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 /* Rearrange the terms so that we get inequality s * i <> c, with s
144 positive. Also cast everything to the unsigned type. */
145 if (tree_int_cst_sign_bit (iv->step))
147 s = fold_convert (niter_type,
148 fold_build1 (NEGATE_EXPR, type, iv->step));
149 c = fold_build2 (MINUS_EXPR, niter_type,
150 fold_convert (niter_type, iv->base),
151 fold_convert (niter_type, final));
155 s = fold_convert (niter_type, iv->step);
156 c = fold_build2 (MINUS_EXPR, niter_type,
157 fold_convert (niter_type, final),
158 fold_convert (niter_type, iv->base));
161 /* First the trivial cases -- when the step is 1. */
162 if (integer_onep (s))
168 /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
169 is infinite. Otherwise, the number of iterations is
170 (inverse(s/d) * (c/d)) mod (size of mode/d). */
171 bits = num_ending_zeros (s);
172 bound = build_low_bits_mask (niter_type,
173 (TYPE_PRECISION (niter_type)
174 - tree_low_cst (bits, 1)));
176 d = fold_binary_to_constant (LSHIFT_EXPR, niter_type,
177 build_int_cst_type (niter_type, 1), bits);
178 s = fold_binary_to_constant (RSHIFT_EXPR, niter_type, s, bits);
182 /* If we cannot assume that the loop is not infinite, record the
183 assumptions for divisibility of c. */
184 assumption = fold_build2 (FLOOR_MOD_EXPR, niter_type, c, d);
185 assumption = fold_build2 (EQ_EXPR, boolean_type_node,
186 assumption, build_int_cst (niter_type, 0));
187 if (!nonzero_p (assumption))
188 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
189 niter->assumptions, assumption);
192 c = fold_build2 (EXACT_DIV_EXPR, niter_type, c, d);
193 tmp = fold_build2 (MULT_EXPR, niter_type, c, inverse (s, bound));
194 niter->niter = fold_build2 (BIT_AND_EXPR, niter_type, tmp, bound);
198 /* Checks whether we can determine the final value of the control variable
199 of the loop with ending condition IV0 < IV1 (computed in TYPE).
200 DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
201 of the step. The assumptions necessary to ensure that the computation
202 of the final value does not overflow are recorded in NITER. If we
203 find the final value, we adjust DELTA and return TRUE. Otherwise
207 number_of_iterations_lt_to_ne (tree type, affine_iv *iv0, affine_iv *iv1,
208 struct tree_niter_desc *niter,
209 tree *delta, tree step)
211 tree niter_type = TREE_TYPE (step);
212 tree mod = fold_build2 (FLOOR_MOD_EXPR, niter_type, *delta, step);
214 tree assumption = boolean_true_node, bound, noloop;
216 if (TREE_CODE (mod) != INTEGER_CST)
219 mod = fold_build2 (MINUS_EXPR, niter_type, step, mod);
220 tmod = fold_convert (type, mod);
222 if (nonzero_p (iv0->step))
224 /* The final value of the iv is iv1->base + MOD, assuming that this
225 computation does not overflow, and that
226 iv0->base <= iv1->base + MOD. */
227 if (!iv1->no_overflow && !zero_p (mod))
229 bound = fold_build2 (MINUS_EXPR, type,
230 TYPE_MAX_VALUE (type), tmod);
231 assumption = fold_build2 (LE_EXPR, boolean_type_node,
233 if (zero_p (assumption))
236 noloop = fold_build2 (GT_EXPR, boolean_type_node,
238 fold_build2 (PLUS_EXPR, type,
243 /* The final value of the iv is iv0->base - MOD, assuming that this
244 computation does not overflow, and that
245 iv0->base - MOD <= iv1->base. */
246 if (!iv0->no_overflow && !zero_p (mod))
248 bound = fold_build2 (PLUS_EXPR, type,
249 TYPE_MIN_VALUE (type), tmod);
250 assumption = fold_build2 (GE_EXPR, boolean_type_node,
252 if (zero_p (assumption))
255 noloop = fold_build2 (GT_EXPR, boolean_type_node,
256 fold_build2 (MINUS_EXPR, type,
261 if (!nonzero_p (assumption))
262 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
265 if (!zero_p (noloop))
266 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
269 *delta = fold_build2 (PLUS_EXPR, niter_type, *delta, mod);
273 /* Add assertions to NITER that ensure that the control variable of the loop
274 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
275 are TYPE. Returns false if we can prove that there is an overflow, true
276 otherwise. STEP is the absolute value of the step. */
279 assert_no_overflow_lt (tree type, affine_iv *iv0, affine_iv *iv1,
280 struct tree_niter_desc *niter, tree step)
282 tree bound, d, assumption, diff;
283 tree niter_type = TREE_TYPE (step);
285 if (nonzero_p (iv0->step))
287 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
288 if (iv0->no_overflow)
291 /* If iv0->base is a constant, we can determine the last value before
292 overflow precisely; otherwise we conservatively assume
295 if (TREE_CODE (iv0->base) == INTEGER_CST)
297 d = fold_build2 (MINUS_EXPR, niter_type,
298 fold_convert (niter_type, TYPE_MAX_VALUE (type)),
299 fold_convert (niter_type, iv0->base));
300 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
303 diff = fold_build2 (MINUS_EXPR, niter_type, step,
304 build_int_cst_type (niter_type, 1));
305 bound = fold_build2 (MINUS_EXPR, type,
306 TYPE_MAX_VALUE (type), fold_convert (type, diff));
307 assumption = fold_build2 (LE_EXPR, boolean_type_node,
312 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
313 if (iv1->no_overflow)
316 if (TREE_CODE (iv1->base) == INTEGER_CST)
318 d = fold_build2 (MINUS_EXPR, niter_type,
319 fold_convert (niter_type, iv1->base),
320 fold_convert (niter_type, TYPE_MIN_VALUE (type)));
321 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
324 diff = fold_build2 (MINUS_EXPR, niter_type, step,
325 build_int_cst_type (niter_type, 1));
326 bound = fold_build2 (PLUS_EXPR, type,
327 TYPE_MIN_VALUE (type), fold_convert (type, diff));
328 assumption = fold_build2 (GE_EXPR, boolean_type_node,
332 if (zero_p (assumption))
334 if (!nonzero_p (assumption))
335 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
336 niter->assumptions, assumption);
338 iv0->no_overflow = true;
339 iv1->no_overflow = true;
343 /* Add an assumption to NITER that a loop whose ending condition
344 is IV0 < IV1 rolls. TYPE is the type of the control iv. */
347 assert_loop_rolls_lt (tree type, affine_iv *iv0, affine_iv *iv1,
348 struct tree_niter_desc *niter)
350 tree assumption = boolean_true_node, bound, diff;
351 tree mbz, mbzl, mbzr;
353 if (nonzero_p (iv0->step))
355 diff = fold_build2 (MINUS_EXPR, type,
356 iv0->step, build_int_cst_type (type, 1));
358 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
359 0 address never belongs to any object, we can assume this for
361 if (!POINTER_TYPE_P (type))
363 bound = fold_build2 (PLUS_EXPR, type,
364 TYPE_MIN_VALUE (type), diff);
365 assumption = fold_build2 (GE_EXPR, boolean_type_node,
369 /* And then we can compute iv0->base - diff, and compare it with
371 mbzl = fold_build2 (MINUS_EXPR, type, iv0->base, diff);
376 diff = fold_build2 (PLUS_EXPR, type,
377 iv1->step, build_int_cst_type (type, 1));
379 if (!POINTER_TYPE_P (type))
381 bound = fold_build2 (PLUS_EXPR, type,
382 TYPE_MAX_VALUE (type), diff);
383 assumption = fold_build2 (LE_EXPR, boolean_type_node,
388 mbzr = fold_build2 (MINUS_EXPR, type, iv1->base, diff);
391 mbz = fold_build2 (GT_EXPR, boolean_type_node, mbzl, mbzr);
393 if (!nonzero_p (assumption))
394 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
395 niter->assumptions, assumption);
397 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
398 niter->may_be_zero, mbz);
401 /* Determines number of iterations of loop whose ending condition
402 is IV0 < IV1. TYPE is the type of the iv. The number of
403 iterations is stored to NITER. */
406 number_of_iterations_lt (tree type, affine_iv *iv0, affine_iv *iv1,
407 struct tree_niter_desc *niter,
408 bool never_infinite ATTRIBUTE_UNUSED)
410 tree niter_type = unsigned_type_for (type);
413 delta = fold_build2 (MINUS_EXPR, niter_type,
414 fold_convert (niter_type, iv1->base),
415 fold_convert (niter_type, iv0->base));
417 /* First handle the special case that the step is +-1. */
418 if ((iv0->step && integer_onep (iv0->step)
419 && zero_p (iv1->step))
420 || (iv1->step && integer_all_onesp (iv1->step)
421 && zero_p (iv0->step)))
423 /* for (i = iv0->base; i < iv1->base; i++)
427 for (i = iv1->base; i > iv0->base; i--).
429 In both cases # of iterations is iv1->base - iv0->base, assuming that
430 iv1->base >= iv0->base. */
431 niter->may_be_zero = fold_build2 (LT_EXPR, boolean_type_node,
432 iv1->base, iv0->base);
433 niter->niter = delta;
437 if (nonzero_p (iv0->step))
438 step = fold_convert (niter_type, iv0->step);
440 step = fold_convert (niter_type,
441 fold_build1 (NEGATE_EXPR, type, iv1->step));
443 /* If we can determine the final value of the control iv exactly, we can
444 transform the condition to != comparison. In particular, this will be
445 the case if DELTA is constant. */
446 if (number_of_iterations_lt_to_ne (type, iv0, iv1, niter, &delta, step))
450 zps.base = build_int_cst_type (niter_type, 0);
452 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
453 zps does not overflow. */
454 zps.no_overflow = true;
456 return number_of_iterations_ne (type, &zps, delta, niter, true);
459 /* Make sure that the control iv does not overflow. */
460 if (!assert_no_overflow_lt (type, iv0, iv1, niter, step))
463 /* We determine the number of iterations as (delta + step - 1) / step. For
464 this to work, we must know that iv1->base >= iv0->base - step + 1,
465 otherwise the loop does not roll. */
466 assert_loop_rolls_lt (type, iv0, iv1, niter);
468 s = fold_build2 (MINUS_EXPR, niter_type,
469 step, build_int_cst_type (niter_type, 1));
470 delta = fold_build2 (PLUS_EXPR, niter_type, delta, s);
471 niter->niter = fold_build2 (FLOOR_DIV_EXPR, niter_type, delta, step);
475 /* Determines number of iterations of loop whose ending condition
476 is IV0 <= IV1. TYPE is the type of the iv. The number of
477 iterations is stored to NITER. NEVER_INFINITE is true if
478 we know that this condition must eventually become false (we derived this
479 earlier, and possibly set NITER->assumptions to make sure this
483 number_of_iterations_le (tree type, affine_iv *iv0, affine_iv *iv1,
484 struct tree_niter_desc *niter, bool never_infinite)
488 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
489 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
490 value of the type. This we must know anyway, since if it is
491 equal to this value, the loop rolls forever. */
495 if (nonzero_p (iv0->step))
496 assumption = fold_build2 (NE_EXPR, boolean_type_node,
497 iv1->base, TYPE_MAX_VALUE (type));
499 assumption = fold_build2 (NE_EXPR, boolean_type_node,
500 iv0->base, TYPE_MIN_VALUE (type));
502 if (zero_p (assumption))
504 if (!nonzero_p (assumption))
505 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
506 niter->assumptions, assumption);
509 if (nonzero_p (iv0->step))
510 iv1->base = fold_build2 (PLUS_EXPR, type,
511 iv1->base, build_int_cst_type (type, 1));
513 iv0->base = fold_build2 (MINUS_EXPR, type,
514 iv0->base, build_int_cst_type (type, 1));
515 return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite);
518 /* Determine the number of iterations according to condition (for staying
519 inside loop) which compares two induction variables using comparison
520 operator CODE. The induction variable on left side of the comparison
521 is IV0, the right-hand side is IV1. Both induction variables must have
522 type TYPE, which must be an integer or pointer type. The steps of the
523 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
525 ONLY_EXIT is true if we are sure this is the only way the loop could be
526 exited (including possibly non-returning function calls, exceptions, etc.)
527 -- in this case we can use the information whether the control induction
528 variables can overflow or not in a more efficient way.
530 The results (number of iterations and assumptions as described in
531 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
532 Returns false if it fails to determine number of iterations, true if it
533 was determined (possibly with some assumptions). */
536 number_of_iterations_cond (tree type, affine_iv *iv0, enum tree_code code,
537 affine_iv *iv1, struct tree_niter_desc *niter,
542 /* The meaning of these assumptions is this:
544 then the rest of information does not have to be valid
545 if may_be_zero then the loop does not roll, even if
547 niter->assumptions = boolean_true_node;
548 niter->may_be_zero = boolean_false_node;
549 niter->niter = NULL_TREE;
550 niter->additional_info = boolean_true_node;
552 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
553 the control variable is on lhs. */
554 if (code == GE_EXPR || code == GT_EXPR
555 || (code == NE_EXPR && zero_p (iv0->step)))
558 code = swap_tree_comparison (code);
563 /* If this is not the only possible exit from the loop, the information
564 that the induction variables cannot overflow as derived from
565 signedness analysis cannot be relied upon. We use them e.g. in the
566 following way: given loop for (i = 0; i <= n; i++), if i is
567 signed, it cannot overflow, thus this loop is equivalent to
568 for (i = 0; i < n + 1; i++); however, if n == MAX, but the loop
569 is exited in some other way before i overflows, this transformation
570 is incorrect (the new loop exits immediately). */
571 iv0->no_overflow = false;
572 iv1->no_overflow = false;
575 if (POINTER_TYPE_P (type))
577 /* Comparison of pointers is undefined unless both iv0 and iv1 point
578 to the same object. If they do, the control variable cannot wrap
579 (as wrap around the bounds of memory will never return a pointer
580 that would be guaranteed to point to the same object, even if we
581 avoid undefined behavior by casting to size_t and back). The
582 restrictions on pointer arithmetics and comparisons of pointers
583 ensure that using the no-overflow assumptions is correct in this
584 case even if ONLY_EXIT is false. */
585 iv0->no_overflow = true;
586 iv1->no_overflow = true;
589 /* If the control induction variable does not overflow, the loop obviously
590 cannot be infinite. */
591 if (!zero_p (iv0->step) && iv0->no_overflow)
592 never_infinite = true;
593 else if (!zero_p (iv1->step) && iv1->no_overflow)
594 never_infinite = true;
596 never_infinite = false;
598 /* We can handle the case when neither of the sides of the comparison is
599 invariant, provided that the test is NE_EXPR. This rarely occurs in
600 practice, but it is simple enough to manage. */
601 if (!zero_p (iv0->step) && !zero_p (iv1->step))
606 iv0->step = fold_binary_to_constant (MINUS_EXPR, type,
607 iv0->step, iv1->step);
608 iv0->no_overflow = false;
609 iv1->step = NULL_TREE;
610 iv1->no_overflow = true;
613 /* If the result of the comparison is a constant, the loop is weird. More
614 precise handling would be possible, but the situation is not common enough
615 to waste time on it. */
616 if (zero_p (iv0->step) && zero_p (iv1->step))
619 /* Ignore loops of while (i-- < 10) type. */
622 if (iv0->step && tree_int_cst_sign_bit (iv0->step))
625 if (!zero_p (iv1->step) && !tree_int_cst_sign_bit (iv1->step))
629 /* If the loop exits immediatelly, there is nothing to do. */
630 if (zero_p (fold_build2 (code, boolean_type_node, iv0->base, iv1->base)))
632 niter->niter = build_int_cst_type (unsigned_type_for (type), 0);
636 /* OK, now we know we have a senseful loop. Handle several cases, depending
637 on what comparison operator is used. */
641 gcc_assert (zero_p (iv1->step));
642 return number_of_iterations_ne (type, iv0, iv1->base, niter, never_infinite);
644 return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite);
646 return number_of_iterations_le (type, iv0, iv1, niter, never_infinite);
652 /* Substitute NEW for OLD in EXPR and fold the result. */
655 simplify_replace_tree (tree expr, tree old, tree new)
658 tree ret = NULL_TREE, e, se;
664 || operand_equal_p (expr, old, 0))
665 return unshare_expr (new);
670 n = TREE_CODE_LENGTH (TREE_CODE (expr));
671 for (i = 0; i < n; i++)
673 e = TREE_OPERAND (expr, i);
674 se = simplify_replace_tree (e, old, new);
679 ret = copy_node (expr);
681 TREE_OPERAND (ret, i) = se;
684 return (ret ? fold (ret) : expr);
687 /* Expand definitions of ssa names in EXPR as long as they are simple
688 enough, and return the new expression. */
691 expand_simple_operations (tree expr)
694 tree ret = NULL_TREE, e, ee, stmt;
697 if (expr == NULL_TREE)
700 if (is_gimple_min_invariant (expr))
703 code = TREE_CODE (expr);
704 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code)))
706 n = TREE_CODE_LENGTH (code);
707 for (i = 0; i < n; i++)
709 e = TREE_OPERAND (expr, i);
710 ee = expand_simple_operations (e);
715 ret = copy_node (expr);
717 TREE_OPERAND (ret, i) = ee;
720 return (ret ? fold (ret) : expr);
723 if (TREE_CODE (expr) != SSA_NAME)
726 stmt = SSA_NAME_DEF_STMT (expr);
727 if (TREE_CODE (stmt) != MODIFY_EXPR)
730 e = TREE_OPERAND (stmt, 1);
731 if (/* Casts are simple. */
732 TREE_CODE (e) != NOP_EXPR
733 && TREE_CODE (e) != CONVERT_EXPR
734 /* Copies are simple. */
735 && TREE_CODE (e) != SSA_NAME
736 /* Assignments of invariants are simple. */
737 && !is_gimple_min_invariant (e)
738 /* And increments and decrements by a constant are simple. */
739 && !((TREE_CODE (e) == PLUS_EXPR
740 || TREE_CODE (e) == MINUS_EXPR)
741 && is_gimple_min_invariant (TREE_OPERAND (e, 1))))
744 return expand_simple_operations (e);
747 /* Tries to simplify EXPR using the condition COND. Returns the simplified
748 expression (or EXPR unchanged, if no simplification was possible). */
751 tree_simplify_using_condition_1 (tree cond, tree expr)
754 tree e, te, e0, e1, e2, notcond;
755 enum tree_code code = TREE_CODE (expr);
757 if (code == INTEGER_CST)
760 if (code == TRUTH_OR_EXPR
761 || code == TRUTH_AND_EXPR
762 || code == COND_EXPR)
766 e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
767 if (TREE_OPERAND (expr, 0) != e0)
770 e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
771 if (TREE_OPERAND (expr, 1) != e1)
774 if (code == COND_EXPR)
776 e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
777 if (TREE_OPERAND (expr, 2) != e2)
785 if (code == COND_EXPR)
786 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
788 expr = fold_build2 (code, boolean_type_node, e0, e1);
794 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
795 propagation, and vice versa. Fold does not handle this, since it is
796 considered too expensive. */
797 if (TREE_CODE (cond) == EQ_EXPR)
799 e0 = TREE_OPERAND (cond, 0);
800 e1 = TREE_OPERAND (cond, 1);
802 /* We know that e0 == e1. Check whether we cannot simplify expr
804 e = simplify_replace_tree (expr, e0, e1);
805 if (zero_p (e) || nonzero_p (e))
808 e = simplify_replace_tree (expr, e1, e0);
809 if (zero_p (e) || nonzero_p (e))
812 if (TREE_CODE (expr) == EQ_EXPR)
814 e0 = TREE_OPERAND (expr, 0);
815 e1 = TREE_OPERAND (expr, 1);
817 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
818 e = simplify_replace_tree (cond, e0, e1);
821 e = simplify_replace_tree (cond, e1, e0);
825 if (TREE_CODE (expr) == NE_EXPR)
827 e0 = TREE_OPERAND (expr, 0);
828 e1 = TREE_OPERAND (expr, 1);
830 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
831 e = simplify_replace_tree (cond, e0, e1);
833 return boolean_true_node;
834 e = simplify_replace_tree (cond, e1, e0);
836 return boolean_true_node;
839 te = expand_simple_operations (expr);
841 /* Check whether COND ==> EXPR. */
842 notcond = invert_truthvalue (cond);
843 e = fold_binary (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
847 /* Check whether COND ==> not EXPR. */
848 e = fold_binary (TRUTH_AND_EXPR, boolean_type_node, cond, te);
855 /* Tries to simplify EXPR using the condition COND. Returns the simplified
856 expression (or EXPR unchanged, if no simplification was possible).
857 Wrapper around tree_simplify_using_condition_1 that ensures that chains
858 of simple operations in definitions of ssa names in COND are expanded,
859 so that things like casts or incrementing the value of the bound before
860 the loop do not cause us to fail. */
863 tree_simplify_using_condition (tree cond, tree expr)
865 cond = expand_simple_operations (cond);
867 return tree_simplify_using_condition_1 (cond, expr);
870 /* Tries to simplify EXPR using the conditions on entry to LOOP.
871 Record the conditions used for simplification to CONDS_USED.
872 Returns the simplified expression (or EXPR unchanged, if no
873 simplification was possible).*/
876 simplify_using_initial_conditions (struct loop *loop, tree expr,
883 if (TREE_CODE (expr) == INTEGER_CST)
886 for (bb = loop->header;
887 bb != ENTRY_BLOCK_PTR;
888 bb = get_immediate_dominator (CDI_DOMINATORS, bb))
890 if (!single_pred_p (bb))
892 e = single_pred_edge (bb);
894 if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
897 cond = COND_EXPR_COND (last_stmt (e->src));
898 if (e->flags & EDGE_FALSE_VALUE)
899 cond = invert_truthvalue (cond);
900 exp = tree_simplify_using_condition (cond, expr);
903 *conds_used = fold_build2 (TRUTH_AND_EXPR,
914 /* Tries to simplify EXPR using the evolutions of the loop invariants
915 in the superloops of LOOP. Returns the simplified expression
916 (or EXPR unchanged, if no simplification was possible). */
919 simplify_using_outer_evolutions (struct loop *loop, tree expr)
921 enum tree_code code = TREE_CODE (expr);
925 if (is_gimple_min_invariant (expr))
928 if (code == TRUTH_OR_EXPR
929 || code == TRUTH_AND_EXPR
930 || code == COND_EXPR)
934 e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
935 if (TREE_OPERAND (expr, 0) != e0)
938 e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
939 if (TREE_OPERAND (expr, 1) != e1)
942 if (code == COND_EXPR)
944 e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
945 if (TREE_OPERAND (expr, 2) != e2)
953 if (code == COND_EXPR)
954 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
956 expr = fold_build2 (code, boolean_type_node, e0, e1);
962 e = instantiate_parameters (loop, expr);
963 if (is_gimple_min_invariant (e))
969 /* Returns true if EXIT is the only possible exit from LOOP. */
972 loop_only_exit_p (struct loop *loop, edge exit)
975 block_stmt_iterator bsi;
979 if (exit != loop->single_exit)
982 body = get_loop_body (loop);
983 for (i = 0; i < loop->num_nodes; i++)
985 for (bsi = bsi_start (body[0]); !bsi_end_p (bsi); bsi_next (&bsi))
987 call = get_call_expr_in (bsi_stmt (bsi));
988 if (call && TREE_SIDE_EFFECTS (call))
1000 /* Stores description of number of iterations of LOOP derived from
1001 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1002 useful information could be derived (and fields of NITER has
1003 meaning described in comments at struct tree_niter_desc
1004 declaration), false otherwise. If WARN is true and
1005 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1006 potentially unsafe assumptions. */
1009 number_of_iterations_exit (struct loop *loop, edge exit,
1010 struct tree_niter_desc *niter,
1013 tree stmt, cond, type;
1015 enum tree_code code;
1018 if (!dominated_by_p (CDI_DOMINATORS, loop->latch, exit->src))
1021 niter->assumptions = boolean_false_node;
1022 stmt = last_stmt (exit->src);
1023 if (!stmt || TREE_CODE (stmt) != COND_EXPR)
1026 /* We want the condition for staying inside loop. */
1027 cond = COND_EXPR_COND (stmt);
1028 if (exit->flags & EDGE_TRUE_VALUE)
1029 cond = invert_truthvalue (cond);
1031 code = TREE_CODE (cond);
1045 op0 = TREE_OPERAND (cond, 0);
1046 op1 = TREE_OPERAND (cond, 1);
1047 type = TREE_TYPE (op0);
1049 if (TREE_CODE (type) != INTEGER_TYPE
1050 && !POINTER_TYPE_P (type))
1053 if (!simple_iv (loop, stmt, op0, &iv0, false))
1055 if (!simple_iv (loop, stmt, op1, &iv1, false))
1058 iv0.base = expand_simple_operations (iv0.base);
1059 iv1.base = expand_simple_operations (iv1.base);
1060 if (!number_of_iterations_cond (type, &iv0, code, &iv1, niter,
1061 loop_only_exit_p (loop, exit)))
1066 niter->assumptions = simplify_using_outer_evolutions (loop,
1067 niter->assumptions);
1068 niter->may_be_zero = simplify_using_outer_evolutions (loop,
1069 niter->may_be_zero);
1070 niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
1073 niter->additional_info = boolean_true_node;
1075 = simplify_using_initial_conditions (loop,
1077 &niter->additional_info);
1079 = simplify_using_initial_conditions (loop,
1081 &niter->additional_info);
1083 if (integer_onep (niter->assumptions))
1086 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1087 But if we can prove that there is overflow or some other source of weird
1088 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1089 if (integer_zerop (niter->assumptions))
1092 if (flag_unsafe_loop_optimizations)
1093 niter->assumptions = boolean_true_node;
1097 const char *wording;
1098 location_t loc = EXPR_LOCATION (stmt);
1100 /* We can provide a more specific warning if one of the operator is
1101 constant and the other advances by +1 or -1. */
1102 if (!zero_p (iv1.step)
1103 ? (zero_p (iv0.step)
1104 && (integer_onep (iv1.step) || integer_all_onesp (iv1.step)))
1106 && (integer_onep (iv0.step) || integer_all_onesp (iv0.step))))
1108 flag_unsafe_loop_optimizations
1109 ? N_("assuming that the loop is not infinite")
1110 : N_("cannot optimize possibly infinite loops");
1113 flag_unsafe_loop_optimizations
1114 ? N_("assuming that the loop counter does not overflow")
1115 : N_("cannot optimize loop, the loop counter may overflow");
1117 if (LOCATION_LINE (loc) > 0)
1118 warning (OPT_Wunsafe_loop_optimizations, "%H%s", &loc, gettext (wording));
1120 warning (OPT_Wunsafe_loop_optimizations, "%s", gettext (wording));
1123 return flag_unsafe_loop_optimizations;
1126 /* Try to determine the number of iterations of LOOP. If we succeed,
1127 expression giving number of iterations is returned and *EXIT is
1128 set to the edge from that the information is obtained. Otherwise
1129 chrec_dont_know is returned. */
1132 find_loop_niter (struct loop *loop, edge *exit)
1134 unsigned n_exits, i;
1135 edge *exits = get_loop_exit_edges (loop, &n_exits);
1137 tree niter = NULL_TREE, aniter;
1138 struct tree_niter_desc desc;
1141 for (i = 0; i < n_exits; i++)
1144 if (!just_once_each_iteration_p (loop, ex->src))
1147 if (!number_of_iterations_exit (loop, ex, &desc, false))
1150 if (nonzero_p (desc.may_be_zero))
1152 /* We exit in the first iteration through this exit.
1153 We won't find anything better. */
1154 niter = build_int_cst_type (unsigned_type_node, 0);
1159 if (!zero_p (desc.may_be_zero))
1162 aniter = desc.niter;
1166 /* Nothing recorded yet. */
1172 /* Prefer constants, the lower the better. */
1173 if (TREE_CODE (aniter) != INTEGER_CST)
1176 if (TREE_CODE (niter) != INTEGER_CST)
1183 if (tree_int_cst_lt (aniter, niter))
1192 return niter ? niter : chrec_dont_know;
1197 Analysis of a number of iterations of a loop by a brute-force evaluation.
1201 /* Bound on the number of iterations we try to evaluate. */
1203 #define MAX_ITERATIONS_TO_TRACK \
1204 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1206 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1207 result by a chain of operations such that all but exactly one of their
1208 operands are constants. */
1211 chain_of_csts_start (struct loop *loop, tree x)
1213 tree stmt = SSA_NAME_DEF_STMT (x);
1215 basic_block bb = bb_for_stmt (stmt);
1218 || !flow_bb_inside_loop_p (loop, bb))
1221 if (TREE_CODE (stmt) == PHI_NODE)
1223 if (bb == loop->header)
1229 if (TREE_CODE (stmt) != MODIFY_EXPR)
1232 if (!ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
1234 if (SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_DEF) == NULL_DEF_OPERAND_P)
1237 use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
1238 if (use == NULL_USE_OPERAND_P)
1241 return chain_of_csts_start (loop, use);
1244 /* Determines whether the expression X is derived from a result of a phi node
1245 in header of LOOP such that
1247 * the derivation of X consists only from operations with constants
1248 * the initial value of the phi node is constant
1249 * the value of the phi node in the next iteration can be derived from the
1250 value in the current iteration by a chain of operations with constants.
1252 If such phi node exists, it is returned. If X is a constant, X is returned
1253 unchanged. Otherwise NULL_TREE is returned. */
1256 get_base_for (struct loop *loop, tree x)
1258 tree phi, init, next;
1260 if (is_gimple_min_invariant (x))
1263 phi = chain_of_csts_start (loop, x);
1267 init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
1268 next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
1270 if (TREE_CODE (next) != SSA_NAME)
1273 if (!is_gimple_min_invariant (init))
1276 if (chain_of_csts_start (loop, next) != phi)
1282 /* Given an expression X, then
1284 * if X is NULL_TREE, we return the constant BASE.
1285 * otherwise X is a SSA name, whose value in the considered loop is derived
1286 by a chain of operations with constant from a result of a phi node in
1287 the header of the loop. Then we return value of X when the value of the
1288 result of this phi node is given by the constant BASE. */
1291 get_val_for (tree x, tree base)
1297 gcc_assert (is_gimple_min_invariant (base));
1302 stmt = SSA_NAME_DEF_STMT (x);
1303 if (TREE_CODE (stmt) == PHI_NODE)
1306 FOR_EACH_SSA_USE_OPERAND (op, stmt, iter, SSA_OP_USE)
1308 nx = USE_FROM_PTR (op);
1309 val = get_val_for (nx, base);
1311 val = fold (TREE_OPERAND (stmt, 1));
1313 /* only iterate loop once. */
1317 /* Should never reach here. */
1321 /* Tries to count the number of iterations of LOOP till it exits by EXIT
1322 by brute force -- i.e. by determining the value of the operands of the
1323 condition at EXIT in first few iterations of the loop (assuming that
1324 these values are constant) and determining the first one in that the
1325 condition is not satisfied. Returns the constant giving the number
1326 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
1329 loop_niter_by_eval (struct loop *loop, edge exit)
1331 tree cond, cnd, acnd;
1332 tree op[2], val[2], next[2], aval[2], phi[2];
1336 cond = last_stmt (exit->src);
1337 if (!cond || TREE_CODE (cond) != COND_EXPR)
1338 return chrec_dont_know;
1340 cnd = COND_EXPR_COND (cond);
1341 if (exit->flags & EDGE_TRUE_VALUE)
1342 cnd = invert_truthvalue (cnd);
1344 cmp = TREE_CODE (cnd);
1353 for (j = 0; j < 2; j++)
1354 op[j] = TREE_OPERAND (cnd, j);
1358 return chrec_dont_know;
1361 for (j = 0; j < 2; j++)
1363 phi[j] = get_base_for (loop, op[j]);
1365 return chrec_dont_know;
1368 for (j = 0; j < 2; j++)
1370 if (TREE_CODE (phi[j]) == PHI_NODE)
1372 val[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_preheader_edge (loop));
1373 next[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_latch_edge (loop));
1378 next[j] = NULL_TREE;
1383 for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
1385 for (j = 0; j < 2; j++)
1386 aval[j] = get_val_for (op[j], val[j]);
1388 acnd = fold_binary (cmp, boolean_type_node, aval[0], aval[1]);
1389 if (acnd && zero_p (acnd))
1391 if (dump_file && (dump_flags & TDF_DETAILS))
1393 "Proved that loop %d iterates %d times using brute force.\n",
1395 return build_int_cst (unsigned_type_node, i);
1398 for (j = 0; j < 2; j++)
1400 val[j] = get_val_for (next[j], val[j]);
1401 if (!is_gimple_min_invariant (val[j]))
1402 return chrec_dont_know;
1406 return chrec_dont_know;
1409 /* Finds the exit of the LOOP by that the loop exits after a constant
1410 number of iterations and stores the exit edge to *EXIT. The constant
1411 giving the number of iterations of LOOP is returned. The number of
1412 iterations is determined using loop_niter_by_eval (i.e. by brute force
1413 evaluation). If we are unable to find the exit for that loop_niter_by_eval
1414 determines the number of iterations, chrec_dont_know is returned. */
1417 find_loop_niter_by_eval (struct loop *loop, edge *exit)
1419 unsigned n_exits, i;
1420 edge *exits = get_loop_exit_edges (loop, &n_exits);
1422 tree niter = NULL_TREE, aniter;
1425 for (i = 0; i < n_exits; i++)
1428 if (!just_once_each_iteration_p (loop, ex->src))
1431 aniter = loop_niter_by_eval (loop, ex);
1432 if (chrec_contains_undetermined (aniter))
1436 && !tree_int_cst_lt (aniter, niter))
1444 return niter ? niter : chrec_dont_know;
1449 Analysis of upper bounds on number of iterations of a loop.
1453 /* Records that AT_STMT is executed at most BOUND times in LOOP. The
1454 additional condition ADDITIONAL is recorded with the bound. */
1457 record_estimate (struct loop *loop, tree bound, tree additional, tree at_stmt)
1459 struct nb_iter_bound *elt = xmalloc (sizeof (struct nb_iter_bound));
1461 if (dump_file && (dump_flags & TDF_DETAILS))
1463 fprintf (dump_file, "Statements after ");
1464 print_generic_expr (dump_file, at_stmt, TDF_SLIM);
1465 fprintf (dump_file, " are executed at most ");
1466 print_generic_expr (dump_file, bound, TDF_SLIM);
1467 fprintf (dump_file, " times in loop %d.\n", loop->num);
1471 elt->at_stmt = at_stmt;
1472 elt->additional = additional;
1473 elt->next = loop->bounds;
1477 /* Initialize LOOP->ESTIMATED_NB_ITERATIONS with the lowest safe
1478 approximation of the number of iterations for LOOP. */
1481 compute_estimated_nb_iterations (struct loop *loop)
1483 struct nb_iter_bound *bound;
1485 for (bound = loop->bounds; bound; bound = bound->next)
1486 if (TREE_CODE (bound->bound) == INTEGER_CST
1487 /* Update only when there is no previous estimation. */
1488 && (chrec_contains_undetermined (loop->estimated_nb_iterations)
1489 /* Or when the current estimation is smaller. */
1490 || tree_int_cst_lt (bound->bound, loop->estimated_nb_iterations)))
1491 loop->estimated_nb_iterations = bound->bound;
1494 /* The following analyzers are extracting informations on the bounds
1495 of LOOP from the following undefined behaviors:
1497 - data references should not access elements over the statically
1500 - signed variables should not overflow when flag_wrapv is not set.
1504 infer_loop_bounds_from_undefined (struct loop *loop)
1507 basic_block bb, *bbs;
1508 block_stmt_iterator bsi;
1510 bbs = get_loop_body (loop);
1512 for (i = 0; i < loop->num_nodes; i++)
1516 for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
1518 tree stmt = bsi_stmt (bsi);
1520 switch (TREE_CODE (stmt))
1524 tree op0 = TREE_OPERAND (stmt, 0);
1525 tree op1 = TREE_OPERAND (stmt, 1);
1527 /* For each array access, analyze its access function
1528 and record a bound on the loop iteration domain. */
1529 if (TREE_CODE (op1) == ARRAY_REF
1530 && !array_ref_contains_indirect_ref (op1))
1531 estimate_iters_using_array (stmt, op1);
1533 if (TREE_CODE (op0) == ARRAY_REF
1534 && !array_ref_contains_indirect_ref (op0))
1535 estimate_iters_using_array (stmt, op0);
1537 /* For each signed type variable in LOOP, analyze its
1538 scalar evolution and record a bound of the loop
1539 based on the type's ranges. */
1540 else if (!flag_wrapv && TREE_CODE (op0) == SSA_NAME)
1542 tree init, step, diff, estimation;
1543 tree scev = instantiate_parameters
1544 (loop, analyze_scalar_evolution (loop, op0));
1545 tree type = chrec_type (scev);
1548 if (chrec_contains_undetermined (scev)
1549 || TYPE_UNSIGNED (type))
1552 init = initial_condition_in_loop_num (scev, loop->num);
1553 step = evolution_part_in_loop_num (scev, loop->num);
1555 if (init == NULL_TREE
1556 || step == NULL_TREE
1557 || TREE_CODE (init) != INTEGER_CST
1558 || TREE_CODE (step) != INTEGER_CST
1559 || TYPE_MIN_VALUE (type) == NULL_TREE
1560 || TYPE_MAX_VALUE (type) == NULL_TREE)
1563 utype = unsigned_type_for (type);
1564 if (tree_int_cst_lt (step, integer_zero_node))
1565 diff = fold_build2 (MINUS_EXPR, type, init,
1566 TYPE_MIN_VALUE (type));
1568 diff = fold_build2 (MINUS_EXPR, type,
1569 TYPE_MAX_VALUE (type), init);
1571 if (integer_nonzerop (step))
1573 estimation = fold_build2 (CEIL_DIV_EXPR, type, diff,
1575 record_estimate (loop,
1576 fold_convert (utype, estimation),
1577 boolean_true_node, stmt);
1588 for (args = TREE_OPERAND (stmt, 1); args;
1589 args = TREE_CHAIN (args))
1590 if (TREE_CODE (TREE_VALUE (args)) == ARRAY_REF
1591 && !array_ref_contains_indirect_ref (TREE_VALUE (args)))
1592 estimate_iters_using_array (stmt, TREE_VALUE (args));
1602 if (chrec_contains_undetermined (loop->estimated_nb_iterations))
1603 compute_estimated_nb_iterations (loop);
1609 /* Records estimates on numbers of iterations of LOOP. */
1612 estimate_numbers_of_iterations_loop (struct loop *loop)
1616 unsigned i, n_exits;
1617 struct tree_niter_desc niter_desc;
1619 /* Give up if we already have tried to compute an estimation. */
1620 if (loop->estimated_nb_iterations == chrec_dont_know
1621 /* Or when we already have an estimation. */
1622 || (loop->estimated_nb_iterations != NULL_TREE
1623 && TREE_CODE (loop->estimated_nb_iterations) == INTEGER_CST))
1626 loop->estimated_nb_iterations = chrec_dont_know;
1628 exits = get_loop_exit_edges (loop, &n_exits);
1629 for (i = 0; i < n_exits; i++)
1631 if (!number_of_iterations_exit (loop, exits[i], &niter_desc, false))
1634 niter = niter_desc.niter;
1635 type = TREE_TYPE (niter);
1636 if (!zero_p (niter_desc.may_be_zero)
1637 && !nonzero_p (niter_desc.may_be_zero))
1638 niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
1639 build_int_cst_type (type, 0),
1641 record_estimate (loop, niter,
1642 niter_desc.additional_info,
1643 last_stmt (exits[i]->src));
1647 if (chrec_contains_undetermined (loop->estimated_nb_iterations))
1648 infer_loop_bounds_from_undefined (loop);
1651 /* Records estimates on numbers of iterations of LOOPS. */
1654 estimate_numbers_of_iterations (struct loops *loops)
1659 for (i = 1; i < loops->num; i++)
1661 loop = loops->parray[i];
1663 estimate_numbers_of_iterations_loop (loop);
1667 /* If A > B, returns -1. If A == B, returns 0. If A < B, returns 1.
1668 If neither of these relations can be proved, returns 2. */
1671 compare_trees (tree a, tree b)
1673 tree typea = TREE_TYPE (a), typeb = TREE_TYPE (b);
1676 if (TYPE_PRECISION (typea) > TYPE_PRECISION (typeb))
1681 a = fold_convert (type, a);
1682 b = fold_convert (type, b);
1684 if (nonzero_p (fold_binary (EQ_EXPR, boolean_type_node, a, b)))
1686 if (nonzero_p (fold_binary (LT_EXPR, boolean_type_node, a, b)))
1688 if (nonzero_p (fold_binary (GT_EXPR, boolean_type_node, a, b)))
1694 /* Returns true if statement S1 dominates statement S2. */
1697 stmt_dominates_stmt_p (tree s1, tree s2)
1699 basic_block bb1 = bb_for_stmt (s1), bb2 = bb_for_stmt (s2);
1707 block_stmt_iterator bsi;
1709 for (bsi = bsi_start (bb1); bsi_stmt (bsi) != s2; bsi_next (&bsi))
1710 if (bsi_stmt (bsi) == s1)
1716 return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
1719 /* Return true when it is possible to prove that the induction
1720 variable does not wrap: vary outside the type specified bounds.
1721 Checks whether BOUND < VALID_NITER that means in the context of iv
1722 conversion that all the iterations in the loop are safe: not
1725 The statement NITER_BOUND->AT_STMT is executed at most
1726 NITER_BOUND->BOUND times in the loop.
1728 NITER_BOUND->ADDITIONAL is the additional condition recorded for
1729 operands of the bound. This is useful in the following case,
1730 created by loop header copying:
1739 If the n > 0 condition is taken into account, the number of iterations of the
1740 loop can be expressed as n - 1. If the type of n is signed, the ADDITIONAL
1741 assumption "n > 0" says us that the value of the number of iterations is at
1742 most MAX_TYPE - 1 (without this assumption, it might overflow). */
1745 proved_non_wrapping_p (tree at_stmt,
1746 struct nb_iter_bound *niter_bound,
1751 tree bound = niter_bound->bound;
1754 if (TYPE_PRECISION (new_type) > TYPE_PRECISION (TREE_TYPE (bound)))
1755 bound = fold_convert (unsigned_type_for (new_type), bound);
1757 valid_niter = fold_convert (TREE_TYPE (bound), valid_niter);
1759 /* Give up if BOUND was not folded to an INTEGER_CST, as in PR23434. */
1760 if (TREE_CODE (bound) != INTEGER_CST)
1763 /* After the statement niter_bound->at_stmt we know that anything is
1764 executed at most BOUND times. */
1765 if (at_stmt && stmt_dominates_stmt_p (niter_bound->at_stmt, at_stmt))
1767 /* Before the statement niter_bound->at_stmt we know that anything
1768 is executed at most BOUND + 1 times. */
1772 cond = fold_binary (cmp, boolean_type_node, valid_niter, bound);
1773 if (nonzero_p (cond))
1776 cond = build2 (cmp, boolean_type_node, valid_niter, bound);
1777 /* Try taking additional conditions into account. */
1778 cond = fold_binary (TRUTH_OR_EXPR, boolean_type_node,
1779 invert_truthvalue (niter_bound->additional),
1782 if (nonzero_p (cond))
1788 /* Checks whether it is correct to count the induction variable BASE +
1789 STEP * I at AT_STMT in a wider type NEW_TYPE, using the bounds on
1790 numbers of iterations of a LOOP. If it is possible, return the
1791 value of step of the induction variable in the NEW_TYPE, otherwise
1792 return NULL_TREE. */
1795 convert_step_widening (struct loop *loop, tree new_type, tree base, tree step,
1798 struct nb_iter_bound *bound;
1799 tree base_in_new_type, base_plus_step_in_new_type, step_in_new_type;
1800 tree delta, step_abs;
1801 tree unsigned_type, valid_niter;
1803 /* Compute the new step. For example, {(uchar) 100, +, (uchar) 240}
1804 is converted to {(uint) 100, +, (uint) 0xfffffff0} in order to
1805 keep the values of the induction variable unchanged: 100, 84, 68,
1808 Another example is: (uint) {(uchar)100, +, (uchar)3} is converted
1809 to {(uint)100, +, (uint)3}.
1811 Before returning the new step, verify that the number of
1812 iterations is less than DELTA / STEP_ABS (i.e. in the previous
1813 example (256 - 100) / 3) such that the iv does not wrap (in which
1814 case the operations are too difficult to be represented and
1815 handled: the values of the iv should be taken modulo 256 in the
1816 wider type; this is not implemented). */
1817 base_in_new_type = fold_convert (new_type, base);
1818 base_plus_step_in_new_type =
1819 fold_convert (new_type,
1820 fold_build2 (PLUS_EXPR, TREE_TYPE (base), base, step));
1821 step_in_new_type = fold_build2 (MINUS_EXPR, new_type,
1822 base_plus_step_in_new_type,
1825 if (TREE_CODE (step_in_new_type) != INTEGER_CST)
1828 switch (compare_trees (base_plus_step_in_new_type, base_in_new_type))
1832 tree extreme = upper_bound_in_type (new_type, TREE_TYPE (base));
1833 delta = fold_build2 (MINUS_EXPR, new_type, extreme,
1835 step_abs = step_in_new_type;
1841 tree extreme = lower_bound_in_type (new_type, TREE_TYPE (base));
1842 delta = fold_build2 (MINUS_EXPR, new_type, base_in_new_type,
1844 step_abs = fold_build1 (NEGATE_EXPR, new_type, step_in_new_type);
1849 return step_in_new_type;
1855 unsigned_type = unsigned_type_for (new_type);
1856 delta = fold_convert (unsigned_type, delta);
1857 step_abs = fold_convert (unsigned_type, step_abs);
1858 valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type,
1861 estimate_numbers_of_iterations_loop (loop);
1862 for (bound = loop->bounds; bound; bound = bound->next)
1863 if (proved_non_wrapping_p (at_stmt, bound, new_type, valid_niter))
1864 return step_in_new_type;
1866 /* Fail when the loop has no bound estimations, or when no bound can
1867 be used for verifying the conversion. */
1871 /* Returns true when VAR is used in pointer arithmetics. DEPTH is
1872 used for limiting the search. */
1875 used_in_pointer_arithmetic_p (tree var, int depth)
1877 use_operand_p use_p;
1878 imm_use_iterator iter;
1881 || TREE_CODE (var) != SSA_NAME
1882 || !has_single_use (var))
1885 FOR_EACH_IMM_USE_FAST (use_p, iter, var)
1887 tree stmt = USE_STMT (use_p);
1889 if (stmt && TREE_CODE (stmt) == MODIFY_EXPR)
1891 tree rhs = TREE_OPERAND (stmt, 1);
1893 if (TREE_CODE (rhs) == NOP_EXPR
1894 || TREE_CODE (rhs) == CONVERT_EXPR)
1896 if (POINTER_TYPE_P (TREE_TYPE (rhs)))
1901 return used_in_pointer_arithmetic_p (TREE_OPERAND (stmt, 0),
1908 /* Return false only when the induction variable BASE + STEP * I is
1909 known to not overflow: i.e. when the number of iterations is small
1910 enough with respect to the step and initial condition in order to
1911 keep the evolution confined in TYPEs bounds. Return true when the
1912 iv is known to overflow or when the property is not computable.
1914 Initialize INIT_IS_MAX to true when the evolution goes from
1915 INIT_IS_MAX to LOWER_BOUND_IN_TYPE, false in the contrary case.
1916 When this property cannot be determined, UNKNOWN_MAX is set to
1920 scev_probably_wraps_p (tree type, tree base, tree step,
1921 tree at_stmt, struct loop *loop,
1922 bool *init_is_max, bool *unknown_max)
1924 struct nb_iter_bound *bound;
1925 tree delta, step_abs;
1926 tree unsigned_type, valid_niter;
1927 tree base_plus_step, bpsps;
1930 /* FIXME: The following code will not be used anymore once
1931 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html is
1934 If AT_STMT is a cast to unsigned that is later used for
1935 referencing a memory location, it is followed by a pointer
1936 conversion just after. Because pointers do not wrap, the
1937 sequences that reference the memory do not wrap either. In the
1938 following example, sequences corresponding to D_13 and to D_14
1939 can be proved to not wrap because they are used for computing a
1942 D.1621_13 = (long unsigned intD.4) D.1620_12;
1943 D.1622_14 = D.1621_13 * 8;
1944 D.1623_15 = (doubleD.29 *) D.1622_14;
1946 if (at_stmt && TREE_CODE (at_stmt) == MODIFY_EXPR)
1948 tree op0 = TREE_OPERAND (at_stmt, 0);
1949 tree op1 = TREE_OPERAND (at_stmt, 1);
1950 tree type_op1 = TREE_TYPE (op1);
1952 if ((TYPE_UNSIGNED (type_op1)
1953 && used_in_pointer_arithmetic_p (op0, 2))
1954 || POINTER_TYPE_P (type_op1))
1956 *unknown_max = true;
1961 if (chrec_contains_undetermined (base)
1962 || chrec_contains_undetermined (step)
1963 || TREE_CODE (base) == REAL_CST
1964 || TREE_CODE (step) == REAL_CST)
1966 *unknown_max = true;
1970 *unknown_max = false;
1971 base_plus_step = fold_build2 (PLUS_EXPR, type, base, step);
1972 bpsps = fold_build2 (PLUS_EXPR, type, base_plus_step, step);
1973 cps = compare_trees (base_plus_step, base);
1974 cpsps = compare_trees (bpsps, base_plus_step);
1976 /* Check that the sequence is not wrapping in the first step: it
1977 should have the same monotonicity for the first two steps. See
1986 tree extreme = upper_bound_in_type (type, TREE_TYPE (base));
1987 delta = fold_build2 (MINUS_EXPR, type, extreme, base);
1989 *init_is_max = false;
1995 tree extreme = lower_bound_in_type (type, TREE_TYPE (base));
1996 delta = fold_build2 (MINUS_EXPR, type, base, extreme);
1997 step_abs = fold_build1 (NEGATE_EXPR, type, step);
1998 *init_is_max = true;
2003 /* This means step is equal to 0. This should not happen. It
2004 could happen in convert step, but not here. Safely answer
2005 don't know as in the default case. */
2008 *unknown_max = true;
2012 /* If AT_STMT represents a cast operation, we may not be able to
2013 take advantage of the undefinedness of signed type evolutions.
2015 implement-c.texi states: "For conversion to a type of width
2016 N, the value is reduced modulo 2^N to be within range of the
2019 See PR 21959 for a test case. Essentially, given a cast
2024 sc = (signed char) uc;
2028 where uc and sc have the scev {0, +, 1}, we would consider uc to
2029 wrap around, but not sc, because it is of a signed type. This
2030 causes VRP to erroneously fold the predicate above because it
2031 thinks that sc cannot be negative. */
2032 if (at_stmt && TREE_CODE (at_stmt) == MODIFY_EXPR)
2034 tree rhs = TREE_OPERAND (at_stmt, 1);
2035 tree outer_t = TREE_TYPE (rhs);
2037 if (!TYPE_UNSIGNED (outer_t)
2038 && (TREE_CODE (rhs) == NOP_EXPR || TREE_CODE (rhs) == CONVERT_EXPR))
2040 tree inner_t = TREE_TYPE (TREE_OPERAND (rhs, 0));
2042 /* If the inner type is unsigned and its size and/or
2043 precision are smaller to that of the outer type, then the
2044 expression may wrap around. */
2045 if (TYPE_UNSIGNED (inner_t)
2046 && (TYPE_SIZE (inner_t) <= TYPE_SIZE (outer_t)
2047 || TYPE_PRECISION (inner_t) <= TYPE_PRECISION (outer_t)))
2049 *unknown_max = true;
2055 /* After having set INIT_IS_MAX, we can return false: when not using
2056 wrapping arithmetic, signed types don't wrap. */
2057 if (!flag_wrapv && !TYPE_UNSIGNED (type))
2060 unsigned_type = unsigned_type_for (type);
2061 delta = fold_convert (unsigned_type, delta);
2062 step_abs = fold_convert (unsigned_type, step_abs);
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)
2067 if (proved_non_wrapping_p (at_stmt, bound, type, valid_niter))
2070 /* At this point we still don't have a proof that the iv does not
2071 overflow: give up. */
2072 *unknown_max = true;
2076 /* Return the conversion to NEW_TYPE of the STEP of an induction
2077 variable BASE + STEP * I at AT_STMT. When it fails, return
2081 convert_step (struct loop *loop, tree new_type, tree base, tree step,
2086 if (chrec_contains_undetermined (base)
2087 || chrec_contains_undetermined (step))
2090 base_type = TREE_TYPE (base);
2092 /* When not using wrapping arithmetic, signed types don't wrap. */
2093 if (!flag_wrapv && !TYPE_UNSIGNED (base_type))
2094 return fold_convert (new_type, step);
2096 if (TYPE_PRECISION (new_type) > TYPE_PRECISION (base_type))
2097 return convert_step_widening (loop, new_type, base, step, at_stmt);
2099 return fold_convert (new_type, step);
2102 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
2105 free_numbers_of_iterations_estimates_loop (struct loop *loop)
2107 struct nb_iter_bound *bound, *next;
2109 loop->nb_iterations = NULL;
2110 loop->estimated_nb_iterations = NULL;
2111 for (bound = loop->bounds; bound; bound = next)
2117 loop->bounds = NULL;
2120 /* Frees the information on upper bounds on numbers of iterations of LOOPS. */
2123 free_numbers_of_iterations_estimates (struct loops *loops)
2128 for (i = 1; i < loops->num; i++)
2130 loop = loops->parray[i];
2132 free_numbers_of_iterations_estimates_loop (loop);
2136 /* Substitute value VAL for ssa name NAME inside expressions held
2140 substitute_in_loop_info (struct loop *loop, tree name, tree val)
2142 struct nb_iter_bound *bound;
2144 loop->nb_iterations = simplify_replace_tree (loop->nb_iterations, name, val);
2145 loop->estimated_nb_iterations
2146 = simplify_replace_tree (loop->estimated_nb_iterations, name, val);
2147 for (bound = loop->bounds; bound; bound = bound->next)
2149 bound->bound = simplify_replace_tree (bound->bound, name, val);
2150 bound->additional = simplify_replace_tree (bound->additional, name, val);