1 /* Chains of recurrences.
2 Copyright (C) 2003-2018 Free Software Foundation, Inc.
3 Contributed by Sebastian Pop <pop@cri.ensmp.fr>
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 3, 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 COPYING3. If not see
19 <http://www.gnu.org/licenses/>. */
20
21 /* This file implements operations on chains of recurrences. Chains
22 of recurrences are used for modeling evolution functions of scalar
23 variables.
24 */
25
26 #include "config.h"
27 #include "system.h"
28 #include "coretypes.h"
29 #include "backend.h"
30 #include "tree.h"
31 #include "gimple-expr.h"
32 #include "tree-pretty-print.h"
33 #include "fold-const.h"
34 #include "cfgloop.h"
35 #include "tree-ssa-loop-ivopts.h"
36 #include "tree-ssa-loop-niter.h"
37 #include "tree-chrec.h"
38 #include "dumpfile.h"
39 #include "params.h"
40 #include "tree-scalar-evolution.h"
41
42 /* Extended folder for chrecs. */
43
44 /* Determines whether CST is not a constant evolution. */
45
46 static inline bool
is_not_constant_evolution(const_tree cst)47 is_not_constant_evolution (const_tree cst)
48 {
49 return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
50 }
51
52 /* Fold CODE for a polynomial function and a constant. */
53
54 static inline tree
chrec_fold_poly_cst(enum tree_code code,tree type,tree poly,tree cst)55 chrec_fold_poly_cst (enum tree_code code,
56 tree type,
57 tree poly,
58 tree cst)
59 {
60 gcc_assert (poly);
61 gcc_assert (cst);
62 gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
63 gcc_checking_assert (!is_not_constant_evolution (cst));
64 gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly)));
65
66 switch (code)
67 {
68 case PLUS_EXPR:
69 return build_polynomial_chrec
70 (CHREC_VARIABLE (poly),
71 chrec_fold_plus (type, CHREC_LEFT (poly), cst),
72 CHREC_RIGHT (poly));
73
74 case MINUS_EXPR:
75 return build_polynomial_chrec
76 (CHREC_VARIABLE (poly),
77 chrec_fold_minus (type, CHREC_LEFT (poly), cst),
78 CHREC_RIGHT (poly));
79
80 case MULT_EXPR:
81 return build_polynomial_chrec
82 (CHREC_VARIABLE (poly),
83 chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
84 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
85
86 default:
87 return chrec_dont_know;
88 }
89 }
90
91 /* Fold the addition of two polynomial functions. */
92
93 static inline tree
chrec_fold_plus_poly_poly(enum tree_code code,tree type,tree poly0,tree poly1)94 chrec_fold_plus_poly_poly (enum tree_code code,
95 tree type,
96 tree poly0,
97 tree poly1)
98 {
99 tree left, right;
100 struct loop *loop0 = get_chrec_loop (poly0);
101 struct loop *loop1 = get_chrec_loop (poly1);
102 tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type;
103
104 gcc_assert (poly0);
105 gcc_assert (poly1);
106 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
107 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
108 if (POINTER_TYPE_P (chrec_type (poly0)))
109 gcc_checking_assert (ptrofftype_p (chrec_type (poly1))
110 && useless_type_conversion_p (type, chrec_type (poly0)));
111 else
112 gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
113 && useless_type_conversion_p (type, chrec_type (poly1)));
114
115 /*
116 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2,
117 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2,
118 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */
119 if (flow_loop_nested_p (loop0, loop1))
120 {
121 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
122 return build_polynomial_chrec
123 (CHREC_VARIABLE (poly1),
124 chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
125 CHREC_RIGHT (poly1));
126 else
127 return build_polynomial_chrec
128 (CHREC_VARIABLE (poly1),
129 chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
130 chrec_fold_multiply (type, CHREC_RIGHT (poly1),
131 SCALAR_FLOAT_TYPE_P (type)
132 ? build_real (type, dconstm1)
133 : build_int_cst_type (type, -1)));
134 }
135
136 if (flow_loop_nested_p (loop1, loop0))
137 {
138 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
139 return build_polynomial_chrec
140 (CHREC_VARIABLE (poly0),
141 chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
142 CHREC_RIGHT (poly0));
143 else
144 return build_polynomial_chrec
145 (CHREC_VARIABLE (poly0),
146 chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
147 CHREC_RIGHT (poly0));
148 }
149
150 /* This function should never be called for chrecs of loops that
151 do not belong to the same loop nest. */
152 if (loop0 != loop1)
153 {
154 /* It still can happen if we are not in loop-closed SSA form. */
155 gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
156 return chrec_dont_know;
157 }
158
159 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
160 {
161 left = chrec_fold_plus
162 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
163 right = chrec_fold_plus
164 (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
165 }
166 else
167 {
168 left = chrec_fold_minus
169 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
170 right = chrec_fold_minus
171 (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
172 }
173
174 if (chrec_zerop (right))
175 return left;
176 else
177 return build_polynomial_chrec
178 (CHREC_VARIABLE (poly0), left, right);
179 }
180
181
182
183 /* Fold the multiplication of two polynomial functions. */
184
185 static inline tree
chrec_fold_multiply_poly_poly(tree type,tree poly0,tree poly1)186 chrec_fold_multiply_poly_poly (tree type,
187 tree poly0,
188 tree poly1)
189 {
190 tree t0, t1, t2;
191 int var;
192 struct loop *loop0 = get_chrec_loop (poly0);
193 struct loop *loop1 = get_chrec_loop (poly1);
194
195 gcc_assert (poly0);
196 gcc_assert (poly1);
197 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
198 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
199 gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
200 && useless_type_conversion_p (type, chrec_type (poly1)));
201
202 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2,
203 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2,
204 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
205 if (flow_loop_nested_p (loop0, loop1))
206 /* poly0 is a constant wrt. poly1. */
207 return build_polynomial_chrec
208 (CHREC_VARIABLE (poly1),
209 chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
210 CHREC_RIGHT (poly1));
211
212 if (flow_loop_nested_p (loop1, loop0))
213 /* poly1 is a constant wrt. poly0. */
214 return build_polynomial_chrec
215 (CHREC_VARIABLE (poly0),
216 chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
217 CHREC_RIGHT (poly0));
218
219 if (loop0 != loop1)
220 {
221 /* It still can happen if we are not in loop-closed SSA form. */
222 gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
223 return chrec_dont_know;
224 }
225
226 /* poly0 and poly1 are two polynomials in the same variable,
227 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
228
229 /* "a*c". */
230 t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
231
232 /* "a*d + b*c". */
233 t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
234 t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
235 CHREC_RIGHT (poly0),
236 CHREC_LEFT (poly1)));
237 /* "b*d". */
238 t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
239 /* "a*d + b*c + b*d". */
240 t1 = chrec_fold_plus (type, t1, t2);
241 /* "2*b*d". */
242 t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
243 ? build_real (type, dconst2)
244 : build_int_cst (type, 2), t2);
245
246 var = CHREC_VARIABLE (poly0);
247 return build_polynomial_chrec (var, t0,
248 build_polynomial_chrec (var, t1, t2));
249 }
250
251 /* When the operands are automatically_generated_chrec_p, the fold has
252 to respect the semantics of the operands. */
253
254 static inline tree
chrec_fold_automatically_generated_operands(tree op0,tree op1)255 chrec_fold_automatically_generated_operands (tree op0,
256 tree op1)
257 {
258 if (op0 == chrec_dont_know
259 || op1 == chrec_dont_know)
260 return chrec_dont_know;
261
262 if (op0 == chrec_known
263 || op1 == chrec_known)
264 return chrec_known;
265
266 if (op0 == chrec_not_analyzed_yet
267 || op1 == chrec_not_analyzed_yet)
268 return chrec_not_analyzed_yet;
269
270 /* The default case produces a safe result. */
271 return chrec_dont_know;
272 }
273
274 /* Fold the addition of two chrecs. */
275
276 static tree
chrec_fold_plus_1(enum tree_code code,tree type,tree op0,tree op1)277 chrec_fold_plus_1 (enum tree_code code, tree type,
278 tree op0, tree op1)
279 {
280 if (automatically_generated_chrec_p (op0)
281 || automatically_generated_chrec_p (op1))
282 return chrec_fold_automatically_generated_operands (op0, op1);
283
284 switch (TREE_CODE (op0))
285 {
286 case POLYNOMIAL_CHREC:
287 gcc_checking_assert
288 (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
289 switch (TREE_CODE (op1))
290 {
291 case POLYNOMIAL_CHREC:
292 gcc_checking_assert
293 (!chrec_contains_symbols_defined_in_loop (op1,
294 CHREC_VARIABLE (op1)));
295 return chrec_fold_plus_poly_poly (code, type, op0, op1);
296
297 CASE_CONVERT:
298 {
299 /* We can strip sign-conversions to signed by performing the
300 operation in unsigned. */
301 tree optype = TREE_TYPE (TREE_OPERAND (op1, 0));
302 if (INTEGRAL_TYPE_P (type)
303 && INTEGRAL_TYPE_P (optype)
304 && tree_nop_conversion_p (type, optype)
305 && TYPE_UNSIGNED (optype))
306 return chrec_convert (type,
307 chrec_fold_plus_1 (code, optype,
308 chrec_convert (optype,
309 op0, NULL),
310 TREE_OPERAND (op1, 0)),
311 NULL);
312 if (tree_contains_chrecs (op1, NULL))
313 return chrec_dont_know;
314 }
315 /* FALLTHRU */
316
317 default:
318 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
319 return build_polynomial_chrec
320 (CHREC_VARIABLE (op0),
321 chrec_fold_plus (type, CHREC_LEFT (op0), op1),
322 CHREC_RIGHT (op0));
323 else
324 return build_polynomial_chrec
325 (CHREC_VARIABLE (op0),
326 chrec_fold_minus (type, CHREC_LEFT (op0), op1),
327 CHREC_RIGHT (op0));
328 }
329
330 CASE_CONVERT:
331 {
332 /* We can strip sign-conversions to signed by performing the
333 operation in unsigned. */
334 tree optype = TREE_TYPE (TREE_OPERAND (op0, 0));
335 if (INTEGRAL_TYPE_P (type)
336 && INTEGRAL_TYPE_P (optype)
337 && tree_nop_conversion_p (type, optype)
338 && TYPE_UNSIGNED (optype))
339 return chrec_convert (type,
340 chrec_fold_plus_1 (code, optype,
341 TREE_OPERAND (op0, 0),
342 chrec_convert (optype,
343 op1, NULL)),
344 NULL);
345 if (tree_contains_chrecs (op0, NULL))
346 return chrec_dont_know;
347 }
348 /* FALLTHRU */
349
350 default:
351 switch (TREE_CODE (op1))
352 {
353 case POLYNOMIAL_CHREC:
354 gcc_checking_assert
355 (!chrec_contains_symbols_defined_in_loop (op1,
356 CHREC_VARIABLE (op1)));
357 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
358 return build_polynomial_chrec
359 (CHREC_VARIABLE (op1),
360 chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
361 CHREC_RIGHT (op1));
362 else
363 return build_polynomial_chrec
364 (CHREC_VARIABLE (op1),
365 chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
366 chrec_fold_multiply (type, CHREC_RIGHT (op1),
367 SCALAR_FLOAT_TYPE_P (type)
368 ? build_real (type, dconstm1)
369 : build_int_cst_type (type, -1)));
370
371 CASE_CONVERT:
372 if (tree_contains_chrecs (op1, NULL))
373 return chrec_dont_know;
374 /* FALLTHRU */
375
376 default:
377 {
378 int size = 0;
379 if ((tree_contains_chrecs (op0, &size)
380 || tree_contains_chrecs (op1, &size))
381 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
382 return build2 (code, type, op0, op1);
383 else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
384 {
385 if (code == POINTER_PLUS_EXPR)
386 return fold_build_pointer_plus (fold_convert (type, op0),
387 op1);
388 else
389 return fold_build2 (code, type,
390 fold_convert (type, op0),
391 fold_convert (type, op1));
392 }
393 else
394 return chrec_dont_know;
395 }
396 }
397 }
398 }
399
400 /* Fold the addition of two chrecs. */
401
402 tree
chrec_fold_plus(tree type,tree op0,tree op1)403 chrec_fold_plus (tree type,
404 tree op0,
405 tree op1)
406 {
407 enum tree_code code;
408 if (automatically_generated_chrec_p (op0)
409 || automatically_generated_chrec_p (op1))
410 return chrec_fold_automatically_generated_operands (op0, op1);
411
412 if (integer_zerop (op0))
413 return chrec_convert (type, op1, NULL);
414 if (integer_zerop (op1))
415 return chrec_convert (type, op0, NULL);
416
417 if (POINTER_TYPE_P (type))
418 code = POINTER_PLUS_EXPR;
419 else
420 code = PLUS_EXPR;
421
422 return chrec_fold_plus_1 (code, type, op0, op1);
423 }
424
425 /* Fold the subtraction of two chrecs. */
426
427 tree
chrec_fold_minus(tree type,tree op0,tree op1)428 chrec_fold_minus (tree type,
429 tree op0,
430 tree op1)
431 {
432 if (automatically_generated_chrec_p (op0)
433 || automatically_generated_chrec_p (op1))
434 return chrec_fold_automatically_generated_operands (op0, op1);
435
436 if (integer_zerop (op1))
437 return op0;
438
439 return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
440 }
441
442 /* Fold the multiplication of two chrecs. */
443
444 tree
chrec_fold_multiply(tree type,tree op0,tree op1)445 chrec_fold_multiply (tree type,
446 tree op0,
447 tree op1)
448 {
449 if (automatically_generated_chrec_p (op0)
450 || automatically_generated_chrec_p (op1))
451 return chrec_fold_automatically_generated_operands (op0, op1);
452
453 switch (TREE_CODE (op0))
454 {
455 case POLYNOMIAL_CHREC:
456 gcc_checking_assert
457 (!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
458 switch (TREE_CODE (op1))
459 {
460 case POLYNOMIAL_CHREC:
461 gcc_checking_assert
462 (!chrec_contains_symbols_defined_in_loop (op1,
463 CHREC_VARIABLE (op1)));
464 return chrec_fold_multiply_poly_poly (type, op0, op1);
465
466 CASE_CONVERT:
467 if (tree_contains_chrecs (op1, NULL))
468 return chrec_dont_know;
469 /* FALLTHRU */
470
471 default:
472 if (integer_onep (op1))
473 return op0;
474 if (integer_zerop (op1))
475 return build_int_cst (type, 0);
476
477 return build_polynomial_chrec
478 (CHREC_VARIABLE (op0),
479 chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
480 chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
481 }
482
483 CASE_CONVERT:
484 if (tree_contains_chrecs (op0, NULL))
485 return chrec_dont_know;
486 /* FALLTHRU */
487
488 default:
489 if (integer_onep (op0))
490 return op1;
491
492 if (integer_zerop (op0))
493 return build_int_cst (type, 0);
494
495 switch (TREE_CODE (op1))
496 {
497 case POLYNOMIAL_CHREC:
498 gcc_checking_assert
499 (!chrec_contains_symbols_defined_in_loop (op1,
500 CHREC_VARIABLE (op1)));
501 return build_polynomial_chrec
502 (CHREC_VARIABLE (op1),
503 chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
504 chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
505
506 CASE_CONVERT:
507 if (tree_contains_chrecs (op1, NULL))
508 return chrec_dont_know;
509 /* FALLTHRU */
510
511 default:
512 if (integer_onep (op1))
513 return op0;
514 if (integer_zerop (op1))
515 return build_int_cst (type, 0);
516 return fold_build2 (MULT_EXPR, type, op0, op1);
517 }
518 }
519 }
520
521
522
523 /* Operations. */
524
525 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate
526 calculation overflows, otherwise return C(n,k) with type TYPE. */
527
528 static tree
tree_fold_binomial(tree type,tree n,unsigned int k)529 tree_fold_binomial (tree type, tree n, unsigned int k)
530 {
531 bool overflow;
532 unsigned int i;
533
534 /* Handle the most frequent cases. */
535 if (k == 0)
536 return build_int_cst (type, 1);
537 if (k == 1)
538 return fold_convert (type, n);
539
540 widest_int num = wi::to_widest (n);
541
542 /* Check that k <= n. */
543 if (wi::ltu_p (num, k))
544 return NULL_TREE;
545
546 /* Denominator = 2. */
547 widest_int denom = 2;
548
549 /* Index = Numerator-1. */
550 widest_int idx = num - 1;
551
552 /* Numerator = Numerator*Index = n*(n-1). */
553 num = wi::smul (num, idx, &overflow);
554 if (overflow)
555 return NULL_TREE;
556
557 for (i = 3; i <= k; i++)
558 {
559 /* Index--. */
560 --idx;
561
562 /* Numerator *= Index. */
563 num = wi::smul (num, idx, &overflow);
564 if (overflow)
565 return NULL_TREE;
566
567 /* Denominator *= i. */
568 denom *= i;
569 }
570
571 /* Result = Numerator / Denominator. */
572 num = wi::udiv_trunc (num, denom);
573 if (! wi::fits_to_tree_p (num, type))
574 return NULL_TREE;
575 return wide_int_to_tree (type, num);
576 }
577
578 /* Helper function. Use the Newton's interpolating formula for
579 evaluating the value of the evolution function.
580 The result may be in an unsigned type of CHREC. */
581
582 static tree
chrec_evaluate(unsigned var,tree chrec,tree n,unsigned int k)583 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
584 {
585 tree arg0, arg1, binomial_n_k;
586 tree type = TREE_TYPE (chrec);
587 struct loop *var_loop = get_loop (cfun, var);
588
589 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
590 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
591 chrec = CHREC_LEFT (chrec);
592
593 /* The formula associates the expression and thus we have to make
594 sure to not introduce undefined overflow. */
595 tree ctype = type;
596 if (INTEGRAL_TYPE_P (type)
597 && ! TYPE_OVERFLOW_WRAPS (type))
598 ctype = unsigned_type_for (type);
599
600 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
601 && CHREC_VARIABLE (chrec) == var)
602 {
603 arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
604 if (arg1 == chrec_dont_know)
605 return chrec_dont_know;
606 binomial_n_k = tree_fold_binomial (ctype, n, k);
607 if (!binomial_n_k)
608 return chrec_dont_know;
609 tree l = chrec_convert (ctype, CHREC_LEFT (chrec), NULL);
610 arg0 = fold_build2 (MULT_EXPR, ctype, l, binomial_n_k);
611 return chrec_fold_plus (ctype, arg0, arg1);
612 }
613
614 binomial_n_k = tree_fold_binomial (ctype, n, k);
615 if (!binomial_n_k)
616 return chrec_dont_know;
617
618 return fold_build2 (MULT_EXPR, ctype,
619 chrec_convert (ctype, chrec, NULL), binomial_n_k);
620 }
621
622 /* Evaluates "CHREC (X)" when the varying variable is VAR.
623 Example: Given the following parameters,
624
625 var = 1
626 chrec = {3, +, 4}_1
627 x = 10
628
629 The result is given by the Newton's interpolating formula:
630 3 * \binom{10}{0} + 4 * \binom{10}{1}.
631 */
632
633 tree
chrec_apply(unsigned var,tree chrec,tree x)634 chrec_apply (unsigned var,
635 tree chrec,
636 tree x)
637 {
638 tree type = chrec_type (chrec);
639 tree res = chrec_dont_know;
640
641 if (automatically_generated_chrec_p (chrec)
642 || automatically_generated_chrec_p (x)
643
644 /* When the symbols are defined in an outer loop, it is possible
645 to symbolically compute the apply, since the symbols are
646 constants with respect to the varying loop. */
647 || chrec_contains_symbols_defined_in_loop (chrec, var))
648 return chrec_dont_know;
649
650 if (dump_file && (dump_flags & TDF_SCEV))
651 fprintf (dump_file, "(chrec_apply \n");
652
653 if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
654 x = build_real_from_int_cst (type, x);
655
656 switch (TREE_CODE (chrec))
657 {
658 case POLYNOMIAL_CHREC:
659 if (evolution_function_is_affine_p (chrec))
660 {
661 if (CHREC_VARIABLE (chrec) != var)
662 return build_polynomial_chrec
663 (CHREC_VARIABLE (chrec),
664 chrec_apply (var, CHREC_LEFT (chrec), x),
665 chrec_apply (var, CHREC_RIGHT (chrec), x));
666
667 /* "{a, +, b} (x)" -> "a + b*x". */
668 x = chrec_convert_rhs (type, x, NULL);
669 res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x);
670 res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
671 }
672 else if (TREE_CODE (x) == INTEGER_CST
673 && tree_int_cst_sgn (x) == 1)
674 /* testsuite/.../ssa-chrec-38.c. */
675 res = chrec_convert (type, chrec_evaluate (var, chrec, x, 0), NULL);
676 else
677 res = chrec_dont_know;
678 break;
679
680 CASE_CONVERT:
681 res = chrec_convert (TREE_TYPE (chrec),
682 chrec_apply (var, TREE_OPERAND (chrec, 0), x),
683 NULL);
684 break;
685
686 default:
687 res = chrec;
688 break;
689 }
690
691 if (dump_file && (dump_flags & TDF_SCEV))
692 {
693 fprintf (dump_file, " (varying_loop = %d\n", var);
694 fprintf (dump_file, ")\n (chrec = ");
695 print_generic_expr (dump_file, chrec);
696 fprintf (dump_file, ")\n (x = ");
697 print_generic_expr (dump_file, x);
698 fprintf (dump_file, ")\n (res = ");
699 print_generic_expr (dump_file, res);
700 fprintf (dump_file, "))\n");
701 }
702
703 return res;
704 }
705
706 /* For a given CHREC and an induction variable map IV_MAP that maps
707 (loop->num, expr) for every loop number of the current_loops an
708 expression, calls chrec_apply when the expression is not NULL. */
709
710 tree
chrec_apply_map(tree chrec,vec<tree> iv_map)711 chrec_apply_map (tree chrec, vec<tree> iv_map)
712 {
713 int i;
714 tree expr;
715
716 FOR_EACH_VEC_ELT (iv_map, i, expr)
717 if (expr)
718 chrec = chrec_apply (i, chrec, expr);
719
720 return chrec;
721 }
722
723 /* Replaces the initial condition in CHREC with INIT_COND. */
724
725 tree
chrec_replace_initial_condition(tree chrec,tree init_cond)726 chrec_replace_initial_condition (tree chrec,
727 tree init_cond)
728 {
729 if (automatically_generated_chrec_p (chrec))
730 return chrec;
731
732 gcc_assert (chrec_type (chrec) == chrec_type (init_cond));
733
734 switch (TREE_CODE (chrec))
735 {
736 case POLYNOMIAL_CHREC:
737 return build_polynomial_chrec
738 (CHREC_VARIABLE (chrec),
739 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
740 CHREC_RIGHT (chrec));
741
742 default:
743 return init_cond;
744 }
745 }
746
747 /* Returns the initial condition of a given CHREC. */
748
749 tree
initial_condition(tree chrec)750 initial_condition (tree chrec)
751 {
752 if (automatically_generated_chrec_p (chrec))
753 return chrec;
754
755 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
756 return initial_condition (CHREC_LEFT (chrec));
757 else
758 return chrec;
759 }
760
761 /* Returns a univariate function that represents the evolution in
762 LOOP_NUM. Mask the evolution of any other loop. */
763
764 tree
hide_evolution_in_other_loops_than_loop(tree chrec,unsigned loop_num)765 hide_evolution_in_other_loops_than_loop (tree chrec,
766 unsigned loop_num)
767 {
768 struct loop *loop = get_loop (cfun, loop_num), *chloop;
769 if (automatically_generated_chrec_p (chrec))
770 return chrec;
771
772 switch (TREE_CODE (chrec))
773 {
774 case POLYNOMIAL_CHREC:
775 chloop = get_chrec_loop (chrec);
776
777 if (chloop == loop)
778 return build_polynomial_chrec
779 (loop_num,
780 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
781 loop_num),
782 CHREC_RIGHT (chrec));
783
784 else if (flow_loop_nested_p (chloop, loop))
785 /* There is no evolution in this loop. */
786 return initial_condition (chrec);
787
788 else if (flow_loop_nested_p (loop, chloop))
789 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
790 loop_num);
791
792 else
793 return chrec_dont_know;
794
795 default:
796 return chrec;
797 }
798 }
799
800 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
801 true, otherwise returns the initial condition in LOOP_NUM. */
802
803 static tree
chrec_component_in_loop_num(tree chrec,unsigned loop_num,bool right)804 chrec_component_in_loop_num (tree chrec,
805 unsigned loop_num,
806 bool right)
807 {
808 tree component;
809 struct loop *loop = get_loop (cfun, loop_num), *chloop;
810
811 if (automatically_generated_chrec_p (chrec))
812 return chrec;
813
814 switch (TREE_CODE (chrec))
815 {
816 case POLYNOMIAL_CHREC:
817 chloop = get_chrec_loop (chrec);
818
819 if (chloop == loop)
820 {
821 if (right)
822 component = CHREC_RIGHT (chrec);
823 else
824 component = CHREC_LEFT (chrec);
825
826 if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
827 || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
828 return component;
829
830 else
831 return build_polynomial_chrec
832 (loop_num,
833 chrec_component_in_loop_num (CHREC_LEFT (chrec),
834 loop_num,
835 right),
836 component);
837 }
838
839 else if (flow_loop_nested_p (chloop, loop))
840 /* There is no evolution part in this loop. */
841 return NULL_TREE;
842
843 else
844 {
845 gcc_assert (flow_loop_nested_p (loop, chloop));
846 return chrec_component_in_loop_num (CHREC_LEFT (chrec),
847 loop_num,
848 right);
849 }
850
851 default:
852 if (right)
853 return NULL_TREE;
854 else
855 return chrec;
856 }
857 }
858
859 /* Returns the evolution part in LOOP_NUM. Example: the call
860 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
861 {1, +, 2}_1 */
862
863 tree
evolution_part_in_loop_num(tree chrec,unsigned loop_num)864 evolution_part_in_loop_num (tree chrec,
865 unsigned loop_num)
866 {
867 return chrec_component_in_loop_num (chrec, loop_num, true);
868 }
869
870 /* Returns the initial condition in LOOP_NUM. Example: the call
871 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
872 {0, +, 1}_1 */
873
874 tree
initial_condition_in_loop_num(tree chrec,unsigned loop_num)875 initial_condition_in_loop_num (tree chrec,
876 unsigned loop_num)
877 {
878 return chrec_component_in_loop_num (chrec, loop_num, false);
879 }
880
881 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
882 This function is essentially used for setting the evolution to
883 chrec_dont_know, for example after having determined that it is
884 impossible to say how many times a loop will execute. */
885
886 tree
reset_evolution_in_loop(unsigned loop_num,tree chrec,tree new_evol)887 reset_evolution_in_loop (unsigned loop_num,
888 tree chrec,
889 tree new_evol)
890 {
891 struct loop *loop = get_loop (cfun, loop_num);
892
893 if (POINTER_TYPE_P (chrec_type (chrec)))
894 gcc_assert (ptrofftype_p (chrec_type (new_evol)));
895 else
896 gcc_assert (chrec_type (chrec) == chrec_type (new_evol));
897
898 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
899 && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
900 {
901 tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
902 new_evol);
903 tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
904 new_evol);
905 return build_polynomial_chrec (CHREC_VARIABLE (chrec), left, right);
906 }
907
908 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
909 && CHREC_VARIABLE (chrec) == loop_num)
910 chrec = CHREC_LEFT (chrec);
911
912 return build_polynomial_chrec (loop_num, chrec, new_evol);
913 }
914
915 /* Merges two evolution functions that were found by following two
916 alternate paths of a conditional expression. */
917
918 tree
chrec_merge(tree chrec1,tree chrec2)919 chrec_merge (tree chrec1,
920 tree chrec2)
921 {
922 if (chrec1 == chrec_dont_know
923 || chrec2 == chrec_dont_know)
924 return chrec_dont_know;
925
926 if (chrec1 == chrec_known
927 || chrec2 == chrec_known)
928 return chrec_known;
929
930 if (chrec1 == chrec_not_analyzed_yet)
931 return chrec2;
932 if (chrec2 == chrec_not_analyzed_yet)
933 return chrec1;
934
935 if (eq_evolutions_p (chrec1, chrec2))
936 return chrec1;
937
938 return chrec_dont_know;
939 }
940
941
942
943 /* Observers. */
944
945 /* Helper function for is_multivariate_chrec. */
946
947 static bool
is_multivariate_chrec_rec(const_tree chrec,unsigned int rec_var)948 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var)
949 {
950 if (chrec == NULL_TREE)
951 return false;
952
953 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
954 {
955 if (CHREC_VARIABLE (chrec) != rec_var)
956 return true;
957 else
958 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var)
959 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
960 }
961 else
962 return false;
963 }
964
965 /* Determine whether the given chrec is multivariate or not. */
966
967 bool
is_multivariate_chrec(const_tree chrec)968 is_multivariate_chrec (const_tree chrec)
969 {
970 if (chrec == NULL_TREE)
971 return false;
972
973 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
974 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec),
975 CHREC_VARIABLE (chrec))
976 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec),
977 CHREC_VARIABLE (chrec)));
978 else
979 return false;
980 }
981
982 /* Determines whether the chrec contains symbolic names or not. */
983
984 bool
chrec_contains_symbols(const_tree chrec)985 chrec_contains_symbols (const_tree chrec)
986 {
987 int i, n;
988
989 if (chrec == NULL_TREE)
990 return false;
991
992 if (TREE_CODE (chrec) == SSA_NAME
993 || VAR_P (chrec)
994 || TREE_CODE (chrec) == POLY_INT_CST
995 || TREE_CODE (chrec) == PARM_DECL
996 || TREE_CODE (chrec) == FUNCTION_DECL
997 || TREE_CODE (chrec) == LABEL_DECL
998 || TREE_CODE (chrec) == RESULT_DECL
999 || TREE_CODE (chrec) == FIELD_DECL)
1000 return true;
1001
1002 n = TREE_OPERAND_LENGTH (chrec);
1003 for (i = 0; i < n; i++)
1004 if (chrec_contains_symbols (TREE_OPERAND (chrec, i)))
1005 return true;
1006 return false;
1007 }
1008
1009 /* Determines whether the chrec contains undetermined coefficients. */
1010
1011 bool
chrec_contains_undetermined(const_tree chrec)1012 chrec_contains_undetermined (const_tree chrec)
1013 {
1014 int i, n;
1015
1016 if (chrec == chrec_dont_know)
1017 return true;
1018
1019 if (chrec == NULL_TREE)
1020 return false;
1021
1022 n = TREE_OPERAND_LENGTH (chrec);
1023 for (i = 0; i < n; i++)
1024 if (chrec_contains_undetermined (TREE_OPERAND (chrec, i)))
1025 return true;
1026 return false;
1027 }
1028
1029 /* Determines whether the tree EXPR contains chrecs, and increment
1030 SIZE if it is not a NULL pointer by an estimation of the depth of
1031 the tree. */
1032
1033 bool
tree_contains_chrecs(const_tree expr,int * size)1034 tree_contains_chrecs (const_tree expr, int *size)
1035 {
1036 int i, n;
1037
1038 if (expr == NULL_TREE)
1039 return false;
1040
1041 if (size)
1042 (*size)++;
1043
1044 if (tree_is_chrec (expr))
1045 return true;
1046
1047 n = TREE_OPERAND_LENGTH (expr);
1048 for (i = 0; i < n; i++)
1049 if (tree_contains_chrecs (TREE_OPERAND (expr, i), size))
1050 return true;
1051 return false;
1052 }
1053
1054 /* Recursive helper function. */
1055
1056 static bool
evolution_function_is_invariant_rec_p(tree chrec,int loopnum)1057 evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
1058 {
1059 if (evolution_function_is_constant_p (chrec))
1060 return true;
1061
1062 if (TREE_CODE (chrec) == SSA_NAME
1063 && (loopnum == 0
1064 || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec)))
1065 return true;
1066
1067 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
1068 {
1069 if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
1070 || flow_loop_nested_p (get_loop (cfun, loopnum),
1071 get_chrec_loop (chrec))
1072 || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
1073 loopnum)
1074 || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
1075 loopnum))
1076 return false;
1077 return true;
1078 }
1079
1080 switch (TREE_OPERAND_LENGTH (chrec))
1081 {
1082 case 2:
1083 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
1084 loopnum))
1085 return false;
1086 /* FALLTHRU */
1087
1088 case 1:
1089 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
1090 loopnum))
1091 return false;
1092 return true;
1093
1094 default:
1095 return false;
1096 }
1097
1098 return false;
1099 }
1100
1101 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
1102
1103 bool
evolution_function_is_invariant_p(tree chrec,int loopnum)1104 evolution_function_is_invariant_p (tree chrec, int loopnum)
1105 {
1106 return evolution_function_is_invariant_rec_p (chrec, loopnum);
1107 }
1108
1109 /* Determine whether the given tree is an affine multivariate
1110 evolution. */
1111
1112 bool
evolution_function_is_affine_multivariate_p(const_tree chrec,int loopnum)1113 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
1114 {
1115 if (chrec == NULL_TREE)
1116 return false;
1117
1118 switch (TREE_CODE (chrec))
1119 {
1120 case POLYNOMIAL_CHREC:
1121 if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
1122 {
1123 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
1124 return true;
1125 else
1126 {
1127 if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
1128 && CHREC_VARIABLE (CHREC_RIGHT (chrec))
1129 != CHREC_VARIABLE (chrec)
1130 && evolution_function_is_affine_multivariate_p
1131 (CHREC_RIGHT (chrec), loopnum))
1132 return true;
1133 else
1134 return false;
1135 }
1136 }
1137 else
1138 {
1139 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
1140 && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
1141 && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
1142 && evolution_function_is_affine_multivariate_p
1143 (CHREC_LEFT (chrec), loopnum))
1144 return true;
1145 else
1146 return false;
1147 }
1148
1149 default:
1150 return false;
1151 }
1152 }
1153
1154 /* Determine whether the given tree is a function in zero or one
1155 variables. */
1156
1157 bool
evolution_function_is_univariate_p(const_tree chrec)1158 evolution_function_is_univariate_p (const_tree chrec)
1159 {
1160 if (chrec == NULL_TREE)
1161 return true;
1162
1163 switch (TREE_CODE (chrec))
1164 {
1165 case POLYNOMIAL_CHREC:
1166 switch (TREE_CODE (CHREC_LEFT (chrec)))
1167 {
1168 case POLYNOMIAL_CHREC:
1169 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
1170 return false;
1171 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
1172 return false;
1173 break;
1174
1175 default:
1176 if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
1177 return false;
1178 break;
1179 }
1180
1181 switch (TREE_CODE (CHREC_RIGHT (chrec)))
1182 {
1183 case POLYNOMIAL_CHREC:
1184 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
1185 return false;
1186 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
1187 return false;
1188 break;
1189
1190 default:
1191 if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
1192 return false;
1193 break;
1194 }
1195 return true;
1196
1197 default:
1198 return true;
1199 }
1200 }
1201
1202 /* Returns the number of variables of CHREC. Example: the call
1203 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */
1204
1205 unsigned
nb_vars_in_chrec(tree chrec)1206 nb_vars_in_chrec (tree chrec)
1207 {
1208 if (chrec == NULL_TREE)
1209 return 0;
1210
1211 switch (TREE_CODE (chrec))
1212 {
1213 case POLYNOMIAL_CHREC:
1214 return 1 + nb_vars_in_chrec
1215 (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));
1216
1217 default:
1218 return 0;
1219 }
1220 }
1221
1222 /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv
1223 the scev corresponds to. AT_STMT is the statement at that the scev is
1224 evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume
1225 that the rules for overflow of the given language apply (e.g., that signed
1226 arithmetics in C does not overflow) -- i.e., to use them to avoid
1227 unnecessary tests, but also to enforce that the result follows them.
1228 FROM is the source variable converted if it's not NULL. Returns true if
1229 the conversion succeeded, false otherwise. */
1230
1231 bool
convert_affine_scev(struct loop * loop,tree type,tree * base,tree * step,gimple * at_stmt,bool use_overflow_semantics,tree from)1232 convert_affine_scev (struct loop *loop, tree type,
1233 tree *base, tree *step, gimple *at_stmt,
1234 bool use_overflow_semantics, tree from)
1235 {
1236 tree ct = TREE_TYPE (*step);
1237 bool enforce_overflow_semantics;
1238 bool must_check_src_overflow, must_check_rslt_overflow;
1239 tree new_base, new_step;
1240 tree step_type = POINTER_TYPE_P (type) ? sizetype : type;
1241
1242 /* In general,
1243 (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1244 but we must check some assumptions.
1245
1246 1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1247 of CT is smaller than the precision of TYPE. For example, when we
1248 cast unsigned char [254, +, 1] to unsigned, the values on left side
1249 are 254, 255, 0, 1, ..., but those on the right side are
1250 254, 255, 256, 257, ...
1251 2) In case that we must also preserve the fact that signed ivs do not
1252 overflow, we must additionally check that the new iv does not wrap.
1253 For example, unsigned char [125, +, 1] casted to signed char could
1254 become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1255 which would confuse optimizers that assume that this does not
1256 happen. */
1257 must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);
1258
1259 enforce_overflow_semantics = (use_overflow_semantics
1260 && nowrap_type_p (type));
1261 if (enforce_overflow_semantics)
1262 {
1263 /* We can avoid checking whether the result overflows in the following
1264 cases:
1265
1266 -- must_check_src_overflow is true, and the range of TYPE is superset
1267 of the range of CT -- i.e., in all cases except if CT signed and
1268 TYPE unsigned.
1269 -- both CT and TYPE have the same precision and signedness, and we
1270 verify instead that the source does not overflow (this may be
1271 easier than verifying it for the result, as we may use the
1272 information about the semantics of overflow in CT). */
1273 if (must_check_src_overflow)
1274 {
1275 if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
1276 must_check_rslt_overflow = true;
1277 else
1278 must_check_rslt_overflow = false;
1279 }
1280 else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
1281 && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
1282 {
1283 must_check_rslt_overflow = false;
1284 must_check_src_overflow = true;
1285 }
1286 else
1287 must_check_rslt_overflow = true;
1288 }
1289 else
1290 must_check_rslt_overflow = false;
1291
1292 if (must_check_src_overflow
1293 && scev_probably_wraps_p (from, *base, *step, at_stmt, loop,
1294 use_overflow_semantics))
1295 return false;
1296
1297 new_base = chrec_convert (type, *base, at_stmt, use_overflow_semantics);
1298 /* The step must be sign extended, regardless of the signedness
1299 of CT and TYPE. This only needs to be handled specially when
1300 CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1301 (with values 100, 99, 98, ...) from becoming signed or unsigned
1302 [100, +, 255] with values 100, 355, ...; the sign-extension is
1303 performed by default when CT is signed. */
1304 new_step = *step;
1305 if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
1306 {
1307 tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
1308 new_step = chrec_convert (signed_ct, new_step, at_stmt,
1309 use_overflow_semantics);
1310 }
1311 new_step = chrec_convert (step_type, new_step, at_stmt,
1312 use_overflow_semantics);
1313
1314 if (automatically_generated_chrec_p (new_base)
1315 || automatically_generated_chrec_p (new_step))
1316 return false;
1317
1318 if (must_check_rslt_overflow
1319 /* Note that in this case we cannot use the fact that signed variables
1320 do not overflow, as this is what we are verifying for the new iv. */
1321 && scev_probably_wraps_p (NULL_TREE, new_base, new_step,
1322 at_stmt, loop, false))
1323 return false;
1324
1325 *base = new_base;
1326 *step = new_step;
1327 return true;
1328 }
1329
1330
1331 /* Convert CHREC for the right hand side of a CHREC.
1332 The increment for a pointer type is always sizetype. */
1333
1334 tree
chrec_convert_rhs(tree type,tree chrec,gimple * at_stmt)1335 chrec_convert_rhs (tree type, tree chrec, gimple *at_stmt)
1336 {
1337 if (POINTER_TYPE_P (type))
1338 type = sizetype;
1339
1340 return chrec_convert (type, chrec, at_stmt);
1341 }
1342
1343 /* Convert CHREC to TYPE. When the analyzer knows the context in
1344 which the CHREC is built, it sets AT_STMT to the statement that
1345 contains the definition of the analyzed variable, otherwise the
1346 conversion is less accurate: the information is used for
1347 determining a more accurate estimation of the number of iterations.
1348 By default AT_STMT could be safely set to NULL_TREE.
1349
1350 USE_OVERFLOW_SEMANTICS is true if this function should assume that
1351 the rules for overflow of the given language apply (e.g., that signed
1352 arithmetics in C does not overflow) -- i.e., to use them to avoid
1353 unnecessary tests, but also to enforce that the result follows them.
1354
1355 FROM is the source variable converted if it's not NULL. */
1356
1357 static tree
chrec_convert_1(tree type,tree chrec,gimple * at_stmt,bool use_overflow_semantics,tree from)1358 chrec_convert_1 (tree type, tree chrec, gimple *at_stmt,
1359 bool use_overflow_semantics, tree from)
1360 {
1361 tree ct, res;
1362 tree base, step;
1363 struct loop *loop;
1364
1365 if (automatically_generated_chrec_p (chrec))
1366 return chrec;
1367
1368 ct = chrec_type (chrec);
1369 if (useless_type_conversion_p (type, ct))
1370 return chrec;
1371
1372 if (!evolution_function_is_affine_p (chrec))
1373 goto keep_cast;
1374
1375 loop = get_chrec_loop (chrec);
1376 base = CHREC_LEFT (chrec);
1377 step = CHREC_RIGHT (chrec);
1378
1379 if (convert_affine_scev (loop, type, &base, &step, at_stmt,
1380 use_overflow_semantics, from))
1381 return build_polynomial_chrec (loop->num, base, step);
1382
1383 /* If we cannot propagate the cast inside the chrec, just keep the cast. */
1384 keep_cast:
1385 /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
1386 may be more expensive. We do want to perform this optimization here
1387 though for canonicalization reasons. */
1388 if (use_overflow_semantics
1389 && (TREE_CODE (chrec) == PLUS_EXPR
1390 || TREE_CODE (chrec) == MINUS_EXPR)
1391 && TREE_CODE (type) == INTEGER_TYPE
1392 && TREE_CODE (ct) == INTEGER_TYPE
1393 && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
1394 && TYPE_OVERFLOW_UNDEFINED (ct))
1395 res = fold_build2 (TREE_CODE (chrec), type,
1396 fold_convert (type, TREE_OPERAND (chrec, 0)),
1397 fold_convert (type, TREE_OPERAND (chrec, 1)));
1398 /* Similar perform the trick that (signed char)((int)x + 2) can be
1399 narrowed to (signed char)((unsigned char)x + 2). */
1400 else if (use_overflow_semantics
1401 && TREE_CODE (chrec) == POLYNOMIAL_CHREC
1402 && TREE_CODE (ct) == INTEGER_TYPE
1403 && TREE_CODE (type) == INTEGER_TYPE
1404 && TYPE_OVERFLOW_UNDEFINED (type)
1405 && TYPE_PRECISION (type) < TYPE_PRECISION (ct))
1406 {
1407 tree utype = unsigned_type_for (type);
1408 res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
1409 fold_convert (utype,
1410 CHREC_LEFT (chrec)),
1411 fold_convert (utype,
1412 CHREC_RIGHT (chrec)));
1413 res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics, from);
1414 }
1415 else
1416 res = fold_convert (type, chrec);
1417
1418 /* Don't propagate overflows. */
1419 if (CONSTANT_CLASS_P (res))
1420 TREE_OVERFLOW (res) = 0;
1421
1422 /* But reject constants that don't fit in their type after conversion.
1423 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1424 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1425 and can cause problems later when computing niters of loops. Note
1426 that we don't do the check before converting because we don't want
1427 to reject conversions of negative chrecs to unsigned types. */
1428 if (TREE_CODE (res) == INTEGER_CST
1429 && TREE_CODE (type) == INTEGER_TYPE
1430 && !int_fits_type_p (res, type))
1431 res = chrec_dont_know;
1432
1433 return res;
1434 }
1435
1436 /* Convert CHREC to TYPE. When the analyzer knows the context in
1437 which the CHREC is built, it sets AT_STMT to the statement that
1438 contains the definition of the analyzed variable, otherwise the
1439 conversion is less accurate: the information is used for
1440 determining a more accurate estimation of the number of iterations.
1441 By default AT_STMT could be safely set to NULL_TREE.
1442
1443 The following rule is always true: TREE_TYPE (chrec) ==
1444 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1445 An example of what could happen when adding two chrecs and the type
1446 of the CHREC_RIGHT is different than CHREC_LEFT is:
1447
1448 {(uint) 0, +, (uchar) 10} +
1449 {(uint) 0, +, (uchar) 250}
1450
1451 that would produce a wrong result if CHREC_RIGHT is not (uint):
1452
1453 {(uint) 0, +, (uchar) 4}
1454
1455 instead of
1456
1457 {(uint) 0, +, (uint) 260}
1458
1459 USE_OVERFLOW_SEMANTICS is true if this function should assume that
1460 the rules for overflow of the given language apply (e.g., that signed
1461 arithmetics in C does not overflow) -- i.e., to use them to avoid
1462 unnecessary tests, but also to enforce that the result follows them.
1463
1464 FROM is the source variable converted if it's not NULL. */
1465
1466 tree
chrec_convert(tree type,tree chrec,gimple * at_stmt,bool use_overflow_semantics,tree from)1467 chrec_convert (tree type, tree chrec, gimple *at_stmt,
1468 bool use_overflow_semantics, tree from)
1469 {
1470 return chrec_convert_1 (type, chrec, at_stmt, use_overflow_semantics, from);
1471 }
1472
1473 /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new
1474 chrec if something else than what chrec_convert would do happens, NULL_TREE
1475 otherwise. This function set TRUE to variable pointed by FOLD_CONVERSIONS
1476 if the result chrec may overflow. */
1477
1478 tree
chrec_convert_aggressive(tree type,tree chrec,bool * fold_conversions)1479 chrec_convert_aggressive (tree type, tree chrec, bool *fold_conversions)
1480 {
1481 tree inner_type, left, right, lc, rc, rtype;
1482
1483 gcc_assert (fold_conversions != NULL);
1484
1485 if (automatically_generated_chrec_p (chrec)
1486 || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1487 return NULL_TREE;
1488
1489 inner_type = TREE_TYPE (chrec);
1490 if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
1491 return NULL_TREE;
1492
1493 if (useless_type_conversion_p (type, inner_type))
1494 return NULL_TREE;
1495
1496 if (!*fold_conversions && evolution_function_is_affine_p (chrec))
1497 {
1498 tree base, step;
1499 struct loop *loop;
1500
1501 loop = get_chrec_loop (chrec);
1502 base = CHREC_LEFT (chrec);
1503 step = CHREC_RIGHT (chrec);
1504 if (convert_affine_scev (loop, type, &base, &step, NULL, true))
1505 return build_polynomial_chrec (loop->num, base, step);
1506 }
1507 rtype = POINTER_TYPE_P (type) ? sizetype : type;
1508
1509 left = CHREC_LEFT (chrec);
1510 right = CHREC_RIGHT (chrec);
1511 lc = chrec_convert_aggressive (type, left, fold_conversions);
1512 if (!lc)
1513 lc = chrec_convert (type, left, NULL);
1514 rc = chrec_convert_aggressive (rtype, right, fold_conversions);
1515 if (!rc)
1516 rc = chrec_convert (rtype, right, NULL);
1517
1518 *fold_conversions = true;
1519
1520 return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
1521 }
1522
1523 /* Returns true when CHREC0 == CHREC1. */
1524
1525 bool
eq_evolutions_p(const_tree chrec0,const_tree chrec1)1526 eq_evolutions_p (const_tree chrec0, const_tree chrec1)
1527 {
1528 if (chrec0 == NULL_TREE
1529 || chrec1 == NULL_TREE
1530 || TREE_CODE (chrec0) != TREE_CODE (chrec1))
1531 return false;
1532
1533 if (chrec0 == chrec1)
1534 return true;
1535
1536 if (! types_compatible_p (TREE_TYPE (chrec0), TREE_TYPE (chrec1)))
1537 return false;
1538
1539 switch (TREE_CODE (chrec0))
1540 {
1541 case POLYNOMIAL_CHREC:
1542 return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
1543 && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
1544 && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));
1545
1546 case PLUS_EXPR:
1547 case MULT_EXPR:
1548 case MINUS_EXPR:
1549 case POINTER_PLUS_EXPR:
1550 return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1551 TREE_OPERAND (chrec1, 0))
1552 && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
1553 TREE_OPERAND (chrec1, 1));
1554
1555 CASE_CONVERT:
1556 return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
1557 TREE_OPERAND (chrec1, 0));
1558
1559 default:
1560 return operand_equal_p (chrec0, chrec1, 0);
1561 }
1562 }
1563
1564 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1565 EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1566 which of these cases happens. */
1567
1568 enum ev_direction
scev_direction(const_tree chrec)1569 scev_direction (const_tree chrec)
1570 {
1571 const_tree step;
1572
1573 if (!evolution_function_is_affine_p (chrec))
1574 return EV_DIR_UNKNOWN;
1575
1576 step = CHREC_RIGHT (chrec);
1577 if (TREE_CODE (step) != INTEGER_CST)
1578 return EV_DIR_UNKNOWN;
1579
1580 if (tree_int_cst_sign_bit (step))
1581 return EV_DIR_DECREASES;
1582 else
1583 return EV_DIR_GROWS;
1584 }
1585
1586 /* Iterates over all the components of SCEV, and calls CBCK. */
1587
1588 void
for_each_scev_op(tree * scev,bool (* cbck)(tree *,void *),void * data)1589 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
1590 {
1591 switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
1592 {
1593 case 3:
1594 for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
1595 /* FALLTHRU */
1596
1597 case 2:
1598 for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
1599 /* FALLTHRU */
1600
1601 case 1:
1602 for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
1603 /* FALLTHRU */
1604
1605 default:
1606 cbck (scev, data);
1607 break;
1608 }
1609 }
1610
1611 /* Returns true when the operation can be part of a linear
1612 expression. */
1613
1614 static inline bool
operator_is_linear(tree scev)1615 operator_is_linear (tree scev)
1616 {
1617 switch (TREE_CODE (scev))
1618 {
1619 case INTEGER_CST:
1620 case POLYNOMIAL_CHREC:
1621 case PLUS_EXPR:
1622 case POINTER_PLUS_EXPR:
1623 case MULT_EXPR:
1624 case MINUS_EXPR:
1625 case NEGATE_EXPR:
1626 case SSA_NAME:
1627 case NON_LVALUE_EXPR:
1628 case BIT_NOT_EXPR:
1629 CASE_CONVERT:
1630 return true;
1631
1632 default:
1633 return false;
1634 }
1635 }
1636
1637 /* Return true when SCEV is a linear expression. Linear expressions
1638 can contain additions, substractions and multiplications.
1639 Multiplications are restricted to constant scaling: "cst * x". */
1640
1641 bool
scev_is_linear_expression(tree scev)1642 scev_is_linear_expression (tree scev)
1643 {
1644 if (evolution_function_is_constant_p (scev))
1645 return true;
1646
1647 if (scev == NULL
1648 || !operator_is_linear (scev))
1649 return false;
1650
1651 if (TREE_CODE (scev) == MULT_EXPR)
1652 return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
1653 && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));
1654
1655 if (TREE_CODE (scev) == POLYNOMIAL_CHREC
1656 && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
1657 return false;
1658
1659 switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
1660 {
1661 case 3:
1662 return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1663 && scev_is_linear_expression (TREE_OPERAND (scev, 1))
1664 && scev_is_linear_expression (TREE_OPERAND (scev, 2));
1665
1666 case 2:
1667 return scev_is_linear_expression (TREE_OPERAND (scev, 0))
1668 && scev_is_linear_expression (TREE_OPERAND (scev, 1));
1669
1670 case 1:
1671 return scev_is_linear_expression (TREE_OPERAND (scev, 0));
1672
1673 case 0:
1674 return true;
1675
1676 default:
1677 return false;
1678 }
1679 }
1680
1681 /* Determines whether the expression CHREC contains only interger consts
1682 in the right parts. */
1683
1684 bool
evolution_function_right_is_integer_cst(const_tree chrec)1685 evolution_function_right_is_integer_cst (const_tree chrec)
1686 {
1687 if (chrec == NULL_TREE)
1688 return false;
1689
1690 switch (TREE_CODE (chrec))
1691 {
1692 case INTEGER_CST:
1693 return true;
1694
1695 case POLYNOMIAL_CHREC:
1696 return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
1697 && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
1698 || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));
1699
1700 CASE_CONVERT:
1701 return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));
1702
1703 default:
1704 return false;
1705 }
1706 }
1707