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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 | ||
c8a2ab6d SP |
39 | \f |
40 | ||
41 | /* Extended folder for chrecs. */ | |
42 | ||
43 | /* Determines whether CST is not a constant evolution. */ | |
44 | ||
45 | static inline bool | |
46 | is_not_constant_evolution (tree cst) | |
47 | { | |
48 | return (TREE_CODE (cst) == POLYNOMIAL_CHREC); | |
49 | } | |
50 | ||
51 | /* Fold CODE for a polynomial function and a constant. */ | |
52 | ||
53 | static inline tree | |
54 | chrec_fold_poly_cst (enum tree_code code, | |
55 | tree type, | |
56 | tree poly, | |
57 | tree cst) | |
58 | { | |
59 | #if defined ENABLE_CHECKING | |
60 | if (poly == NULL_TREE | |
61 | || cst == NULL_TREE | |
62 | || TREE_CODE (poly) != POLYNOMIAL_CHREC | |
63 | || is_not_constant_evolution (cst)) | |
64 | abort (); | |
65 | #endif | |
66 | ||
67 | switch (code) | |
68 | { | |
69 | case PLUS_EXPR: | |
70 | return build_polynomial_chrec | |
71 | (CHREC_VARIABLE (poly), | |
72 | chrec_fold_plus (type, CHREC_LEFT (poly), cst), | |
73 | CHREC_RIGHT (poly)); | |
74 | ||
75 | case MINUS_EXPR: | |
76 | return build_polynomial_chrec | |
77 | (CHREC_VARIABLE (poly), | |
78 | chrec_fold_minus (type, CHREC_LEFT (poly), cst), | |
79 | CHREC_RIGHT (poly)); | |
80 | ||
81 | case MULT_EXPR: | |
82 | return build_polynomial_chrec | |
83 | (CHREC_VARIABLE (poly), | |
84 | chrec_fold_multiply (type, CHREC_LEFT (poly), cst), | |
85 | chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); | |
86 | ||
87 | default: | |
88 | return chrec_dont_know; | |
89 | } | |
90 | } | |
91 | ||
92 | /* Fold the addition of two polynomial functions. */ | |
93 | ||
94 | static inline tree | |
95 | chrec_fold_plus_poly_poly (enum tree_code code, | |
96 | tree type, | |
97 | tree poly0, | |
98 | tree poly1) | |
99 | { | |
100 | tree left, right; | |
101 | ||
102 | #if defined ENABLE_CHECKING | |
103 | if (poly0 == NULL_TREE | |
104 | || poly1 == NULL_TREE | |
105 | || TREE_CODE (poly0) != POLYNOMIAL_CHREC | |
106 | || TREE_CODE (poly1) != POLYNOMIAL_CHREC) | |
107 | abort (); | |
108 | #endif | |
109 | ||
110 | /* | |
111 | {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2, | |
112 | {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2, | |
113 | {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */ | |
114 | if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) | |
115 | { | |
116 | if (code == PLUS_EXPR) | |
117 | return build_polynomial_chrec | |
118 | (CHREC_VARIABLE (poly1), | |
119 | chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)), | |
120 | CHREC_RIGHT (poly1)); | |
121 | else | |
122 | return build_polynomial_chrec | |
123 | (CHREC_VARIABLE (poly1), | |
124 | chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)), | |
125 | chrec_fold_multiply (type, CHREC_RIGHT (poly1), | |
126 | convert (type, integer_minus_one_node))); | |
127 | } | |
128 | ||
129 | if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1)) | |
130 | { | |
131 | if (code == PLUS_EXPR) | |
132 | return build_polynomial_chrec | |
133 | (CHREC_VARIABLE (poly0), | |
134 | chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), | |
135 | CHREC_RIGHT (poly0)); | |
136 | else | |
137 | return build_polynomial_chrec | |
138 | (CHREC_VARIABLE (poly0), | |
139 | chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), | |
140 | CHREC_RIGHT (poly0)); | |
141 | } | |
142 | ||
143 | if (code == PLUS_EXPR) | |
144 | { | |
145 | left = chrec_fold_plus | |
146 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
147 | right = chrec_fold_plus | |
148 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
149 | } | |
150 | else | |
151 | { | |
152 | left = chrec_fold_minus | |
153 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
154 | right = chrec_fold_minus | |
155 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
156 | } | |
157 | ||
158 | if (chrec_zerop (right)) | |
159 | return left; | |
160 | else | |
161 | return build_polynomial_chrec | |
162 | (CHREC_VARIABLE (poly0), left, right); | |
163 | } | |
164 | ||
165 | \f | |
166 | ||
167 | /* Fold the multiplication of two polynomial functions. */ | |
168 | ||
169 | static inline tree | |
170 | chrec_fold_multiply_poly_poly (tree type, | |
171 | tree poly0, | |
172 | tree poly1) | |
173 | { | |
174 | #if defined ENABLE_CHECKING | |
175 | if (poly0 == NULL_TREE | |
176 | || poly1 == NULL_TREE | |
177 | || TREE_CODE (poly0) != POLYNOMIAL_CHREC | |
178 | || TREE_CODE (poly1) != POLYNOMIAL_CHREC) | |
179 | abort (); | |
180 | #endif | |
181 | ||
182 | /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, | |
183 | {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, | |
184 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
185 | if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) | |
186 | /* poly0 is a constant wrt. poly1. */ | |
187 | return build_polynomial_chrec | |
188 | (CHREC_VARIABLE (poly1), | |
189 | chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), | |
190 | CHREC_RIGHT (poly1)); | |
191 | ||
192 | if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0)) | |
193 | /* poly1 is a constant wrt. poly0. */ | |
194 | return build_polynomial_chrec | |
195 | (CHREC_VARIABLE (poly0), | |
196 | chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), | |
197 | CHREC_RIGHT (poly0)); | |
198 | ||
199 | /* poly0 and poly1 are two polynomials in the same variable, | |
200 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
201 | return | |
202 | build_polynomial_chrec | |
203 | (CHREC_VARIABLE (poly0), | |
204 | build_polynomial_chrec | |
205 | (CHREC_VARIABLE (poly0), | |
206 | ||
207 | /* "a*c". */ | |
208 | chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)), | |
209 | ||
210 | /* "a*d + b*c + b*d". */ | |
211 | chrec_fold_plus | |
212 | (type, chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)), | |
213 | ||
214 | chrec_fold_plus | |
215 | (type, | |
216 | chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_LEFT (poly1)), | |
217 | chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1))))), | |
218 | ||
219 | /* "2*b*d". */ | |
220 | chrec_fold_multiply | |
7d60be94 | 221 | (type, build_int_cst (NULL_TREE, 2), |
c8a2ab6d SP |
222 | chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)))); |
223 | } | |
224 | ||
225 | /* When the operands are automatically_generated_chrec_p, the fold has | |
226 | to respect the semantics of the operands. */ | |
227 | ||
228 | static inline tree | |
229 | chrec_fold_automatically_generated_operands (tree op0, | |
230 | tree op1) | |
231 | { | |
232 | if (op0 == chrec_dont_know | |
233 | || op1 == chrec_dont_know) | |
234 | return chrec_dont_know; | |
235 | ||
236 | if (op0 == chrec_known | |
237 | || op1 == chrec_known) | |
238 | return chrec_known; | |
239 | ||
240 | if (op0 == chrec_not_analyzed_yet | |
241 | || op1 == chrec_not_analyzed_yet) | |
242 | return chrec_not_analyzed_yet; | |
243 | ||
8c27b7d4 | 244 | /* The default case produces a safe result. */ |
c8a2ab6d SP |
245 | return chrec_dont_know; |
246 | } | |
247 | ||
248 | /* Fold the addition of two chrecs. */ | |
249 | ||
250 | static tree | |
251 | chrec_fold_plus_1 (enum tree_code code, | |
252 | tree type, | |
253 | tree op0, | |
254 | tree op1) | |
255 | { | |
256 | if (automatically_generated_chrec_p (op0) | |
257 | || automatically_generated_chrec_p (op1)) | |
258 | return chrec_fold_automatically_generated_operands (op0, op1); | |
259 | ||
260 | switch (TREE_CODE (op0)) | |
261 | { | |
262 | case POLYNOMIAL_CHREC: | |
263 | switch (TREE_CODE (op1)) | |
264 | { | |
265 | case POLYNOMIAL_CHREC: | |
266 | return chrec_fold_plus_poly_poly (code, type, op0, op1); | |
267 | ||
268 | default: | |
269 | if (code == PLUS_EXPR) | |
270 | return build_polynomial_chrec | |
271 | (CHREC_VARIABLE (op0), | |
272 | chrec_fold_plus (type, CHREC_LEFT (op0), op1), | |
273 | CHREC_RIGHT (op0)); | |
274 | else | |
275 | return build_polynomial_chrec | |
276 | (CHREC_VARIABLE (op0), | |
277 | chrec_fold_minus (type, CHREC_LEFT (op0), op1), | |
278 | CHREC_RIGHT (op0)); | |
279 | } | |
280 | ||
281 | default: | |
282 | switch (TREE_CODE (op1)) | |
283 | { | |
284 | case POLYNOMIAL_CHREC: | |
285 | if (code == PLUS_EXPR) | |
286 | return build_polynomial_chrec | |
287 | (CHREC_VARIABLE (op1), | |
288 | chrec_fold_plus (type, op0, CHREC_LEFT (op1)), | |
289 | CHREC_RIGHT (op1)); | |
290 | else | |
291 | return build_polynomial_chrec | |
292 | (CHREC_VARIABLE (op1), | |
293 | chrec_fold_minus (type, op0, CHREC_LEFT (op1)), | |
294 | chrec_fold_multiply (type, CHREC_RIGHT (op1), | |
295 | convert (type, | |
296 | integer_minus_one_node))); | |
297 | ||
298 | default: | |
299 | if (tree_contains_chrecs (op0) | |
300 | || tree_contains_chrecs (op1)) | |
301 | return build (code, type, op0, op1); | |
302 | else | |
303 | return fold (build (code, type, op0, op1)); | |
304 | } | |
305 | } | |
306 | } | |
307 | ||
308 | /* Fold the addition of two chrecs. */ | |
309 | ||
310 | tree | |
311 | chrec_fold_plus (tree type, | |
312 | tree op0, | |
313 | tree op1) | |
314 | { | |
315 | if (integer_zerop (op0)) | |
316 | return op1; | |
317 | if (integer_zerop (op1)) | |
318 | return op0; | |
319 | ||
320 | return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1); | |
321 | } | |
322 | ||
323 | /* Fold the subtraction of two chrecs. */ | |
324 | ||
325 | tree | |
326 | chrec_fold_minus (tree type, | |
327 | tree op0, | |
328 | tree op1) | |
329 | { | |
330 | if (integer_zerop (op1)) | |
331 | return op0; | |
332 | ||
333 | return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); | |
334 | } | |
335 | ||
336 | /* Fold the multiplication of two chrecs. */ | |
337 | ||
338 | tree | |
339 | chrec_fold_multiply (tree type, | |
340 | tree op0, | |
341 | tree op1) | |
342 | { | |
343 | if (automatically_generated_chrec_p (op0) | |
344 | || automatically_generated_chrec_p (op1)) | |
345 | return chrec_fold_automatically_generated_operands (op0, op1); | |
346 | ||
347 | switch (TREE_CODE (op0)) | |
348 | { | |
349 | case POLYNOMIAL_CHREC: | |
350 | switch (TREE_CODE (op1)) | |
351 | { | |
352 | case POLYNOMIAL_CHREC: | |
353 | return chrec_fold_multiply_poly_poly (type, op0, op1); | |
354 | ||
355 | default: | |
356 | if (integer_onep (op1)) | |
357 | return op0; | |
358 | if (integer_zerop (op1)) | |
359 | return convert (type, integer_zero_node); | |
360 | ||
361 | return build_polynomial_chrec | |
362 | (CHREC_VARIABLE (op0), | |
363 | chrec_fold_multiply (type, CHREC_LEFT (op0), op1), | |
364 | chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); | |
365 | } | |
366 | ||
367 | default: | |
368 | if (integer_onep (op0)) | |
369 | return op1; | |
370 | ||
371 | if (integer_zerop (op0)) | |
372 | return convert (type, integer_zero_node); | |
373 | ||
374 | switch (TREE_CODE (op1)) | |
375 | { | |
376 | case POLYNOMIAL_CHREC: | |
377 | return build_polynomial_chrec | |
378 | (CHREC_VARIABLE (op1), | |
379 | chrec_fold_multiply (type, CHREC_LEFT (op1), op0), | |
380 | chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); | |
381 | ||
382 | default: | |
383 | if (integer_onep (op1)) | |
384 | return op0; | |
385 | if (integer_zerop (op1)) | |
386 | return convert (type, integer_zero_node); | |
387 | return fold (build (MULT_EXPR, type, op0, op1)); | |
388 | } | |
389 | } | |
390 | } | |
391 | ||
392 | \f | |
393 | ||
394 | /* Operations. */ | |
395 | ||
396 | /* The factorial. */ | |
397 | ||
398 | static tree | |
399 | tree_fold_factorial (tree f) | |
400 | { | |
401 | if (tree_int_cst_sgn (f) <= 0) | |
402 | return integer_one_node; | |
403 | else | |
404 | return fold | |
405 | (build (MULT_EXPR, integer_type_node, f, | |
406 | tree_fold_factorial (fold (build (MINUS_EXPR, integer_type_node, | |
407 | f, integer_one_node))))); | |
408 | } | |
409 | ||
410 | /* The binomial coefficient. */ | |
411 | ||
412 | static tree | |
413 | tree_fold_binomial (tree n, | |
414 | tree k) | |
415 | { | |
416 | return fold | |
417 | (build (EXACT_DIV_EXPR, integer_type_node, tree_fold_factorial (n), | |
418 | fold (build (MULT_EXPR, integer_type_node, | |
419 | tree_fold_factorial (k), | |
420 | tree_fold_factorial | |
421 | (fold (build (MINUS_EXPR, integer_type_node, | |
422 | n, k))))))); | |
423 | } | |
424 | ||
425 | /* Helper function. Use the Newton's interpolating formula for | |
426 | evaluating the value of the evolution function. */ | |
427 | ||
428 | static tree | |
429 | chrec_evaluate (unsigned var, | |
430 | tree chrec, | |
431 | tree n, | |
432 | tree k) | |
433 | { | |
434 | tree type = chrec_type (chrec); | |
435 | tree binomial_n_k = tree_fold_binomial (n, k); | |
436 | ||
437 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
438 | { | |
439 | if (CHREC_VARIABLE (chrec) > var) | |
440 | return chrec_evaluate (var, CHREC_LEFT (chrec), n, k); | |
441 | ||
442 | if (CHREC_VARIABLE (chrec) == var) | |
443 | return chrec_fold_plus | |
444 | (type, | |
445 | fold (build (MULT_EXPR, type, binomial_n_k, CHREC_LEFT (chrec))), | |
446 | chrec_evaluate (var, CHREC_RIGHT (chrec), n, | |
447 | fold (build (PLUS_EXPR, type, k, integer_one_node)))); | |
448 | ||
449 | return fold (build (MULT_EXPR, type, binomial_n_k, chrec)); | |
450 | } | |
451 | else | |
452 | return fold (build (MULT_EXPR, type, binomial_n_k, chrec)); | |
453 | } | |
454 | ||
455 | /* Evaluates "CHREC (X)" when the varying variable is VAR. | |
456 | Example: Given the following parameters, | |
457 | ||
458 | var = 1 | |
459 | chrec = {3, +, 4}_1 | |
460 | x = 10 | |
461 | ||
462 | The result is given by the Newton's interpolating formula: | |
463 | 3 * \binom{10}{0} + 4 * \binom{10}{1}. | |
464 | */ | |
465 | ||
466 | tree | |
467 | chrec_apply (unsigned var, | |
468 | tree chrec, | |
469 | tree x) | |
470 | { | |
471 | tree type = chrec_type (chrec); | |
472 | tree res = chrec_dont_know; | |
473 | ||
474 | if (automatically_generated_chrec_p (chrec) | |
475 | || automatically_generated_chrec_p (x) | |
476 | ||
477 | /* When the symbols are defined in an outer loop, it is possible | |
478 | to symbolically compute the apply, since the symbols are | |
479 | constants with respect to the varying loop. */ | |
480 | || chrec_contains_symbols_defined_in_loop (chrec, var) | |
481 | || chrec_contains_symbols (x)) | |
482 | return chrec_dont_know; | |
483 | ||
484 | if (dump_file && (dump_flags & TDF_DETAILS)) | |
485 | fprintf (dump_file, "(chrec_apply \n"); | |
486 | ||
487 | if (evolution_function_is_affine_p (chrec)) | |
488 | { | |
489 | /* "{a, +, b} (x)" -> "a + b*x". */ | |
490 | if (TREE_CODE (CHREC_LEFT (chrec)) == INTEGER_CST | |
491 | && integer_zerop (CHREC_LEFT (chrec))) | |
492 | res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x); | |
493 | ||
494 | else | |
495 | res = chrec_fold_plus (type, CHREC_LEFT (chrec), | |
496 | chrec_fold_multiply (type, | |
497 | CHREC_RIGHT (chrec), x)); | |
498 | } | |
499 | ||
500 | else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
501 | res = chrec; | |
502 | ||
503 | else if (TREE_CODE (x) == INTEGER_CST | |
504 | && tree_int_cst_sgn (x) == 1) | |
505 | /* testsuite/.../ssa-chrec-38.c. */ | |
506 | res = chrec_evaluate (var, chrec, x, integer_zero_node); | |
507 | ||
508 | else | |
509 | res = chrec_dont_know; | |
510 | ||
511 | if (dump_file && (dump_flags & TDF_DETAILS)) | |
512 | { | |
513 | fprintf (dump_file, " (varying_loop = %d\n", var); | |
514 | fprintf (dump_file, ")\n (chrec = "); | |
515 | print_generic_expr (dump_file, chrec, 0); | |
516 | fprintf (dump_file, ")\n (x = "); | |
517 | print_generic_expr (dump_file, x, 0); | |
518 | fprintf (dump_file, ")\n (res = "); | |
519 | print_generic_expr (dump_file, res, 0); | |
520 | fprintf (dump_file, "))\n"); | |
521 | } | |
522 | ||
523 | return res; | |
524 | } | |
525 | ||
526 | /* Replaces the initial condition in CHREC with INIT_COND. */ | |
527 | ||
528 | tree | |
529 | chrec_replace_initial_condition (tree chrec, | |
530 | tree init_cond) | |
531 | { | |
532 | if (automatically_generated_chrec_p (chrec)) | |
533 | return chrec; | |
534 | ||
535 | switch (TREE_CODE (chrec)) | |
536 | { | |
537 | case POLYNOMIAL_CHREC: | |
538 | return build_polynomial_chrec | |
539 | (CHREC_VARIABLE (chrec), | |
540 | chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), | |
541 | CHREC_RIGHT (chrec)); | |
542 | ||
543 | default: | |
544 | return init_cond; | |
545 | } | |
546 | } | |
547 | ||
548 | /* Returns the initial condition of a given CHREC. */ | |
549 | ||
550 | tree | |
551 | initial_condition (tree chrec) | |
552 | { | |
553 | if (automatically_generated_chrec_p (chrec)) | |
554 | return chrec; | |
555 | ||
556 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
557 | return initial_condition (CHREC_LEFT (chrec)); | |
558 | else | |
559 | return chrec; | |
560 | } | |
561 | ||
562 | /* Returns a univariate function that represents the evolution in | |
563 | LOOP_NUM. Mask the evolution of any other loop. */ | |
564 | ||
565 | tree | |
566 | hide_evolution_in_other_loops_than_loop (tree chrec, | |
567 | unsigned loop_num) | |
568 | { | |
569 | if (automatically_generated_chrec_p (chrec)) | |
570 | return chrec; | |
571 | ||
572 | switch (TREE_CODE (chrec)) | |
573 | { | |
574 | case POLYNOMIAL_CHREC: | |
575 | if (CHREC_VARIABLE (chrec) == loop_num) | |
576 | return build_polynomial_chrec | |
577 | (loop_num, | |
578 | hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
579 | loop_num), | |
580 | CHREC_RIGHT (chrec)); | |
581 | ||
582 | else if (CHREC_VARIABLE (chrec) < loop_num) | |
583 | /* There is no evolution in this loop. */ | |
584 | return initial_condition (chrec); | |
585 | ||
586 | else | |
587 | return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
588 | loop_num); | |
589 | ||
590 | default: | |
591 | return chrec; | |
592 | } | |
593 | } | |
594 | ||
595 | /* Returns the evolution part in LOOP_NUM. Example: the call | |
596 | get_evolution_in_loop (1, {{0, +, 1}_1, +, 2}_1) returns | |
597 | {1, +, 2}_1 */ | |
598 | ||
599 | tree | |
600 | evolution_part_in_loop_num (tree chrec, | |
601 | unsigned loop_num) | |
602 | { | |
603 | if (automatically_generated_chrec_p (chrec)) | |
604 | return chrec; | |
605 | ||
606 | switch (TREE_CODE (chrec)) | |
607 | { | |
608 | case POLYNOMIAL_CHREC: | |
609 | if (CHREC_VARIABLE (chrec) == loop_num) | |
610 | { | |
611 | if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC | |
612 | || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) | |
613 | return CHREC_RIGHT (chrec); | |
614 | ||
615 | else | |
616 | return build_polynomial_chrec | |
617 | (loop_num, | |
618 | evolution_part_in_loop_num (CHREC_LEFT (chrec), loop_num), | |
619 | CHREC_RIGHT (chrec)); | |
620 | } | |
621 | ||
622 | else if (CHREC_VARIABLE (chrec) < loop_num) | |
623 | /* There is no evolution part in this loop. */ | |
624 | return NULL_TREE; | |
625 | ||
626 | else | |
627 | return evolution_part_in_loop_num (CHREC_LEFT (chrec), loop_num); | |
628 | ||
629 | default: | |
630 | return NULL_TREE; | |
631 | } | |
632 | } | |
633 | ||
634 | /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. | |
635 | This function is essentially used for setting the evolution to | |
636 | chrec_dont_know, for example after having determined that it is | |
637 | impossible to say how many times a loop will execute. */ | |
638 | ||
639 | tree | |
640 | reset_evolution_in_loop (unsigned loop_num, | |
641 | tree chrec, | |
642 | tree new_evol) | |
643 | { | |
644 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
645 | && CHREC_VARIABLE (chrec) > loop_num) | |
646 | return build | |
647 | (TREE_CODE (chrec), | |
7d60be94 | 648 | build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)), |
c8a2ab6d SP |
649 | reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), new_evol), |
650 | reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), new_evol)); | |
651 | ||
652 | while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
653 | && CHREC_VARIABLE (chrec) == loop_num) | |
654 | chrec = CHREC_LEFT (chrec); | |
655 | ||
656 | return build_polynomial_chrec (loop_num, chrec, new_evol); | |
657 | } | |
658 | ||
659 | /* Merges two evolution functions that were found by following two | |
660 | alternate paths of a conditional expression. */ | |
661 | ||
662 | tree | |
663 | chrec_merge (tree chrec1, | |
664 | tree chrec2) | |
665 | { | |
666 | if (chrec1 == chrec_dont_know | |
667 | || chrec2 == chrec_dont_know) | |
668 | return chrec_dont_know; | |
669 | ||
670 | if (chrec1 == chrec_known | |
671 | || chrec2 == chrec_known) | |
672 | return chrec_known; | |
673 | ||
674 | if (chrec1 == chrec_not_analyzed_yet) | |
675 | return chrec2; | |
676 | if (chrec2 == chrec_not_analyzed_yet) | |
677 | return chrec1; | |
678 | ||
679 | if (operand_equal_p (chrec1, chrec2, 0)) | |
680 | return chrec1; | |
681 | ||
682 | return chrec_dont_know; | |
683 | } | |
684 | ||
685 | \f | |
686 | ||
687 | /* Observers. */ | |
688 | ||
689 | /* Helper function for is_multivariate_chrec. */ | |
690 | ||
691 | static bool | |
692 | is_multivariate_chrec_rec (tree chrec, unsigned int rec_var) | |
693 | { | |
694 | if (chrec == NULL_TREE) | |
695 | return false; | |
696 | ||
697 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
698 | { | |
699 | if (CHREC_VARIABLE (chrec) != rec_var) | |
700 | return true; | |
701 | else | |
702 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) | |
703 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); | |
704 | } | |
705 | else | |
706 | return false; | |
707 | } | |
708 | ||
709 | /* Determine whether the given chrec is multivariate or not. */ | |
710 | ||
711 | bool | |
712 | is_multivariate_chrec (tree chrec) | |
713 | { | |
714 | if (chrec == NULL_TREE) | |
715 | return false; | |
716 | ||
717 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
718 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), | |
719 | CHREC_VARIABLE (chrec)) | |
720 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), | |
721 | CHREC_VARIABLE (chrec))); | |
722 | else | |
723 | return false; | |
724 | } | |
725 | ||
726 | /* Determines whether the chrec contains symbolic names or not. */ | |
727 | ||
728 | bool | |
729 | chrec_contains_symbols (tree chrec) | |
730 | { | |
731 | if (chrec == NULL_TREE) | |
732 | return false; | |
733 | ||
734 | if (TREE_CODE (chrec) == SSA_NAME | |
735 | || TREE_CODE (chrec) == VAR_DECL | |
736 | || TREE_CODE (chrec) == PARM_DECL | |
737 | || TREE_CODE (chrec) == FUNCTION_DECL | |
738 | || TREE_CODE (chrec) == LABEL_DECL | |
739 | || TREE_CODE (chrec) == RESULT_DECL | |
740 | || TREE_CODE (chrec) == FIELD_DECL) | |
741 | return true; | |
742 | ||
743 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
744 | { | |
745 | case 3: | |
746 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 2))) | |
747 | return true; | |
748 | ||
749 | case 2: | |
750 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 1))) | |
751 | return true; | |
752 | ||
753 | case 1: | |
754 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 0))) | |
755 | return true; | |
756 | ||
757 | default: | |
758 | return false; | |
759 | } | |
760 | } | |
761 | ||
762 | /* Determines whether the chrec contains undetermined coefficients. */ | |
763 | ||
764 | bool | |
765 | chrec_contains_undetermined (tree chrec) | |
766 | { | |
767 | if (chrec == chrec_dont_know | |
768 | || chrec == chrec_not_analyzed_yet | |
769 | || chrec == NULL_TREE) | |
770 | return true; | |
771 | ||
772 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
773 | { | |
774 | case 3: | |
775 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2))) | |
776 | return true; | |
777 | ||
778 | case 2: | |
779 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1))) | |
780 | return true; | |
781 | ||
782 | case 1: | |
783 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0))) | |
784 | return true; | |
785 | ||
786 | default: | |
787 | return false; | |
788 | } | |
789 | } | |
790 | ||
791 | /* Determines whether the tree EXPR contains chrecs. */ | |
792 | ||
793 | bool | |
794 | tree_contains_chrecs (tree expr) | |
795 | { | |
796 | if (expr == NULL_TREE) | |
797 | return false; | |
798 | ||
799 | if (tree_is_chrec (expr)) | |
800 | return true; | |
801 | ||
802 | switch (TREE_CODE_LENGTH (TREE_CODE (expr))) | |
803 | { | |
804 | case 3: | |
805 | if (tree_contains_chrecs (TREE_OPERAND (expr, 2))) | |
806 | return true; | |
807 | ||
808 | case 2: | |
809 | if (tree_contains_chrecs (TREE_OPERAND (expr, 1))) | |
810 | return true; | |
811 | ||
812 | case 1: | |
813 | if (tree_contains_chrecs (TREE_OPERAND (expr, 0))) | |
814 | return true; | |
815 | ||
816 | default: | |
817 | return false; | |
818 | } | |
819 | } | |
820 | ||
821 | /* Determine whether the given tree is an affine multivariate | |
822 | evolution. */ | |
823 | ||
824 | bool | |
825 | evolution_function_is_affine_multivariate_p (tree chrec) | |
826 | { | |
827 | if (chrec == NULL_TREE) | |
828 | return false; | |
829 | ||
830 | switch (TREE_CODE (chrec)) | |
831 | { | |
832 | case POLYNOMIAL_CHREC: | |
833 | if (evolution_function_is_constant_p (CHREC_LEFT (chrec))) | |
834 | { | |
835 | if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))) | |
836 | return true; | |
837 | else | |
838 | { | |
839 | if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC | |
840 | && CHREC_VARIABLE (CHREC_RIGHT (chrec)) | |
841 | != CHREC_VARIABLE (chrec) | |
842 | && evolution_function_is_affine_multivariate_p | |
843 | (CHREC_RIGHT (chrec))) | |
844 | return true; | |
845 | else | |
846 | return false; | |
847 | } | |
848 | } | |
849 | else | |
850 | { | |
851 | if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)) | |
852 | && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC | |
853 | && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) | |
854 | && evolution_function_is_affine_multivariate_p | |
855 | (CHREC_LEFT (chrec))) | |
856 | return true; | |
857 | else | |
858 | return false; | |
859 | } | |
860 | ||
861 | default: | |
862 | return false; | |
863 | } | |
864 | } | |
865 | ||
866 | /* Determine whether the given tree is a function in zero or one | |
867 | variables. */ | |
868 | ||
869 | bool | |
870 | evolution_function_is_univariate_p (tree chrec) | |
871 | { | |
872 | if (chrec == NULL_TREE) | |
873 | return true; | |
874 | ||
875 | switch (TREE_CODE (chrec)) | |
876 | { | |
877 | case POLYNOMIAL_CHREC: | |
878 | switch (TREE_CODE (CHREC_LEFT (chrec))) | |
879 | { | |
880 | case POLYNOMIAL_CHREC: | |
881 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) | |
882 | return false; | |
883 | if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) | |
884 | return false; | |
885 | break; | |
886 | ||
887 | default: | |
888 | break; | |
889 | } | |
890 | ||
891 | switch (TREE_CODE (CHREC_RIGHT (chrec))) | |
892 | { | |
893 | case POLYNOMIAL_CHREC: | |
894 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) | |
895 | return false; | |
896 | if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) | |
897 | return false; | |
898 | break; | |
899 | ||
900 | default: | |
901 | break; | |
902 | } | |
903 | ||
904 | default: | |
905 | return true; | |
906 | } | |
907 | } | |
908 | ||
909 | \f | |
910 | ||
911 | /* Convert the initial condition of chrec to type. */ | |
912 | ||
913 | tree | |
914 | chrec_convert (tree type, | |
915 | tree chrec) | |
916 | { | |
917 | tree ct; | |
918 | ||
919 | if (automatically_generated_chrec_p (chrec)) | |
920 | return chrec; | |
921 | ||
922 | ct = chrec_type (chrec); | |
923 | if (ct == type) | |
924 | return chrec; | |
925 | ||
926 | if (TYPE_PRECISION (ct) < TYPE_PRECISION (type)) | |
927 | return count_ev_in_wider_type (type, chrec); | |
928 | ||
929 | switch (TREE_CODE (chrec)) | |
930 | { | |
931 | case POLYNOMIAL_CHREC: | |
932 | return build_polynomial_chrec (CHREC_VARIABLE (chrec), | |
933 | chrec_convert (type, | |
934 | CHREC_LEFT (chrec)), | |
935 | chrec_convert (type, | |
936 | CHREC_RIGHT (chrec))); | |
937 | ||
938 | default: | |
939 | { | |
940 | tree res = convert (type, chrec); | |
941 | ||
942 | /* Don't propagate overflows. */ | |
943 | TREE_OVERFLOW (res) = 0; | |
944 | if (TREE_CODE_CLASS (TREE_CODE (res)) == 'c') | |
945 | TREE_CONSTANT_OVERFLOW (res) = 0; | |
946 | return res; | |
947 | } | |
948 | } | |
949 | } | |
950 | ||
951 | /* Returns the type of the chrec. */ | |
952 | ||
953 | tree | |
954 | chrec_type (tree chrec) | |
955 | { | |
956 | if (automatically_generated_chrec_p (chrec)) | |
957 | return NULL_TREE; | |
958 | ||
959 | return TREE_TYPE (chrec); | |
960 | } | |
961 | ||
962 | extern void initialize_scalar_evolutions_analyzer (void); | |
963 | ||
964 | /* Initializer. */ | |
965 | ||
966 | void | |
967 | initialize_scalar_evolutions_analyzer (void) | |
968 | { | |
969 | /* The elements below are unique. */ | |
970 | if (chrec_dont_know == NULL_TREE) | |
971 | { | |
972 | chrec_not_analyzed_yet = NULL_TREE; | |
973 | chrec_dont_know = make_node (SCEV_NOT_KNOWN); | |
974 | chrec_known = make_node (SCEV_KNOWN); | |
975 | TREE_TYPE (chrec_dont_know) = NULL_TREE; | |
976 | TREE_TYPE (chrec_known) = NULL_TREE; | |
977 | } | |
978 | } |