1 /* Functions to determine/estimate number of iterations of a loop.
2 Copyright (C) 2004, 2005 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 (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_type (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_type (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_type (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 (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 (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_type (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_type (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 (type, 1));
530 iv0->base = fold_build2 (MINUS_EXPR, type,
531 iv0->base, build_int_cst_type (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_type (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;
740 return (ret ? fold (ret) : expr);
743 if (TREE_CODE (expr) != SSA_NAME)
746 stmt = SSA_NAME_DEF_STMT (expr);
747 if (TREE_CODE (stmt) != MODIFY_EXPR)
750 e = TREE_OPERAND (stmt, 1);
751 if (/* Casts are simple. */
752 TREE_CODE (e) != NOP_EXPR
753 && TREE_CODE (e) != CONVERT_EXPR
754 /* Copies are simple. */
755 && TREE_CODE (e) != SSA_NAME
756 /* Assignments of invariants are simple. */
757 && !is_gimple_min_invariant (e)
758 /* And increments and decrements by a constant are simple. */
759 && !((TREE_CODE (e) == PLUS_EXPR
760 || TREE_CODE (e) == MINUS_EXPR)
761 && is_gimple_min_invariant (TREE_OPERAND (e, 1))))
764 return expand_simple_operations (e);
767 /* Tries to simplify EXPR using the condition COND. Returns the simplified
768 expression (or EXPR unchanged, if no simplification was possible). */
771 tree_simplify_using_condition_1 (tree cond, tree expr)
774 tree e, te, e0, e1, e2, notcond;
775 enum tree_code code = TREE_CODE (expr);
777 if (code == INTEGER_CST)
780 if (code == TRUTH_OR_EXPR
781 || code == TRUTH_AND_EXPR
782 || code == COND_EXPR)
786 e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
787 if (TREE_OPERAND (expr, 0) != e0)
790 e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
791 if (TREE_OPERAND (expr, 1) != e1)
794 if (code == COND_EXPR)
796 e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
797 if (TREE_OPERAND (expr, 2) != e2)
805 if (code == COND_EXPR)
806 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
808 expr = fold_build2 (code, boolean_type_node, e0, e1);
814 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
815 propagation, and vice versa. Fold does not handle this, since it is
816 considered too expensive. */
817 if (TREE_CODE (cond) == EQ_EXPR)
819 e0 = TREE_OPERAND (cond, 0);
820 e1 = TREE_OPERAND (cond, 1);
822 /* We know that e0 == e1. Check whether we cannot simplify expr
824 e = simplify_replace_tree (expr, e0, e1);
825 if (zero_p (e) || nonzero_p (e))
828 e = simplify_replace_tree (expr, e1, e0);
829 if (zero_p (e) || nonzero_p (e))
832 if (TREE_CODE (expr) == EQ_EXPR)
834 e0 = TREE_OPERAND (expr, 0);
835 e1 = TREE_OPERAND (expr, 1);
837 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
838 e = simplify_replace_tree (cond, e0, e1);
841 e = simplify_replace_tree (cond, e1, e0);
845 if (TREE_CODE (expr) == NE_EXPR)
847 e0 = TREE_OPERAND (expr, 0);
848 e1 = TREE_OPERAND (expr, 1);
850 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
851 e = simplify_replace_tree (cond, e0, e1);
853 return boolean_true_node;
854 e = simplify_replace_tree (cond, e1, e0);
856 return boolean_true_node;
859 te = expand_simple_operations (expr);
861 /* Check whether COND ==> EXPR. */
862 notcond = invert_truthvalue (cond);
863 e = fold_binary (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
867 /* Check whether COND ==> not EXPR. */
868 e = fold_binary (TRUTH_AND_EXPR, boolean_type_node, cond, te);
875 /* Tries to simplify EXPR using the condition COND. Returns the simplified
876 expression (or EXPR unchanged, if no simplification was possible).
877 Wrapper around tree_simplify_using_condition_1 that ensures that chains
878 of simple operations in definitions of ssa names in COND are expanded,
879 so that things like casts or incrementing the value of the bound before
880 the loop do not cause us to fail. */
883 tree_simplify_using_condition (tree cond, tree expr)
885 cond = expand_simple_operations (cond);
887 return tree_simplify_using_condition_1 (cond, expr);
890 /* Tries to simplify EXPR using the conditions on entry to LOOP.
891 Record the conditions used for simplification to CONDS_USED.
892 Returns the simplified expression (or EXPR unchanged, if no
893 simplification was possible).*/
896 simplify_using_initial_conditions (struct loop *loop, tree expr,
903 if (TREE_CODE (expr) == INTEGER_CST)
906 for (bb = loop->header;
907 bb != ENTRY_BLOCK_PTR;
908 bb = get_immediate_dominator (CDI_DOMINATORS, bb))
910 if (!single_pred_p (bb))
912 e = single_pred_edge (bb);
914 if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
917 cond = COND_EXPR_COND (last_stmt (e->src));
918 if (e->flags & EDGE_FALSE_VALUE)
919 cond = invert_truthvalue (cond);
920 exp = tree_simplify_using_condition (cond, expr);
923 *conds_used = fold_build2 (TRUTH_AND_EXPR,
934 /* Tries to simplify EXPR using the evolutions of the loop invariants
935 in the superloops of LOOP. Returns the simplified expression
936 (or EXPR unchanged, if no simplification was possible). */
939 simplify_using_outer_evolutions (struct loop *loop, tree expr)
941 enum tree_code code = TREE_CODE (expr);
945 if (is_gimple_min_invariant (expr))
948 if (code == TRUTH_OR_EXPR
949 || code == TRUTH_AND_EXPR
950 || code == COND_EXPR)
954 e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
955 if (TREE_OPERAND (expr, 0) != e0)
958 e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
959 if (TREE_OPERAND (expr, 1) != e1)
962 if (code == COND_EXPR)
964 e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
965 if (TREE_OPERAND (expr, 2) != e2)
973 if (code == COND_EXPR)
974 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
976 expr = fold_build2 (code, boolean_type_node, e0, e1);
982 e = instantiate_parameters (loop, expr);
983 if (is_gimple_min_invariant (e))
989 /* Returns true if EXIT is the only possible exit from LOOP. */
992 loop_only_exit_p (struct loop *loop, edge exit)
995 block_stmt_iterator bsi;
999 if (exit != loop->single_exit)
1002 body = get_loop_body (loop);
1003 for (i = 0; i < loop->num_nodes; i++)
1005 for (bsi = bsi_start (body[0]); !bsi_end_p (bsi); bsi_next (&bsi))
1007 call = get_call_expr_in (bsi_stmt (bsi));
1008 if (call && TREE_SIDE_EFFECTS (call))
1020 /* Stores description of number of iterations of LOOP derived from
1021 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1022 useful information could be derived (and fields of NITER has
1023 meaning described in comments at struct tree_niter_desc
1024 declaration), false otherwise. If WARN is true and
1025 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1026 potentially unsafe assumptions. */
1029 number_of_iterations_exit (struct loop *loop, edge exit,
1030 struct tree_niter_desc *niter,
1033 tree stmt, cond, type;
1035 enum tree_code code;
1038 if (!dominated_by_p (CDI_DOMINATORS, loop->latch, exit->src))
1041 niter->assumptions = boolean_false_node;
1042 stmt = last_stmt (exit->src);
1043 if (!stmt || TREE_CODE (stmt) != COND_EXPR)
1046 /* We want the condition for staying inside loop. */
1047 cond = COND_EXPR_COND (stmt);
1048 if (exit->flags & EDGE_TRUE_VALUE)
1049 cond = invert_truthvalue (cond);
1051 code = TREE_CODE (cond);
1065 op0 = TREE_OPERAND (cond, 0);
1066 op1 = TREE_OPERAND (cond, 1);
1067 type = TREE_TYPE (op0);
1069 if (TREE_CODE (type) != INTEGER_TYPE
1070 && !POINTER_TYPE_P (type))
1073 if (!simple_iv (loop, stmt, op0, &iv0, false))
1075 if (!simple_iv (loop, stmt, op1, &iv1, false))
1078 iv0.base = expand_simple_operations (iv0.base);
1079 iv1.base = expand_simple_operations (iv1.base);
1080 if (!number_of_iterations_cond (type, &iv0, code, &iv1, niter,
1081 loop_only_exit_p (loop, exit)))
1086 niter->assumptions = simplify_using_outer_evolutions (loop,
1087 niter->assumptions);
1088 niter->may_be_zero = simplify_using_outer_evolutions (loop,
1089 niter->may_be_zero);
1090 niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
1093 niter->additional_info = boolean_true_node;
1095 = simplify_using_initial_conditions (loop,
1097 &niter->additional_info);
1099 = simplify_using_initial_conditions (loop,
1101 &niter->additional_info);
1103 if (integer_onep (niter->assumptions))
1106 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1107 But if we can prove that there is overflow or some other source of weird
1108 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1109 if (integer_zerop (niter->assumptions))
1112 if (flag_unsafe_loop_optimizations)
1113 niter->assumptions = boolean_true_node;
1117 const char *wording;
1118 location_t loc = EXPR_LOCATION (stmt);
1120 /* We can provide a more specific warning if one of the operator is
1121 constant and the other advances by +1 or -1. */
1122 if (!zero_p (iv1.step)
1123 ? (zero_p (iv0.step)
1124 && (integer_onep (iv1.step) || integer_all_onesp (iv1.step)))
1126 && (integer_onep (iv0.step) || integer_all_onesp (iv0.step))))
1128 flag_unsafe_loop_optimizations
1129 ? N_("assuming that the loop is not infinite")
1130 : N_("cannot optimize possibly infinite loops");
1133 flag_unsafe_loop_optimizations
1134 ? N_("assuming that the loop counter does not overflow")
1135 : N_("cannot optimize loop, the loop counter may overflow");
1137 if (LOCATION_LINE (loc) > 0)
1138 warning (OPT_Wunsafe_loop_optimizations, "%H%s", &loc, gettext (wording));
1140 warning (OPT_Wunsafe_loop_optimizations, "%s", gettext (wording));
1143 return flag_unsafe_loop_optimizations;
1146 /* Try to determine the number of iterations of LOOP. If we succeed,
1147 expression giving number of iterations is returned and *EXIT is
1148 set to the edge from that the information is obtained. Otherwise
1149 chrec_dont_know is returned. */
1152 find_loop_niter (struct loop *loop, edge *exit)
1154 unsigned n_exits, i;
1155 edge *exits = get_loop_exit_edges (loop, &n_exits);
1157 tree niter = NULL_TREE, aniter;
1158 struct tree_niter_desc desc;
1161 for (i = 0; i < n_exits; i++)
1164 if (!just_once_each_iteration_p (loop, ex->src))
1167 if (!number_of_iterations_exit (loop, ex, &desc, false))
1170 if (nonzero_p (desc.may_be_zero))
1172 /* We exit in the first iteration through this exit.
1173 We won't find anything better. */
1174 niter = build_int_cst_type (unsigned_type_node, 0);
1179 if (!zero_p (desc.may_be_zero))
1182 aniter = desc.niter;
1186 /* Nothing recorded yet. */
1192 /* Prefer constants, the lower the better. */
1193 if (TREE_CODE (aniter) != INTEGER_CST)
1196 if (TREE_CODE (niter) != INTEGER_CST)
1203 if (tree_int_cst_lt (aniter, niter))
1212 return niter ? niter : chrec_dont_know;
1217 Analysis of a number of iterations of a loop by a brute-force evaluation.
1221 /* Bound on the number of iterations we try to evaluate. */
1223 #define MAX_ITERATIONS_TO_TRACK \
1224 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1226 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1227 result by a chain of operations such that all but exactly one of their
1228 operands are constants. */
1231 chain_of_csts_start (struct loop *loop, tree x)
1233 tree stmt = SSA_NAME_DEF_STMT (x);
1235 basic_block bb = bb_for_stmt (stmt);
1238 || !flow_bb_inside_loop_p (loop, bb))
1241 if (TREE_CODE (stmt) == PHI_NODE)
1243 if (bb == loop->header)
1249 if (TREE_CODE (stmt) != MODIFY_EXPR)
1252 if (!ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
1254 if (SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_DEF) == NULL_DEF_OPERAND_P)
1257 use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
1258 if (use == NULL_USE_OPERAND_P)
1261 return chain_of_csts_start (loop, use);
1264 /* Determines whether the expression X is derived from a result of a phi node
1265 in header of LOOP such that
1267 * the derivation of X consists only from operations with constants
1268 * the initial value of the phi node is constant
1269 * the value of the phi node in the next iteration can be derived from the
1270 value in the current iteration by a chain of operations with constants.
1272 If such phi node exists, it is returned. If X is a constant, X is returned
1273 unchanged. Otherwise NULL_TREE is returned. */
1276 get_base_for (struct loop *loop, tree x)
1278 tree phi, init, next;
1280 if (is_gimple_min_invariant (x))
1283 phi = chain_of_csts_start (loop, x);
1287 init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
1288 next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
1290 if (TREE_CODE (next) != SSA_NAME)
1293 if (!is_gimple_min_invariant (init))
1296 if (chain_of_csts_start (loop, next) != phi)
1302 /* Given an expression X, then
1304 * if BASE is NULL_TREE, X must be a constant and we return X.
1305 * otherwise X is a SSA name, whose value in the considered loop is derived
1306 by a chain of operations with constant from a result of a phi node in
1307 the header of the loop. Then we return value of X when the value of the
1308 result of this phi node is given by the constant BASE. */
1311 get_val_for (tree x, tree base)
1320 stmt = SSA_NAME_DEF_STMT (x);
1321 if (TREE_CODE (stmt) == PHI_NODE)
1324 FOR_EACH_SSA_USE_OPERAND (op, stmt, iter, SSA_OP_USE)
1326 nx = USE_FROM_PTR (op);
1327 val = get_val_for (nx, base);
1329 val = fold (TREE_OPERAND (stmt, 1));
1331 /* only iterate loop once. */
1335 /* Should never reach here. */
1339 /* Tries to count the number of iterations of LOOP till it exits by EXIT
1340 by brute force -- i.e. by determining the value of the operands of the
1341 condition at EXIT in first few iterations of the loop (assuming that
1342 these values are constant) and determining the first one in that the
1343 condition is not satisfied. Returns the constant giving the number
1344 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
1347 loop_niter_by_eval (struct loop *loop, edge exit)
1349 tree cond, cnd, acnd;
1350 tree op[2], val[2], next[2], aval[2], phi[2];
1354 cond = last_stmt (exit->src);
1355 if (!cond || TREE_CODE (cond) != COND_EXPR)
1356 return chrec_dont_know;
1358 cnd = COND_EXPR_COND (cond);
1359 if (exit->flags & EDGE_TRUE_VALUE)
1360 cnd = invert_truthvalue (cnd);
1362 cmp = TREE_CODE (cnd);
1371 for (j = 0; j < 2; j++)
1372 op[j] = TREE_OPERAND (cnd, j);
1376 return chrec_dont_know;
1379 for (j = 0; j < 2; j++)
1381 phi[j] = get_base_for (loop, op[j]);
1383 return chrec_dont_know;
1386 for (j = 0; j < 2; j++)
1388 if (TREE_CODE (phi[j]) == PHI_NODE)
1390 val[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_preheader_edge (loop));
1391 next[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_latch_edge (loop));
1396 next[j] = NULL_TREE;
1401 for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
1403 for (j = 0; j < 2; j++)
1404 aval[j] = get_val_for (op[j], val[j]);
1406 acnd = fold_binary (cmp, boolean_type_node, aval[0], aval[1]);
1407 if (acnd && zero_p (acnd))
1409 if (dump_file && (dump_flags & TDF_DETAILS))
1411 "Proved that loop %d iterates %d times using brute force.\n",
1413 return build_int_cst (unsigned_type_node, i);
1416 for (j = 0; j < 2; j++)
1417 val[j] = get_val_for (next[j], val[j]);
1420 return chrec_dont_know;
1423 /* Finds the exit of the LOOP by that the loop exits after a constant
1424 number of iterations and stores the exit edge to *EXIT. The constant
1425 giving the number of iterations of LOOP is returned. The number of
1426 iterations is determined using loop_niter_by_eval (i.e. by brute force
1427 evaluation). If we are unable to find the exit for that loop_niter_by_eval
1428 determines the number of iterations, chrec_dont_know is returned. */
1431 find_loop_niter_by_eval (struct loop *loop, edge *exit)
1433 unsigned n_exits, i;
1434 edge *exits = get_loop_exit_edges (loop, &n_exits);
1436 tree niter = NULL_TREE, aniter;
1439 for (i = 0; i < n_exits; i++)
1442 if (!just_once_each_iteration_p (loop, ex->src))
1445 aniter = loop_niter_by_eval (loop, ex);
1446 if (chrec_contains_undetermined (aniter))
1450 && !tree_int_cst_lt (aniter, niter))
1458 return niter ? niter : chrec_dont_know;
1463 Analysis of upper bounds on number of iterations of a loop.
1467 /* Records that AT_STMT is executed at most BOUND times in LOOP. The
1468 additional condition ADDITIONAL is recorded with the bound. */
1471 record_estimate (struct loop *loop, tree bound, tree additional, tree at_stmt)
1473 struct nb_iter_bound *elt = xmalloc (sizeof (struct nb_iter_bound));
1475 if (dump_file && (dump_flags & TDF_DETAILS))
1477 fprintf (dump_file, "Statements after ");
1478 print_generic_expr (dump_file, at_stmt, TDF_SLIM);
1479 fprintf (dump_file, " are executed at most ");
1480 print_generic_expr (dump_file, bound, TDF_SLIM);
1481 fprintf (dump_file, " times in loop %d.\n", loop->num);
1485 elt->at_stmt = at_stmt;
1486 elt->additional = additional;
1487 elt->next = loop->bounds;
1491 /* Initialize LOOP->ESTIMATED_NB_ITERATIONS with the lowest safe
1492 approximation of the number of iterations for LOOP. */
1495 compute_estimated_nb_iterations (struct loop *loop)
1497 struct nb_iter_bound *bound;
1499 for (bound = loop->bounds; bound; bound = bound->next)
1500 if (TREE_CODE (bound->bound) == INTEGER_CST
1501 /* Update only when there is no previous estimation. */
1502 && (chrec_contains_undetermined (loop->estimated_nb_iterations)
1503 /* Or when the current estimation is smaller. */
1504 || tree_int_cst_lt (bound->bound, loop->estimated_nb_iterations)))
1505 loop->estimated_nb_iterations = bound->bound;
1508 /* The following analyzers are extracting informations on the bounds
1509 of LOOP from the following undefined behaviors:
1511 - data references should not access elements over the statically
1514 - signed variables should not overflow when flag_wrapv is not set.
1518 infer_loop_bounds_from_undefined (struct loop *loop)
1521 basic_block bb, *bbs;
1522 block_stmt_iterator bsi;
1524 bbs = get_loop_body (loop);
1526 for (i = 0; i < loop->num_nodes; i++)
1530 for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
1532 tree stmt = bsi_stmt (bsi);
1534 switch (TREE_CODE (stmt))
1538 tree op0 = TREE_OPERAND (stmt, 0);
1539 tree op1 = TREE_OPERAND (stmt, 1);
1541 /* For each array access, analyze its access function
1542 and record a bound on the loop iteration domain. */
1543 if (TREE_CODE (op1) == ARRAY_REF
1544 && !array_ref_contains_indirect_ref (op1))
1545 estimate_iters_using_array (stmt, op1);
1547 if (TREE_CODE (op0) == ARRAY_REF
1548 && !array_ref_contains_indirect_ref (op0))
1549 estimate_iters_using_array (stmt, op0);
1551 /* For each signed type variable in LOOP, analyze its
1552 scalar evolution and record a bound of the loop
1553 based on the type's ranges. */
1554 else if (!flag_wrapv && TREE_CODE (op0) == SSA_NAME)
1556 tree init, step, diff, estimation;
1557 tree scev = instantiate_parameters
1558 (loop, analyze_scalar_evolution (loop, op0));
1559 tree type = chrec_type (scev);
1562 if (chrec_contains_undetermined (scev)
1563 || TYPE_UNSIGNED (type))
1566 init = initial_condition_in_loop_num (scev, loop->num);
1567 step = evolution_part_in_loop_num (scev, loop->num);
1569 if (init == NULL_TREE
1570 || step == NULL_TREE
1571 || TREE_CODE (init) != INTEGER_CST
1572 || TREE_CODE (step) != INTEGER_CST
1573 || TYPE_MIN_VALUE (type) == NULL_TREE
1574 || TYPE_MAX_VALUE (type) == NULL_TREE)
1577 utype = unsigned_type_for (type);
1578 if (tree_int_cst_lt (step, integer_zero_node))
1579 diff = fold_build2 (MINUS_EXPR, utype, init,
1580 TYPE_MIN_VALUE (type));
1582 diff = fold_build2 (MINUS_EXPR, utype,
1583 TYPE_MAX_VALUE (type), init);
1585 estimation = fold_build2 (CEIL_DIV_EXPR, utype, diff,
1587 record_estimate (loop, estimation, boolean_true_node, stmt);
1597 for (args = TREE_OPERAND (stmt, 1); args;
1598 args = TREE_CHAIN (args))
1599 if (TREE_CODE (TREE_VALUE (args)) == ARRAY_REF
1600 && !array_ref_contains_indirect_ref (TREE_VALUE (args)))
1601 estimate_iters_using_array (stmt, TREE_VALUE (args));
1611 if (chrec_contains_undetermined (loop->estimated_nb_iterations))
1612 compute_estimated_nb_iterations (loop);
1618 /* Records estimates on numbers of iterations of LOOP. */
1621 estimate_numbers_of_iterations_loop (struct loop *loop)
1625 unsigned i, n_exits;
1626 struct tree_niter_desc niter_desc;
1628 /* Give up if we already have tried to compute an estimation. */
1629 if (loop->estimated_nb_iterations == chrec_dont_know
1630 /* Or when we already have an estimation. */
1631 || (loop->estimated_nb_iterations != NULL_TREE
1632 && TREE_CODE (loop->estimated_nb_iterations) == INTEGER_CST))
1635 loop->estimated_nb_iterations = chrec_dont_know;
1637 exits = get_loop_exit_edges (loop, &n_exits);
1638 for (i = 0; i < n_exits; i++)
1640 if (!number_of_iterations_exit (loop, exits[i], &niter_desc, false))
1643 niter = niter_desc.niter;
1644 type = TREE_TYPE (niter);
1645 if (!zero_p (niter_desc.may_be_zero)
1646 && !nonzero_p (niter_desc.may_be_zero))
1647 niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
1648 build_int_cst_type (type, 0),
1650 record_estimate (loop, niter,
1651 niter_desc.additional_info,
1652 last_stmt (exits[i]->src));
1656 if (chrec_contains_undetermined (loop->estimated_nb_iterations))
1657 infer_loop_bounds_from_undefined (loop);
1660 /* Records estimates on numbers of iterations of LOOPS. */
1663 estimate_numbers_of_iterations (struct loops *loops)
1668 for (i = 1; i < loops->num; i++)
1670 loop = loops->parray[i];
1672 estimate_numbers_of_iterations_loop (loop);
1676 /* If A > B, returns -1. If A == B, returns 0. If A < B, returns 1.
1677 If neither of these relations can be proved, returns 2. */
1680 compare_trees (tree a, tree b)
1682 tree typea = TREE_TYPE (a), typeb = TREE_TYPE (b);
1685 if (TYPE_PRECISION (typea) > TYPE_PRECISION (typeb))
1690 a = fold_convert (type, a);
1691 b = fold_convert (type, b);
1693 if (nonzero_p (fold_binary (EQ_EXPR, boolean_type_node, a, b)))
1695 if (nonzero_p (fold_binary (LT_EXPR, boolean_type_node, a, b)))
1697 if (nonzero_p (fold_binary (GT_EXPR, boolean_type_node, a, b)))
1703 /* Returns true if statement S1 dominates statement S2. */
1706 stmt_dominates_stmt_p (tree s1, tree s2)
1708 basic_block bb1 = bb_for_stmt (s1), bb2 = bb_for_stmt (s2);
1716 block_stmt_iterator bsi;
1718 for (bsi = bsi_start (bb1); bsi_stmt (bsi) != s2; bsi_next (&bsi))
1719 if (bsi_stmt (bsi) == s1)
1725 return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
1728 /* Return true when it is possible to prove that the induction
1729 variable does not wrap: vary outside the type specified bounds.
1730 Checks whether BOUND < VALID_NITER that means in the context of iv
1731 conversion that all the iterations in the loop are safe: not
1734 The statement NITER_BOUND->AT_STMT is executed at most
1735 NITER_BOUND->BOUND times in the loop.
1737 NITER_BOUND->ADDITIONAL is the additional condition recorded for
1738 operands of the bound. This is useful in the following case,
1739 created by loop header copying:
1748 If the n > 0 condition is taken into account, the number of iterations of the
1749 loop can be expressed as n - 1. If the type of n is signed, the ADDITIONAL
1750 assumption "n > 0" says us that the value of the number of iterations is at
1751 most MAX_TYPE - 1 (without this assumption, it might overflow). */
1754 proved_non_wrapping_p (tree at_stmt,
1755 struct nb_iter_bound *niter_bound,
1760 tree bound = niter_bound->bound;
1763 if (TYPE_PRECISION (new_type) > TYPE_PRECISION (TREE_TYPE (bound)))
1764 bound = fold_convert (unsigned_type_for (new_type), bound);
1766 valid_niter = fold_convert (TREE_TYPE (bound), valid_niter);
1768 /* Give up if BOUND was not folded to an INTEGER_CST, as in PR23434. */
1769 if (TREE_CODE (bound) != INTEGER_CST)
1772 /* After the statement niter_bound->at_stmt we know that anything is
1773 executed at most BOUND times. */
1774 if (at_stmt && stmt_dominates_stmt_p (niter_bound->at_stmt, at_stmt))
1776 /* Before the statement niter_bound->at_stmt we know that anything
1777 is executed at most BOUND + 1 times. */
1781 cond = fold_binary (cmp, boolean_type_node, valid_niter, bound);
1782 if (nonzero_p (cond))
1785 cond = build2 (cmp, boolean_type_node, valid_niter, bound);
1786 /* Try taking additional conditions into account. */
1787 cond = fold_binary (TRUTH_OR_EXPR, boolean_type_node,
1788 invert_truthvalue (niter_bound->additional),
1791 if (nonzero_p (cond))
1797 /* Checks whether it is correct to count the induction variable BASE +
1798 STEP * I at AT_STMT in a wider type NEW_TYPE, using the bounds on
1799 numbers of iterations of a LOOP. If it is possible, return the
1800 value of step of the induction variable in the NEW_TYPE, otherwise
1801 return NULL_TREE. */
1804 convert_step_widening (struct loop *loop, tree new_type, tree base, tree step,
1807 struct nb_iter_bound *bound;
1808 tree base_in_new_type, base_plus_step_in_new_type, step_in_new_type;
1809 tree delta, step_abs;
1810 tree unsigned_type, valid_niter;
1812 /* Compute the new step. For example, {(uchar) 100, +, (uchar) 240}
1813 is converted to {(uint) 100, +, (uint) 0xfffffff0} in order to
1814 keep the values of the induction variable unchanged: 100, 84, 68,
1817 Another example is: (uint) {(uchar)100, +, (uchar)3} is converted
1818 to {(uint)100, +, (uint)3}.
1820 Before returning the new step, verify that the number of
1821 iterations is less than DELTA / STEP_ABS (i.e. in the previous
1822 example (256 - 100) / 3) such that the iv does not wrap (in which
1823 case the operations are too difficult to be represented and
1824 handled: the values of the iv should be taken modulo 256 in the
1825 wider type; this is not implemented). */
1826 base_in_new_type = fold_convert (new_type, base);
1827 base_plus_step_in_new_type =
1828 fold_convert (new_type,
1829 fold_build2 (PLUS_EXPR, TREE_TYPE (base), base, step));
1830 step_in_new_type = fold_build2 (MINUS_EXPR, new_type,
1831 base_plus_step_in_new_type,
1834 if (TREE_CODE (step_in_new_type) != INTEGER_CST)
1837 switch (compare_trees (base_plus_step_in_new_type, base_in_new_type))
1841 tree extreme = upper_bound_in_type (new_type, TREE_TYPE (base));
1842 delta = fold_build2 (MINUS_EXPR, new_type, extreme,
1844 step_abs = step_in_new_type;
1850 tree extreme = lower_bound_in_type (new_type, TREE_TYPE (base));
1851 delta = fold_build2 (MINUS_EXPR, new_type, base_in_new_type,
1853 step_abs = fold_build1 (NEGATE_EXPR, new_type, step_in_new_type);
1858 return step_in_new_type;
1864 unsigned_type = unsigned_type_for (new_type);
1865 delta = fold_convert (unsigned_type, delta);
1866 step_abs = fold_convert (unsigned_type, step_abs);
1867 valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type,
1870 estimate_numbers_of_iterations_loop (loop);
1871 for (bound = loop->bounds; bound; bound = bound->next)
1872 if (proved_non_wrapping_p (at_stmt, bound, new_type, valid_niter))
1873 return step_in_new_type;
1875 /* Fail when the loop has no bound estimations, or when no bound can
1876 be used for verifying the conversion. */
1880 /* Returns true when VAR is used in pointer arithmetics. DEPTH is
1881 used for limiting the search. */
1884 used_in_pointer_arithmetic_p (tree var, int depth)
1886 use_operand_p use_p;
1887 imm_use_iterator iter;
1890 || TREE_CODE (var) != SSA_NAME
1891 || !has_single_use (var))
1894 FOR_EACH_IMM_USE_FAST (use_p, iter, var)
1896 tree stmt = USE_STMT (use_p);
1898 if (stmt && TREE_CODE (stmt) == MODIFY_EXPR)
1900 tree rhs = TREE_OPERAND (stmt, 1);
1902 if (TREE_CODE (rhs) == NOP_EXPR
1903 || TREE_CODE (rhs) == CONVERT_EXPR)
1905 if (POINTER_TYPE_P (TREE_TYPE (rhs)))
1910 return used_in_pointer_arithmetic_p (TREE_OPERAND (stmt, 0),
1917 /* Return false only when the induction variable BASE + STEP * I is
1918 known to not overflow: i.e. when the number of iterations is small
1919 enough with respect to the step and initial condition in order to
1920 keep the evolution confined in TYPEs bounds. Return true when the
1921 iv is known to overflow or when the property is not computable.
1923 Initialize INIT_IS_MAX to true when the evolution goes from
1924 INIT_IS_MAX to LOWER_BOUND_IN_TYPE, false in the contrary case.
1925 When this property cannot be determined, UNKNOWN_MAX is set to
1929 scev_probably_wraps_p (tree type, tree base, tree step,
1930 tree at_stmt, struct loop *loop,
1931 bool *init_is_max, bool *unknown_max)
1933 struct nb_iter_bound *bound;
1934 tree delta, step_abs;
1935 tree unsigned_type, valid_niter;
1936 tree base_plus_step, bpsps;
1939 /* FIXME: The following code will not be used anymore once
1940 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html is
1943 If AT_STMT is a cast to unsigned that is later used for
1944 referencing a memory location, it is followed by a pointer
1945 conversion just after. Because pointers do not wrap, the
1946 sequences that reference the memory do not wrap either. In the
1947 following example, sequences corresponding to D_13 and to D_14
1948 can be proved to not wrap because they are used for computing a
1951 D.1621_13 = (long unsigned intD.4) D.1620_12;
1952 D.1622_14 = D.1621_13 * 8;
1953 D.1623_15 = (doubleD.29 *) D.1622_14;
1955 if (at_stmt && TREE_CODE (at_stmt) == MODIFY_EXPR)
1957 tree op0 = TREE_OPERAND (at_stmt, 0);
1958 tree op1 = TREE_OPERAND (at_stmt, 1);
1959 tree type_op1 = TREE_TYPE (op1);
1961 if ((TYPE_UNSIGNED (type_op1)
1962 && used_in_pointer_arithmetic_p (op0, 2))
1963 || POINTER_TYPE_P (type_op1))
1965 *unknown_max = true;
1970 if (chrec_contains_undetermined (base)
1971 || chrec_contains_undetermined (step)
1972 || TREE_CODE (base) == REAL_CST
1973 || TREE_CODE (step) == REAL_CST)
1975 *unknown_max = true;
1979 *unknown_max = false;
1980 base_plus_step = fold_build2 (PLUS_EXPR, type, base, step);
1981 bpsps = fold_build2 (PLUS_EXPR, type, base_plus_step, step);
1982 cps = compare_trees (base_plus_step, base);
1983 cpsps = compare_trees (bpsps, base_plus_step);
1985 /* Check that the sequence is not wrapping in the first step: it
1986 should have the same monotonicity for the first two steps. See
1995 tree extreme = upper_bound_in_type (type, TREE_TYPE (base));
1996 delta = fold_build2 (MINUS_EXPR, type, extreme, base);
1998 *init_is_max = false;
2004 tree extreme = lower_bound_in_type (type, TREE_TYPE (base));
2005 delta = fold_build2 (MINUS_EXPR, type, base, extreme);
2006 step_abs = fold_build1 (NEGATE_EXPR, type, step);
2007 *init_is_max = true;
2012 /* This means step is equal to 0. This should not happen. It
2013 could happen in convert step, but not here. Safely answer
2014 don't know as in the default case. */
2017 *unknown_max = true;
2021 /* If AT_STMT represents a cast operation, we may not be able to
2022 take advantage of the undefinedness of signed type evolutions.
2024 implement-c.texi states: "For conversion to a type of width
2025 N, the value is reduced modulo 2^N to be within range of the
2028 See PR 21959 for a test case. Essentially, given a cast
2033 sc = (signed char) uc;
2037 where uc and sc have the scev {0, +, 1}, we would consider uc to
2038 wrap around, but not sc, because it is of a signed type. This
2039 causes VRP to erroneously fold the predicate above because it
2040 thinks that sc cannot be negative. */
2041 if (at_stmt && TREE_CODE (at_stmt) == MODIFY_EXPR)
2043 tree rhs = TREE_OPERAND (at_stmt, 1);
2044 tree outer_t = TREE_TYPE (rhs);
2046 if (!TYPE_UNSIGNED (outer_t)
2047 && (TREE_CODE (rhs) == NOP_EXPR || TREE_CODE (rhs) == CONVERT_EXPR))
2049 tree inner_t = TREE_TYPE (TREE_OPERAND (rhs, 0));
2051 /* If the inner type is unsigned and its size and/or
2052 precision are smaller to that of the outer type, then the
2053 expression may wrap around. */
2054 if (TYPE_UNSIGNED (inner_t)
2055 && (TYPE_SIZE (inner_t) <= TYPE_SIZE (outer_t)
2056 || TYPE_PRECISION (inner_t) <= TYPE_PRECISION (outer_t)))
2058 *unknown_max = true;
2064 /* After having set INIT_IS_MAX, we can return false: when not using
2065 wrapping arithmetic, signed types don't wrap. */
2066 if (!flag_wrapv && !TYPE_UNSIGNED (type))
2069 unsigned_type = unsigned_type_for (type);
2070 delta = fold_convert (unsigned_type, delta);
2071 step_abs = fold_convert (unsigned_type, step_abs);
2072 valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step_abs);
2074 estimate_numbers_of_iterations_loop (loop);
2075 for (bound = loop->bounds; bound; bound = bound->next)
2076 if (proved_non_wrapping_p (at_stmt, bound, type, valid_niter))
2079 /* At this point we still don't have a proof that the iv does not
2080 overflow: give up. */
2081 *unknown_max = true;
2085 /* Return the conversion to NEW_TYPE of the STEP of an induction
2086 variable BASE + STEP * I at AT_STMT. When it fails, return
2090 convert_step (struct loop *loop, tree new_type, tree base, tree step,
2095 if (chrec_contains_undetermined (base)
2096 || chrec_contains_undetermined (step))
2099 base_type = TREE_TYPE (base);
2101 /* When not using wrapping arithmetic, signed types don't wrap. */
2102 if (!flag_wrapv && !TYPE_UNSIGNED (base_type))
2103 return fold_convert (new_type, step);
2105 if (TYPE_PRECISION (new_type) > TYPE_PRECISION (base_type))
2106 return convert_step_widening (loop, new_type, base, step, at_stmt);
2108 return fold_convert (new_type, step);
2111 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
2114 free_numbers_of_iterations_estimates_loop (struct loop *loop)
2116 struct nb_iter_bound *bound, *next;
2118 loop->nb_iterations = NULL;
2119 loop->estimated_nb_iterations = NULL;
2120 for (bound = loop->bounds; bound; bound = next)
2126 loop->bounds = NULL;
2129 /* Frees the information on upper bounds on numbers of iterations of LOOPS. */
2132 free_numbers_of_iterations_estimates (struct loops *loops)
2137 for (i = 1; i < loops->num; i++)
2139 loop = loops->parray[i];
2141 free_numbers_of_iterations_estimates_loop (loop);
2145 /* Substitute value VAL for ssa name NAME inside expressions held
2149 substitute_in_loop_info (struct loop *loop, tree name, tree val)
2151 struct nb_iter_bound *bound;
2153 loop->nb_iterations = simplify_replace_tree (loop->nb_iterations, name, val);
2154 loop->estimated_nb_iterations
2155 = simplify_replace_tree (loop->estimated_nb_iterations, name, val);
2156 for (bound = loop->bounds; bound; bound = bound->next)
2158 bound->bound = simplify_replace_tree (bound->bound, name, val);
2159 bound->additional = simplify_replace_tree (bound->additional, name, val);