1 /* Functions to determine/estimate number of iterations of a loop.
2 Copyright (C) 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
4 This file is part of GCC.
6 GCC is free software; you can redistribute it and/or modify it
7 under the terms of the GNU General Public License as published by the
8 Free Software Foundation; either version 2, or (at your option) any
11 GCC is distributed in the hope that it will be useful, but WITHOUT
12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
16 You should have received a copy of the GNU General Public License
17 along with GCC; see the file COPYING. If not, write to the Free
18 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
23 #include "coretypes.h"
28 #include "hard-reg-set.h"
29 #include "basic-block.h"
31 #include "diagnostic.h"
33 #include "tree-flow.h"
34 #include "tree-dump.h"
36 #include "tree-pass.h"
38 #include "tree-chrec.h"
39 #include "tree-scalar-evolution.h"
40 #include "tree-data-ref.h"
44 #include "tree-inline.h"
46 #define SWAP(X, Y) do { void *tmp = (X); (X) = (Y); (Y) = tmp; } while (0)
51 Analysis of number of iterations of an affine exit test.
55 /* Returns true if ARG is either NULL_TREE or constant zero. Unlike
56 integer_zerop, it does not care about overflow flags. */
64 if (TREE_CODE (arg) != INTEGER_CST)
67 return (TREE_INT_CST_LOW (arg) == 0 && TREE_INT_CST_HIGH (arg) == 0);
70 /* Returns true if ARG a nonzero constant. Unlike integer_nonzerop, it does
71 not care about overflow flags. */
79 if (TREE_CODE (arg) != INTEGER_CST)
82 return (TREE_INT_CST_LOW (arg) != 0 || TREE_INT_CST_HIGH (arg) != 0);
85 /* Returns inverse of X modulo 2^s, where MASK = 2^s-1. */
88 inverse (tree x, tree mask)
90 tree type = TREE_TYPE (x);
92 unsigned ctr = tree_floor_log2 (mask);
94 if (TYPE_PRECISION (type) <= HOST_BITS_PER_WIDE_INT)
96 unsigned HOST_WIDE_INT ix;
97 unsigned HOST_WIDE_INT imask;
98 unsigned HOST_WIDE_INT irslt = 1;
100 gcc_assert (cst_and_fits_in_hwi (x));
101 gcc_assert (cst_and_fits_in_hwi (mask));
103 ix = int_cst_value (x);
104 imask = int_cst_value (mask);
113 rslt = build_int_cst_type (type, irslt);
117 rslt = build_int_cst (type, 1);
120 rslt = int_const_binop (MULT_EXPR, rslt, x, 0);
121 x = int_const_binop (MULT_EXPR, x, x, 0);
123 rslt = int_const_binop (BIT_AND_EXPR, rslt, mask, 0);
129 /* Determines number of iterations of loop whose ending condition
130 is IV <> FINAL. TYPE is the type of the iv. The number of
131 iterations is stored to NITER. NEVER_INFINITE is true if
132 we know that the exit must be taken eventually, i.e., that the IV
133 ever reaches the value FINAL (we derived this earlier, and possibly set
134 NITER->assumptions to make sure this is the case). */
137 number_of_iterations_ne (tree type, affine_iv *iv, tree final,
138 struct tree_niter_desc *niter, bool never_infinite)
140 tree niter_type = unsigned_type_for (type);
141 tree s, c, d, bits, assumption, tmp, bound;
143 niter->control = *iv;
144 niter->bound = final;
145 niter->cmp = NE_EXPR;
147 /* Rearrange the terms so that we get inequality s * i <> c, with s
148 positive. Also cast everything to the unsigned type. */
149 if (tree_int_cst_sign_bit (iv->step))
151 s = fold_convert (niter_type,
152 fold_build1 (NEGATE_EXPR, type, iv->step));
153 c = fold_build2 (MINUS_EXPR, niter_type,
154 fold_convert (niter_type, iv->base),
155 fold_convert (niter_type, final));
159 s = fold_convert (niter_type, iv->step);
160 c = fold_build2 (MINUS_EXPR, niter_type,
161 fold_convert (niter_type, final),
162 fold_convert (niter_type, iv->base));
165 /* First the trivial cases -- when the step is 1. */
166 if (integer_onep (s))
172 /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
173 is infinite. Otherwise, the number of iterations is
174 (inverse(s/d) * (c/d)) mod (size of mode/d). */
175 bits = num_ending_zeros (s);
176 bound = build_low_bits_mask (niter_type,
177 (TYPE_PRECISION (niter_type)
178 - tree_low_cst (bits, 1)));
180 d = fold_binary_to_constant (LSHIFT_EXPR, niter_type,
181 build_int_cst (niter_type, 1), bits);
182 s = fold_binary_to_constant (RSHIFT_EXPR, niter_type, s, bits);
186 /* If we cannot assume that the loop is not infinite, record the
187 assumptions for divisibility of c. */
188 assumption = fold_build2 (FLOOR_MOD_EXPR, niter_type, c, d);
189 assumption = fold_build2 (EQ_EXPR, boolean_type_node,
190 assumption, build_int_cst (niter_type, 0));
191 if (!nonzero_p (assumption))
192 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
193 niter->assumptions, assumption);
196 c = fold_build2 (EXACT_DIV_EXPR, niter_type, c, d);
197 tmp = fold_build2 (MULT_EXPR, niter_type, c, inverse (s, bound));
198 niter->niter = fold_build2 (BIT_AND_EXPR, niter_type, tmp, bound);
202 /* Checks whether we can determine the final value of the control variable
203 of the loop with ending condition IV0 < IV1 (computed in TYPE).
204 DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
205 of the step. The assumptions necessary to ensure that the computation
206 of the final value does not overflow are recorded in NITER. If we
207 find the final value, we adjust DELTA and return TRUE. Otherwise
211 number_of_iterations_lt_to_ne (tree type, affine_iv *iv0, affine_iv *iv1,
212 struct tree_niter_desc *niter,
213 tree *delta, tree step)
215 tree niter_type = TREE_TYPE (step);
216 tree mod = fold_build2 (FLOOR_MOD_EXPR, niter_type, *delta, step);
218 tree assumption = boolean_true_node, bound, noloop;
220 if (TREE_CODE (mod) != INTEGER_CST)
223 mod = fold_build2 (MINUS_EXPR, niter_type, step, mod);
224 tmod = fold_convert (type, mod);
226 if (nonzero_p (iv0->step))
228 /* The final value of the iv is iv1->base + MOD, assuming that this
229 computation does not overflow, and that
230 iv0->base <= iv1->base + MOD. */
231 if (!iv1->no_overflow && !zero_p (mod))
233 bound = fold_build2 (MINUS_EXPR, type,
234 TYPE_MAX_VALUE (type), tmod);
235 assumption = fold_build2 (LE_EXPR, boolean_type_node,
237 if (zero_p (assumption))
240 noloop = fold_build2 (GT_EXPR, boolean_type_node,
242 fold_build2 (PLUS_EXPR, type,
247 /* The final value of the iv is iv0->base - MOD, assuming that this
248 computation does not overflow, and that
249 iv0->base - MOD <= iv1->base. */
250 if (!iv0->no_overflow && !zero_p (mod))
252 bound = fold_build2 (PLUS_EXPR, type,
253 TYPE_MIN_VALUE (type), tmod);
254 assumption = fold_build2 (GE_EXPR, boolean_type_node,
256 if (zero_p (assumption))
259 noloop = fold_build2 (GT_EXPR, boolean_type_node,
260 fold_build2 (MINUS_EXPR, type,
265 if (!nonzero_p (assumption))
266 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
269 if (!zero_p (noloop))
270 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
273 *delta = fold_build2 (PLUS_EXPR, niter_type, *delta, mod);
277 /* Add assertions to NITER that ensure that the control variable of the loop
278 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
279 are TYPE. Returns false if we can prove that there is an overflow, true
280 otherwise. STEP is the absolute value of the step. */
283 assert_no_overflow_lt (tree type, affine_iv *iv0, affine_iv *iv1,
284 struct tree_niter_desc *niter, tree step)
286 tree bound, d, assumption, diff;
287 tree niter_type = TREE_TYPE (step);
289 if (nonzero_p (iv0->step))
291 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
292 if (iv0->no_overflow)
295 /* If iv0->base is a constant, we can determine the last value before
296 overflow precisely; otherwise we conservatively assume
299 if (TREE_CODE (iv0->base) == INTEGER_CST)
301 d = fold_build2 (MINUS_EXPR, niter_type,
302 fold_convert (niter_type, TYPE_MAX_VALUE (type)),
303 fold_convert (niter_type, iv0->base));
304 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
307 diff = fold_build2 (MINUS_EXPR, niter_type, step,
308 build_int_cst (niter_type, 1));
309 bound = fold_build2 (MINUS_EXPR, type,
310 TYPE_MAX_VALUE (type), fold_convert (type, diff));
311 assumption = fold_build2 (LE_EXPR, boolean_type_node,
316 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
317 if (iv1->no_overflow)
320 if (TREE_CODE (iv1->base) == INTEGER_CST)
322 d = fold_build2 (MINUS_EXPR, niter_type,
323 fold_convert (niter_type, iv1->base),
324 fold_convert (niter_type, TYPE_MIN_VALUE (type)));
325 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
328 diff = fold_build2 (MINUS_EXPR, niter_type, step,
329 build_int_cst (niter_type, 1));
330 bound = fold_build2 (PLUS_EXPR, type,
331 TYPE_MIN_VALUE (type), fold_convert (type, diff));
332 assumption = fold_build2 (GE_EXPR, boolean_type_node,
336 if (zero_p (assumption))
338 if (!nonzero_p (assumption))
339 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
340 niter->assumptions, assumption);
342 iv0->no_overflow = true;
343 iv1->no_overflow = true;
347 /* Add an assumption to NITER that a loop whose ending condition
348 is IV0 < IV1 rolls. TYPE is the type of the control iv. */
351 assert_loop_rolls_lt (tree type, affine_iv *iv0, affine_iv *iv1,
352 struct tree_niter_desc *niter)
354 tree assumption = boolean_true_node, bound, diff;
355 tree mbz, mbzl, mbzr;
357 if (nonzero_p (iv0->step))
359 diff = fold_build2 (MINUS_EXPR, type,
360 iv0->step, build_int_cst (type, 1));
362 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
363 0 address never belongs to any object, we can assume this for
365 if (!POINTER_TYPE_P (type))
367 bound = fold_build2 (PLUS_EXPR, type,
368 TYPE_MIN_VALUE (type), diff);
369 assumption = fold_build2 (GE_EXPR, boolean_type_node,
373 /* And then we can compute iv0->base - diff, and compare it with
375 mbzl = fold_build2 (MINUS_EXPR, type, iv0->base, diff);
380 diff = fold_build2 (PLUS_EXPR, type,
381 iv1->step, build_int_cst (type, 1));
383 if (!POINTER_TYPE_P (type))
385 bound = fold_build2 (PLUS_EXPR, type,
386 TYPE_MAX_VALUE (type), diff);
387 assumption = fold_build2 (LE_EXPR, boolean_type_node,
392 mbzr = fold_build2 (MINUS_EXPR, type, iv1->base, diff);
395 mbz = fold_build2 (GT_EXPR, boolean_type_node, mbzl, mbzr);
397 if (!nonzero_p (assumption))
398 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
399 niter->assumptions, assumption);
401 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
402 niter->may_be_zero, mbz);
405 /* Determines number of iterations of loop whose ending condition
406 is IV0 < IV1. TYPE is the type of the iv. The number of
407 iterations is stored to NITER. */
410 number_of_iterations_lt (tree type, affine_iv *iv0, affine_iv *iv1,
411 struct tree_niter_desc *niter,
412 bool never_infinite ATTRIBUTE_UNUSED)
414 tree niter_type = unsigned_type_for (type);
417 if (nonzero_p (iv0->step))
419 niter->control = *iv0;
420 niter->cmp = LT_EXPR;
421 niter->bound = iv1->base;
425 niter->control = *iv1;
426 niter->cmp = GT_EXPR;
427 niter->bound = iv0->base;
430 delta = fold_build2 (MINUS_EXPR, niter_type,
431 fold_convert (niter_type, iv1->base),
432 fold_convert (niter_type, iv0->base));
434 /* First handle the special case that the step is +-1. */
435 if ((iv0->step && integer_onep (iv0->step)
436 && zero_p (iv1->step))
437 || (iv1->step && integer_all_onesp (iv1->step)
438 && zero_p (iv0->step)))
440 /* for (i = iv0->base; i < iv1->base; i++)
444 for (i = iv1->base; i > iv0->base; i--).
446 In both cases # of iterations is iv1->base - iv0->base, assuming that
447 iv1->base >= iv0->base. */
448 niter->may_be_zero = fold_build2 (LT_EXPR, boolean_type_node,
449 iv1->base, iv0->base);
450 niter->niter = delta;
454 if (nonzero_p (iv0->step))
455 step = fold_convert (niter_type, iv0->step);
457 step = fold_convert (niter_type,
458 fold_build1 (NEGATE_EXPR, type, iv1->step));
460 /* If we can determine the final value of the control iv exactly, we can
461 transform the condition to != comparison. In particular, this will be
462 the case if DELTA is constant. */
463 if (number_of_iterations_lt_to_ne (type, iv0, iv1, niter, &delta, step))
467 zps.base = build_int_cst (niter_type, 0);
469 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
470 zps does not overflow. */
471 zps.no_overflow = true;
473 return number_of_iterations_ne (type, &zps, delta, niter, true);
476 /* Make sure that the control iv does not overflow. */
477 if (!assert_no_overflow_lt (type, iv0, iv1, niter, step))
480 /* We determine the number of iterations as (delta + step - 1) / step. For
481 this to work, we must know that iv1->base >= iv0->base - step + 1,
482 otherwise the loop does not roll. */
483 assert_loop_rolls_lt (type, iv0, iv1, niter);
485 s = fold_build2 (MINUS_EXPR, niter_type,
486 step, build_int_cst (niter_type, 1));
487 delta = fold_build2 (PLUS_EXPR, niter_type, delta, s);
488 niter->niter = fold_build2 (FLOOR_DIV_EXPR, niter_type, delta, step);
492 /* Determines number of iterations of loop whose ending condition
493 is IV0 <= IV1. TYPE is the type of the iv. The number of
494 iterations is stored to NITER. NEVER_INFINITE is true if
495 we know that this condition must eventually become false (we derived this
496 earlier, and possibly set NITER->assumptions to make sure this
500 number_of_iterations_le (tree type, affine_iv *iv0, affine_iv *iv1,
501 struct tree_niter_desc *niter, bool never_infinite)
505 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
506 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
507 value of the type. This we must know anyway, since if it is
508 equal to this value, the loop rolls forever. */
512 if (nonzero_p (iv0->step))
513 assumption = fold_build2 (NE_EXPR, boolean_type_node,
514 iv1->base, TYPE_MAX_VALUE (type));
516 assumption = fold_build2 (NE_EXPR, boolean_type_node,
517 iv0->base, TYPE_MIN_VALUE (type));
519 if (zero_p (assumption))
521 if (!nonzero_p (assumption))
522 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
523 niter->assumptions, assumption);
526 if (nonzero_p (iv0->step))
527 iv1->base = fold_build2 (PLUS_EXPR, type,
528 iv1->base, build_int_cst (type, 1));
530 iv0->base = fold_build2 (MINUS_EXPR, type,
531 iv0->base, build_int_cst (type, 1));
532 return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite);
535 /* Determine the number of iterations according to condition (for staying
536 inside loop) which compares two induction variables using comparison
537 operator CODE. The induction variable on left side of the comparison
538 is IV0, the right-hand side is IV1. Both induction variables must have
539 type TYPE, which must be an integer or pointer type. The steps of the
540 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
542 ONLY_EXIT is true if we are sure this is the only way the loop could be
543 exited (including possibly non-returning function calls, exceptions, etc.)
544 -- in this case we can use the information whether the control induction
545 variables can overflow or not in a more efficient way.
547 The results (number of iterations and assumptions as described in
548 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
549 Returns false if it fails to determine number of iterations, true if it
550 was determined (possibly with some assumptions). */
553 number_of_iterations_cond (tree type, affine_iv *iv0, enum tree_code code,
554 affine_iv *iv1, struct tree_niter_desc *niter,
559 /* The meaning of these assumptions is this:
561 then the rest of information does not have to be valid
562 if may_be_zero then the loop does not roll, even if
564 niter->assumptions = boolean_true_node;
565 niter->may_be_zero = boolean_false_node;
566 niter->niter = NULL_TREE;
567 niter->additional_info = boolean_true_node;
569 niter->bound = NULL_TREE;
570 niter->cmp = ERROR_MARK;
572 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
573 the control variable is on lhs. */
574 if (code == GE_EXPR || code == GT_EXPR
575 || (code == NE_EXPR && zero_p (iv0->step)))
578 code = swap_tree_comparison (code);
583 /* If this is not the only possible exit from the loop, the information
584 that the induction variables cannot overflow as derived from
585 signedness analysis cannot be relied upon. We use them e.g. in the
586 following way: given loop for (i = 0; i <= n; i++), if i is
587 signed, it cannot overflow, thus this loop is equivalent to
588 for (i = 0; i < n + 1; i++); however, if n == MAX, but the loop
589 is exited in some other way before i overflows, this transformation
590 is incorrect (the new loop exits immediately). */
591 iv0->no_overflow = false;
592 iv1->no_overflow = false;
595 if (POINTER_TYPE_P (type))
597 /* Comparison of pointers is undefined unless both iv0 and iv1 point
598 to the same object. If they do, the control variable cannot wrap
599 (as wrap around the bounds of memory will never return a pointer
600 that would be guaranteed to point to the same object, even if we
601 avoid undefined behavior by casting to size_t and back). The
602 restrictions on pointer arithmetics and comparisons of pointers
603 ensure that using the no-overflow assumptions is correct in this
604 case even if ONLY_EXIT is false. */
605 iv0->no_overflow = true;
606 iv1->no_overflow = true;
609 /* If the control induction variable does not overflow, the loop obviously
610 cannot be infinite. */
611 if (!zero_p (iv0->step) && iv0->no_overflow)
612 never_infinite = true;
613 else if (!zero_p (iv1->step) && iv1->no_overflow)
614 never_infinite = true;
616 never_infinite = false;
618 /* We can handle the case when neither of the sides of the comparison is
619 invariant, provided that the test is NE_EXPR. This rarely occurs in
620 practice, but it is simple enough to manage. */
621 if (!zero_p (iv0->step) && !zero_p (iv1->step))
626 iv0->step = fold_binary_to_constant (MINUS_EXPR, type,
627 iv0->step, iv1->step);
628 iv0->no_overflow = false;
629 iv1->step = NULL_TREE;
630 iv1->no_overflow = true;
633 /* If the result of the comparison is a constant, the loop is weird. More
634 precise handling would be possible, but the situation is not common enough
635 to waste time on it. */
636 if (zero_p (iv0->step) && zero_p (iv1->step))
639 /* Ignore loops of while (i-- < 10) type. */
642 if (iv0->step && tree_int_cst_sign_bit (iv0->step))
645 if (!zero_p (iv1->step) && !tree_int_cst_sign_bit (iv1->step))
649 /* If the loop exits immediately, there is nothing to do. */
650 if (zero_p (fold_build2 (code, boolean_type_node, iv0->base, iv1->base)))
652 niter->niter = build_int_cst (unsigned_type_for (type), 0);
656 /* OK, now we know we have a senseful loop. Handle several cases, depending
657 on what comparison operator is used. */
661 gcc_assert (zero_p (iv1->step));
662 return number_of_iterations_ne (type, iv0, iv1->base, niter, never_infinite);
664 return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite);
666 return number_of_iterations_le (type, iv0, iv1, niter, never_infinite);
672 /* Substitute NEW for OLD in EXPR and fold the result. */
675 simplify_replace_tree (tree expr, tree old, tree new)
678 tree ret = NULL_TREE, e, se;
684 || operand_equal_p (expr, old, 0))
685 return unshare_expr (new);
690 n = TREE_CODE_LENGTH (TREE_CODE (expr));
691 for (i = 0; i < n; i++)
693 e = TREE_OPERAND (expr, i);
694 se = simplify_replace_tree (e, old, new);
699 ret = copy_node (expr);
701 TREE_OPERAND (ret, i) = se;
704 return (ret ? fold (ret) : expr);
707 /* Expand definitions of ssa names in EXPR as long as they are simple
708 enough, and return the new expression. */
711 expand_simple_operations (tree expr)
714 tree ret = NULL_TREE, e, ee, stmt;
717 if (expr == NULL_TREE)
720 if (is_gimple_min_invariant (expr))
723 code = TREE_CODE (expr);
724 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code)))
726 n = TREE_CODE_LENGTH (code);
727 for (i = 0; i < n; i++)
729 e = TREE_OPERAND (expr, i);
730 ee = expand_simple_operations (e);
735 ret = copy_node (expr);
737 TREE_OPERAND (ret, i) = ee;
743 fold_defer_overflow_warnings ();
745 fold_undefer_and_ignore_overflow_warnings ();
749 if (TREE_CODE (expr) != SSA_NAME)
752 stmt = SSA_NAME_DEF_STMT (expr);
753 if (TREE_CODE (stmt) != MODIFY_EXPR)
756 e = TREE_OPERAND (stmt, 1);
757 if (/* Casts are simple. */
758 TREE_CODE (e) != NOP_EXPR
759 && TREE_CODE (e) != CONVERT_EXPR
760 /* Copies are simple. */
761 && TREE_CODE (e) != SSA_NAME
762 /* Assignments of invariants are simple. */
763 && !is_gimple_min_invariant (e)
764 /* And increments and decrements by a constant are simple. */
765 && !((TREE_CODE (e) == PLUS_EXPR
766 || TREE_CODE (e) == MINUS_EXPR)
767 && is_gimple_min_invariant (TREE_OPERAND (e, 1))))
770 return expand_simple_operations (e);
773 /* Tries to simplify EXPR using the condition COND. Returns the simplified
774 expression (or EXPR unchanged, if no simplification was possible). */
777 tree_simplify_using_condition_1 (tree cond, tree expr)
780 tree e, te, e0, e1, e2, notcond;
781 enum tree_code code = TREE_CODE (expr);
783 if (code == INTEGER_CST)
786 if (code == TRUTH_OR_EXPR
787 || code == TRUTH_AND_EXPR
788 || code == COND_EXPR)
792 e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
793 if (TREE_OPERAND (expr, 0) != e0)
796 e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
797 if (TREE_OPERAND (expr, 1) != e1)
800 if (code == COND_EXPR)
802 e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
803 if (TREE_OPERAND (expr, 2) != e2)
811 if (code == COND_EXPR)
812 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
814 expr = fold_build2 (code, boolean_type_node, e0, e1);
820 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
821 propagation, and vice versa. Fold does not handle this, since it is
822 considered too expensive. */
823 if (TREE_CODE (cond) == EQ_EXPR)
825 e0 = TREE_OPERAND (cond, 0);
826 e1 = TREE_OPERAND (cond, 1);
828 /* We know that e0 == e1. Check whether we cannot simplify expr
830 e = simplify_replace_tree (expr, e0, e1);
831 if (zero_p (e) || nonzero_p (e))
834 e = simplify_replace_tree (expr, e1, e0);
835 if (zero_p (e) || nonzero_p (e))
838 if (TREE_CODE (expr) == EQ_EXPR)
840 e0 = TREE_OPERAND (expr, 0);
841 e1 = TREE_OPERAND (expr, 1);
843 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
844 e = simplify_replace_tree (cond, e0, e1);
847 e = simplify_replace_tree (cond, e1, e0);
851 if (TREE_CODE (expr) == NE_EXPR)
853 e0 = TREE_OPERAND (expr, 0);
854 e1 = TREE_OPERAND (expr, 1);
856 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
857 e = simplify_replace_tree (cond, e0, e1);
859 return boolean_true_node;
860 e = simplify_replace_tree (cond, e1, e0);
862 return boolean_true_node;
865 te = expand_simple_operations (expr);
867 /* Check whether COND ==> EXPR. */
868 notcond = invert_truthvalue (cond);
869 e = fold_binary (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
873 /* Check whether COND ==> not EXPR. */
874 e = fold_binary (TRUTH_AND_EXPR, boolean_type_node, cond, te);
881 /* Tries to simplify EXPR using the condition COND. Returns the simplified
882 expression (or EXPR unchanged, if no simplification was possible).
883 Wrapper around tree_simplify_using_condition_1 that ensures that chains
884 of simple operations in definitions of ssa names in COND are expanded,
885 so that things like casts or incrementing the value of the bound before
886 the loop do not cause us to fail. */
889 tree_simplify_using_condition (tree cond, tree expr)
891 cond = expand_simple_operations (cond);
893 return tree_simplify_using_condition_1 (cond, expr);
896 /* The maximum number of dominator BBs we search for conditions
897 of loop header copies we use for simplifying a conditional
899 #define MAX_DOMINATORS_TO_WALK 8
901 /* Tries to simplify EXPR using the conditions on entry to LOOP.
902 Record the conditions used for simplification to CONDS_USED.
903 Returns the simplified expression (or EXPR unchanged, if no
904 simplification was possible).*/
907 simplify_using_initial_conditions (struct loop *loop, tree expr,
915 if (TREE_CODE (expr) == INTEGER_CST)
918 /* Limit walking the dominators to avoid quadraticness in
919 the number of BBs times the number of loops in degenerate
921 for (bb = loop->header;
922 bb != ENTRY_BLOCK_PTR && cnt < MAX_DOMINATORS_TO_WALK;
923 bb = get_immediate_dominator (CDI_DOMINATORS, bb))
925 if (!single_pred_p (bb))
927 e = single_pred_edge (bb);
929 if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
932 cond = COND_EXPR_COND (last_stmt (e->src));
933 if (e->flags & EDGE_FALSE_VALUE)
934 cond = invert_truthvalue (cond);
935 exp = tree_simplify_using_condition (cond, expr);
938 *conds_used = fold_build2 (TRUTH_AND_EXPR,
950 /* Tries to simplify EXPR using the evolutions of the loop invariants
951 in the superloops of LOOP. Returns the simplified expression
952 (or EXPR unchanged, if no simplification was possible). */
955 simplify_using_outer_evolutions (struct loop *loop, tree expr)
957 enum tree_code code = TREE_CODE (expr);
961 if (is_gimple_min_invariant (expr))
964 if (code == TRUTH_OR_EXPR
965 || code == TRUTH_AND_EXPR
966 || code == COND_EXPR)
970 e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
971 if (TREE_OPERAND (expr, 0) != e0)
974 e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
975 if (TREE_OPERAND (expr, 1) != e1)
978 if (code == COND_EXPR)
980 e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
981 if (TREE_OPERAND (expr, 2) != e2)
989 if (code == COND_EXPR)
990 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
992 expr = fold_build2 (code, boolean_type_node, e0, e1);
998 e = instantiate_parameters (loop, expr);
999 if (is_gimple_min_invariant (e))
1005 /* Returns true if EXIT is the only possible exit from LOOP. */
1008 loop_only_exit_p (struct loop *loop, edge exit)
1011 block_stmt_iterator bsi;
1015 if (exit != loop->single_exit)
1018 body = get_loop_body (loop);
1019 for (i = 0; i < loop->num_nodes; i++)
1021 for (bsi = bsi_start (body[0]); !bsi_end_p (bsi); bsi_next (&bsi))
1023 call = get_call_expr_in (bsi_stmt (bsi));
1024 if (call && TREE_SIDE_EFFECTS (call))
1036 /* Stores description of number of iterations of LOOP derived from
1037 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1038 useful information could be derived (and fields of NITER has
1039 meaning described in comments at struct tree_niter_desc
1040 declaration), false otherwise. If WARN is true and
1041 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1042 potentially unsafe assumptions. */
1045 number_of_iterations_exit (struct loop *loop, edge exit,
1046 struct tree_niter_desc *niter,
1049 tree stmt, cond, type;
1051 enum tree_code code;
1054 if (!dominated_by_p (CDI_DOMINATORS, loop->latch, exit->src))
1057 niter->assumptions = boolean_false_node;
1058 stmt = last_stmt (exit->src);
1059 if (!stmt || TREE_CODE (stmt) != COND_EXPR)
1062 /* We want the condition for staying inside loop. */
1063 cond = COND_EXPR_COND (stmt);
1064 if (exit->flags & EDGE_TRUE_VALUE)
1065 cond = invert_truthvalue (cond);
1067 code = TREE_CODE (cond);
1081 op0 = TREE_OPERAND (cond, 0);
1082 op1 = TREE_OPERAND (cond, 1);
1083 type = TREE_TYPE (op0);
1085 if (TREE_CODE (type) != INTEGER_TYPE
1086 && !POINTER_TYPE_P (type))
1089 if (!simple_iv (loop, stmt, op0, &iv0, false))
1091 if (!simple_iv (loop, stmt, op1, &iv1, false))
1094 /* We don't want to see undefined signed overflow warnings while
1095 computing the nmber of iterations. */
1096 fold_defer_overflow_warnings ();
1098 iv0.base = expand_simple_operations (iv0.base);
1099 iv1.base = expand_simple_operations (iv1.base);
1100 if (!number_of_iterations_cond (type, &iv0, code, &iv1, niter,
1101 loop_only_exit_p (loop, exit)))
1103 fold_undefer_and_ignore_overflow_warnings ();
1109 niter->assumptions = simplify_using_outer_evolutions (loop,
1110 niter->assumptions);
1111 niter->may_be_zero = simplify_using_outer_evolutions (loop,
1112 niter->may_be_zero);
1113 niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
1116 niter->additional_info = boolean_true_node;
1118 = simplify_using_initial_conditions (loop,
1120 &niter->additional_info);
1122 = simplify_using_initial_conditions (loop,
1124 &niter->additional_info);
1126 fold_undefer_and_ignore_overflow_warnings ();
1128 if (integer_onep (niter->assumptions))
1131 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1132 But if we can prove that there is overflow or some other source of weird
1133 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1134 if (integer_zerop (niter->assumptions))
1137 if (flag_unsafe_loop_optimizations)
1138 niter->assumptions = boolean_true_node;
1142 const char *wording;
1143 location_t loc = EXPR_LOCATION (stmt);
1145 /* We can provide a more specific warning if one of the operator is
1146 constant and the other advances by +1 or -1. */
1147 if (!zero_p (iv1.step)
1148 ? (zero_p (iv0.step)
1149 && (integer_onep (iv1.step) || integer_all_onesp (iv1.step)))
1151 && (integer_onep (iv0.step) || integer_all_onesp (iv0.step))))
1153 flag_unsafe_loop_optimizations
1154 ? N_("assuming that the loop is not infinite")
1155 : N_("cannot optimize possibly infinite loops");
1158 flag_unsafe_loop_optimizations
1159 ? N_("assuming that the loop counter does not overflow")
1160 : N_("cannot optimize loop, the loop counter may overflow");
1162 if (LOCATION_LINE (loc) > 0)
1163 warning (OPT_Wunsafe_loop_optimizations, "%H%s", &loc, gettext (wording));
1165 warning (OPT_Wunsafe_loop_optimizations, "%s", gettext (wording));
1168 return flag_unsafe_loop_optimizations;
1171 /* Try to determine the number of iterations of LOOP. If we succeed,
1172 expression giving number of iterations is returned and *EXIT is
1173 set to the edge from that the information is obtained. Otherwise
1174 chrec_dont_know is returned. */
1177 find_loop_niter (struct loop *loop, edge *exit)
1179 unsigned n_exits, i;
1180 edge *exits = get_loop_exit_edges (loop, &n_exits);
1182 tree niter = NULL_TREE, aniter;
1183 struct tree_niter_desc desc;
1186 for (i = 0; i < n_exits; i++)
1189 if (!just_once_each_iteration_p (loop, ex->src))
1192 if (!number_of_iterations_exit (loop, ex, &desc, false))
1195 if (nonzero_p (desc.may_be_zero))
1197 /* We exit in the first iteration through this exit.
1198 We won't find anything better. */
1199 niter = build_int_cst (unsigned_type_node, 0);
1204 if (!zero_p (desc.may_be_zero))
1207 aniter = desc.niter;
1211 /* Nothing recorded yet. */
1217 /* Prefer constants, the lower the better. */
1218 if (TREE_CODE (aniter) != INTEGER_CST)
1221 if (TREE_CODE (niter) != INTEGER_CST)
1228 if (tree_int_cst_lt (aniter, niter))
1237 return niter ? niter : chrec_dont_know;
1242 Analysis of a number of iterations of a loop by a brute-force evaluation.
1246 /* Bound on the number of iterations we try to evaluate. */
1248 #define MAX_ITERATIONS_TO_TRACK \
1249 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1251 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1252 result by a chain of operations such that all but exactly one of their
1253 operands are constants. */
1256 chain_of_csts_start (struct loop *loop, tree x)
1258 tree stmt = SSA_NAME_DEF_STMT (x);
1260 basic_block bb = bb_for_stmt (stmt);
1263 || !flow_bb_inside_loop_p (loop, bb))
1266 if (TREE_CODE (stmt) == PHI_NODE)
1268 if (bb == loop->header)
1274 if (TREE_CODE (stmt) != MODIFY_EXPR)
1277 if (!ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
1279 if (SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_DEF) == NULL_DEF_OPERAND_P)
1282 use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
1283 if (use == NULL_USE_OPERAND_P)
1286 return chain_of_csts_start (loop, use);
1289 /* Determines whether the expression X is derived from a result of a phi node
1290 in header of LOOP such that
1292 * the derivation of X consists only from operations with constants
1293 * the initial value of the phi node is constant
1294 * the value of the phi node in the next iteration can be derived from the
1295 value in the current iteration by a chain of operations with constants.
1297 If such phi node exists, it is returned. If X is a constant, X is returned
1298 unchanged. Otherwise NULL_TREE is returned. */
1301 get_base_for (struct loop *loop, tree x)
1303 tree phi, init, next;
1305 if (is_gimple_min_invariant (x))
1308 phi = chain_of_csts_start (loop, x);
1312 init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
1313 next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
1315 if (TREE_CODE (next) != SSA_NAME)
1318 if (!is_gimple_min_invariant (init))
1321 if (chain_of_csts_start (loop, next) != phi)
1327 /* Given an expression X, then
1329 * if X is NULL_TREE, we return the constant BASE.
1330 * otherwise X is a SSA name, whose value in the considered loop is derived
1331 by a chain of operations with constant from a result of a phi node in
1332 the header of the loop. Then we return value of X when the value of the
1333 result of this phi node is given by the constant BASE. */
1336 get_val_for (tree x, tree base)
1342 gcc_assert (is_gimple_min_invariant (base));
1347 stmt = SSA_NAME_DEF_STMT (x);
1348 if (TREE_CODE (stmt) == PHI_NODE)
1351 FOR_EACH_SSA_USE_OPERAND (op, stmt, iter, SSA_OP_USE)
1353 nx = USE_FROM_PTR (op);
1354 val = get_val_for (nx, base);
1356 val = fold (TREE_OPERAND (stmt, 1));
1358 /* only iterate loop once. */
1362 /* Should never reach here. */
1366 /* Tries to count the number of iterations of LOOP till it exits by EXIT
1367 by brute force -- i.e. by determining the value of the operands of the
1368 condition at EXIT in first few iterations of the loop (assuming that
1369 these values are constant) and determining the first one in that the
1370 condition is not satisfied. Returns the constant giving the number
1371 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
1374 loop_niter_by_eval (struct loop *loop, edge exit)
1376 tree cond, cnd, acnd;
1377 tree op[2], val[2], next[2], aval[2], phi[2];
1381 cond = last_stmt (exit->src);
1382 if (!cond || TREE_CODE (cond) != COND_EXPR)
1383 return chrec_dont_know;
1385 cnd = COND_EXPR_COND (cond);
1386 if (exit->flags & EDGE_TRUE_VALUE)
1387 cnd = invert_truthvalue (cnd);
1389 cmp = TREE_CODE (cnd);
1398 for (j = 0; j < 2; j++)
1399 op[j] = TREE_OPERAND (cnd, j);
1403 return chrec_dont_know;
1406 for (j = 0; j < 2; j++)
1408 phi[j] = get_base_for (loop, op[j]);
1410 return chrec_dont_know;
1413 for (j = 0; j < 2; j++)
1415 if (TREE_CODE (phi[j]) == PHI_NODE)
1417 val[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_preheader_edge (loop));
1418 next[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_latch_edge (loop));
1423 next[j] = NULL_TREE;
1428 /* Don't issue signed overflow warnings. */
1429 fold_defer_overflow_warnings ();
1431 for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
1433 for (j = 0; j < 2; j++)
1434 aval[j] = get_val_for (op[j], val[j]);
1436 acnd = fold_binary (cmp, boolean_type_node, aval[0], aval[1]);
1437 if (acnd && zero_p (acnd))
1439 fold_undefer_and_ignore_overflow_warnings ();
1440 if (dump_file && (dump_flags & TDF_DETAILS))
1442 "Proved that loop %d iterates %d times using brute force.\n",
1444 return build_int_cst (unsigned_type_node, i);
1447 for (j = 0; j < 2; j++)
1449 val[j] = get_val_for (next[j], val[j]);
1450 if (!is_gimple_min_invariant (val[j]))
1452 fold_undefer_and_ignore_overflow_warnings ();
1453 return chrec_dont_know;
1458 fold_undefer_and_ignore_overflow_warnings ();
1460 return chrec_dont_know;
1463 /* Finds the exit of the LOOP by that the loop exits after a constant
1464 number of iterations and stores the exit edge to *EXIT. The constant
1465 giving the number of iterations of LOOP is returned. The number of
1466 iterations is determined using loop_niter_by_eval (i.e. by brute force
1467 evaluation). If we are unable to find the exit for that loop_niter_by_eval
1468 determines the number of iterations, chrec_dont_know is returned. */
1471 find_loop_niter_by_eval (struct loop *loop, edge *exit)
1473 unsigned n_exits, i;
1474 edge *exits = get_loop_exit_edges (loop, &n_exits);
1476 tree niter = NULL_TREE, aniter;
1479 for (i = 0; i < n_exits; i++)
1482 if (!just_once_each_iteration_p (loop, ex->src))
1485 aniter = loop_niter_by_eval (loop, ex);
1486 if (chrec_contains_undetermined (aniter))
1490 && !tree_int_cst_lt (aniter, niter))
1498 return niter ? niter : chrec_dont_know;
1503 Analysis of upper bounds on number of iterations of a loop.
1507 /* Returns true if we can prove that COND ==> VAL >= 0. */
1510 implies_nonnegative_p (tree cond, tree val)
1512 tree type = TREE_TYPE (val);
1515 if (tree_expr_nonnegative_p (val))
1518 if (nonzero_p (cond))
1521 compare = fold_build2 (GE_EXPR,
1522 boolean_type_node, val, build_int_cst (type, 0));
1523 compare = tree_simplify_using_condition_1 (cond, compare);
1525 return nonzero_p (compare);
1528 /* Returns true if we can prove that COND ==> A >= B. */
1531 implies_ge_p (tree cond, tree a, tree b)
1533 tree compare = fold_build2 (GE_EXPR, boolean_type_node, a, b);
1535 if (nonzero_p (compare))
1538 if (nonzero_p (cond))
1541 compare = tree_simplify_using_condition_1 (cond, compare);
1543 return nonzero_p (compare);
1546 /* Returns a constant upper bound on the value of expression VAL. VAL
1547 is considered to be unsigned. If its type is signed, its value must
1550 The condition ADDITIONAL must be satisfied (for example, if VAL is
1551 "(unsigned) n" and ADDITIONAL is "n > 0", then we can derive that
1552 VAL is at most (unsigned) MAX_INT). */
1555 derive_constant_upper_bound (tree val, tree additional)
1557 tree type = TREE_TYPE (val);
1558 tree op0, op1, subtype, maxt;
1559 double_int bnd, max, mmax, cst;
1561 if (INTEGRAL_TYPE_P (type))
1562 maxt = TYPE_MAX_VALUE (type);
1564 maxt = upper_bound_in_type (type, type);
1566 max = tree_to_double_int (maxt);
1568 switch (TREE_CODE (val))
1571 return tree_to_double_int (val);
1575 op0 = TREE_OPERAND (val, 0);
1576 subtype = TREE_TYPE (op0);
1577 if (!TYPE_UNSIGNED (subtype)
1578 /* If TYPE is also signed, the fact that VAL is nonnegative implies
1579 that OP0 is nonnegative. */
1580 && TYPE_UNSIGNED (type)
1581 && !implies_nonnegative_p (additional, op0))
1583 /* If we cannot prove that the casted expression is nonnegative,
1584 we cannot establish more useful upper bound than the precision
1585 of the type gives us. */
1589 /* We now know that op0 is an nonnegative value. Try deriving an upper
1591 bnd = derive_constant_upper_bound (op0, additional);
1593 /* If the bound does not fit in TYPE, max. value of TYPE could be
1595 if (double_int_ucmp (max, bnd) < 0)
1602 op0 = TREE_OPERAND (val, 0);
1603 op1 = TREE_OPERAND (val, 1);
1605 if (TREE_CODE (op1) != INTEGER_CST
1606 || !implies_nonnegative_p (additional, op0))
1609 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
1610 choose the most logical way how to treat this constant regardless
1611 of the signedness of the type. */
1612 cst = tree_to_double_int (op1);
1613 cst = double_int_sext (cst, TYPE_PRECISION (type));
1614 if (TREE_CODE (val) == PLUS_EXPR)
1615 cst = double_int_neg (cst);
1617 bnd = derive_constant_upper_bound (op0, additional);
1619 if (double_int_negative_p (cst))
1621 cst = double_int_neg (cst);
1622 /* Avoid CST == 0x80000... */
1623 if (double_int_negative_p (cst))
1626 /* OP0 + CST. We need to check that
1627 BND <= MAX (type) - CST. */
1629 mmax = double_int_add (max, double_int_neg (cst));
1630 if (double_int_ucmp (bnd, mmax) > 0)
1633 return double_int_add (bnd, cst);
1637 /* OP0 - CST, where CST >= 0.
1639 If TYPE is signed, we have already verified that OP0 >= 0, and we
1640 know that the result is nonnegative. This implies that
1643 If TYPE is unsigned, we must additionally know that OP0 >= CST,
1644 otherwise the operation underflows.
1647 /* This should only happen if the type is unsigned; however, for
1648 programs that use overflowing signed arithmetics even with
1649 -fno-wrapv, this condition may also be true for signed values. */
1650 if (double_int_ucmp (bnd, cst) < 0)
1653 if (TYPE_UNSIGNED (type)
1654 && !implies_ge_p (additional,
1655 op0, double_int_to_tree (type, cst)))
1658 bnd = double_int_add (bnd, double_int_neg (cst));
1663 case FLOOR_DIV_EXPR:
1664 case EXACT_DIV_EXPR:
1665 op0 = TREE_OPERAND (val, 0);
1666 op1 = TREE_OPERAND (val, 1);
1667 if (TREE_CODE (op1) != INTEGER_CST
1668 || tree_int_cst_sign_bit (op1))
1671 bnd = derive_constant_upper_bound (op0, additional);
1672 return double_int_udiv (bnd, tree_to_double_int (op1), FLOOR_DIV_EXPR);
1679 /* Records that AT_STMT is executed at most BOUND times in LOOP. The
1680 additional condition ADDITIONAL is recorded with the bound. */
1683 record_estimate (struct loop *loop, tree bound, tree additional, tree at_stmt)
1685 struct nb_iter_bound *elt = xmalloc (sizeof (struct nb_iter_bound));
1686 double_int i_bound = derive_constant_upper_bound (bound, additional);
1687 tree c_bound = double_int_to_tree (unsigned_type_for (TREE_TYPE (bound)),
1690 if (dump_file && (dump_flags & TDF_DETAILS))
1692 fprintf (dump_file, "Statements after ");
1693 print_generic_expr (dump_file, at_stmt, TDF_SLIM);
1694 fprintf (dump_file, " are executed at most ");
1695 print_generic_expr (dump_file, bound, TDF_SLIM);
1696 fprintf (dump_file, " (bounded by ");
1697 print_generic_expr (dump_file, c_bound, TDF_SLIM);
1698 fprintf (dump_file, ") times in loop %d.\n", loop->num);
1701 elt->bound = c_bound;
1702 elt->at_stmt = at_stmt;
1703 elt->next = loop->bounds;
1707 /* Initialize LOOP->ESTIMATED_NB_ITERATIONS with the lowest safe
1708 approximation of the number of iterations for LOOP. */
1711 compute_estimated_nb_iterations (struct loop *loop)
1713 struct nb_iter_bound *bound;
1715 for (bound = loop->bounds; bound; bound = bound->next)
1717 if (TREE_CODE (bound->bound) != INTEGER_CST)
1720 /* Update only when there is no previous estimation, or when the current
1721 estimation is smaller. */
1722 if (chrec_contains_undetermined (loop->estimated_nb_iterations)
1723 || tree_int_cst_lt (bound->bound, loop->estimated_nb_iterations))
1724 loop->estimated_nb_iterations = bound->bound;
1728 /* The following analyzers are extracting informations on the bounds
1729 of LOOP from the following undefined behaviors:
1731 - data references should not access elements over the statically
1734 - signed variables should not overflow when flag_wrapv is not set.
1738 infer_loop_bounds_from_undefined (struct loop *loop)
1741 basic_block bb, *bbs;
1742 block_stmt_iterator bsi;
1744 bbs = get_loop_body (loop);
1746 for (i = 0; i < loop->num_nodes; i++)
1750 /* If BB is not executed in each iteration of the loop, we cannot
1751 use the operations in it to infer reliable upper bound on the
1752 # of iterations of the loop. */
1753 if (!dominated_by_p (CDI_DOMINATORS, loop->latch, bb))
1756 for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
1758 tree stmt = bsi_stmt (bsi);
1760 switch (TREE_CODE (stmt))
1764 tree op0 = TREE_OPERAND (stmt, 0);
1765 tree op1 = TREE_OPERAND (stmt, 1);
1767 /* For each array access, analyze its access function
1768 and record a bound on the loop iteration domain. */
1769 if (TREE_CODE (op1) == ARRAY_REF
1770 && !array_ref_contains_indirect_ref (op1))
1771 estimate_iters_using_array (stmt, op1);
1773 if (TREE_CODE (op0) == ARRAY_REF
1774 && !array_ref_contains_indirect_ref (op0))
1775 estimate_iters_using_array (stmt, op0);
1777 /* For each signed type variable in LOOP, analyze its
1778 scalar evolution and record a bound of the loop
1779 based on the type's ranges. */
1780 else if (!flag_wrapv && TREE_CODE (op0) == SSA_NAME)
1782 tree init, step, diff, estimation;
1783 tree scev = instantiate_parameters
1784 (loop, analyze_scalar_evolution (loop, op0));
1785 tree type = chrec_type (scev);
1787 if (chrec_contains_undetermined (scev)
1788 || TYPE_OVERFLOW_WRAPS (type))
1791 init = initial_condition_in_loop_num (scev, loop->num);
1792 step = evolution_part_in_loop_num (scev, loop->num);
1794 if (init == NULL_TREE
1795 || step == NULL_TREE
1796 || TREE_CODE (init) != INTEGER_CST
1797 || TREE_CODE (step) != INTEGER_CST
1798 || TYPE_MIN_VALUE (type) == NULL_TREE
1799 || TYPE_MAX_VALUE (type) == NULL_TREE)
1802 if (integer_nonzerop (step))
1806 if (tree_int_cst_lt (step, integer_zero_node))
1807 diff = fold_build2 (MINUS_EXPR, type, init,
1808 TYPE_MIN_VALUE (type));
1810 diff = fold_build2 (MINUS_EXPR, type,
1811 TYPE_MAX_VALUE (type), init);
1813 utype = unsigned_type_for (type);
1814 estimation = fold_build2 (CEIL_DIV_EXPR, type, diff,
1816 record_estimate (loop,
1817 fold_convert (utype, estimation),
1818 boolean_true_node, stmt);
1829 for (args = TREE_OPERAND (stmt, 1); args;
1830 args = TREE_CHAIN (args))
1831 if (TREE_CODE (TREE_VALUE (args)) == ARRAY_REF
1832 && !array_ref_contains_indirect_ref (TREE_VALUE (args)))
1833 estimate_iters_using_array (stmt, TREE_VALUE (args));
1844 compute_estimated_nb_iterations (loop);
1848 /* Records estimates on numbers of iterations of LOOP. */
1851 estimate_numbers_of_iterations_loop (struct loop *loop)
1855 unsigned i, n_exits;
1856 struct tree_niter_desc niter_desc;
1858 /* Give up if we already have tried to compute an estimation. */
1859 if (loop->estimated_nb_iterations == chrec_dont_know
1860 /* Or when we already have an estimation. */
1861 || (loop->estimated_nb_iterations != NULL_TREE
1862 && TREE_CODE (loop->estimated_nb_iterations) == INTEGER_CST))
1865 loop->estimated_nb_iterations = chrec_dont_know;
1867 exits = get_loop_exit_edges (loop, &n_exits);
1868 for (i = 0; i < n_exits; i++)
1870 if (!number_of_iterations_exit (loop, exits[i], &niter_desc, false))
1873 niter = niter_desc.niter;
1874 type = TREE_TYPE (niter);
1875 if (!zero_p (niter_desc.may_be_zero)
1876 && !nonzero_p (niter_desc.may_be_zero))
1877 niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
1878 build_int_cst (type, 0),
1880 record_estimate (loop, niter,
1881 niter_desc.additional_info,
1882 last_stmt (exits[i]->src));
1886 if (chrec_contains_undetermined (loop->estimated_nb_iterations))
1887 infer_loop_bounds_from_undefined (loop);
1890 /* Records estimates on numbers of iterations of LOOPS. */
1893 estimate_numbers_of_iterations (struct loops *loops)
1898 /* We don't want to issue signed overflow warnings while getting
1899 loop iteration estimates. */
1900 fold_defer_overflow_warnings ();
1902 for (i = 1; i < loops->num; i++)
1904 loop = loops->parray[i];
1906 estimate_numbers_of_iterations_loop (loop);
1909 fold_undefer_and_ignore_overflow_warnings ();
1912 /* Returns true if statement S1 dominates statement S2. */
1915 stmt_dominates_stmt_p (tree s1, tree s2)
1917 basic_block bb1 = bb_for_stmt (s1), bb2 = bb_for_stmt (s2);
1925 block_stmt_iterator bsi;
1927 for (bsi = bsi_start (bb1); bsi_stmt (bsi) != s2; bsi_next (&bsi))
1928 if (bsi_stmt (bsi) == s1)
1934 return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
1937 /* Returns true when we can prove that the number of executions of
1938 STMT in the loop is at most NITER, according to the fact
1939 that the statement NITER_BOUND->at_stmt is executed at most
1940 NITER_BOUND->bound times. */
1943 n_of_executions_at_most (tree stmt,
1944 struct nb_iter_bound *niter_bound,
1948 tree bound = niter_bound->bound;
1949 tree bound_type = TREE_TYPE (bound);
1950 tree nit_type = TREE_TYPE (niter);
1953 gcc_assert (TYPE_UNSIGNED (bound_type)
1954 && TYPE_UNSIGNED (nit_type)
1955 && is_gimple_min_invariant (bound));
1956 if (TYPE_PRECISION (nit_type) > TYPE_PRECISION (bound_type))
1957 bound = fold_convert (nit_type, bound);
1959 niter = fold_convert (bound_type, niter);
1961 /* After the statement niter_bound->at_stmt we know that anything is
1962 executed at most BOUND times. */
1963 if (stmt && stmt_dominates_stmt_p (niter_bound->at_stmt, stmt))
1965 /* Before the statement niter_bound->at_stmt we know that anything
1966 is executed at most BOUND + 1 times. */
1970 cond = fold_binary (cmp, boolean_type_node, niter, bound);
1971 return nonzero_p (cond);
1974 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
1977 nowrap_type_p (tree type)
1979 if (INTEGRAL_TYPE_P (type)
1980 && TYPE_OVERFLOW_UNDEFINED (type))
1983 if (POINTER_TYPE_P (type))
1989 /* Return false only when the induction variable BASE + STEP * I is
1990 known to not overflow: i.e. when the number of iterations is small
1991 enough with respect to the step and initial condition in order to
1992 keep the evolution confined in TYPEs bounds. Return true when the
1993 iv is known to overflow or when the property is not computable.
1995 USE_OVERFLOW_SEMANTICS is true if this function should assume that
1996 the rules for overflow of the given language apply (e.g., that signed
1997 arithmetics in C does not overflow). */
2000 scev_probably_wraps_p (tree base, tree step,
2001 tree at_stmt, struct loop *loop,
2002 bool use_overflow_semantics)
2004 struct nb_iter_bound *bound;
2005 tree delta, step_abs;
2006 tree unsigned_type, valid_niter;
2007 tree type = TREE_TYPE (step);
2009 /* FIXME: We really need something like
2010 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
2012 We used to test for the following situation that frequently appears
2013 during address arithmetics:
2015 D.1621_13 = (long unsigned intD.4) D.1620_12;
2016 D.1622_14 = D.1621_13 * 8;
2017 D.1623_15 = (doubleD.29 *) D.1622_14;
2019 And derived that the sequence corresponding to D_14
2020 can be proved to not wrap because it is used for computing a
2021 memory access; however, this is not really the case -- for example,
2022 if D_12 = (unsigned char) [254,+,1], then D_14 has values
2023 2032, 2040, 0, 8, ..., but the code is still legal. */
2025 if (chrec_contains_undetermined (base)
2026 || chrec_contains_undetermined (step)
2027 || TREE_CODE (step) != INTEGER_CST)
2033 /* If we can use the fact that signed and pointer arithmetics does not
2034 wrap, we are done. */
2035 if (use_overflow_semantics && nowrap_type_p (type))
2038 /* Don't issue signed overflow warnings. */
2039 fold_defer_overflow_warnings ();
2041 /* Otherwise, compute the number of iterations before we reach the
2042 bound of the type, and verify that the loop is exited before this
2044 unsigned_type = unsigned_type_for (type);
2045 base = fold_convert (unsigned_type, base);
2047 if (tree_int_cst_sign_bit (step))
2049 tree extreme = fold_convert (unsigned_type,
2050 lower_bound_in_type (type, type));
2051 delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
2052 step_abs = fold_build1 (NEGATE_EXPR, unsigned_type,
2053 fold_convert (unsigned_type, step));
2057 tree extreme = fold_convert (unsigned_type,
2058 upper_bound_in_type (type, type));
2059 delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
2060 step_abs = fold_convert (unsigned_type, step);
2063 valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step_abs);
2065 estimate_numbers_of_iterations_loop (loop);
2066 for (bound = loop->bounds; bound; bound = bound->next)
2068 if (n_of_executions_at_most (at_stmt, bound, valid_niter))
2070 fold_undefer_and_ignore_overflow_warnings ();
2075 fold_undefer_and_ignore_overflow_warnings ();
2077 /* At this point we still don't have a proof that the iv does not
2078 overflow: give up. */
2082 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
2085 free_numbers_of_iterations_estimates_loop (struct loop *loop)
2087 struct nb_iter_bound *bound, *next;
2089 loop->nb_iterations = NULL;
2090 loop->estimated_nb_iterations = NULL;
2091 for (bound = loop->bounds; bound; bound = next)
2097 loop->bounds = NULL;
2100 /* Frees the information on upper bounds on numbers of iterations of LOOPS. */
2103 free_numbers_of_iterations_estimates (struct loops *loops)
2108 for (i = 1; i < loops->num; i++)
2110 loop = loops->parray[i];
2112 free_numbers_of_iterations_estimates_loop (loop);
2116 /* Substitute value VAL for ssa name NAME inside expressions held
2120 substitute_in_loop_info (struct loop *loop, tree name, tree val)
2122 loop->nb_iterations = simplify_replace_tree (loop->nb_iterations, name, val);
2123 loop->estimated_nb_iterations
2124 = simplify_replace_tree (loop->estimated_nb_iterations, name, val);