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c8a2ab6d | 1 | /* Chains of recurrences. |
0ff4040e SP |
2 | Copyright (C) 2003, 2004, 2005, 2006 Free Software Foundation, Inc. |
3 | Contributed by Sebastian Pop <pop@cri.ensmp.fr> | |
c8a2ab6d SP |
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 | |
366ccddb KC |
19 | Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA |
20 | 02110-1301, USA. */ | |
c8a2ab6d SP |
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" | |
c8a2ab6d SP |
31 | #include "ggc.h" |
32 | #include "tree.h" | |
7e0923cd | 33 | #include "real.h" |
c8a2ab6d | 34 | #include "diagnostic.h" |
1e8552eb SP |
35 | #include "cfgloop.h" |
36 | #include "tree-flow.h" | |
c8a2ab6d SP |
37 | #include "tree-chrec.h" |
38 | #include "tree-pass.h" | |
2412d35c | 39 | #include "params.h" |
18aed06a | 40 | #include "tree-scalar-evolution.h" |
c8a2ab6d | 41 | |
c8a2ab6d SP |
42 | \f |
43 | ||
44 | /* Extended folder for chrecs. */ | |
45 | ||
46 | /* Determines whether CST is not a constant evolution. */ | |
47 | ||
48 | static inline bool | |
49 | is_not_constant_evolution (tree cst) | |
50 | { | |
51 | return (TREE_CODE (cst) == POLYNOMIAL_CHREC); | |
52 | } | |
53 | ||
54 | /* Fold CODE for a polynomial function and a constant. */ | |
55 | ||
56 | static inline tree | |
57 | chrec_fold_poly_cst (enum tree_code code, | |
58 | tree type, | |
59 | tree poly, | |
60 | tree cst) | |
61 | { | |
1e128c5f GB |
62 | gcc_assert (poly); |
63 | gcc_assert (cst); | |
64 | gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC); | |
65 | gcc_assert (!is_not_constant_evolution (cst)); | |
e2157b49 SP |
66 | gcc_assert (type == chrec_type (poly)); |
67 | ||
c8a2ab6d SP |
68 | switch (code) |
69 | { | |
70 | case PLUS_EXPR: | |
71 | return build_polynomial_chrec | |
72 | (CHREC_VARIABLE (poly), | |
73 | chrec_fold_plus (type, CHREC_LEFT (poly), cst), | |
74 | CHREC_RIGHT (poly)); | |
75 | ||
76 | case MINUS_EXPR: | |
77 | return build_polynomial_chrec | |
78 | (CHREC_VARIABLE (poly), | |
79 | chrec_fold_minus (type, CHREC_LEFT (poly), cst), | |
80 | CHREC_RIGHT (poly)); | |
81 | ||
82 | case MULT_EXPR: | |
83 | return build_polynomial_chrec | |
84 | (CHREC_VARIABLE (poly), | |
85 | chrec_fold_multiply (type, CHREC_LEFT (poly), cst), | |
86 | chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); | |
87 | ||
88 | default: | |
89 | return chrec_dont_know; | |
90 | } | |
91 | } | |
92 | ||
93 | /* Fold the addition of two polynomial functions. */ | |
94 | ||
95 | static inline tree | |
96 | chrec_fold_plus_poly_poly (enum tree_code code, | |
97 | tree type, | |
98 | tree poly0, | |
99 | tree poly1) | |
100 | { | |
101 | tree left, right; | |
1e128c5f GB |
102 | |
103 | gcc_assert (poly0); | |
104 | gcc_assert (poly1); | |
105 | gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); | |
106 | gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); | |
e2157b49 SP |
107 | gcc_assert (chrec_type (poly0) == chrec_type (poly1)); |
108 | gcc_assert (type == chrec_type (poly0)); | |
c8a2ab6d SP |
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), | |
7e0923cd SP |
126 | SCALAR_FLOAT_TYPE_P (type) |
127 | ? build_real (type, dconstm1) | |
128 | : build_int_cst_type (type, -1))); | |
c8a2ab6d SP |
129 | } |
130 | ||
131 | if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1)) | |
132 | { | |
133 | if (code == PLUS_EXPR) | |
134 | return build_polynomial_chrec | |
135 | (CHREC_VARIABLE (poly0), | |
136 | chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), | |
137 | CHREC_RIGHT (poly0)); | |
138 | else | |
139 | return build_polynomial_chrec | |
140 | (CHREC_VARIABLE (poly0), | |
141 | chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), | |
142 | CHREC_RIGHT (poly0)); | |
143 | } | |
144 | ||
145 | if (code == PLUS_EXPR) | |
146 | { | |
147 | left = chrec_fold_plus | |
148 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
149 | right = chrec_fold_plus | |
150 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
151 | } | |
152 | else | |
153 | { | |
154 | left = chrec_fold_minus | |
155 | (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
156 | right = chrec_fold_minus | |
157 | (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
158 | } | |
159 | ||
160 | if (chrec_zerop (right)) | |
161 | return left; | |
162 | else | |
163 | return build_polynomial_chrec | |
164 | (CHREC_VARIABLE (poly0), left, right); | |
165 | } | |
166 | ||
167 | \f | |
168 | ||
169 | /* Fold the multiplication of two polynomial functions. */ | |
170 | ||
171 | static inline tree | |
172 | chrec_fold_multiply_poly_poly (tree type, | |
173 | tree poly0, | |
174 | tree poly1) | |
175 | { | |
2c5f025d ZD |
176 | tree t0, t1, t2; |
177 | int var; | |
178 | ||
1e128c5f GB |
179 | gcc_assert (poly0); |
180 | gcc_assert (poly1); | |
181 | gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); | |
182 | gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); | |
e2157b49 SP |
183 | gcc_assert (chrec_type (poly0) == chrec_type (poly1)); |
184 | gcc_assert (type == chrec_type (poly0)); | |
c8a2ab6d SP |
185 | |
186 | /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, | |
187 | {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, | |
188 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
189 | if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1)) | |
190 | /* poly0 is a constant wrt. poly1. */ | |
191 | return build_polynomial_chrec | |
192 | (CHREC_VARIABLE (poly1), | |
193 | chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), | |
194 | CHREC_RIGHT (poly1)); | |
195 | ||
196 | if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0)) | |
197 | /* poly1 is a constant wrt. poly0. */ | |
198 | return build_polynomial_chrec | |
199 | (CHREC_VARIABLE (poly0), | |
200 | chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), | |
201 | CHREC_RIGHT (poly0)); | |
202 | ||
203 | /* poly0 and poly1 are two polynomials in the same variable, | |
204 | {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
c8a2ab6d | 205 | |
2c5f025d ZD |
206 | /* "a*c". */ |
207 | t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
208 | ||
209 | /* "a*d + b*c + b*d". */ | |
210 | t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)); | |
211 | t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, | |
212 | CHREC_RIGHT (poly0), | |
213 | CHREC_LEFT (poly1))); | |
214 | t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, | |
215 | CHREC_RIGHT (poly0), | |
216 | CHREC_RIGHT (poly1))); | |
217 | /* "2*b*d". */ | |
218 | t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); | |
7e0923cd SP |
219 | t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type) |
220 | ? build_real (type, dconst2) | |
ff5e9a94 | 221 | : build_int_cst (type, 2), t2); |
2c5f025d ZD |
222 | |
223 | var = CHREC_VARIABLE (poly0); | |
224 | return build_polynomial_chrec (var, t0, | |
225 | build_polynomial_chrec (var, t1, t2)); | |
c8a2ab6d SP |
226 | } |
227 | ||
228 | /* When the operands are automatically_generated_chrec_p, the fold has | |
229 | to respect the semantics of the operands. */ | |
230 | ||
231 | static inline tree | |
232 | chrec_fold_automatically_generated_operands (tree op0, | |
233 | tree op1) | |
234 | { | |
235 | if (op0 == chrec_dont_know | |
236 | || op1 == chrec_dont_know) | |
237 | return chrec_dont_know; | |
238 | ||
239 | if (op0 == chrec_known | |
240 | || op1 == chrec_known) | |
241 | return chrec_known; | |
242 | ||
243 | if (op0 == chrec_not_analyzed_yet | |
244 | || op1 == chrec_not_analyzed_yet) | |
245 | return chrec_not_analyzed_yet; | |
246 | ||
8c27b7d4 | 247 | /* The default case produces a safe result. */ |
c8a2ab6d SP |
248 | return chrec_dont_know; |
249 | } | |
250 | ||
251 | /* Fold the addition of two chrecs. */ | |
252 | ||
253 | static tree | |
e2157b49 SP |
254 | chrec_fold_plus_1 (enum tree_code code, tree type, |
255 | tree op0, tree op1) | |
c8a2ab6d SP |
256 | { |
257 | if (automatically_generated_chrec_p (op0) | |
258 | || automatically_generated_chrec_p (op1)) | |
259 | return chrec_fold_automatically_generated_operands (op0, op1); | |
260 | ||
261 | switch (TREE_CODE (op0)) | |
262 | { | |
263 | case POLYNOMIAL_CHREC: | |
264 | switch (TREE_CODE (op1)) | |
265 | { | |
266 | case POLYNOMIAL_CHREC: | |
267 | return chrec_fold_plus_poly_poly (code, type, op0, op1); | |
268 | ||
269 | default: | |
270 | if (code == PLUS_EXPR) | |
271 | return build_polynomial_chrec | |
272 | (CHREC_VARIABLE (op0), | |
273 | chrec_fold_plus (type, CHREC_LEFT (op0), op1), | |
274 | CHREC_RIGHT (op0)); | |
275 | else | |
276 | return build_polynomial_chrec | |
277 | (CHREC_VARIABLE (op0), | |
278 | chrec_fold_minus (type, CHREC_LEFT (op0), op1), | |
279 | CHREC_RIGHT (op0)); | |
280 | } | |
281 | ||
282 | default: | |
283 | switch (TREE_CODE (op1)) | |
284 | { | |
285 | case POLYNOMIAL_CHREC: | |
286 | if (code == PLUS_EXPR) | |
287 | return build_polynomial_chrec | |
288 | (CHREC_VARIABLE (op1), | |
289 | chrec_fold_plus (type, op0, CHREC_LEFT (op1)), | |
290 | CHREC_RIGHT (op1)); | |
291 | else | |
292 | return build_polynomial_chrec | |
293 | (CHREC_VARIABLE (op1), | |
294 | chrec_fold_minus (type, op0, CHREC_LEFT (op1)), | |
7e0923cd SP |
295 | chrec_fold_multiply (type, CHREC_RIGHT (op1), |
296 | SCALAR_FLOAT_TYPE_P (type) | |
297 | ? build_real (type, dconstm1) | |
298 | : build_int_cst_type (type, -1))); | |
c8a2ab6d SP |
299 | |
300 | default: | |
2412d35c SP |
301 | { |
302 | int size = 0; | |
303 | if ((tree_contains_chrecs (op0, &size) | |
304 | || tree_contains_chrecs (op1, &size)) | |
305 | && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) | |
306 | return build2 (code, type, op0, op1); | |
307 | else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) | |
1c1205fb RG |
308 | return fold_build2 (code, type, |
309 | fold_convert (type, op0), | |
310 | fold_convert (type, op1)); | |
2412d35c SP |
311 | else |
312 | return chrec_dont_know; | |
313 | } | |
c8a2ab6d SP |
314 | } |
315 | } | |
316 | } | |
317 | ||
318 | /* Fold the addition of two chrecs. */ | |
319 | ||
320 | tree | |
321 | chrec_fold_plus (tree type, | |
322 | tree op0, | |
323 | tree op1) | |
324 | { | |
e2157b49 SP |
325 | if (automatically_generated_chrec_p (op0) |
326 | || automatically_generated_chrec_p (op1)) | |
327 | return chrec_fold_automatically_generated_operands (op0, op1); | |
328 | ||
c8a2ab6d SP |
329 | if (integer_zerop (op0)) |
330 | return op1; | |
331 | if (integer_zerop (op1)) | |
332 | return op0; | |
333 | ||
334 | return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1); | |
335 | } | |
336 | ||
337 | /* Fold the subtraction of two chrecs. */ | |
338 | ||
339 | tree | |
340 | chrec_fold_minus (tree type, | |
341 | tree op0, | |
342 | tree op1) | |
343 | { | |
e2157b49 SP |
344 | if (automatically_generated_chrec_p (op0) |
345 | || automatically_generated_chrec_p (op1)) | |
346 | return chrec_fold_automatically_generated_operands (op0, op1); | |
347 | ||
c8a2ab6d SP |
348 | if (integer_zerop (op1)) |
349 | return op0; | |
350 | ||
351 | return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); | |
352 | } | |
353 | ||
354 | /* Fold the multiplication of two chrecs. */ | |
355 | ||
356 | tree | |
357 | chrec_fold_multiply (tree type, | |
358 | tree op0, | |
359 | tree op1) | |
360 | { | |
361 | if (automatically_generated_chrec_p (op0) | |
362 | || automatically_generated_chrec_p (op1)) | |
363 | return chrec_fold_automatically_generated_operands (op0, op1); | |
364 | ||
365 | switch (TREE_CODE (op0)) | |
366 | { | |
367 | case POLYNOMIAL_CHREC: | |
368 | switch (TREE_CODE (op1)) | |
369 | { | |
370 | case POLYNOMIAL_CHREC: | |
371 | return chrec_fold_multiply_poly_poly (type, op0, op1); | |
372 | ||
373 | default: | |
374 | if (integer_onep (op1)) | |
375 | return op0; | |
376 | if (integer_zerop (op1)) | |
ff5e9a94 | 377 | return build_int_cst (type, 0); |
c8a2ab6d SP |
378 | |
379 | return build_polynomial_chrec | |
380 | (CHREC_VARIABLE (op0), | |
381 | chrec_fold_multiply (type, CHREC_LEFT (op0), op1), | |
382 | chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); | |
383 | } | |
384 | ||
385 | default: | |
386 | if (integer_onep (op0)) | |
387 | return op1; | |
388 | ||
389 | if (integer_zerop (op0)) | |
ff5e9a94 | 390 | return build_int_cst (type, 0); |
c8a2ab6d SP |
391 | |
392 | switch (TREE_CODE (op1)) | |
393 | { | |
394 | case POLYNOMIAL_CHREC: | |
395 | return build_polynomial_chrec | |
396 | (CHREC_VARIABLE (op1), | |
397 | chrec_fold_multiply (type, CHREC_LEFT (op1), op0), | |
398 | chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); | |
399 | ||
400 | default: | |
401 | if (integer_onep (op1)) | |
402 | return op0; | |
403 | if (integer_zerop (op1)) | |
ff5e9a94 | 404 | return build_int_cst (type, 0); |
2412d35c | 405 | return fold_build2 (MULT_EXPR, type, op0, op1); |
c8a2ab6d SP |
406 | } |
407 | } | |
408 | } | |
409 | ||
410 | \f | |
411 | ||
412 | /* Operations. */ | |
413 | ||
1a9dddad RS |
414 | /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate |
415 | calculation overflows, otherwise return C(n,k) with type TYPE. */ | |
416 | ||
c8a2ab6d | 417 | static tree |
1a9dddad | 418 | tree_fold_binomial (tree type, tree n, unsigned int k) |
c8a2ab6d | 419 | { |
1a9dddad RS |
420 | unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum; |
421 | HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum; | |
422 | unsigned int i; | |
423 | tree res; | |
424 | ||
425 | /* Handle the most frequent cases. */ | |
426 | if (k == 0) | |
427 | return build_int_cst (type, 1); | |
428 | if (k == 1) | |
429 | return fold_convert (type, n); | |
430 | ||
431 | /* Check that k <= n. */ | |
432 | if (TREE_INT_CST_HIGH (n) == 0 | |
433 | && TREE_INT_CST_LOW (n) < k) | |
434 | return NULL_TREE; | |
435 | ||
436 | /* Numerator = n. */ | |
437 | lnum = TREE_INT_CST_LOW (n); | |
438 | hnum = TREE_INT_CST_HIGH (n); | |
439 | ||
440 | /* Denominator = 2. */ | |
441 | ldenom = 2; | |
442 | hdenom = 0; | |
443 | ||
444 | /* Index = Numerator-1. */ | |
445 | if (lnum == 0) | |
446 | { | |
447 | hidx = hnum - 1; | |
448 | lidx = ~ (unsigned HOST_WIDE_INT) 0; | |
449 | } | |
c8a2ab6d | 450 | else |
1a9dddad RS |
451 | { |
452 | hidx = hnum; | |
453 | lidx = lnum - 1; | |
454 | } | |
c8a2ab6d | 455 | |
1a9dddad RS |
456 | /* Numerator = Numerator*Index = n*(n-1). */ |
457 | if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) | |
458 | return NULL_TREE; | |
c8a2ab6d | 459 | |
1a9dddad RS |
460 | for (i = 3; i <= k; i++) |
461 | { | |
462 | /* Index--. */ | |
463 | if (lidx == 0) | |
464 | { | |
465 | hidx--; | |
466 | lidx = ~ (unsigned HOST_WIDE_INT) 0; | |
467 | } | |
468 | else | |
469 | lidx--; | |
470 | ||
471 | /* Numerator *= Index. */ | |
472 | if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) | |
473 | return NULL_TREE; | |
474 | ||
475 | /* Denominator *= i. */ | |
476 | mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom); | |
477 | } | |
478 | ||
479 | /* Result = Numerator / Denominator. */ | |
480 | div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom, | |
481 | &lres, &hres, &ldum, &hdum); | |
482 | ||
483 | res = build_int_cst_wide (type, lres, hres); | |
484 | return int_fits_type_p (res, type) ? res : NULL_TREE; | |
c8a2ab6d SP |
485 | } |
486 | ||
487 | /* Helper function. Use the Newton's interpolating formula for | |
488 | evaluating the value of the evolution function. */ | |
489 | ||
490 | static tree | |
1a9dddad | 491 | chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k) |
c8a2ab6d | 492 | { |
1a9dddad RS |
493 | tree arg0, arg1, binomial_n_k; |
494 | tree type = TREE_TYPE (chrec); | |
495 | ||
496 | while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
497 | && CHREC_VARIABLE (chrec) > var) | |
498 | chrec = CHREC_LEFT (chrec); | |
499 | ||
500 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
501 | && CHREC_VARIABLE (chrec) == var) | |
c8a2ab6d | 502 | { |
1a9dddad RS |
503 | arg0 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1); |
504 | if (arg0 == chrec_dont_know) | |
505 | return chrec_dont_know; | |
506 | binomial_n_k = tree_fold_binomial (type, n, k); | |
507 | if (!binomial_n_k) | |
508 | return chrec_dont_know; | |
2412d35c SP |
509 | arg1 = fold_build2 (MULT_EXPR, type, |
510 | CHREC_LEFT (chrec), binomial_n_k); | |
1a9dddad | 511 | return chrec_fold_plus (type, arg0, arg1); |
c8a2ab6d | 512 | } |
1a9dddad RS |
513 | |
514 | binomial_n_k = tree_fold_binomial (type, n, k); | |
515 | if (!binomial_n_k) | |
516 | return chrec_dont_know; | |
517 | ||
2412d35c | 518 | return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k); |
c8a2ab6d SP |
519 | } |
520 | ||
521 | /* Evaluates "CHREC (X)" when the varying variable is VAR. | |
522 | Example: Given the following parameters, | |
523 | ||
524 | var = 1 | |
525 | chrec = {3, +, 4}_1 | |
526 | x = 10 | |
527 | ||
528 | The result is given by the Newton's interpolating formula: | |
529 | 3 * \binom{10}{0} + 4 * \binom{10}{1}. | |
530 | */ | |
531 | ||
532 | tree | |
533 | chrec_apply (unsigned var, | |
534 | tree chrec, | |
535 | tree x) | |
536 | { | |
537 | tree type = chrec_type (chrec); | |
538 | tree res = chrec_dont_know; | |
539 | ||
540 | if (automatically_generated_chrec_p (chrec) | |
541 | || automatically_generated_chrec_p (x) | |
542 | ||
543 | /* When the symbols are defined in an outer loop, it is possible | |
544 | to symbolically compute the apply, since the symbols are | |
545 | constants with respect to the varying loop. */ | |
a6f778b2 | 546 | || chrec_contains_symbols_defined_in_loop (chrec, var)) |
c8a2ab6d | 547 | return chrec_dont_know; |
a6f778b2 | 548 | |
c8a2ab6d SP |
549 | if (dump_file && (dump_flags & TDF_DETAILS)) |
550 | fprintf (dump_file, "(chrec_apply \n"); | |
551 | ||
3c0c8f9d SP |
552 | if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type)) |
553 | x = build_real_from_int_cst (type, x); | |
554 | ||
c8a2ab6d SP |
555 | if (evolution_function_is_affine_p (chrec)) |
556 | { | |
557 | /* "{a, +, b} (x)" -> "a + b*x". */ | |
a6f778b2 ZD |
558 | x = chrec_convert (type, x, NULL_TREE); |
559 | res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x); | |
560 | if (!integer_zerop (CHREC_LEFT (chrec))) | |
561 | res = chrec_fold_plus (type, CHREC_LEFT (chrec), res); | |
c8a2ab6d SP |
562 | } |
563 | ||
564 | else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
565 | res = chrec; | |
566 | ||
567 | else if (TREE_CODE (x) == INTEGER_CST | |
568 | && tree_int_cst_sgn (x) == 1) | |
569 | /* testsuite/.../ssa-chrec-38.c. */ | |
1a9dddad | 570 | res = chrec_evaluate (var, chrec, x, 0); |
c8a2ab6d SP |
571 | else |
572 | res = chrec_dont_know; | |
573 | ||
574 | if (dump_file && (dump_flags & TDF_DETAILS)) | |
575 | { | |
576 | fprintf (dump_file, " (varying_loop = %d\n", var); | |
577 | fprintf (dump_file, ")\n (chrec = "); | |
578 | print_generic_expr (dump_file, chrec, 0); | |
579 | fprintf (dump_file, ")\n (x = "); | |
580 | print_generic_expr (dump_file, x, 0); | |
581 | fprintf (dump_file, ")\n (res = "); | |
582 | print_generic_expr (dump_file, res, 0); | |
583 | fprintf (dump_file, "))\n"); | |
584 | } | |
585 | ||
586 | return res; | |
587 | } | |
588 | ||
589 | /* Replaces the initial condition in CHREC with INIT_COND. */ | |
590 | ||
591 | tree | |
592 | chrec_replace_initial_condition (tree chrec, | |
593 | tree init_cond) | |
594 | { | |
595 | if (automatically_generated_chrec_p (chrec)) | |
596 | return chrec; | |
e2157b49 SP |
597 | |
598 | gcc_assert (chrec_type (chrec) == chrec_type (init_cond)); | |
599 | ||
c8a2ab6d SP |
600 | switch (TREE_CODE (chrec)) |
601 | { | |
602 | case POLYNOMIAL_CHREC: | |
603 | return build_polynomial_chrec | |
604 | (CHREC_VARIABLE (chrec), | |
605 | chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), | |
606 | CHREC_RIGHT (chrec)); | |
607 | ||
608 | default: | |
609 | return init_cond; | |
610 | } | |
611 | } | |
612 | ||
613 | /* Returns the initial condition of a given CHREC. */ | |
614 | ||
615 | tree | |
616 | initial_condition (tree chrec) | |
617 | { | |
618 | if (automatically_generated_chrec_p (chrec)) | |
619 | return chrec; | |
620 | ||
621 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
622 | return initial_condition (CHREC_LEFT (chrec)); | |
623 | else | |
624 | return chrec; | |
625 | } | |
626 | ||
627 | /* Returns a univariate function that represents the evolution in | |
628 | LOOP_NUM. Mask the evolution of any other loop. */ | |
629 | ||
630 | tree | |
631 | hide_evolution_in_other_loops_than_loop (tree chrec, | |
632 | unsigned loop_num) | |
633 | { | |
634 | if (automatically_generated_chrec_p (chrec)) | |
635 | return chrec; | |
636 | ||
637 | switch (TREE_CODE (chrec)) | |
638 | { | |
639 | case POLYNOMIAL_CHREC: | |
640 | if (CHREC_VARIABLE (chrec) == loop_num) | |
641 | return build_polynomial_chrec | |
642 | (loop_num, | |
643 | hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
644 | loop_num), | |
645 | CHREC_RIGHT (chrec)); | |
646 | ||
647 | else if (CHREC_VARIABLE (chrec) < loop_num) | |
648 | /* There is no evolution in this loop. */ | |
649 | return initial_condition (chrec); | |
650 | ||
651 | else | |
652 | return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), | |
653 | loop_num); | |
654 | ||
655 | default: | |
656 | return chrec; | |
657 | } | |
658 | } | |
659 | ||
6775f1f3 IR |
660 | /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is |
661 | true, otherwise returns the initial condition in LOOP_NUM. */ | |
c8a2ab6d | 662 | |
6775f1f3 IR |
663 | static tree |
664 | chrec_component_in_loop_num (tree chrec, | |
665 | unsigned loop_num, | |
666 | bool right) | |
c8a2ab6d | 667 | { |
6775f1f3 IR |
668 | tree component; |
669 | ||
c8a2ab6d SP |
670 | if (automatically_generated_chrec_p (chrec)) |
671 | return chrec; | |
672 | ||
673 | switch (TREE_CODE (chrec)) | |
674 | { | |
675 | case POLYNOMIAL_CHREC: | |
676 | if (CHREC_VARIABLE (chrec) == loop_num) | |
677 | { | |
6775f1f3 IR |
678 | if (right) |
679 | component = CHREC_RIGHT (chrec); | |
680 | else | |
681 | component = CHREC_LEFT (chrec); | |
682 | ||
c8a2ab6d SP |
683 | if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC |
684 | || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) | |
6775f1f3 | 685 | return component; |
c8a2ab6d SP |
686 | |
687 | else | |
688 | return build_polynomial_chrec | |
689 | (loop_num, | |
6775f1f3 IR |
690 | chrec_component_in_loop_num (CHREC_LEFT (chrec), |
691 | loop_num, | |
692 | right), | |
693 | component); | |
c8a2ab6d SP |
694 | } |
695 | ||
696 | else if (CHREC_VARIABLE (chrec) < loop_num) | |
697 | /* There is no evolution part in this loop. */ | |
698 | return NULL_TREE; | |
699 | ||
700 | else | |
6775f1f3 IR |
701 | return chrec_component_in_loop_num (CHREC_LEFT (chrec), |
702 | loop_num, | |
703 | right); | |
c8a2ab6d | 704 | |
6775f1f3 IR |
705 | default: |
706 | if (right) | |
707 | return NULL_TREE; | |
708 | else | |
709 | return chrec; | |
c8a2ab6d SP |
710 | } |
711 | } | |
712 | ||
6775f1f3 | 713 | /* Returns the evolution part in LOOP_NUM. Example: the call |
86df10e3 | 714 | evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns |
6775f1f3 IR |
715 | {1, +, 2}_1 */ |
716 | ||
717 | tree | |
718 | evolution_part_in_loop_num (tree chrec, | |
719 | unsigned loop_num) | |
720 | { | |
721 | return chrec_component_in_loop_num (chrec, loop_num, true); | |
722 | } | |
723 | ||
724 | /* Returns the initial condition in LOOP_NUM. Example: the call | |
86df10e3 | 725 | initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns |
6775f1f3 IR |
726 | {0, +, 1}_1 */ |
727 | ||
728 | tree | |
729 | initial_condition_in_loop_num (tree chrec, | |
730 | unsigned loop_num) | |
731 | { | |
732 | return chrec_component_in_loop_num (chrec, loop_num, false); | |
733 | } | |
734 | ||
c8a2ab6d SP |
735 | /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. |
736 | This function is essentially used for setting the evolution to | |
737 | chrec_dont_know, for example after having determined that it is | |
738 | impossible to say how many times a loop will execute. */ | |
739 | ||
740 | tree | |
741 | reset_evolution_in_loop (unsigned loop_num, | |
742 | tree chrec, | |
743 | tree new_evol) | |
744 | { | |
e2157b49 SP |
745 | gcc_assert (chrec_type (chrec) == chrec_type (new_evol)); |
746 | ||
c8a2ab6d SP |
747 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC |
748 | && CHREC_VARIABLE (chrec) > loop_num) | |
6be74c4f JJ |
749 | { |
750 | tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), | |
751 | new_evol); | |
752 | tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), | |
753 | new_evol); | |
754 | return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left), | |
755 | build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)), | |
756 | left, right); | |
757 | } | |
758 | ||
c8a2ab6d SP |
759 | while (TREE_CODE (chrec) == POLYNOMIAL_CHREC |
760 | && CHREC_VARIABLE (chrec) == loop_num) | |
761 | chrec = CHREC_LEFT (chrec); | |
762 | ||
763 | return build_polynomial_chrec (loop_num, chrec, new_evol); | |
764 | } | |
765 | ||
766 | /* Merges two evolution functions that were found by following two | |
767 | alternate paths of a conditional expression. */ | |
768 | ||
769 | tree | |
770 | chrec_merge (tree chrec1, | |
771 | tree chrec2) | |
772 | { | |
773 | if (chrec1 == chrec_dont_know | |
774 | || chrec2 == chrec_dont_know) | |
775 | return chrec_dont_know; | |
776 | ||
777 | if (chrec1 == chrec_known | |
778 | || chrec2 == chrec_known) | |
779 | return chrec_known; | |
780 | ||
781 | if (chrec1 == chrec_not_analyzed_yet) | |
782 | return chrec2; | |
783 | if (chrec2 == chrec_not_analyzed_yet) | |
784 | return chrec1; | |
785 | ||
ace23abf | 786 | if (eq_evolutions_p (chrec1, chrec2)) |
c8a2ab6d SP |
787 | return chrec1; |
788 | ||
789 | return chrec_dont_know; | |
790 | } | |
791 | ||
792 | \f | |
793 | ||
794 | /* Observers. */ | |
795 | ||
796 | /* Helper function for is_multivariate_chrec. */ | |
797 | ||
798 | static bool | |
799 | is_multivariate_chrec_rec (tree chrec, unsigned int rec_var) | |
800 | { | |
801 | if (chrec == NULL_TREE) | |
802 | return false; | |
803 | ||
804 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
805 | { | |
806 | if (CHREC_VARIABLE (chrec) != rec_var) | |
807 | return true; | |
808 | else | |
809 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) | |
810 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); | |
811 | } | |
812 | else | |
813 | return false; | |
814 | } | |
815 | ||
816 | /* Determine whether the given chrec is multivariate or not. */ | |
817 | ||
818 | bool | |
819 | is_multivariate_chrec (tree chrec) | |
820 | { | |
821 | if (chrec == NULL_TREE) | |
822 | return false; | |
823 | ||
824 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
825 | return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), | |
826 | CHREC_VARIABLE (chrec)) | |
827 | || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), | |
828 | CHREC_VARIABLE (chrec))); | |
829 | else | |
830 | return false; | |
831 | } | |
832 | ||
833 | /* Determines whether the chrec contains symbolic names or not. */ | |
834 | ||
835 | bool | |
836 | chrec_contains_symbols (tree chrec) | |
837 | { | |
838 | if (chrec == NULL_TREE) | |
839 | return false; | |
840 | ||
841 | if (TREE_CODE (chrec) == SSA_NAME | |
842 | || TREE_CODE (chrec) == VAR_DECL | |
843 | || TREE_CODE (chrec) == PARM_DECL | |
844 | || TREE_CODE (chrec) == FUNCTION_DECL | |
845 | || TREE_CODE (chrec) == LABEL_DECL | |
846 | || TREE_CODE (chrec) == RESULT_DECL | |
847 | || TREE_CODE (chrec) == FIELD_DECL) | |
848 | return true; | |
849 | ||
850 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
851 | { | |
852 | case 3: | |
853 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 2))) | |
854 | return true; | |
855 | ||
856 | case 2: | |
857 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 1))) | |
858 | return true; | |
859 | ||
860 | case 1: | |
861 | if (chrec_contains_symbols (TREE_OPERAND (chrec, 0))) | |
862 | return true; | |
863 | ||
864 | default: | |
865 | return false; | |
866 | } | |
867 | } | |
868 | ||
869 | /* Determines whether the chrec contains undetermined coefficients. */ | |
870 | ||
871 | bool | |
872 | chrec_contains_undetermined (tree chrec) | |
873 | { | |
874 | if (chrec == chrec_dont_know | |
875 | || chrec == chrec_not_analyzed_yet | |
876 | || chrec == NULL_TREE) | |
877 | return true; | |
878 | ||
879 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
880 | { | |
881 | case 3: | |
882 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2))) | |
883 | return true; | |
884 | ||
885 | case 2: | |
886 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1))) | |
887 | return true; | |
888 | ||
889 | case 1: | |
890 | if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0))) | |
891 | return true; | |
892 | ||
893 | default: | |
894 | return false; | |
895 | } | |
896 | } | |
897 | ||
2412d35c SP |
898 | /* Determines whether the tree EXPR contains chrecs, and increment |
899 | SIZE if it is not a NULL pointer by an estimation of the depth of | |
900 | the tree. */ | |
c8a2ab6d SP |
901 | |
902 | bool | |
2412d35c | 903 | tree_contains_chrecs (tree expr, int *size) |
c8a2ab6d SP |
904 | { |
905 | if (expr == NULL_TREE) | |
906 | return false; | |
2412d35c SP |
907 | |
908 | if (size) | |
909 | (*size)++; | |
c8a2ab6d SP |
910 | |
911 | if (tree_is_chrec (expr)) | |
912 | return true; | |
2412d35c | 913 | |
c8a2ab6d SP |
914 | switch (TREE_CODE_LENGTH (TREE_CODE (expr))) |
915 | { | |
916 | case 3: | |
2412d35c | 917 | if (tree_contains_chrecs (TREE_OPERAND (expr, 2), size)) |
c8a2ab6d SP |
918 | return true; |
919 | ||
920 | case 2: | |
2412d35c | 921 | if (tree_contains_chrecs (TREE_OPERAND (expr, 1), size)) |
c8a2ab6d SP |
922 | return true; |
923 | ||
924 | case 1: | |
2412d35c | 925 | if (tree_contains_chrecs (TREE_OPERAND (expr, 0), size)) |
c8a2ab6d SP |
926 | return true; |
927 | ||
928 | default: | |
929 | return false; | |
930 | } | |
931 | } | |
932 | ||
1e8552eb SP |
933 | /* Recursive helper function. */ |
934 | ||
935 | static bool | |
936 | evolution_function_is_invariant_rec_p (tree chrec, int loopnum) | |
937 | { | |
938 | if (evolution_function_is_constant_p (chrec)) | |
939 | return true; | |
940 | ||
941 | if (TREE_CODE (chrec) == SSA_NAME | |
942 | && expr_invariant_in_loop_p (current_loops->parray[loopnum], | |
943 | chrec)) | |
944 | return true; | |
945 | ||
7ce7896c SP |
946 | if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |
947 | { | |
948 | if (CHREC_VARIABLE (chrec) == (unsigned) loopnum | |
949 | || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), | |
950 | loopnum) | |
951 | || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), | |
952 | loopnum)) | |
953 | return false; | |
954 | return true; | |
955 | } | |
1e8552eb SP |
956 | |
957 | switch (TREE_CODE_LENGTH (TREE_CODE (chrec))) | |
958 | { | |
959 | case 2: | |
960 | if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1), | |
961 | loopnum)) | |
962 | return false; | |
963 | ||
964 | case 1: | |
965 | if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0), | |
966 | loopnum)) | |
967 | return false; | |
968 | return true; | |
969 | ||
970 | default: | |
971 | return false; | |
972 | } | |
973 | ||
974 | return false; | |
975 | } | |
976 | ||
977 | /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */ | |
978 | ||
979 | bool | |
980 | evolution_function_is_invariant_p (tree chrec, int loopnum) | |
981 | { | |
982 | if (evolution_function_is_constant_p (chrec)) | |
983 | return true; | |
984 | ||
985 | if (current_loops != NULL) | |
986 | return evolution_function_is_invariant_rec_p (chrec, loopnum); | |
987 | ||
988 | return false; | |
989 | } | |
990 | ||
c8a2ab6d SP |
991 | /* Determine whether the given tree is an affine multivariate |
992 | evolution. */ | |
993 | ||
994 | bool | |
995 | evolution_function_is_affine_multivariate_p (tree chrec) | |
996 | { | |
997 | if (chrec == NULL_TREE) | |
998 | return false; | |
999 | ||
1000 | switch (TREE_CODE (chrec)) | |
1001 | { | |
1002 | case POLYNOMIAL_CHREC: | |
1003 | if (evolution_function_is_constant_p (CHREC_LEFT (chrec))) | |
1004 | { | |
1005 | if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))) | |
1006 | return true; | |
1007 | else | |
1008 | { | |
1009 | if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC | |
1010 | && CHREC_VARIABLE (CHREC_RIGHT (chrec)) | |
1011 | != CHREC_VARIABLE (chrec) | |
1012 | && evolution_function_is_affine_multivariate_p | |
1013 | (CHREC_RIGHT (chrec))) | |
1014 | return true; | |
1015 | else | |
1016 | return false; | |
1017 | } | |
1018 | } | |
1019 | else | |
1020 | { | |
1021 | if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)) | |
1022 | && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC | |
1023 | && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) | |
1024 | && evolution_function_is_affine_multivariate_p | |
1025 | (CHREC_LEFT (chrec))) | |
1026 | return true; | |
1027 | else | |
1028 | return false; | |
1029 | } | |
1030 | ||
1031 | default: | |
1032 | return false; | |
1033 | } | |
1034 | } | |
1035 | ||
1036 | /* Determine whether the given tree is a function in zero or one | |
1037 | variables. */ | |
1038 | ||
1039 | bool | |
1040 | evolution_function_is_univariate_p (tree chrec) | |
1041 | { | |
1042 | if (chrec == NULL_TREE) | |
1043 | return true; | |
1044 | ||
1045 | switch (TREE_CODE (chrec)) | |
1046 | { | |
1047 | case POLYNOMIAL_CHREC: | |
1048 | switch (TREE_CODE (CHREC_LEFT (chrec))) | |
1049 | { | |
1050 | case POLYNOMIAL_CHREC: | |
1051 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) | |
1052 | return false; | |
1053 | if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) | |
1054 | return false; | |
1055 | break; | |
1056 | ||
1057 | default: | |
1058 | break; | |
1059 | } | |
1060 | ||
1061 | switch (TREE_CODE (CHREC_RIGHT (chrec))) | |
1062 | { | |
1063 | case POLYNOMIAL_CHREC: | |
1064 | if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) | |
1065 | return false; | |
1066 | if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) | |
1067 | return false; | |
1068 | break; | |
1069 | ||
1070 | default: | |
1071 | break; | |
1072 | } | |
1073 | ||
1074 | default: | |
1075 | return true; | |
1076 | } | |
1077 | } | |
1078 | ||
86df10e3 SP |
1079 | /* Returns the number of variables of CHREC. Example: the call |
1080 | nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */ | |
1081 | ||
1082 | unsigned | |
1083 | nb_vars_in_chrec (tree chrec) | |
1084 | { | |
1085 | if (chrec == NULL_TREE) | |
1086 | return 0; | |
1087 | ||
1088 | switch (TREE_CODE (chrec)) | |
1089 | { | |
1090 | case POLYNOMIAL_CHREC: | |
1091 | return 1 + nb_vars_in_chrec | |
1092 | (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec))); | |
1093 | ||
1094 | default: | |
1095 | return 0; | |
1096 | } | |
1097 | } | |
1098 | ||
64a7ab5f ZD |
1099 | /* Returns true if TYPE is a type in that we cannot directly perform |
1100 | arithmetics, even though it is a scalar type. */ | |
1101 | ||
1102 | static bool | |
1103 | avoid_arithmetics_in_type_p (tree type) | |
1104 | { | |
1105 | /* Ada frontend uses subtypes -- an arithmetic cannot be directly performed | |
1106 | in the subtype, but a base type must be used, and the result then can | |
1107 | be casted to the subtype. */ | |
1108 | if (TREE_CODE (type) == INTEGER_TYPE && TREE_TYPE (type) != NULL_TREE) | |
1109 | return true; | |
1110 | ||
1111 | return false; | |
1112 | } | |
1113 | ||
d7f5de76 ZD |
1114 | static tree chrec_convert_1 (tree, tree, tree, bool); |
1115 | ||
1116 | /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv | |
1117 | the scev corresponds to. AT_STMT is the statement at that the scev is | |
1118 | evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that | |
1119 | the rules for overflow of the given language apply (e.g., that signed | |
1120 | arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary | |
1121 | tests, but also to enforce that the result follows them. Returns true if the | |
1122 | conversion succeeded, false otherwise. */ | |
1123 | ||
1124 | bool | |
1125 | convert_affine_scev (struct loop *loop, tree type, | |
1126 | tree *base, tree *step, tree at_stmt, | |
1127 | bool use_overflow_semantics) | |
1128 | { | |
1129 | tree ct = TREE_TYPE (*step); | |
1130 | bool enforce_overflow_semantics; | |
1131 | bool must_check_src_overflow, must_check_rslt_overflow; | |
1132 | tree new_base, new_step; | |
1133 | ||
64a7ab5f ZD |
1134 | /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */ |
1135 | if (avoid_arithmetics_in_type_p (type)) | |
1136 | return false; | |
1137 | ||
d7f5de76 ZD |
1138 | /* In general, |
1139 | (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i, | |
1140 | but we must check some assumptions. | |
1141 | ||
1142 | 1) If [BASE, +, STEP] wraps, the equation is not valid when precision | |
1143 | of CT is smaller than the precision of TYPE. For example, when we | |
1144 | cast unsigned char [254, +, 1] to unsigned, the values on left side | |
1145 | are 254, 255, 0, 1, ..., but those on the right side are | |
1146 | 254, 255, 256, 257, ... | |
1147 | 2) In case that we must also preserve the fact that signed ivs do not | |
1148 | overflow, we must additionally check that the new iv does not wrap. | |
1149 | For example, unsigned char [125, +, 1] casted to signed char could | |
1150 | become a wrapping variable with values 125, 126, 127, -128, -127, ..., | |
1151 | which would confuse optimizers that assume that this does not | |
1152 | happen. */ | |
1153 | must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type); | |
1154 | ||
1155 | enforce_overflow_semantics = (use_overflow_semantics | |
1156 | && nowrap_type_p (type)); | |
1157 | if (enforce_overflow_semantics) | |
1158 | { | |
1159 | /* We can avoid checking whether the result overflows in the following | |
1160 | cases: | |
1161 | ||
1162 | -- must_check_src_overflow is true, and the range of TYPE is superset | |
1163 | of the range of CT -- i.e., in all cases except if CT signed and | |
1164 | TYPE unsigned. | |
1165 | -- both CT and TYPE have the same precision and signedness. */ | |
1166 | if (must_check_src_overflow) | |
1167 | { | |
1168 | if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct)) | |
1169 | must_check_rslt_overflow = true; | |
1170 | else | |
1171 | must_check_rslt_overflow = false; | |
1172 | } | |
1173 | else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type) | |
1174 | && TYPE_PRECISION (ct) == TYPE_PRECISION (type)) | |
1175 | must_check_rslt_overflow = false; | |
1176 | else | |
1177 | must_check_rslt_overflow = true; | |
1178 | } | |
1179 | else | |
1180 | must_check_rslt_overflow = false; | |
1181 | ||
1182 | if (must_check_src_overflow | |
1183 | && scev_probably_wraps_p (*base, *step, at_stmt, loop, | |
1184 | use_overflow_semantics)) | |
1185 | return false; | |
1186 | ||
1187 | new_base = chrec_convert_1 (type, *base, at_stmt, | |
1188 | use_overflow_semantics); | |
1189 | /* The step must be sign extended, regardless of the signedness | |
1190 | of CT and TYPE. This only needs to be handled specially when | |
1191 | CT is unsigned -- to avoid e.g. unsigned char [100, +, 255] | |
1192 | (with values 100, 99, 98, ...) from becoming signed or unsigned | |
1193 | [100, +, 255] with values 100, 355, ...; the sign-extension is | |
1194 | performed by default when CT is signed. */ | |
1195 | new_step = *step; | |
1196 | if (TYPE_PRECISION (type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct)) | |
1197 | new_step = chrec_convert_1 (signed_type_for (ct), new_step, at_stmt, | |
1198 | use_overflow_semantics); | |
1199 | new_step = chrec_convert_1 (type, new_step, at_stmt, use_overflow_semantics); | |
1200 | ||
1201 | if (automatically_generated_chrec_p (new_base) | |
1202 | || automatically_generated_chrec_p (new_step)) | |
1203 | return false; | |
1204 | ||
1205 | if (must_check_rslt_overflow | |
1206 | /* Note that in this case we cannot use the fact that signed variables | |
1207 | do not overflow, as this is what we are verifying for the new iv. */ | |
1208 | && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false)) | |
1209 | return false; | |
1210 | ||
1211 | *base = new_base; | |
1212 | *step = new_step; | |
1213 | return true; | |
1214 | } | |
c8a2ab6d SP |
1215 | \f |
1216 | ||
1e8552eb SP |
1217 | /* Convert CHREC to TYPE. When the analyzer knows the context in |
1218 | which the CHREC is built, it sets AT_STMT to the statement that | |
1219 | contains the definition of the analyzed variable, otherwise the | |
1220 | conversion is less accurate: the information is used for | |
1221 | determining a more accurate estimation of the number of iterations. | |
1222 | By default AT_STMT could be safely set to NULL_TREE. | |
1223 | ||
1224 | The following rule is always true: TREE_TYPE (chrec) == | |
1225 | TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)). | |
1226 | An example of what could happen when adding two chrecs and the type | |
1227 | of the CHREC_RIGHT is different than CHREC_LEFT is: | |
c4cdbeb4 EB |
1228 | |
1229 | {(uint) 0, +, (uchar) 10} + | |
1230 | {(uint) 0, +, (uchar) 250} | |
1231 | ||
1232 | that would produce a wrong result if CHREC_RIGHT is not (uint): | |
1233 | ||
1234 | {(uint) 0, +, (uchar) 4} | |
1235 | ||
1236 | instead of | |
1237 | ||
1238 | {(uint) 0, +, (uint) 260} | |
1239 | */ | |
c8a2ab6d SP |
1240 | |
1241 | tree | |
1e8552eb | 1242 | chrec_convert (tree type, tree chrec, tree at_stmt) |
d7f5de76 ZD |
1243 | { |
1244 | return chrec_convert_1 (type, chrec, at_stmt, true); | |
1245 | } | |
1246 | ||
1247 | /* Convert CHREC to TYPE. When the analyzer knows the context in | |
1248 | which the CHREC is built, it sets AT_STMT to the statement that | |
1249 | contains the definition of the analyzed variable, otherwise the | |
1250 | conversion is less accurate: the information is used for | |
1251 | determining a more accurate estimation of the number of iterations. | |
1252 | By default AT_STMT could be safely set to NULL_TREE. | |
1253 | ||
1254 | USE_OVERFLOW_SEMANTICS is true if this function should assume that | |
1255 | the rules for overflow of the given language apply (e.g., that signed | |
1256 | arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary | |
1257 | tests, but also to enforce that the result follows them. */ | |
1258 | ||
1259 | static tree | |
1260 | chrec_convert_1 (tree type, tree chrec, tree at_stmt, | |
1261 | bool use_overflow_semantics) | |
c8a2ab6d | 1262 | { |
1e8552eb | 1263 | tree ct, res; |
d7f5de76 ZD |
1264 | tree base, step; |
1265 | struct loop *loop; | |
1e8552eb | 1266 | |
c8a2ab6d SP |
1267 | if (automatically_generated_chrec_p (chrec)) |
1268 | return chrec; | |
1269 | ||
1270 | ct = chrec_type (chrec); | |
1271 | if (ct == type) | |
1272 | return chrec; | |
1273 | ||
d7f5de76 ZD |
1274 | if (!evolution_function_is_affine_p (chrec)) |
1275 | goto keep_cast; | |
18aed06a | 1276 | |
d7f5de76 ZD |
1277 | loop = current_loops->parray[CHREC_VARIABLE (chrec)]; |
1278 | base = CHREC_LEFT (chrec); | |
1279 | step = CHREC_RIGHT (chrec); | |
1e8552eb | 1280 | |
d7f5de76 ZD |
1281 | if (convert_affine_scev (loop, type, &base, &step, at_stmt, |
1282 | use_overflow_semantics)) | |
1283 | return build_polynomial_chrec (loop->num, base, step); | |
c8a2ab6d | 1284 | |
d7f5de76 ZD |
1285 | /* If we cannot propagate the cast inside the chrec, just keep the cast. */ |
1286 | keep_cast: | |
1e8552eb | 1287 | res = fold_convert (type, chrec); |
c4cdbeb4 | 1288 | |
1e8552eb SP |
1289 | /* Don't propagate overflows. */ |
1290 | if (CONSTANT_CLASS_P (res)) | |
1291 | { | |
1292 | TREE_CONSTANT_OVERFLOW (res) = 0; | |
1293 | TREE_OVERFLOW (res) = 0; | |
c8a2ab6d | 1294 | } |
1e8552eb SP |
1295 | |
1296 | /* But reject constants that don't fit in their type after conversion. | |
1297 | This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the | |
1298 | natural values associated with TYPE_PRECISION and TYPE_UNSIGNED, | |
1299 | and can cause problems later when computing niters of loops. Note | |
1300 | that we don't do the check before converting because we don't want | |
1301 | to reject conversions of negative chrecs to unsigned types. */ | |
1302 | if (TREE_CODE (res) == INTEGER_CST | |
1303 | && TREE_CODE (type) == INTEGER_TYPE | |
1304 | && !int_fits_type_p (res, type)) | |
1305 | res = chrec_dont_know; | |
1306 | ||
1307 | return res; | |
c8a2ab6d SP |
1308 | } |
1309 | ||
2282a0e6 ZD |
1310 | /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new |
1311 | chrec if something else than what chrec_convert would do happens, NULL_TREE | |
1312 | otherwise. */ | |
1313 | ||
1314 | tree | |
1315 | chrec_convert_aggressive (tree type, tree chrec) | |
1316 | { | |
1317 | tree inner_type, left, right, lc, rc; | |
1318 | ||
1319 | if (automatically_generated_chrec_p (chrec) | |
1320 | || TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
1321 | return NULL_TREE; | |
1322 | ||
1323 | inner_type = TREE_TYPE (chrec); | |
1324 | if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type)) | |
1325 | return NULL_TREE; | |
1326 | ||
64a7ab5f ZD |
1327 | /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */ |
1328 | if (avoid_arithmetics_in_type_p (type)) | |
cdc30c45 | 1329 | return NULL_TREE; |
64a7ab5f | 1330 | |
2282a0e6 ZD |
1331 | left = CHREC_LEFT (chrec); |
1332 | right = CHREC_RIGHT (chrec); | |
1333 | lc = chrec_convert_aggressive (type, left); | |
1334 | if (!lc) | |
1335 | lc = chrec_convert (type, left, NULL_TREE); | |
1336 | rc = chrec_convert_aggressive (type, right); | |
1337 | if (!rc) | |
1338 | rc = chrec_convert (type, right, NULL_TREE); | |
64a7ab5f | 1339 | |
2282a0e6 ZD |
1340 | return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc); |
1341 | } | |
1342 | ||
0ff4040e SP |
1343 | /* Returns true when CHREC0 == CHREC1. */ |
1344 | ||
1345 | bool | |
1346 | eq_evolutions_p (tree chrec0, | |
1347 | tree chrec1) | |
1348 | { | |
1349 | if (chrec0 == NULL_TREE | |
1350 | || chrec1 == NULL_TREE | |
1351 | || TREE_CODE (chrec0) != TREE_CODE (chrec1)) | |
1352 | return false; | |
1353 | ||
1354 | if (chrec0 == chrec1) | |
1355 | return true; | |
1356 | ||
1357 | switch (TREE_CODE (chrec0)) | |
1358 | { | |
1359 | case INTEGER_CST: | |
e2157b49 SP |
1360 | return operand_equal_p (chrec0, chrec1, 0); |
1361 | ||
0ff4040e SP |
1362 | case POLYNOMIAL_CHREC: |
1363 | return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1) | |
1364 | && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1)) | |
1365 | && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1))); | |
1366 | default: | |
1367 | return false; | |
1368 | } | |
1369 | } | |
1370 | ||
d7f5de76 ZD |
1371 | /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow), |
1372 | EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine | |
1373 | which of these cases happens. */ | |
1374 | ||
1375 | enum ev_direction | |
1376 | scev_direction (tree chrec) | |
1377 | { | |
1378 | tree step; | |
1379 | ||
1380 | if (!evolution_function_is_affine_p (chrec)) | |
1381 | return EV_DIR_UNKNOWN; | |
1382 | ||
1383 | step = CHREC_RIGHT (chrec); | |
1384 | if (TREE_CODE (step) != INTEGER_CST) | |
1385 | return EV_DIR_UNKNOWN; | |
1386 | ||
1387 | if (tree_int_cst_sign_bit (step)) | |
1388 | return EV_DIR_DECREASES; | |
1389 | else | |
1390 | return EV_DIR_GROWS; | |
1391 | } |