ||
567 | /* Replaces the initial condition in CHREC with INIT_COND. */ | |
568 | ||
569 | tree | |
570 | chrec_replace_initial_condition (tree chrec, | |
571 | tree init_cond) | |
572 | { | |
573 | if (automatically_generated_chrec_p (chrec)) | |
574 | return chrec; | |
575 | ||
576 | switch (TREE_CODE (chrec)) | |
577 | { | |
578 | case POLYNOMIAL_CHREC: | |
579 | return build_polynomial_chrec | |
580 | (CHREC_VARIABLE (chrec), | |
581 | chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), | |
582 | CHREC_RIGHT (chrec)); | |
583 | ||
584 | default: | |
585 | return init_cond; | |
586 | } | |
587 | } | |
588 | ||
589 | /* Returns the initial condition of a given CHREC. */ | |
590 | ||
591 | tree | |
592 | initial_condition (tree chrec) | |
593 | { | |
594 | if (automatically_generated_chrec_p (chrec)) | |
595 | return chrec; | |
596 | ||
597 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
598 | return initial_condition (CHREC_LEFT (chrec)); | |
599 | else | |
600 | return chrec; | |
601 | } | |
602 | ||
603 | /* Returns a univariate function that represents the evolution in | |
604 | LOOP_NUM. Mask the evolution of any other loop. */ | |
605 | ||
606 | tree | |
607 | hide_evolution_in_other_loops_than_loop (tree chrec, | |
608 | unsigned loop_num) | |
609 | { | |
610 | if (automatically_generated_chrec_p (chrec)) | |
611 | return chrec; | |
612 | ||
613 | switch (TREE_CODE (chrec)) | |
614 | { | |
615 | case POLYNOMIAL_CHREC: | |
616 | if (CHREC_VARIABLE (chrec) == loop_num) | |
617 | return build_polynomial_chrec | |
618 | (loop_num, | |
619 | hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
620 | loop_num), | |
621 | CHREC_RIGHT (chrec)); | |
622 | ||
623 | else if (CHREC_VARIABLE (chrec) < loop_num) | |
624 | /* There is no evolution in this loop. */ | |
625 | return initial_condition (chrec); | |
626 | ||
627 | else | |
628 | return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
629 | loop_num); | |
630 | ||
631 | default: | |
632 | return chrec; | |
633 | } | |
634 | } | |
635 | ||
636 | /* Returns the evolution part in LOOP_NUM. Example: the call | |
637 | get_evolution_in_loop (1, {{0, +, 1}_1, +, 2}_1) returns | |
638 | {1, +, 2}_1 */ | |
639 | ||
640 | tree | |
641 | evolution_part_in_loop_num (tree chrec, | |
642 | unsigned loop_num) | |
643 | { | |
644 | if (automatically_generated_chrec_p (chrec)) | |
645 | return chrec; | |
646 | ||
647 | switch (TREE_CODE (chrec)) | |
648 | { | |
649 | case POLYNOMIAL_CHREC: | |
650 | if (CHREC_VARIABLE (chrec) == loop_num) | |
651 | { | |
652 | if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC | |
653 | || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) | |
654 | return CHREC_RIGHT (chrec); | |
655 | ||
656 | else | |
657 | return build_polynomial_chrec | |
658 | (loop_num, | |
659 | evolution_part_in_loop_num (CHREC_LEFT (chrec), loop_num), | |
660 | CHREC_RIGHT (chrec)); | |
661 | } | |
662 | ||
663 | else if (CHREC_VARIABLE (chrec) < loop_num) | |
664 | /* There is no evolution part in this loop. */ | |
665 | return NULL_TREE; | |
666 | ||
667 | else | |
668 | return evolution_part_in_loop_num (CHREC_LEFT (chrec), loop_num); | |
669 | ||
670 | default: | |
671 | return NULL_TREE; | |
672 | } | |
673 | } | |
674 | ||
675 | /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. | |
676 | This function is essentially used for setting the evolution to | |
677 | chrec_dont_know, for example after having determined that it is | |
678 | impossible to say how many times a loop will execute. */ | |
679 | ||
680 | tree | |
681 | reset_evolution_in_loop (unsigned loop_num, | |
682 | tree chrec, | |
683 | tree new_evol) | |
684 | { | |
685 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
686 | && CHREC_VARIABLE (chrec) > loop_num) | |
687 | return build | |
688 | (TREE_CODE (chrec), | |
689 | build_int_2 (CHREC_VARIABLE (chrec), 0), | |
690 | reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), new_evol), | |
691 | reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), new_evol)); | |
692 | ||
693 | while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
694 | && CHREC_VARIABLE (chrec) == loop_num) | |
695 | chrec = CHREC_LEFT (chrec); | |
696 | ||
697 | return build_polynomial_chrec (loop_num, chrec, new_evol); | |
698 | } | |
699 | ||
700 | /* Merges two evolution functions that were found by following two | |
701 | alternate paths of a conditional expression. */ | |
702 | ||
703 | tree | |
704 | chrec_merge (tree chrec1, | |
705 | tree chrec2) | |
706 | { | |
707 | if (chrec1 == chrec_dont_know | |
708 | || chrec2 == chrec_dont_know) | |
709 | return chrec_dont_know; | |
710 | ||
711 | if (chrec1 == chrec_known | |
712 | || chrec2 == chrec_known) | |
713 | return chrec_known; | |
714 | ||
715 | if (chrec1 == chrec_not_analyzed_yet) | |
716 | return chrec2; | |
717 | if (chrec2 == chrec_not_analyzed_yet) | |
718 | return chrec1; | |
719 | ||
720 | if (operand_equal_p (chrec1, chrec2, 0)) | |
721 | return chrec1; | |
722 | ||
723 | return chrec_dont_know; | |
724 | } | |
725 | ||
726 | \f | |
727 | ||
728 | /* Observers. */ | |
729 | ||
730 | /* Helper function for is_multivariate_chrec. */ | |
731 | ||
732 | static bool | |
733 | is_multivariate_chrec_rec (tree chrec, unsigned int rec_var) | |
734 | { | |
735 | if (chrec == NULL_TREE) | |
736 | return false; | |
737 | ||
738 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
739 | { | |
740 | if (CHREC_VARIABLE (chrec) != rec_var) | |
741 | return true; | |
742 | else | |
743 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) | |
744 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); | |
745 | } | |
746 | else | |
747 | return false; | |
748 | } | |
749 | ||
750 | /* Determine whether the given chrec is multivariate or not. */ | |
751 | ||
752 | bool | |
753 | is_multivariate_chrec (tree chrec) | |
754 | { | |
755 | if (chrec == NULL_TREE) | |
756 | return false; | |
757 | ||
758 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
759 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), | |
760 | CHREC_VARIABLE (chrec)) | |
761 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), | |
762 | CHREC_VARIABLE (chrec))); | |
763 | else | |
764 | return false; | |
765 | } | |
766 | ||
767 | /* Determines whether the chrec contains symbolic names or not. */ | |
768 | ||
769 | bool | |
770 | chrec_contains_symbols (tree chrec) | |
771 | { | |
772 | if (chrec == NULL_TREE) | |
773 | return false; | |
774 | ||
775 | if (TREE_CODE (chrec) == SSA_NAME | |
776 | || TREE_CODE (chrec) == VAR_DECL | |
777 | || TREE_CODE (chrec) == PARM_DECL | |
778 | || TREE_CODE (chrec) == FUNCTION_DECL | |
779 | || TREE_CODE (chrec) == LABEL_DECL | |
780 | || TREE_CODE (chrec) == RESULT_DECL | |
781 | || TREE_CODE (chrec) == FIELD_DECL) | |
782 | return true; | |
783 | ||
784 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
785 | { | |
786 | case 3: | |
787 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 2))) | |
788 | return true; | |
789 | ||
790 | case 2: | |
791 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 1))) | |
792 | return true; | |
793 | ||
794 | case 1: | |
795 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 0))) | |
796 | return true; | |
797 | ||
798 | default: | |
799 | return false; | |
800 | } | |
801 | } | |
802 | ||
803 | /* Determines whether the chrec contains undetermined coefficients. */ | |
804 | ||
805 | bool | |
806 | chrec_contains_undetermined (tree chrec) | |
807 | { | |
808 | if (chrec == chrec_dont_know | |
809 | || chrec == chrec_not_analyzed_yet | |
810 | || chrec == NULL_TREE) | |
811 | return true; | |
812 | ||
813 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
814 | { | |
815 | case 3: | |
816 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2))) | |
817 | return true; | |
818 | ||
819 | case 2: | |
820 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1))) | |
821 | return true; | |
822 | ||
823 | case 1: | |
824 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0))) | |
825 | return true; | |
826 | ||
827 | default: | |
828 | return false; | |
829 | } | |
830 | } | |
831 | ||
832 | /* Determines whether the tree EXPR contains chrecs. */ | |
833 | ||
834 | bool | |
835 | tree_contains_chrecs (tree expr) | |
836 | { | |
837 | if (expr == NULL_TREE) | |
838 | return false; | |
839 | ||
840 | if (tree_is_chrec (expr)) | |
841 | return true; | |
842 | ||
843 | switch (TREE_CODE_LENGTH (TREE_CODE (expr))) | |
844 | { | |
845 | case 3: | |
846 | if (tree_contains_chrecs (TREE_OPERAND (expr, 2))) | |
847 | return true; | |
848 | ||
849 | case 2: | |
850 | if (tree_contains_chrecs (TREE_OPERAND (expr, 1))) | |
851 | return true; | |
852 | ||
853 | case 1: | |
854 | if (tree_contains_chrecs (TREE_OPERAND (expr, 0))) | |
855 | return true; | |
856 | ||
857 | default: | |
858 | return false; | |
859 | } | |
860 | } | |
861 | ||
862 | /* Determine whether the given tree is an affine multivariate | |
863 | evolution. */ | |
864 | ||
865 | bool | |
866 | evolution_function_is_affine_multivariate_p (tree chrec) | |
867 | { | |
868 | if (chrec == NULL_TREE) | |
869 | return false; | |
870 | ||
871 | switch (TREE_CODE (chrec)) | |
872 | { | |
873 | case POLYNOMIAL_CHREC: | |
874 | if (evolution_function_is_constant_p (CHREC_LEFT (chrec))) | |
875 | { | |
876 | if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))) | |
877 | return true; | |
878 | else | |
879 | { | |
880 | if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC | |
881 | && CHREC_VARIABLE (CHREC_RIGHT (chrec)) | |
882 | != CHREC_VARIABLE (chrec) | |
883 | && evolution_function_is_affine_multivariate_p | |
884 | (CHREC_RIGHT (chrec))) | |
885 | return true; | |
886 | else | |
887 | return false; | |
888 | } | |
889 | } | |
890 | else | |
891 | { | |
892 | if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)) | |
893 | && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC | |
894 | && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) | |
895 | && evolution_function_is_affine_multivariate_p | |
896 | (CHREC_LEFT (chrec))) | |
897 | return true; | |
898 | else | |
899 | return false; | |
900 | } | |
901 | ||
902 | default: | |
903 | return false; | |
904 | } | |
905 | } | |
906 | ||
907 | /* Determine whether the given tree is a function in zero or one | |
908 | variables. */ | |
909 | ||
910 | bool | |
911 | evolution_function_is_univariate_p (tree chrec) | |
912 | { | |
913 | if (chrec == NULL_TREE) | |
914 | return true; | |
915 | ||
916 | switch (TREE_CODE (chrec)) | |
917 | { | |
918 | case POLYNOMIAL_CHREC: | |
919 | switch (TREE_CODE (CHREC_LEFT (chrec))) | |
920 | { | |
921 | case POLYNOMIAL_CHREC: | |
922 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) | |
923 | return false; | |
924 | if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) | |
925 | return false; | |
926 | break; | |
927 | ||
928 | default: | |
929 | break; | |
930 | } | |
931 | ||
932 | switch (TREE_CODE (CHREC_RIGHT (chrec))) | |
933 | { | |
934 | case POLYNOMIAL_CHREC: | |
935 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) | |
936 | return false; | |
937 | if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) | |
938 | return false; | |
939 | break; | |
940 | ||
941 | default: | |
942 | break; | |
943 | } | |
944 | ||
945 | default: | |
946 | return true; | |
947 | } | |
948 | } | |
949 | ||
950 | \f | |
951 | ||
952 | /* Convert the initial condition of chrec to type. */ | |
953 | ||
954 | tree | |
955 | chrec_convert (tree type, | |
956 | tree chrec) | |
957 | { | |
958 | tree ct; | |
959 | ||
960 | if (automatically_generated_chrec_p (chrec)) | |
961 | return chrec; | |
962 | ||
963 | ct = chrec_type (chrec); | |
964 | if (ct == type) | |
965 | return chrec; | |
966 | ||
967 | if (TYPE_PRECISION (ct) < TYPE_PRECISION (type)) | |
968 | return count_ev_in_wider_type (type, chrec); | |
969 | ||
970 | switch (TREE_CODE (chrec)) | |
971 | { | |
972 | case POLYNOMIAL_CHREC: | |
973 | return build_polynomial_chrec (CHREC_VARIABLE (chrec), | |
974 | chrec_convert (type, | |
975 | CHREC_LEFT (chrec)), | |
976 | chrec_convert (type, | |
977 | CHREC_RIGHT (chrec))); | |
978 | ||
979 | default: | |
980 | { | |
981 | tree res = convert (type, chrec); | |
982 | ||
983 | /* Don't propagate overflows. */ | |
984 | TREE_OVERFLOW (res) = 0; | |
985 | if (TREE_CODE_CLASS (TREE_CODE (res)) == 'c') | |
986 | TREE_CONSTANT_OVERFLOW (res) = 0; | |
987 | return res; | |
988 | } | |
989 | } | |
990 | } | |
991 | ||
992 | /* Returns the type of the chrec. */ | |
993 | ||
994 | tree | |
995 | chrec_type (tree chrec) | |
996 | { | |
997 | if (automatically_generated_chrec_p (chrec)) | |
998 | return NULL_TREE; | |
999 | ||
1000 | return TREE_TYPE (chrec); | |
1001 | } | |
1002 | ||
1003 | extern void initialize_scalar_evolutions_analyzer (void); | |
1004 | ||
1005 | /* Initializer. */ | |
1006 | ||
1007 | void | |
1008 | initialize_scalar_evolutions_analyzer (void) | |
1009 | { | |
1010 | /* The elements below are unique. */ | |
1011 | if (chrec_dont_know == NULL_TREE) | |
1012 | { | |
1013 | chrec_not_analyzed_yet = NULL_TREE; | |
1014 | chrec_dont_know = make_node (SCEV_NOT_KNOWN); | |
1015 | chrec_known = make_node (SCEV_KNOWN); | |
1016 | TREE_TYPE (chrec_dont_know) = NULL_TREE; | |
1017 | TREE_TYPE (chrec_known) = NULL_TREE; | |
1018 | } | |
1019 | } |