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 loop cannot be infinite (we derived this
133 earlier, and possibly set NITER->assumptions to make sure this
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 the loop cannot be infinite (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 The results (number of iterations and assumptions as described in
526 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
527 Returns false if it fails to determine number of iterations, true if it
528 was determined (possibly with some assumptions). */
531 number_of_iterations_cond (tree type
, affine_iv
*iv0
, enum tree_code code
,
532 affine_iv
*iv1
, struct tree_niter_desc
*niter
)
536 /* The meaning of these assumptions is this:
538 then the rest of information does not have to be valid
539 if may_be_zero then the loop does not roll, even if
541 niter
->assumptions
= boolean_true_node
;
542 niter
->may_be_zero
= boolean_false_node
;
543 niter
->niter
= NULL_TREE
;
544 niter
->additional_info
= boolean_true_node
;
546 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
547 the control variable is on lhs. */
548 if (code
== GE_EXPR
|| code
== GT_EXPR
549 || (code
== NE_EXPR
&& zero_p (iv0
->step
)))
552 code
= swap_tree_comparison (code
);
555 if (POINTER_TYPE_P (type
))
557 /* Comparison of pointers is undefined unless both iv0 and iv1 point
558 to the same object. If they do, the control variable cannot wrap
559 (as wrap around the bounds of memory will never return a pointer
560 that would be guaranteed to point to the same object, even if we
561 avoid undefined behavior by casting to size_t and back). */
562 iv0
->no_overflow
= true;
563 iv1
->no_overflow
= true;
566 /* If the control induction variable does not overflow, the loop obviously
567 cannot be infinite. */
568 if (!zero_p (iv0
->step
) && iv0
->no_overflow
)
569 never_infinite
= true;
570 else if (!zero_p (iv1
->step
) && iv1
->no_overflow
)
571 never_infinite
= true;
573 never_infinite
= false;
575 /* We can handle the case when neither of the sides of the comparison is
576 invariant, provided that the test is NE_EXPR. This rarely occurs in
577 practice, but it is simple enough to manage. */
578 if (!zero_p (iv0
->step
) && !zero_p (iv1
->step
))
583 iv0
->step
= fold_binary_to_constant (MINUS_EXPR
, type
,
584 iv0
->step
, iv1
->step
);
585 iv0
->no_overflow
= false;
586 iv1
->step
= NULL_TREE
;
587 iv1
->no_overflow
= true;
590 /* If the result of the comparison is a constant, the loop is weird. More
591 precise handling would be possible, but the situation is not common enough
592 to waste time on it. */
593 if (zero_p (iv0
->step
) && zero_p (iv1
->step
))
596 /* Ignore loops of while (i-- < 10) type. */
599 if (iv0
->step
&& tree_int_cst_sign_bit (iv0
->step
))
602 if (!zero_p (iv1
->step
) && !tree_int_cst_sign_bit (iv1
->step
))
606 /* If the loop exits immediatelly, there is nothing to do. */
607 if (zero_p (fold_build2 (code
, boolean_type_node
, iv0
->base
, iv1
->base
)))
609 niter
->niter
= build_int_cst_type (unsigned_type_for (type
), 0);
613 /* OK, now we know we have a senseful loop. Handle several cases, depending
614 on what comparison operator is used. */
618 gcc_assert (zero_p (iv1
->step
));
619 return number_of_iterations_ne (type
, iv0
, iv1
->base
, niter
, never_infinite
);
621 return number_of_iterations_lt (type
, iv0
, iv1
, niter
, never_infinite
);
623 return number_of_iterations_le (type
, iv0
, iv1
, niter
, never_infinite
);
629 /* Substitute NEW for OLD in EXPR and fold the result. */
632 simplify_replace_tree (tree expr
, tree old
, tree
new)
635 tree ret
= NULL_TREE
, e
, se
;
641 || operand_equal_p (expr
, old
, 0))
642 return unshare_expr (new);
647 n
= TREE_CODE_LENGTH (TREE_CODE (expr
));
648 for (i
= 0; i
< n
; i
++)
650 e
= TREE_OPERAND (expr
, i
);
651 se
= simplify_replace_tree (e
, old
, new);
656 ret
= copy_node (expr
);
658 TREE_OPERAND (ret
, i
) = se
;
661 return (ret
? fold (ret
) : expr
);
664 /* Expand definitions of ssa names in EXPR as long as they are simple
665 enough, and return the new expression. */
668 expand_simple_operations (tree expr
)
671 tree ret
= NULL_TREE
, e
, ee
, stmt
;
674 if (expr
== NULL_TREE
)
677 if (is_gimple_min_invariant (expr
))
680 code
= TREE_CODE (expr
);
681 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code
)))
683 n
= TREE_CODE_LENGTH (code
);
684 for (i
= 0; i
< n
; i
++)
686 e
= TREE_OPERAND (expr
, i
);
687 ee
= expand_simple_operations (e
);
692 ret
= copy_node (expr
);
694 TREE_OPERAND (ret
, i
) = ee
;
697 return (ret
? fold (ret
) : expr
);
700 if (TREE_CODE (expr
) != SSA_NAME
)
703 stmt
= SSA_NAME_DEF_STMT (expr
);
704 if (TREE_CODE (stmt
) != MODIFY_EXPR
)
707 e
= TREE_OPERAND (stmt
, 1);
708 if (/* Casts are simple. */
709 TREE_CODE (e
) != NOP_EXPR
710 && TREE_CODE (e
) != CONVERT_EXPR
711 /* Copies are simple. */
712 && TREE_CODE (e
) != SSA_NAME
713 /* Assignments of invariants are simple. */
714 && !is_gimple_min_invariant (e
)
715 /* And increments and decrements by a constant are simple. */
716 && !((TREE_CODE (e
) == PLUS_EXPR
717 || TREE_CODE (e
) == MINUS_EXPR
)
718 && is_gimple_min_invariant (TREE_OPERAND (e
, 1))))
721 return expand_simple_operations (e
);
724 /* Tries to simplify EXPR using the condition COND. Returns the simplified
725 expression (or EXPR unchanged, if no simplification was possible). */
728 tree_simplify_using_condition_1 (tree cond
, tree expr
)
731 tree e
, te
, e0
, e1
, e2
, notcond
;
732 enum tree_code code
= TREE_CODE (expr
);
734 if (code
== INTEGER_CST
)
737 if (code
== TRUTH_OR_EXPR
738 || code
== TRUTH_AND_EXPR
739 || code
== COND_EXPR
)
743 e0
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 0));
744 if (TREE_OPERAND (expr
, 0) != e0
)
747 e1
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 1));
748 if (TREE_OPERAND (expr
, 1) != e1
)
751 if (code
== COND_EXPR
)
753 e2
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 2));
754 if (TREE_OPERAND (expr
, 2) != e2
)
762 if (code
== COND_EXPR
)
763 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
765 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
771 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
772 propagation, and vice versa. Fold does not handle this, since it is
773 considered too expensive. */
774 if (TREE_CODE (cond
) == EQ_EXPR
)
776 e0
= TREE_OPERAND (cond
, 0);
777 e1
= TREE_OPERAND (cond
, 1);
779 /* We know that e0 == e1. Check whether we cannot simplify expr
781 e
= simplify_replace_tree (expr
, e0
, e1
);
782 if (zero_p (e
) || nonzero_p (e
))
785 e
= simplify_replace_tree (expr
, e1
, e0
);
786 if (zero_p (e
) || nonzero_p (e
))
789 if (TREE_CODE (expr
) == EQ_EXPR
)
791 e0
= TREE_OPERAND (expr
, 0);
792 e1
= TREE_OPERAND (expr
, 1);
794 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
795 e
= simplify_replace_tree (cond
, e0
, e1
);
798 e
= simplify_replace_tree (cond
, e1
, e0
);
802 if (TREE_CODE (expr
) == NE_EXPR
)
804 e0
= TREE_OPERAND (expr
, 0);
805 e1
= TREE_OPERAND (expr
, 1);
807 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
808 e
= simplify_replace_tree (cond
, e0
, e1
);
810 return boolean_true_node
;
811 e
= simplify_replace_tree (cond
, e1
, e0
);
813 return boolean_true_node
;
816 te
= expand_simple_operations (expr
);
818 /* Check whether COND ==> EXPR. */
819 notcond
= invert_truthvalue (cond
);
820 e
= fold_binary (TRUTH_OR_EXPR
, boolean_type_node
, notcond
, te
);
824 /* Check whether COND ==> not EXPR. */
825 e
= fold_binary (TRUTH_AND_EXPR
, boolean_type_node
, cond
, te
);
832 /* Tries to simplify EXPR using the condition COND. Returns the simplified
833 expression (or EXPR unchanged, if no simplification was possible).
834 Wrapper around tree_simplify_using_condition_1 that ensures that chains
835 of simple operations in definitions of ssa names in COND are expanded,
836 so that things like casts or incrementing the value of the bound before
837 the loop do not cause us to fail. */
840 tree_simplify_using_condition (tree cond
, tree expr
)
842 cond
= expand_simple_operations (cond
);
844 return tree_simplify_using_condition_1 (cond
, expr
);
847 /* Tries to simplify EXPR using the conditions on entry to LOOP.
848 Record the conditions used for simplification to CONDS_USED.
849 Returns the simplified expression (or EXPR unchanged, if no
850 simplification was possible).*/
853 simplify_using_initial_conditions (struct loop
*loop
, tree expr
,
860 if (TREE_CODE (expr
) == INTEGER_CST
)
863 for (bb
= loop
->header
;
864 bb
!= ENTRY_BLOCK_PTR
;
865 bb
= get_immediate_dominator (CDI_DOMINATORS
, bb
))
867 if (!single_pred_p (bb
))
869 e
= single_pred_edge (bb
);
871 if (!(e
->flags
& (EDGE_TRUE_VALUE
| EDGE_FALSE_VALUE
)))
874 cond
= COND_EXPR_COND (last_stmt (e
->src
));
875 if (e
->flags
& EDGE_FALSE_VALUE
)
876 cond
= invert_truthvalue (cond
);
877 exp
= tree_simplify_using_condition (cond
, expr
);
880 *conds_used
= fold_build2 (TRUTH_AND_EXPR
,
891 /* Tries to simplify EXPR using the evolutions of the loop invariants
892 in the superloops of LOOP. Returns the simplified expression
893 (or EXPR unchanged, if no simplification was possible). */
896 simplify_using_outer_evolutions (struct loop
*loop
, tree expr
)
898 enum tree_code code
= TREE_CODE (expr
);
902 if (is_gimple_min_invariant (expr
))
905 if (code
== TRUTH_OR_EXPR
906 || code
== TRUTH_AND_EXPR
907 || code
== COND_EXPR
)
911 e0
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 0));
912 if (TREE_OPERAND (expr
, 0) != e0
)
915 e1
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 1));
916 if (TREE_OPERAND (expr
, 1) != e1
)
919 if (code
== COND_EXPR
)
921 e2
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 2));
922 if (TREE_OPERAND (expr
, 2) != e2
)
930 if (code
== COND_EXPR
)
931 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
933 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
939 e
= instantiate_parameters (loop
, expr
);
940 if (is_gimple_min_invariant (e
))
946 /* Stores description of number of iterations of LOOP derived from
947 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
948 useful information could be derived (and fields of NITER has
949 meaning described in comments at struct tree_niter_desc
950 declaration), false otherwise. If WARN is true and
951 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
952 potentially unsafe assumptions. */
955 number_of_iterations_exit (struct loop
*loop
, edge exit
,
956 struct tree_niter_desc
*niter
,
959 tree stmt
, cond
, type
;
964 if (!dominated_by_p (CDI_DOMINATORS
, loop
->latch
, exit
->src
))
967 niter
->assumptions
= boolean_false_node
;
968 stmt
= last_stmt (exit
->src
);
969 if (!stmt
|| TREE_CODE (stmt
) != COND_EXPR
)
972 /* We want the condition for staying inside loop. */
973 cond
= COND_EXPR_COND (stmt
);
974 if (exit
->flags
& EDGE_TRUE_VALUE
)
975 cond
= invert_truthvalue (cond
);
977 code
= TREE_CODE (cond
);
991 op0
= TREE_OPERAND (cond
, 0);
992 op1
= TREE_OPERAND (cond
, 1);
993 type
= TREE_TYPE (op0
);
995 if (TREE_CODE (type
) != INTEGER_TYPE
996 && !POINTER_TYPE_P (type
))
999 if (!simple_iv (loop
, stmt
, op0
, &iv0
, false))
1001 if (!simple_iv (loop
, stmt
, op1
, &iv1
, false))
1004 iv0
.base
= expand_simple_operations (iv0
.base
);
1005 iv1
.base
= expand_simple_operations (iv1
.base
);
1006 if (!number_of_iterations_cond (type
, &iv0
, code
, &iv1
, niter
))
1011 niter
->assumptions
= simplify_using_outer_evolutions (loop
,
1012 niter
->assumptions
);
1013 niter
->may_be_zero
= simplify_using_outer_evolutions (loop
,
1014 niter
->may_be_zero
);
1015 niter
->niter
= simplify_using_outer_evolutions (loop
, niter
->niter
);
1018 niter
->additional_info
= boolean_true_node
;
1020 = simplify_using_initial_conditions (loop
,
1022 &niter
->additional_info
);
1024 = simplify_using_initial_conditions (loop
,
1026 &niter
->additional_info
);
1028 if (integer_onep (niter
->assumptions
))
1031 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1032 But if we can prove that there is overflow or some other source of weird
1033 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1034 if (integer_zerop (niter
->assumptions
))
1037 if (flag_unsafe_loop_optimizations
)
1038 niter
->assumptions
= boolean_true_node
;
1042 const char *wording
;
1043 location_t loc
= EXPR_LOCATION (stmt
);
1045 /* We can provide a more specific warning if one of the operator is
1046 constant and the other advances by +1 or -1. */
1047 if (!zero_p (iv1
.step
)
1048 ? (zero_p (iv0
.step
)
1049 && (integer_onep (iv1
.step
) || integer_all_onesp (iv1
.step
)))
1051 && (integer_onep (iv0
.step
) || integer_all_onesp (iv0
.step
))))
1053 flag_unsafe_loop_optimizations
1054 ? N_("assuming that the loop is not infinite")
1055 : N_("cannot optimize possibly infinite loops");
1058 flag_unsafe_loop_optimizations
1059 ? N_("assuming that the loop counter does not overflow")
1060 : N_("cannot optimize loop, the loop counter may overflow");
1062 if (LOCATION_LINE (loc
) > 0)
1063 warning (OPT_Wunsafe_loop_optimizations
, "%H%s", &loc
, gettext (wording
));
1065 warning (OPT_Wunsafe_loop_optimizations
, "%s", gettext (wording
));
1068 return flag_unsafe_loop_optimizations
;
1071 /* Try to determine the number of iterations of LOOP. If we succeed,
1072 expression giving number of iterations is returned and *EXIT is
1073 set to the edge from that the information is obtained. Otherwise
1074 chrec_dont_know is returned. */
1077 find_loop_niter (struct loop
*loop
, edge
*exit
)
1079 unsigned n_exits
, i
;
1080 edge
*exits
= get_loop_exit_edges (loop
, &n_exits
);
1082 tree niter
= NULL_TREE
, aniter
;
1083 struct tree_niter_desc desc
;
1086 for (i
= 0; i
< n_exits
; i
++)
1089 if (!just_once_each_iteration_p (loop
, ex
->src
))
1092 if (!number_of_iterations_exit (loop
, ex
, &desc
, false))
1095 if (nonzero_p (desc
.may_be_zero
))
1097 /* We exit in the first iteration through this exit.
1098 We won't find anything better. */
1099 niter
= build_int_cst_type (unsigned_type_node
, 0);
1104 if (!zero_p (desc
.may_be_zero
))
1107 aniter
= desc
.niter
;
1111 /* Nothing recorded yet. */
1117 /* Prefer constants, the lower the better. */
1118 if (TREE_CODE (aniter
) != INTEGER_CST
)
1121 if (TREE_CODE (niter
) != INTEGER_CST
)
1128 if (tree_int_cst_lt (aniter
, niter
))
1137 return niter
? niter
: chrec_dont_know
;
1142 Analysis of a number of iterations of a loop by a brute-force evaluation.
1146 /* Bound on the number of iterations we try to evaluate. */
1148 #define MAX_ITERATIONS_TO_TRACK \
1149 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1151 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1152 result by a chain of operations such that all but exactly one of their
1153 operands are constants. */
1156 chain_of_csts_start (struct loop
*loop
, tree x
)
1158 tree stmt
= SSA_NAME_DEF_STMT (x
);
1160 basic_block bb
= bb_for_stmt (stmt
);
1163 || !flow_bb_inside_loop_p (loop
, bb
))
1166 if (TREE_CODE (stmt
) == PHI_NODE
)
1168 if (bb
== loop
->header
)
1174 if (TREE_CODE (stmt
) != MODIFY_EXPR
)
1177 if (!ZERO_SSA_OPERANDS (stmt
, SSA_OP_ALL_VIRTUALS
))
1179 if (SINGLE_SSA_DEF_OPERAND (stmt
, SSA_OP_DEF
) == NULL_DEF_OPERAND_P
)
1182 use
= SINGLE_SSA_TREE_OPERAND (stmt
, SSA_OP_USE
);
1183 if (use
== NULL_USE_OPERAND_P
)
1186 return chain_of_csts_start (loop
, use
);
1189 /* Determines whether the expression X is derived from a result of a phi node
1190 in header of LOOP such that
1192 * the derivation of X consists only from operations with constants
1193 * the initial value of the phi node is constant
1194 * the value of the phi node in the next iteration can be derived from the
1195 value in the current iteration by a chain of operations with constants.
1197 If such phi node exists, it is returned. If X is a constant, X is returned
1198 unchanged. Otherwise NULL_TREE is returned. */
1201 get_base_for (struct loop
*loop
, tree x
)
1203 tree phi
, init
, next
;
1205 if (is_gimple_min_invariant (x
))
1208 phi
= chain_of_csts_start (loop
, x
);
1212 init
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
1213 next
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
1215 if (TREE_CODE (next
) != SSA_NAME
)
1218 if (!is_gimple_min_invariant (init
))
1221 if (chain_of_csts_start (loop
, next
) != phi
)
1227 /* Given an expression X, then
1229 * if BASE is NULL_TREE, X must be a constant and we return X.
1230 * otherwise X is a SSA name, whose value in the considered loop is derived
1231 by a chain of operations with constant from a result of a phi node in
1232 the header of the loop. Then we return value of X when the value of the
1233 result of this phi node is given by the constant BASE. */
1236 get_val_for (tree x
, tree base
)
1245 stmt
= SSA_NAME_DEF_STMT (x
);
1246 if (TREE_CODE (stmt
) == PHI_NODE
)
1249 FOR_EACH_SSA_USE_OPERAND (op
, stmt
, iter
, SSA_OP_USE
)
1251 nx
= USE_FROM_PTR (op
);
1252 val
= get_val_for (nx
, base
);
1254 val
= fold (TREE_OPERAND (stmt
, 1));
1256 /* only iterate loop once. */
1260 /* Should never reach here. */
1264 /* Tries to count the number of iterations of LOOP till it exits by EXIT
1265 by brute force -- i.e. by determining the value of the operands of the
1266 condition at EXIT in first few iterations of the loop (assuming that
1267 these values are constant) and determining the first one in that the
1268 condition is not satisfied. Returns the constant giving the number
1269 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
1272 loop_niter_by_eval (struct loop
*loop
, edge exit
)
1274 tree cond
, cnd
, acnd
;
1275 tree op
[2], val
[2], next
[2], aval
[2], phi
[2];
1279 cond
= last_stmt (exit
->src
);
1280 if (!cond
|| TREE_CODE (cond
) != COND_EXPR
)
1281 return chrec_dont_know
;
1283 cnd
= COND_EXPR_COND (cond
);
1284 if (exit
->flags
& EDGE_TRUE_VALUE
)
1285 cnd
= invert_truthvalue (cnd
);
1287 cmp
= TREE_CODE (cnd
);
1296 for (j
= 0; j
< 2; j
++)
1297 op
[j
] = TREE_OPERAND (cnd
, j
);
1301 return chrec_dont_know
;
1304 for (j
= 0; j
< 2; j
++)
1306 phi
[j
] = get_base_for (loop
, op
[j
]);
1308 return chrec_dont_know
;
1311 for (j
= 0; j
< 2; j
++)
1313 if (TREE_CODE (phi
[j
]) == PHI_NODE
)
1315 val
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
[j
], loop_preheader_edge (loop
));
1316 next
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
[j
], loop_latch_edge (loop
));
1321 next
[j
] = NULL_TREE
;
1326 for (i
= 0; i
< MAX_ITERATIONS_TO_TRACK
; i
++)
1328 for (j
= 0; j
< 2; j
++)
1329 aval
[j
] = get_val_for (op
[j
], val
[j
]);
1331 acnd
= fold_binary (cmp
, boolean_type_node
, aval
[0], aval
[1]);
1332 if (acnd
&& zero_p (acnd
))
1334 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1336 "Proved that loop %d iterates %d times using brute force.\n",
1338 return build_int_cst (unsigned_type_node
, i
);
1341 for (j
= 0; j
< 2; j
++)
1342 val
[j
] = get_val_for (next
[j
], val
[j
]);
1345 return chrec_dont_know
;
1348 /* Finds the exit of the LOOP by that the loop exits after a constant
1349 number of iterations and stores the exit edge to *EXIT. The constant
1350 giving the number of iterations of LOOP is returned. The number of
1351 iterations is determined using loop_niter_by_eval (i.e. by brute force
1352 evaluation). If we are unable to find the exit for that loop_niter_by_eval
1353 determines the number of iterations, chrec_dont_know is returned. */
1356 find_loop_niter_by_eval (struct loop
*loop
, edge
*exit
)
1358 unsigned n_exits
, i
;
1359 edge
*exits
= get_loop_exit_edges (loop
, &n_exits
);
1361 tree niter
= NULL_TREE
, aniter
;
1364 for (i
= 0; i
< n_exits
; i
++)
1367 if (!just_once_each_iteration_p (loop
, ex
->src
))
1370 aniter
= loop_niter_by_eval (loop
, ex
);
1371 if (chrec_contains_undetermined (aniter
))
1375 && !tree_int_cst_lt (aniter
, niter
))
1383 return niter
? niter
: chrec_dont_know
;
1388 Analysis of upper bounds on number of iterations of a loop.
1392 /* Records that AT_STMT is executed at most BOUND times in LOOP. The
1393 additional condition ADDITIONAL is recorded with the bound. */
1396 record_estimate (struct loop
*loop
, tree bound
, tree additional
, tree at_stmt
)
1398 struct nb_iter_bound
*elt
= xmalloc (sizeof (struct nb_iter_bound
));
1400 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1402 fprintf (dump_file
, "Statements after ");
1403 print_generic_expr (dump_file
, at_stmt
, TDF_SLIM
);
1404 fprintf (dump_file
, " are executed at most ");
1405 print_generic_expr (dump_file
, bound
, TDF_SLIM
);
1406 fprintf (dump_file
, " times in loop %d.\n", loop
->num
);
1410 elt
->at_stmt
= at_stmt
;
1411 elt
->additional
= additional
;
1412 elt
->next
= loop
->bounds
;
1416 /* Initialize LOOP->ESTIMATED_NB_ITERATIONS with the lowest safe
1417 approximation of the number of iterations for LOOP. */
1420 compute_estimated_nb_iterations (struct loop
*loop
)
1422 struct nb_iter_bound
*bound
;
1424 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
1425 if (TREE_CODE (bound
->bound
) == INTEGER_CST
1426 /* Update only when there is no previous estimation. */
1427 && (chrec_contains_undetermined (loop
->estimated_nb_iterations
)
1428 /* Or when the current estimation is smaller. */
1429 || tree_int_cst_lt (bound
->bound
, loop
->estimated_nb_iterations
)))
1430 loop
->estimated_nb_iterations
= bound
->bound
;
1433 /* The following analyzers are extracting informations on the bounds
1434 of LOOP from the following undefined behaviors:
1436 - data references should not access elements over the statically
1439 - signed variables should not overflow when flag_wrapv is not set.
1443 infer_loop_bounds_from_undefined (struct loop
*loop
)
1446 basic_block bb
, *bbs
;
1447 block_stmt_iterator bsi
;
1449 bbs
= get_loop_body (loop
);
1451 for (i
= 0; i
< loop
->num_nodes
; i
++)
1455 for (bsi
= bsi_start (bb
); !bsi_end_p (bsi
); bsi_next (&bsi
))
1457 tree stmt
= bsi_stmt (bsi
);
1459 switch (TREE_CODE (stmt
))
1463 tree op0
= TREE_OPERAND (stmt
, 0);
1464 tree op1
= TREE_OPERAND (stmt
, 1);
1466 /* For each array access, analyze its access function
1467 and record a bound on the loop iteration domain. */
1468 if (TREE_CODE (op1
) == ARRAY_REF
1469 && !array_ref_contains_indirect_ref (op1
))
1470 estimate_iters_using_array (stmt
, op1
);
1472 if (TREE_CODE (op0
) == ARRAY_REF
1473 && !array_ref_contains_indirect_ref (op0
))
1474 estimate_iters_using_array (stmt
, op0
);
1476 /* For each signed type variable in LOOP, analyze its
1477 scalar evolution and record a bound of the loop
1478 based on the type's ranges. */
1479 else if (!flag_wrapv
&& TREE_CODE (op0
) == SSA_NAME
)
1481 tree init
, step
, diff
, estimation
;
1482 tree scev
= instantiate_parameters
1483 (loop
, analyze_scalar_evolution (loop
, op0
));
1484 tree type
= chrec_type (scev
);
1487 if (chrec_contains_undetermined (scev
)
1488 || TYPE_UNSIGNED (type
))
1491 init
= initial_condition_in_loop_num (scev
, loop
->num
);
1492 step
= evolution_part_in_loop_num (scev
, loop
->num
);
1494 if (init
== NULL_TREE
1495 || step
== NULL_TREE
1496 || TREE_CODE (init
) != INTEGER_CST
1497 || TREE_CODE (step
) != INTEGER_CST
1498 || TYPE_MIN_VALUE (type
) == NULL_TREE
1499 || TYPE_MAX_VALUE (type
) == NULL_TREE
)
1502 utype
= unsigned_type_for (type
);
1503 if (tree_int_cst_lt (step
, integer_zero_node
))
1504 diff
= fold_build2 (MINUS_EXPR
, utype
, init
,
1505 TYPE_MIN_VALUE (type
));
1507 diff
= fold_build2 (MINUS_EXPR
, utype
,
1508 TYPE_MAX_VALUE (type
), init
);
1510 estimation
= fold_build2 (CEIL_DIV_EXPR
, utype
, diff
,
1512 record_estimate (loop
, estimation
, boolean_true_node
, stmt
);
1522 for (args
= TREE_OPERAND (stmt
, 1); args
;
1523 args
= TREE_CHAIN (args
))
1524 if (TREE_CODE (TREE_VALUE (args
)) == ARRAY_REF
1525 && !array_ref_contains_indirect_ref (TREE_VALUE (args
)))
1526 estimate_iters_using_array (stmt
, TREE_VALUE (args
));
1536 if (chrec_contains_undetermined (loop
->estimated_nb_iterations
))
1537 compute_estimated_nb_iterations (loop
);
1543 /* Records estimates on numbers of iterations of LOOP. */
1546 estimate_numbers_of_iterations_loop (struct loop
*loop
)
1550 unsigned i
, n_exits
;
1551 struct tree_niter_desc niter_desc
;
1553 /* Give up if we already have tried to compute an estimation. */
1554 if (loop
->estimated_nb_iterations
== chrec_dont_know
1555 /* Or when we already have an estimation. */
1556 || (loop
->estimated_nb_iterations
!= NULL_TREE
1557 && TREE_CODE (loop
->estimated_nb_iterations
) == INTEGER_CST
))
1560 loop
->estimated_nb_iterations
= chrec_dont_know
;
1562 exits
= get_loop_exit_edges (loop
, &n_exits
);
1563 for (i
= 0; i
< n_exits
; i
++)
1565 if (!number_of_iterations_exit (loop
, exits
[i
], &niter_desc
, false))
1568 niter
= niter_desc
.niter
;
1569 type
= TREE_TYPE (niter
);
1570 if (!zero_p (niter_desc
.may_be_zero
)
1571 && !nonzero_p (niter_desc
.may_be_zero
))
1572 niter
= build3 (COND_EXPR
, type
, niter_desc
.may_be_zero
,
1573 build_int_cst_type (type
, 0),
1575 record_estimate (loop
, niter
,
1576 niter_desc
.additional_info
,
1577 last_stmt (exits
[i
]->src
));
1581 if (chrec_contains_undetermined (loop
->estimated_nb_iterations
))
1582 infer_loop_bounds_from_undefined (loop
);
1585 /* Records estimates on numbers of iterations of LOOPS. */
1588 estimate_numbers_of_iterations (struct loops
*loops
)
1593 for (i
= 1; i
< loops
->num
; i
++)
1595 loop
= loops
->parray
[i
];
1597 estimate_numbers_of_iterations_loop (loop
);
1601 /* If A > B, returns -1. If A == B, returns 0. If A < B, returns 1.
1602 If neither of these relations can be proved, returns 2. */
1605 compare_trees (tree a
, tree b
)
1607 tree typea
= TREE_TYPE (a
), typeb
= TREE_TYPE (b
);
1610 if (TYPE_PRECISION (typea
) > TYPE_PRECISION (typeb
))
1615 a
= fold_convert (type
, a
);
1616 b
= fold_convert (type
, b
);
1618 if (nonzero_p (fold_binary (EQ_EXPR
, boolean_type_node
, a
, b
)))
1620 if (nonzero_p (fold_binary (LT_EXPR
, boolean_type_node
, a
, b
)))
1622 if (nonzero_p (fold_binary (GT_EXPR
, boolean_type_node
, a
, b
)))
1628 /* Returns true if statement S1 dominates statement S2. */
1631 stmt_dominates_stmt_p (tree s1
, tree s2
)
1633 basic_block bb1
= bb_for_stmt (s1
), bb2
= bb_for_stmt (s2
);
1641 block_stmt_iterator bsi
;
1643 for (bsi
= bsi_start (bb1
); bsi_stmt (bsi
) != s2
; bsi_next (&bsi
))
1644 if (bsi_stmt (bsi
) == s1
)
1650 return dominated_by_p (CDI_DOMINATORS
, bb2
, bb1
);
1653 /* Return true when it is possible to prove that the induction
1654 variable does not wrap: vary outside the type specified bounds.
1655 Checks whether BOUND < VALID_NITER that means in the context of iv
1656 conversion that all the iterations in the loop are safe: not
1659 The statement NITER_BOUND->AT_STMT is executed at most
1660 NITER_BOUND->BOUND times in the loop.
1662 NITER_BOUND->ADDITIONAL is the additional condition recorded for
1663 operands of the bound. This is useful in the following case,
1664 created by loop header copying:
1673 If the n > 0 condition is taken into account, the number of iterations of the
1674 loop can be expressed as n - 1. If the type of n is signed, the ADDITIONAL
1675 assumption "n > 0" says us that the value of the number of iterations is at
1676 most MAX_TYPE - 1 (without this assumption, it might overflow). */
1679 proved_non_wrapping_p (tree at_stmt
,
1680 struct nb_iter_bound
*niter_bound
,
1685 tree bound
= niter_bound
->bound
;
1688 if (TYPE_PRECISION (new_type
) > TYPE_PRECISION (TREE_TYPE (bound
)))
1689 bound
= fold_convert (unsigned_type_for (new_type
), bound
);
1691 valid_niter
= fold_convert (TREE_TYPE (bound
), valid_niter
);
1693 /* Give up if BOUND was not folded to an INTEGER_CST, as in PR23434. */
1694 if (TREE_CODE (bound
) != INTEGER_CST
)
1697 /* After the statement niter_bound->at_stmt we know that anything is
1698 executed at most BOUND times. */
1699 if (at_stmt
&& stmt_dominates_stmt_p (niter_bound
->at_stmt
, at_stmt
))
1701 /* Before the statement niter_bound->at_stmt we know that anything
1702 is executed at most BOUND + 1 times. */
1706 cond
= fold_binary (cmp
, boolean_type_node
, valid_niter
, bound
);
1707 if (nonzero_p (cond
))
1710 cond
= build2 (cmp
, boolean_type_node
, valid_niter
, bound
);
1711 /* Try taking additional conditions into account. */
1712 cond
= fold_binary (TRUTH_OR_EXPR
, boolean_type_node
,
1713 invert_truthvalue (niter_bound
->additional
),
1716 if (nonzero_p (cond
))
1722 /* Checks whether it is correct to count the induction variable BASE +
1723 STEP * I at AT_STMT in a wider type NEW_TYPE, using the bounds on
1724 numbers of iterations of a LOOP. If it is possible, return the
1725 value of step of the induction variable in the NEW_TYPE, otherwise
1726 return NULL_TREE. */
1729 convert_step_widening (struct loop
*loop
, tree new_type
, tree base
, tree step
,
1732 struct nb_iter_bound
*bound
;
1733 tree base_in_new_type
, base_plus_step_in_new_type
, step_in_new_type
;
1734 tree delta
, step_abs
;
1735 tree unsigned_type
, valid_niter
;
1737 /* Compute the new step. For example, {(uchar) 100, +, (uchar) 240}
1738 is converted to {(uint) 100, +, (uint) 0xfffffff0} in order to
1739 keep the values of the induction variable unchanged: 100, 84, 68,
1742 Another example is: (uint) {(uchar)100, +, (uchar)3} is converted
1743 to {(uint)100, +, (uint)3}.
1745 Before returning the new step, verify that the number of
1746 iterations is less than DELTA / STEP_ABS (i.e. in the previous
1747 example (256 - 100) / 3) such that the iv does not wrap (in which
1748 case the operations are too difficult to be represented and
1749 handled: the values of the iv should be taken modulo 256 in the
1750 wider type; this is not implemented). */
1751 base_in_new_type
= fold_convert (new_type
, base
);
1752 base_plus_step_in_new_type
=
1753 fold_convert (new_type
,
1754 fold_build2 (PLUS_EXPR
, TREE_TYPE (base
), base
, step
));
1755 step_in_new_type
= fold_build2 (MINUS_EXPR
, new_type
,
1756 base_plus_step_in_new_type
,
1759 if (TREE_CODE (step_in_new_type
) != INTEGER_CST
)
1762 switch (compare_trees (base_plus_step_in_new_type
, base_in_new_type
))
1766 tree extreme
= upper_bound_in_type (new_type
, TREE_TYPE (base
));
1767 delta
= fold_build2 (MINUS_EXPR
, new_type
, extreme
,
1769 step_abs
= step_in_new_type
;
1775 tree extreme
= lower_bound_in_type (new_type
, TREE_TYPE (base
));
1776 delta
= fold_build2 (MINUS_EXPR
, new_type
, base_in_new_type
,
1778 step_abs
= fold_build1 (NEGATE_EXPR
, new_type
, step_in_new_type
);
1783 return step_in_new_type
;
1789 unsigned_type
= unsigned_type_for (new_type
);
1790 delta
= fold_convert (unsigned_type
, delta
);
1791 step_abs
= fold_convert (unsigned_type
, step_abs
);
1792 valid_niter
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
,
1795 estimate_numbers_of_iterations_loop (loop
);
1796 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
1797 if (proved_non_wrapping_p (at_stmt
, bound
, new_type
, valid_niter
))
1798 return step_in_new_type
;
1800 /* Fail when the loop has no bound estimations, or when no bound can
1801 be used for verifying the conversion. */
1805 /* Returns true when VAR is used in pointer arithmetics. DEPTH is
1806 used for limiting the search. */
1809 used_in_pointer_arithmetic_p (tree var
, int depth
)
1811 use_operand_p use_p
;
1812 imm_use_iterator iter
;
1815 || TREE_CODE (var
) != SSA_NAME
1816 || !has_single_use (var
))
1819 FOR_EACH_IMM_USE_FAST (use_p
, iter
, var
)
1821 tree stmt
= USE_STMT (use_p
);
1823 if (stmt
&& TREE_CODE (stmt
) == MODIFY_EXPR
)
1825 tree rhs
= TREE_OPERAND (stmt
, 1);
1827 if (TREE_CODE (rhs
) == NOP_EXPR
1828 || TREE_CODE (rhs
) == CONVERT_EXPR
)
1830 if (POINTER_TYPE_P (TREE_TYPE (rhs
)))
1835 return used_in_pointer_arithmetic_p (TREE_OPERAND (stmt
, 0),
1842 /* Return false only when the induction variable BASE + STEP * I is
1843 known to not overflow: i.e. when the number of iterations is small
1844 enough with respect to the step and initial condition in order to
1845 keep the evolution confined in TYPEs bounds. Return true when the
1846 iv is known to overflow or when the property is not computable.
1848 Initialize INIT_IS_MAX to true when the evolution goes from
1849 INIT_IS_MAX to LOWER_BOUND_IN_TYPE, false in the contrary case.
1850 When this property cannot be determined, UNKNOWN_MAX is set to
1854 scev_probably_wraps_p (tree type
, tree base
, tree step
,
1855 tree at_stmt
, struct loop
*loop
,
1856 bool *init_is_max
, bool *unknown_max
)
1858 struct nb_iter_bound
*bound
;
1859 tree delta
, step_abs
;
1860 tree unsigned_type
, valid_niter
;
1861 tree base_plus_step
, bpsps
;
1864 /* FIXME: The following code will not be used anymore once
1865 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html is
1868 If AT_STMT is a cast to unsigned that is later used for
1869 referencing a memory location, it is followed by a pointer
1870 conversion just after. Because pointers do not wrap, the
1871 sequences that reference the memory do not wrap either. In the
1872 following example, sequences corresponding to D_13 and to D_14
1873 can be proved to not wrap because they are used for computing a
1876 D.1621_13 = (long unsigned intD.4) D.1620_12;
1877 D.1622_14 = D.1621_13 * 8;
1878 D.1623_15 = (doubleD.29 *) D.1622_14;
1880 if (at_stmt
&& TREE_CODE (at_stmt
) == MODIFY_EXPR
)
1882 tree op0
= TREE_OPERAND (at_stmt
, 0);
1883 tree op1
= TREE_OPERAND (at_stmt
, 1);
1884 tree type_op1
= TREE_TYPE (op1
);
1886 if ((TYPE_UNSIGNED (type_op1
)
1887 && used_in_pointer_arithmetic_p (op0
, 2))
1888 || POINTER_TYPE_P (type_op1
))
1890 *unknown_max
= true;
1895 if (chrec_contains_undetermined (base
)
1896 || chrec_contains_undetermined (step
)
1897 || TREE_CODE (base
) == REAL_CST
1898 || TREE_CODE (step
) == REAL_CST
)
1900 *unknown_max
= true;
1904 *unknown_max
= false;
1905 base_plus_step
= fold_build2 (PLUS_EXPR
, type
, base
, step
);
1906 bpsps
= fold_build2 (PLUS_EXPR
, type
, base_plus_step
, step
);
1907 cps
= compare_trees (base_plus_step
, base
);
1908 cpsps
= compare_trees (bpsps
, base_plus_step
);
1910 /* Check that the sequence is not wrapping in the first step: it
1911 should have the same monotonicity for the first two steps. See
1920 tree extreme
= upper_bound_in_type (type
, TREE_TYPE (base
));
1921 delta
= fold_build2 (MINUS_EXPR
, type
, extreme
, base
);
1923 *init_is_max
= false;
1929 tree extreme
= lower_bound_in_type (type
, TREE_TYPE (base
));
1930 delta
= fold_build2 (MINUS_EXPR
, type
, base
, extreme
);
1931 step_abs
= fold_build1 (NEGATE_EXPR
, type
, step
);
1932 *init_is_max
= true;
1937 /* This means step is equal to 0. This should not happen. It
1938 could happen in convert step, but not here. Safely answer
1939 don't know as in the default case. */
1942 *unknown_max
= true;
1946 /* If AT_STMT represents a cast operation, we may not be able to
1947 take advantage of the undefinedness of signed type evolutions.
1949 implement-c.texi states: "For conversion to a type of width
1950 N, the value is reduced modulo 2^N to be within range of the
1953 See PR 21959 for a test case. Essentially, given a cast
1958 sc = (signed char) uc;
1962 where uc and sc have the scev {0, +, 1}, we would consider uc to
1963 wrap around, but not sc, because it is of a signed type. This
1964 causes VRP to erroneously fold the predicate above because it
1965 thinks that sc cannot be negative. */
1966 if (at_stmt
&& TREE_CODE (at_stmt
) == MODIFY_EXPR
)
1968 tree rhs
= TREE_OPERAND (at_stmt
, 1);
1969 tree outer_t
= TREE_TYPE (rhs
);
1971 if (!TYPE_UNSIGNED (outer_t
)
1972 && (TREE_CODE (rhs
) == NOP_EXPR
|| TREE_CODE (rhs
) == CONVERT_EXPR
))
1974 tree inner_t
= TREE_TYPE (TREE_OPERAND (rhs
, 0));
1976 /* If the inner type is unsigned and its size and/or
1977 precision are smaller to that of the outer type, then the
1978 expression may wrap around. */
1979 if (TYPE_UNSIGNED (inner_t
)
1980 && (TYPE_SIZE (inner_t
) <= TYPE_SIZE (outer_t
)
1981 || TYPE_PRECISION (inner_t
) <= TYPE_PRECISION (outer_t
)))
1983 *unknown_max
= true;
1989 /* After having set INIT_IS_MAX, we can return false: when not using
1990 wrapping arithmetic, signed types don't wrap. */
1991 if (!flag_wrapv
&& !TYPE_UNSIGNED (type
))
1994 unsigned_type
= unsigned_type_for (type
);
1995 delta
= fold_convert (unsigned_type
, delta
);
1996 step_abs
= fold_convert (unsigned_type
, step_abs
);
1997 valid_niter
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step_abs
);
1999 estimate_numbers_of_iterations_loop (loop
);
2000 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
2001 if (proved_non_wrapping_p (at_stmt
, bound
, type
, valid_niter
))
2004 /* At this point we still don't have a proof that the iv does not
2005 overflow: give up. */
2006 *unknown_max
= true;
2010 /* Return the conversion to NEW_TYPE of the STEP of an induction
2011 variable BASE + STEP * I at AT_STMT. When it fails, return
2015 convert_step (struct loop
*loop
, tree new_type
, tree base
, tree step
,
2020 if (chrec_contains_undetermined (base
)
2021 || chrec_contains_undetermined (step
))
2024 base_type
= TREE_TYPE (base
);
2026 /* When not using wrapping arithmetic, signed types don't wrap. */
2027 if (!flag_wrapv
&& !TYPE_UNSIGNED (base_type
))
2028 return fold_convert (new_type
, step
);
2030 if (TYPE_PRECISION (new_type
) > TYPE_PRECISION (base_type
))
2031 return convert_step_widening (loop
, new_type
, base
, step
, at_stmt
);
2033 return fold_convert (new_type
, step
);
2036 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
2039 free_numbers_of_iterations_estimates_loop (struct loop
*loop
)
2041 struct nb_iter_bound
*bound
, *next
;
2043 loop
->nb_iterations
= NULL
;
2044 loop
->estimated_nb_iterations
= NULL
;
2045 for (bound
= loop
->bounds
; bound
; bound
= next
)
2051 loop
->bounds
= NULL
;
2054 /* Frees the information on upper bounds on numbers of iterations of LOOPS. */
2057 free_numbers_of_iterations_estimates (struct loops
*loops
)
2062 for (i
= 1; i
< loops
->num
; i
++)
2064 loop
= loops
->parray
[i
];
2066 free_numbers_of_iterations_estimates_loop (loop
);
2070 /* Substitute value VAL for ssa name NAME inside expressions held
2074 substitute_in_loop_info (struct loop
*loop
, tree name
, tree val
)
2076 struct nb_iter_bound
*bound
;
2078 loop
->nb_iterations
= simplify_replace_tree (loop
->nb_iterations
, name
, val
);
2079 loop
->estimated_nb_iterations
2080 = simplify_replace_tree (loop
->estimated_nb_iterations
, name
, val
);
2081 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
2083 bound
->bound
= simplify_replace_tree (bound
->bound
, name
, val
);
2084 bound
->additional
= simplify_replace_tree (bound
->additional
, name
, val
);