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
, 1);
120 rslt
= int_const_binop (MULT_EXPR
, rslt
, x
, 0);
121 x
= int_const_binop (MULT_EXPR
, x
, x
, 0);
123 rslt
= int_const_binop (BIT_AND_EXPR
, rslt
, mask
, 0);
129 /* Determines number of iterations of loop whose ending condition
130 is IV <> FINAL. TYPE is the type of the iv. The number of
131 iterations is stored to NITER. NEVER_INFINITE is true if
132 we know that the exit must be taken eventually, i.e., that the IV
133 ever reaches the value FINAL (we derived this earlier, and possibly set
134 NITER->assumptions to make sure this is the case). */
137 number_of_iterations_ne (tree type
, affine_iv
*iv
, tree final
,
138 struct tree_niter_desc
*niter
, bool never_infinite
)
140 tree niter_type
= unsigned_type_for (type
);
141 tree s
, c
, d
, bits
, assumption
, tmp
, bound
;
143 niter
->control
= *iv
;
144 niter
->bound
= final
;
145 niter
->cmp
= NE_EXPR
;
147 /* Rearrange the terms so that we get inequality s * i <> c, with s
148 positive. Also cast everything to the unsigned type. */
149 if (tree_int_cst_sign_bit (iv
->step
))
151 s
= fold_convert (niter_type
,
152 fold_build1 (NEGATE_EXPR
, type
, iv
->step
));
153 c
= fold_build2 (MINUS_EXPR
, niter_type
,
154 fold_convert (niter_type
, iv
->base
),
155 fold_convert (niter_type
, final
));
159 s
= fold_convert (niter_type
, iv
->step
);
160 c
= fold_build2 (MINUS_EXPR
, niter_type
,
161 fold_convert (niter_type
, final
),
162 fold_convert (niter_type
, iv
->base
));
165 /* First the trivial cases -- when the step is 1. */
166 if (integer_onep (s
))
172 /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
173 is infinite. Otherwise, the number of iterations is
174 (inverse(s/d) * (c/d)) mod (size of mode/d). */
175 bits
= num_ending_zeros (s
);
176 bound
= build_low_bits_mask (niter_type
,
177 (TYPE_PRECISION (niter_type
)
178 - tree_low_cst (bits
, 1)));
180 d
= fold_binary_to_constant (LSHIFT_EXPR
, niter_type
,
181 build_int_cst (niter_type
, 1), bits
);
182 s
= fold_binary_to_constant (RSHIFT_EXPR
, niter_type
, s
, bits
);
186 /* If we cannot assume that the loop is not infinite, record the
187 assumptions for divisibility of c. */
188 assumption
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, c
, d
);
189 assumption
= fold_build2 (EQ_EXPR
, boolean_type_node
,
190 assumption
, build_int_cst (niter_type
, 0));
191 if (!nonzero_p (assumption
))
192 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
193 niter
->assumptions
, assumption
);
196 c
= fold_build2 (EXACT_DIV_EXPR
, niter_type
, c
, d
);
197 tmp
= fold_build2 (MULT_EXPR
, niter_type
, c
, inverse (s
, bound
));
198 niter
->niter
= fold_build2 (BIT_AND_EXPR
, niter_type
, tmp
, bound
);
202 /* Checks whether we can determine the final value of the control variable
203 of the loop with ending condition IV0 < IV1 (computed in TYPE).
204 DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
205 of the step. The assumptions necessary to ensure that the computation
206 of the final value does not overflow are recorded in NITER. If we
207 find the final value, we adjust DELTA and return TRUE. Otherwise
211 number_of_iterations_lt_to_ne (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
212 struct tree_niter_desc
*niter
,
213 tree
*delta
, tree step
)
215 tree niter_type
= TREE_TYPE (step
);
216 tree mod
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, *delta
, step
);
218 tree assumption
= boolean_true_node
, bound
, noloop
;
220 if (TREE_CODE (mod
) != INTEGER_CST
)
223 mod
= fold_build2 (MINUS_EXPR
, niter_type
, step
, mod
);
224 tmod
= fold_convert (type
, mod
);
226 if (nonzero_p (iv0
->step
))
228 /* The final value of the iv is iv1->base + MOD, assuming that this
229 computation does not overflow, and that
230 iv0->base <= iv1->base + MOD. */
231 if (!iv1
->no_overflow
&& !zero_p (mod
))
233 bound
= fold_build2 (MINUS_EXPR
, type
,
234 TYPE_MAX_VALUE (type
), tmod
);
235 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
237 if (zero_p (assumption
))
240 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
242 fold_build2 (PLUS_EXPR
, type
,
247 /* The final value of the iv is iv0->base - MOD, assuming that this
248 computation does not overflow, and that
249 iv0->base - MOD <= iv1->base. */
250 if (!iv0
->no_overflow
&& !zero_p (mod
))
252 bound
= fold_build2 (PLUS_EXPR
, type
,
253 TYPE_MIN_VALUE (type
), tmod
);
254 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
256 if (zero_p (assumption
))
259 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
260 fold_build2 (MINUS_EXPR
, type
,
265 if (!nonzero_p (assumption
))
266 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
269 if (!zero_p (noloop
))
270 niter
->may_be_zero
= fold_build2 (TRUTH_OR_EXPR
, boolean_type_node
,
273 *delta
= fold_build2 (PLUS_EXPR
, niter_type
, *delta
, mod
);
277 /* Add assertions to NITER that ensure that the control variable of the loop
278 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
279 are TYPE. Returns false if we can prove that there is an overflow, true
280 otherwise. STEP is the absolute value of the step. */
283 assert_no_overflow_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
284 struct tree_niter_desc
*niter
, tree step
)
286 tree bound
, d
, assumption
, diff
;
287 tree niter_type
= TREE_TYPE (step
);
289 if (nonzero_p (iv0
->step
))
291 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
292 if (iv0
->no_overflow
)
295 /* If iv0->base is a constant, we can determine the last value before
296 overflow precisely; otherwise we conservatively assume
299 if (TREE_CODE (iv0
->base
) == INTEGER_CST
)
301 d
= fold_build2 (MINUS_EXPR
, niter_type
,
302 fold_convert (niter_type
, TYPE_MAX_VALUE (type
)),
303 fold_convert (niter_type
, iv0
->base
));
304 diff
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, d
, step
);
307 diff
= fold_build2 (MINUS_EXPR
, niter_type
, step
,
308 build_int_cst (niter_type
, 1));
309 bound
= fold_build2 (MINUS_EXPR
, type
,
310 TYPE_MAX_VALUE (type
), fold_convert (type
, diff
));
311 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
316 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
317 if (iv1
->no_overflow
)
320 if (TREE_CODE (iv1
->base
) == INTEGER_CST
)
322 d
= fold_build2 (MINUS_EXPR
, niter_type
,
323 fold_convert (niter_type
, iv1
->base
),
324 fold_convert (niter_type
, TYPE_MIN_VALUE (type
)));
325 diff
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, d
, step
);
328 diff
= fold_build2 (MINUS_EXPR
, niter_type
, step
,
329 build_int_cst (niter_type
, 1));
330 bound
= fold_build2 (PLUS_EXPR
, type
,
331 TYPE_MIN_VALUE (type
), fold_convert (type
, diff
));
332 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
336 if (zero_p (assumption
))
338 if (!nonzero_p (assumption
))
339 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
340 niter
->assumptions
, assumption
);
342 iv0
->no_overflow
= true;
343 iv1
->no_overflow
= true;
347 /* Add an assumption to NITER that a loop whose ending condition
348 is IV0 < IV1 rolls. TYPE is the type of the control iv. */
351 assert_loop_rolls_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
352 struct tree_niter_desc
*niter
)
354 tree assumption
= boolean_true_node
, bound
, diff
;
355 tree mbz
, mbzl
, mbzr
;
357 if (nonzero_p (iv0
->step
))
359 diff
= fold_build2 (MINUS_EXPR
, type
,
360 iv0
->step
, build_int_cst (type
, 1));
362 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
363 0 address never belongs to any object, we can assume this for
365 if (!POINTER_TYPE_P (type
))
367 bound
= fold_build2 (PLUS_EXPR
, type
,
368 TYPE_MIN_VALUE (type
), diff
);
369 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
373 /* And then we can compute iv0->base - diff, and compare it with
375 mbzl
= fold_build2 (MINUS_EXPR
, type
, iv0
->base
, diff
);
380 diff
= fold_build2 (PLUS_EXPR
, type
,
381 iv1
->step
, build_int_cst (type
, 1));
383 if (!POINTER_TYPE_P (type
))
385 bound
= fold_build2 (PLUS_EXPR
, type
,
386 TYPE_MAX_VALUE (type
), diff
);
387 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
392 mbzr
= fold_build2 (MINUS_EXPR
, type
, iv1
->base
, diff
);
395 mbz
= fold_build2 (GT_EXPR
, boolean_type_node
, mbzl
, mbzr
);
397 if (!nonzero_p (assumption
))
398 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
399 niter
->assumptions
, assumption
);
401 niter
->may_be_zero
= fold_build2 (TRUTH_OR_EXPR
, boolean_type_node
,
402 niter
->may_be_zero
, mbz
);
405 /* Determines number of iterations of loop whose ending condition
406 is IV0 < IV1. TYPE is the type of the iv. The number of
407 iterations is stored to NITER. */
410 number_of_iterations_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
411 struct tree_niter_desc
*niter
,
412 bool never_infinite ATTRIBUTE_UNUSED
)
414 tree niter_type
= unsigned_type_for (type
);
417 if (nonzero_p (iv0
->step
))
419 niter
->control
= *iv0
;
420 niter
->cmp
= LT_EXPR
;
421 niter
->bound
= iv1
->base
;
425 niter
->control
= *iv1
;
426 niter
->cmp
= GT_EXPR
;
427 niter
->bound
= iv0
->base
;
430 delta
= fold_build2 (MINUS_EXPR
, niter_type
,
431 fold_convert (niter_type
, iv1
->base
),
432 fold_convert (niter_type
, iv0
->base
));
434 /* First handle the special case that the step is +-1. */
435 if ((iv0
->step
&& integer_onep (iv0
->step
)
436 && zero_p (iv1
->step
))
437 || (iv1
->step
&& integer_all_onesp (iv1
->step
)
438 && zero_p (iv0
->step
)))
440 /* for (i = iv0->base; i < iv1->base; i++)
444 for (i = iv1->base; i > iv0->base; i--).
446 In both cases # of iterations is iv1->base - iv0->base, assuming that
447 iv1->base >= iv0->base. */
448 niter
->may_be_zero
= fold_build2 (LT_EXPR
, boolean_type_node
,
449 iv1
->base
, iv0
->base
);
450 niter
->niter
= delta
;
454 if (nonzero_p (iv0
->step
))
455 step
= fold_convert (niter_type
, iv0
->step
);
457 step
= fold_convert (niter_type
,
458 fold_build1 (NEGATE_EXPR
, type
, iv1
->step
));
460 /* If we can determine the final value of the control iv exactly, we can
461 transform the condition to != comparison. In particular, this will be
462 the case if DELTA is constant. */
463 if (number_of_iterations_lt_to_ne (type
, iv0
, iv1
, niter
, &delta
, step
))
467 zps
.base
= build_int_cst (niter_type
, 0);
469 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
470 zps does not overflow. */
471 zps
.no_overflow
= true;
473 return number_of_iterations_ne (type
, &zps
, delta
, niter
, true);
476 /* Make sure that the control iv does not overflow. */
477 if (!assert_no_overflow_lt (type
, iv0
, iv1
, niter
, step
))
480 /* We determine the number of iterations as (delta + step - 1) / step. For
481 this to work, we must know that iv1->base >= iv0->base - step + 1,
482 otherwise the loop does not roll. */
483 assert_loop_rolls_lt (type
, iv0
, iv1
, niter
);
485 s
= fold_build2 (MINUS_EXPR
, niter_type
,
486 step
, build_int_cst (niter_type
, 1));
487 delta
= fold_build2 (PLUS_EXPR
, niter_type
, delta
, s
);
488 niter
->niter
= fold_build2 (FLOOR_DIV_EXPR
, niter_type
, delta
, step
);
492 /* Determines number of iterations of loop whose ending condition
493 is IV0 <= IV1. TYPE is the type of the iv. The number of
494 iterations is stored to NITER. NEVER_INFINITE is true if
495 we know that this condition must eventually become false (we derived this
496 earlier, and possibly set NITER->assumptions to make sure this
500 number_of_iterations_le (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
501 struct tree_niter_desc
*niter
, bool never_infinite
)
505 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
506 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
507 value of the type. This we must know anyway, since if it is
508 equal to this value, the loop rolls forever. */
512 if (nonzero_p (iv0
->step
))
513 assumption
= fold_build2 (NE_EXPR
, boolean_type_node
,
514 iv1
->base
, TYPE_MAX_VALUE (type
));
516 assumption
= fold_build2 (NE_EXPR
, boolean_type_node
,
517 iv0
->base
, TYPE_MIN_VALUE (type
));
519 if (zero_p (assumption
))
521 if (!nonzero_p (assumption
))
522 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
523 niter
->assumptions
, assumption
);
526 if (nonzero_p (iv0
->step
))
527 iv1
->base
= fold_build2 (PLUS_EXPR
, type
,
528 iv1
->base
, build_int_cst (type
, 1));
530 iv0
->base
= fold_build2 (MINUS_EXPR
, type
,
531 iv0
->base
, build_int_cst (type
, 1));
532 return number_of_iterations_lt (type
, iv0
, iv1
, niter
, never_infinite
);
535 /* Determine the number of iterations according to condition (for staying
536 inside loop) which compares two induction variables using comparison
537 operator CODE. The induction variable on left side of the comparison
538 is IV0, the right-hand side is IV1. Both induction variables must have
539 type TYPE, which must be an integer or pointer type. The steps of the
540 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
542 ONLY_EXIT is true if we are sure this is the only way the loop could be
543 exited (including possibly non-returning function calls, exceptions, etc.)
544 -- in this case we can use the information whether the control induction
545 variables can overflow or not in a more efficient way.
547 The results (number of iterations and assumptions as described in
548 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
549 Returns false if it fails to determine number of iterations, true if it
550 was determined (possibly with some assumptions). */
553 number_of_iterations_cond (tree type
, affine_iv
*iv0
, enum tree_code code
,
554 affine_iv
*iv1
, struct tree_niter_desc
*niter
,
559 /* The meaning of these assumptions is this:
561 then the rest of information does not have to be valid
562 if may_be_zero then the loop does not roll, even if
564 niter
->assumptions
= boolean_true_node
;
565 niter
->may_be_zero
= boolean_false_node
;
566 niter
->niter
= NULL_TREE
;
567 niter
->additional_info
= boolean_true_node
;
569 niter
->bound
= NULL_TREE
;
570 niter
->cmp
= ERROR_MARK
;
572 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
573 the control variable is on lhs. */
574 if (code
== GE_EXPR
|| code
== GT_EXPR
575 || (code
== NE_EXPR
&& zero_p (iv0
->step
)))
578 code
= swap_tree_comparison (code
);
583 /* If this is not the only possible exit from the loop, the information
584 that the induction variables cannot overflow as derived from
585 signedness analysis cannot be relied upon. We use them e.g. in the
586 following way: given loop for (i = 0; i <= n; i++), if i is
587 signed, it cannot overflow, thus this loop is equivalent to
588 for (i = 0; i < n + 1; i++); however, if n == MAX, but the loop
589 is exited in some other way before i overflows, this transformation
590 is incorrect (the new loop exits immediately). */
591 iv0
->no_overflow
= false;
592 iv1
->no_overflow
= false;
595 if (POINTER_TYPE_P (type
))
597 /* Comparison of pointers is undefined unless both iv0 and iv1 point
598 to the same object. If they do, the control variable cannot wrap
599 (as wrap around the bounds of memory will never return a pointer
600 that would be guaranteed to point to the same object, even if we
601 avoid undefined behavior by casting to size_t and back). The
602 restrictions on pointer arithmetics and comparisons of pointers
603 ensure that using the no-overflow assumptions is correct in this
604 case even if ONLY_EXIT is false. */
605 iv0
->no_overflow
= true;
606 iv1
->no_overflow
= true;
609 /* If the control induction variable does not overflow, the loop obviously
610 cannot be infinite. */
611 if (!zero_p (iv0
->step
) && iv0
->no_overflow
)
612 never_infinite
= true;
613 else if (!zero_p (iv1
->step
) && iv1
->no_overflow
)
614 never_infinite
= true;
616 never_infinite
= false;
618 /* We can handle the case when neither of the sides of the comparison is
619 invariant, provided that the test is NE_EXPR. This rarely occurs in
620 practice, but it is simple enough to manage. */
621 if (!zero_p (iv0
->step
) && !zero_p (iv1
->step
))
626 iv0
->step
= fold_binary_to_constant (MINUS_EXPR
, type
,
627 iv0
->step
, iv1
->step
);
628 iv0
->no_overflow
= false;
629 iv1
->step
= NULL_TREE
;
630 iv1
->no_overflow
= true;
633 /* If the result of the comparison is a constant, the loop is weird. More
634 precise handling would be possible, but the situation is not common enough
635 to waste time on it. */
636 if (zero_p (iv0
->step
) && zero_p (iv1
->step
))
639 /* Ignore loops of while (i-- < 10) type. */
642 if (iv0
->step
&& tree_int_cst_sign_bit (iv0
->step
))
645 if (!zero_p (iv1
->step
) && !tree_int_cst_sign_bit (iv1
->step
))
649 /* If the loop exits immediately, there is nothing to do. */
650 if (zero_p (fold_build2 (code
, boolean_type_node
, iv0
->base
, iv1
->base
)))
652 niter
->niter
= build_int_cst (unsigned_type_for (type
), 0);
656 /* OK, now we know we have a senseful loop. Handle several cases, depending
657 on what comparison operator is used. */
661 gcc_assert (zero_p (iv1
->step
));
662 return number_of_iterations_ne (type
, iv0
, iv1
->base
, niter
, never_infinite
);
664 return number_of_iterations_lt (type
, iv0
, iv1
, niter
, never_infinite
);
666 return number_of_iterations_le (type
, iv0
, iv1
, niter
, never_infinite
);
672 /* Substitute NEW for OLD in EXPR and fold the result. */
675 simplify_replace_tree (tree expr
, tree old
, tree
new)
678 tree ret
= NULL_TREE
, e
, se
;
684 || operand_equal_p (expr
, old
, 0))
685 return unshare_expr (new);
687 if (!EXPR_P (expr
) && !GIMPLE_STMT_P (expr
))
690 n
= TREE_CODE_LENGTH (TREE_CODE (expr
));
691 for (i
= 0; i
< n
; i
++)
693 e
= TREE_OPERAND (expr
, i
);
694 se
= simplify_replace_tree (e
, old
, new);
699 ret
= copy_node (expr
);
701 TREE_OPERAND (ret
, i
) = se
;
704 return (ret
? fold (ret
) : expr
);
707 /* Expand definitions of ssa names in EXPR as long as they are simple
708 enough, and return the new expression. */
711 expand_simple_operations (tree expr
)
714 tree ret
= NULL_TREE
, e
, ee
, stmt
;
717 if (expr
== NULL_TREE
)
720 if (is_gimple_min_invariant (expr
))
723 code
= TREE_CODE (expr
);
724 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code
)))
726 n
= TREE_CODE_LENGTH (code
);
727 for (i
= 0; i
< n
; i
++)
729 e
= TREE_OPERAND (expr
, i
);
730 ee
= expand_simple_operations (e
);
735 ret
= copy_node (expr
);
737 TREE_OPERAND (ret
, i
) = ee
;
740 return (ret
? fold (ret
) : expr
);
743 if (TREE_CODE (expr
) != SSA_NAME
)
746 stmt
= SSA_NAME_DEF_STMT (expr
);
747 if (TREE_CODE (stmt
) != GIMPLE_MODIFY_STMT
)
750 e
= GIMPLE_STMT_OPERAND (stmt
, 1);
751 if (/* Casts are simple. */
752 TREE_CODE (e
) != NOP_EXPR
753 && TREE_CODE (e
) != CONVERT_EXPR
754 /* Copies are simple. */
755 && TREE_CODE (e
) != SSA_NAME
756 /* Assignments of invariants are simple. */
757 && !is_gimple_min_invariant (e
)
758 /* And increments and decrements by a constant are simple. */
759 && !((TREE_CODE (e
) == PLUS_EXPR
760 || TREE_CODE (e
) == MINUS_EXPR
)
761 && is_gimple_min_invariant (TREE_OPERAND (e
, 1))))
764 return expand_simple_operations (e
);
767 /* Tries to simplify EXPR using the condition COND. Returns the simplified
768 expression (or EXPR unchanged, if no simplification was possible). */
771 tree_simplify_using_condition_1 (tree cond
, tree expr
)
774 tree e
, te
, e0
, e1
, e2
, notcond
;
775 enum tree_code code
= TREE_CODE (expr
);
777 if (code
== INTEGER_CST
)
780 if (code
== TRUTH_OR_EXPR
781 || code
== TRUTH_AND_EXPR
782 || code
== COND_EXPR
)
786 e0
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 0));
787 if (TREE_OPERAND (expr
, 0) != e0
)
790 e1
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 1));
791 if (TREE_OPERAND (expr
, 1) != e1
)
794 if (code
== COND_EXPR
)
796 e2
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 2));
797 if (TREE_OPERAND (expr
, 2) != e2
)
805 if (code
== COND_EXPR
)
806 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
808 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
814 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
815 propagation, and vice versa. Fold does not handle this, since it is
816 considered too expensive. */
817 if (TREE_CODE (cond
) == EQ_EXPR
)
819 e0
= TREE_OPERAND (cond
, 0);
820 e1
= TREE_OPERAND (cond
, 1);
822 /* We know that e0 == e1. Check whether we cannot simplify expr
824 e
= simplify_replace_tree (expr
, e0
, e1
);
825 if (zero_p (e
) || nonzero_p (e
))
828 e
= simplify_replace_tree (expr
, e1
, e0
);
829 if (zero_p (e
) || nonzero_p (e
))
832 if (TREE_CODE (expr
) == EQ_EXPR
)
834 e0
= TREE_OPERAND (expr
, 0);
835 e1
= TREE_OPERAND (expr
, 1);
837 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
838 e
= simplify_replace_tree (cond
, e0
, e1
);
841 e
= simplify_replace_tree (cond
, e1
, e0
);
845 if (TREE_CODE (expr
) == NE_EXPR
)
847 e0
= TREE_OPERAND (expr
, 0);
848 e1
= TREE_OPERAND (expr
, 1);
850 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
851 e
= simplify_replace_tree (cond
, e0
, e1
);
853 return boolean_true_node
;
854 e
= simplify_replace_tree (cond
, e1
, e0
);
856 return boolean_true_node
;
859 te
= expand_simple_operations (expr
);
861 /* Check whether COND ==> EXPR. */
862 notcond
= invert_truthvalue (cond
);
863 e
= fold_binary (TRUTH_OR_EXPR
, boolean_type_node
, notcond
, te
);
867 /* Check whether COND ==> not EXPR. */
868 e
= fold_binary (TRUTH_AND_EXPR
, boolean_type_node
, cond
, te
);
875 /* Tries to simplify EXPR using the condition COND. Returns the simplified
876 expression (or EXPR unchanged, if no simplification was possible).
877 Wrapper around tree_simplify_using_condition_1 that ensures that chains
878 of simple operations in definitions of ssa names in COND are expanded,
879 so that things like casts or incrementing the value of the bound before
880 the loop do not cause us to fail. */
883 tree_simplify_using_condition (tree cond
, tree expr
)
885 cond
= expand_simple_operations (cond
);
887 return tree_simplify_using_condition_1 (cond
, expr
);
890 /* The maximum number of dominator BBs we search for conditions
891 of loop header copies we use for simplifying a conditional
893 #define MAX_DOMINATORS_TO_WALK 8
895 /* Tries to simplify EXPR using the conditions on entry to LOOP.
896 Record the conditions used for simplification to CONDS_USED.
897 Returns the simplified expression (or EXPR unchanged, if no
898 simplification was possible).*/
901 simplify_using_initial_conditions (struct loop
*loop
, tree expr
,
909 if (TREE_CODE (expr
) == INTEGER_CST
)
912 /* Limit walking the dominators to avoid quadraticness in
913 the number of BBs times the number of loops in degenerate
915 for (bb
= loop
->header
;
916 bb
!= ENTRY_BLOCK_PTR
&& cnt
< MAX_DOMINATORS_TO_WALK
;
917 bb
= get_immediate_dominator (CDI_DOMINATORS
, bb
))
919 if (!single_pred_p (bb
))
921 e
= single_pred_edge (bb
);
923 if (!(e
->flags
& (EDGE_TRUE_VALUE
| EDGE_FALSE_VALUE
)))
926 cond
= COND_EXPR_COND (last_stmt (e
->src
));
927 if (e
->flags
& EDGE_FALSE_VALUE
)
928 cond
= invert_truthvalue (cond
);
929 exp
= tree_simplify_using_condition (cond
, expr
);
932 *conds_used
= fold_build2 (TRUTH_AND_EXPR
,
944 /* Tries to simplify EXPR using the evolutions of the loop invariants
945 in the superloops of LOOP. Returns the simplified expression
946 (or EXPR unchanged, if no simplification was possible). */
949 simplify_using_outer_evolutions (struct loop
*loop
, tree expr
)
951 enum tree_code code
= TREE_CODE (expr
);
955 if (is_gimple_min_invariant (expr
))
958 if (code
== TRUTH_OR_EXPR
959 || code
== TRUTH_AND_EXPR
960 || code
== COND_EXPR
)
964 e0
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 0));
965 if (TREE_OPERAND (expr
, 0) != e0
)
968 e1
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 1));
969 if (TREE_OPERAND (expr
, 1) != e1
)
972 if (code
== COND_EXPR
)
974 e2
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 2));
975 if (TREE_OPERAND (expr
, 2) != e2
)
983 if (code
== COND_EXPR
)
984 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
986 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
992 e
= instantiate_parameters (loop
, expr
);
993 if (is_gimple_min_invariant (e
))
999 /* Returns true if EXIT is the only possible exit from LOOP. */
1002 loop_only_exit_p (struct loop
*loop
, edge exit
)
1005 block_stmt_iterator bsi
;
1009 if (exit
!= single_exit (loop
))
1012 body
= get_loop_body (loop
);
1013 for (i
= 0; i
< loop
->num_nodes
; i
++)
1015 for (bsi
= bsi_start (body
[0]); !bsi_end_p (bsi
); bsi_next (&bsi
))
1017 call
= get_call_expr_in (bsi_stmt (bsi
));
1018 if (call
&& TREE_SIDE_EFFECTS (call
))
1030 /* Stores description of number of iterations of LOOP derived from
1031 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1032 useful information could be derived (and fields of NITER has
1033 meaning described in comments at struct tree_niter_desc
1034 declaration), false otherwise. If WARN is true and
1035 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1036 potentially unsafe assumptions. */
1039 number_of_iterations_exit (struct loop
*loop
, edge exit
,
1040 struct tree_niter_desc
*niter
,
1043 tree stmt
, cond
, type
;
1045 enum tree_code code
;
1048 if (!dominated_by_p (CDI_DOMINATORS
, loop
->latch
, exit
->src
))
1051 niter
->assumptions
= boolean_false_node
;
1052 stmt
= last_stmt (exit
->src
);
1053 if (!stmt
|| TREE_CODE (stmt
) != COND_EXPR
)
1056 /* We want the condition for staying inside loop. */
1057 cond
= COND_EXPR_COND (stmt
);
1058 if (exit
->flags
& EDGE_TRUE_VALUE
)
1059 cond
= invert_truthvalue (cond
);
1061 code
= TREE_CODE (cond
);
1075 op0
= TREE_OPERAND (cond
, 0);
1076 op1
= TREE_OPERAND (cond
, 1);
1077 type
= TREE_TYPE (op0
);
1079 if (TREE_CODE (type
) != INTEGER_TYPE
1080 && !POINTER_TYPE_P (type
))
1083 if (!simple_iv (loop
, stmt
, op0
, &iv0
, false))
1085 if (!simple_iv (loop
, stmt
, op1
, &iv1
, false))
1088 iv0
.base
= expand_simple_operations (iv0
.base
);
1089 iv1
.base
= expand_simple_operations (iv1
.base
);
1090 if (!number_of_iterations_cond (type
, &iv0
, code
, &iv1
, niter
,
1091 loop_only_exit_p (loop
, exit
)))
1096 niter
->assumptions
= simplify_using_outer_evolutions (loop
,
1097 niter
->assumptions
);
1098 niter
->may_be_zero
= simplify_using_outer_evolutions (loop
,
1099 niter
->may_be_zero
);
1100 niter
->niter
= simplify_using_outer_evolutions (loop
, niter
->niter
);
1103 niter
->additional_info
= boolean_true_node
;
1105 = simplify_using_initial_conditions (loop
,
1107 &niter
->additional_info
);
1109 = simplify_using_initial_conditions (loop
,
1111 &niter
->additional_info
);
1113 if (integer_onep (niter
->assumptions
))
1116 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1117 But if we can prove that there is overflow or some other source of weird
1118 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1119 if (integer_zerop (niter
->assumptions
))
1122 if (flag_unsafe_loop_optimizations
)
1123 niter
->assumptions
= boolean_true_node
;
1127 const char *wording
;
1128 location_t loc
= EXPR_LOCATION (stmt
);
1130 /* We can provide a more specific warning if one of the operator is
1131 constant and the other advances by +1 or -1. */
1132 if (!zero_p (iv1
.step
)
1133 ? (zero_p (iv0
.step
)
1134 && (integer_onep (iv1
.step
) || integer_all_onesp (iv1
.step
)))
1136 && (integer_onep (iv0
.step
) || integer_all_onesp (iv0
.step
))))
1138 flag_unsafe_loop_optimizations
1139 ? N_("assuming that the loop is not infinite")
1140 : N_("cannot optimize possibly infinite loops");
1143 flag_unsafe_loop_optimizations
1144 ? N_("assuming that the loop counter does not overflow")
1145 : N_("cannot optimize loop, the loop counter may overflow");
1147 if (LOCATION_LINE (loc
) > 0)
1148 warning (OPT_Wunsafe_loop_optimizations
, "%H%s", &loc
, gettext (wording
));
1150 warning (OPT_Wunsafe_loop_optimizations
, "%s", gettext (wording
));
1153 return flag_unsafe_loop_optimizations
;
1156 /* Try to determine the number of iterations of LOOP. If we succeed,
1157 expression giving number of iterations is returned and *EXIT is
1158 set to the edge from that the information is obtained. Otherwise
1159 chrec_dont_know is returned. */
1162 find_loop_niter (struct loop
*loop
, edge
*exit
)
1165 VEC (edge
, heap
) *exits
= get_loop_exit_edges (loop
);
1167 tree niter
= NULL_TREE
, aniter
;
1168 struct tree_niter_desc desc
;
1171 for (i
= 0; VEC_iterate (edge
, exits
, i
, ex
); i
++)
1173 if (!just_once_each_iteration_p (loop
, ex
->src
))
1176 if (!number_of_iterations_exit (loop
, ex
, &desc
, false))
1179 if (nonzero_p (desc
.may_be_zero
))
1181 /* We exit in the first iteration through this exit.
1182 We won't find anything better. */
1183 niter
= build_int_cst (unsigned_type_node
, 0);
1188 if (!zero_p (desc
.may_be_zero
))
1191 aniter
= desc
.niter
;
1195 /* Nothing recorded yet. */
1201 /* Prefer constants, the lower the better. */
1202 if (TREE_CODE (aniter
) != INTEGER_CST
)
1205 if (TREE_CODE (niter
) != INTEGER_CST
)
1212 if (tree_int_cst_lt (aniter
, niter
))
1219 VEC_free (edge
, heap
, exits
);
1221 return niter
? niter
: chrec_dont_know
;
1226 Analysis of a number of iterations of a loop by a brute-force evaluation.
1230 /* Bound on the number of iterations we try to evaluate. */
1232 #define MAX_ITERATIONS_TO_TRACK \
1233 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1235 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1236 result by a chain of operations such that all but exactly one of their
1237 operands are constants. */
1240 chain_of_csts_start (struct loop
*loop
, tree x
)
1242 tree stmt
= SSA_NAME_DEF_STMT (x
);
1244 basic_block bb
= bb_for_stmt (stmt
);
1247 || !flow_bb_inside_loop_p (loop
, bb
))
1250 if (TREE_CODE (stmt
) == PHI_NODE
)
1252 if (bb
== loop
->header
)
1258 if (TREE_CODE (stmt
) != GIMPLE_MODIFY_STMT
)
1261 if (!ZERO_SSA_OPERANDS (stmt
, SSA_OP_ALL_VIRTUALS
))
1263 if (SINGLE_SSA_DEF_OPERAND (stmt
, SSA_OP_DEF
) == NULL_DEF_OPERAND_P
)
1266 use
= SINGLE_SSA_TREE_OPERAND (stmt
, SSA_OP_USE
);
1267 if (use
== NULL_USE_OPERAND_P
)
1270 return chain_of_csts_start (loop
, use
);
1273 /* Determines whether the expression X is derived from a result of a phi node
1274 in header of LOOP such that
1276 * the derivation of X consists only from operations with constants
1277 * the initial value of the phi node is constant
1278 * the value of the phi node in the next iteration can be derived from the
1279 value in the current iteration by a chain of operations with constants.
1281 If such phi node exists, it is returned. If X is a constant, X is returned
1282 unchanged. Otherwise NULL_TREE is returned. */
1285 get_base_for (struct loop
*loop
, tree x
)
1287 tree phi
, init
, next
;
1289 if (is_gimple_min_invariant (x
))
1292 phi
= chain_of_csts_start (loop
, x
);
1296 init
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
1297 next
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
1299 if (TREE_CODE (next
) != SSA_NAME
)
1302 if (!is_gimple_min_invariant (init
))
1305 if (chain_of_csts_start (loop
, next
) != phi
)
1311 /* Given an expression X, then
1313 * if X is NULL_TREE, we return the constant BASE.
1314 * otherwise X is a SSA name, whose value in the considered loop is derived
1315 by a chain of operations with constant from a result of a phi node in
1316 the header of the loop. Then we return value of X when the value of the
1317 result of this phi node is given by the constant BASE. */
1320 get_val_for (tree x
, tree base
)
1326 gcc_assert (is_gimple_min_invariant (base
));
1331 stmt
= SSA_NAME_DEF_STMT (x
);
1332 if (TREE_CODE (stmt
) == PHI_NODE
)
1335 FOR_EACH_SSA_USE_OPERAND (op
, stmt
, iter
, SSA_OP_USE
)
1337 nx
= USE_FROM_PTR (op
);
1338 val
= get_val_for (nx
, base
);
1340 val
= fold (GIMPLE_STMT_OPERAND (stmt
, 1));
1342 /* only iterate loop once. */
1346 /* Should never reach here. */
1350 /* Tries to count the number of iterations of LOOP till it exits by EXIT
1351 by brute force -- i.e. by determining the value of the operands of the
1352 condition at EXIT in first few iterations of the loop (assuming that
1353 these values are constant) and determining the first one in that the
1354 condition is not satisfied. Returns the constant giving the number
1355 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
1358 loop_niter_by_eval (struct loop
*loop
, edge exit
)
1360 tree cond
, cnd
, acnd
;
1361 tree op
[2], val
[2], next
[2], aval
[2], phi
[2];
1365 cond
= last_stmt (exit
->src
);
1366 if (!cond
|| TREE_CODE (cond
) != COND_EXPR
)
1367 return chrec_dont_know
;
1369 cnd
= COND_EXPR_COND (cond
);
1370 if (exit
->flags
& EDGE_TRUE_VALUE
)
1371 cnd
= invert_truthvalue (cnd
);
1373 cmp
= TREE_CODE (cnd
);
1382 for (j
= 0; j
< 2; j
++)
1383 op
[j
] = TREE_OPERAND (cnd
, j
);
1387 return chrec_dont_know
;
1390 for (j
= 0; j
< 2; j
++)
1392 phi
[j
] = get_base_for (loop
, op
[j
]);
1394 return chrec_dont_know
;
1397 for (j
= 0; j
< 2; j
++)
1399 if (TREE_CODE (phi
[j
]) == PHI_NODE
)
1401 val
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
[j
], loop_preheader_edge (loop
));
1402 next
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
[j
], loop_latch_edge (loop
));
1407 next
[j
] = NULL_TREE
;
1412 for (i
= 0; i
< MAX_ITERATIONS_TO_TRACK
; i
++)
1414 for (j
= 0; j
< 2; j
++)
1415 aval
[j
] = get_val_for (op
[j
], val
[j
]);
1417 acnd
= fold_binary (cmp
, boolean_type_node
, aval
[0], aval
[1]);
1418 if (acnd
&& zero_p (acnd
))
1420 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1422 "Proved that loop %d iterates %d times using brute force.\n",
1424 return build_int_cst (unsigned_type_node
, i
);
1427 for (j
= 0; j
< 2; j
++)
1429 val
[j
] = get_val_for (next
[j
], val
[j
]);
1430 if (!is_gimple_min_invariant (val
[j
]))
1431 return chrec_dont_know
;
1435 return chrec_dont_know
;
1438 /* Finds the exit of the LOOP by that the loop exits after a constant
1439 number of iterations and stores the exit edge to *EXIT. The constant
1440 giving the number of iterations of LOOP is returned. The number of
1441 iterations is determined using loop_niter_by_eval (i.e. by brute force
1442 evaluation). If we are unable to find the exit for that loop_niter_by_eval
1443 determines the number of iterations, chrec_dont_know is returned. */
1446 find_loop_niter_by_eval (struct loop
*loop
, edge
*exit
)
1449 VEC (edge
, heap
) *exits
= get_loop_exit_edges (loop
);
1451 tree niter
= NULL_TREE
, aniter
;
1454 for (i
= 0; VEC_iterate (edge
, exits
, i
, ex
); i
++)
1456 if (!just_once_each_iteration_p (loop
, ex
->src
))
1459 aniter
= loop_niter_by_eval (loop
, ex
);
1460 if (chrec_contains_undetermined (aniter
))
1464 && !tree_int_cst_lt (aniter
, niter
))
1470 VEC_free (edge
, heap
, exits
);
1472 return niter
? niter
: chrec_dont_know
;
1477 Analysis of upper bounds on number of iterations of a loop.
1481 /* Returns true if we can prove that COND ==> VAL >= 0. */
1484 implies_nonnegative_p (tree cond
, tree val
)
1486 tree type
= TREE_TYPE (val
);
1489 if (tree_expr_nonnegative_p (val
))
1492 if (nonzero_p (cond
))
1495 compare
= fold_build2 (GE_EXPR
,
1496 boolean_type_node
, val
, build_int_cst (type
, 0));
1497 compare
= tree_simplify_using_condition_1 (cond
, compare
);
1499 return nonzero_p (compare
);
1502 /* Returns true if we can prove that COND ==> A >= B. */
1505 implies_ge_p (tree cond
, tree a
, tree b
)
1507 tree compare
= fold_build2 (GE_EXPR
, boolean_type_node
, a
, b
);
1509 if (nonzero_p (compare
))
1512 if (nonzero_p (cond
))
1515 compare
= tree_simplify_using_condition_1 (cond
, compare
);
1517 return nonzero_p (compare
);
1520 /* Returns a constant upper bound on the value of expression VAL. VAL
1521 is considered to be unsigned. If its type is signed, its value must
1524 The condition ADDITIONAL must be satisfied (for example, if VAL is
1525 "(unsigned) n" and ADDITIONAL is "n > 0", then we can derive that
1526 VAL is at most (unsigned) MAX_INT). */
1529 derive_constant_upper_bound (tree val
, tree additional
)
1531 tree type
= TREE_TYPE (val
);
1532 tree op0
, op1
, subtype
, maxt
;
1533 double_int bnd
, max
, mmax
, cst
;
1536 if (INTEGRAL_TYPE_P (type
))
1537 maxt
= TYPE_MAX_VALUE (type
);
1539 maxt
= upper_bound_in_type (type
, type
);
1541 max
= tree_to_double_int (maxt
);
1543 switch (TREE_CODE (val
))
1546 return tree_to_double_int (val
);
1550 op0
= TREE_OPERAND (val
, 0);
1551 subtype
= TREE_TYPE (op0
);
1552 if (!TYPE_UNSIGNED (subtype
)
1553 /* If TYPE is also signed, the fact that VAL is nonnegative implies
1554 that OP0 is nonnegative. */
1555 && TYPE_UNSIGNED (type
)
1556 && !implies_nonnegative_p (additional
, op0
))
1558 /* If we cannot prove that the casted expression is nonnegative,
1559 we cannot establish more useful upper bound than the precision
1560 of the type gives us. */
1564 /* We now know that op0 is an nonnegative value. Try deriving an upper
1566 bnd
= derive_constant_upper_bound (op0
, additional
);
1568 /* If the bound does not fit in TYPE, max. value of TYPE could be
1570 if (double_int_ucmp (max
, bnd
) < 0)
1577 op0
= TREE_OPERAND (val
, 0);
1578 op1
= TREE_OPERAND (val
, 1);
1580 if (TREE_CODE (op1
) != INTEGER_CST
1581 || !implies_nonnegative_p (additional
, op0
))
1584 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
1585 choose the most logical way how to treat this constant regardless
1586 of the signedness of the type. */
1587 cst
= tree_to_double_int (op1
);
1588 cst
= double_int_sext (cst
, TYPE_PRECISION (type
));
1589 if (TREE_CODE (val
) == PLUS_EXPR
)
1590 cst
= double_int_neg (cst
);
1592 bnd
= derive_constant_upper_bound (op0
, additional
);
1594 if (double_int_negative_p (cst
))
1596 cst
= double_int_neg (cst
);
1597 /* Avoid CST == 0x80000... */
1598 if (double_int_negative_p (cst
))
1601 /* OP0 + CST. We need to check that
1602 BND <= MAX (type) - CST. */
1604 mmax
= double_int_add (max
, double_int_neg (cst
));
1605 if (double_int_ucmp (bnd
, mmax
) > 0)
1608 return double_int_add (bnd
, cst
);
1612 /* OP0 - CST, where CST >= 0.
1614 If TYPE is signed, we have already verified that OP0 >= 0, and we
1615 know that the result is nonnegative. This implies that
1618 If TYPE is unsigned, we must additionally know that OP0 >= CST,
1619 otherwise the operation underflows.
1622 /* This should only happen if the type is unsigned; however, for
1623 programs that use overflowing signed arithmetics even with
1624 -fno-wrapv, this condition may also be true for signed values. */
1625 if (double_int_ucmp (bnd
, cst
) < 0)
1628 if (TYPE_UNSIGNED (type
)
1629 && !implies_ge_p (additional
,
1630 op0
, double_int_to_tree (type
, cst
)))
1633 bnd
= double_int_add (bnd
, double_int_neg (cst
));
1638 case FLOOR_DIV_EXPR
:
1639 case EXACT_DIV_EXPR
:
1640 op0
= TREE_OPERAND (val
, 0);
1641 op1
= TREE_OPERAND (val
, 1);
1642 if (TREE_CODE (op1
) != INTEGER_CST
1643 || tree_int_cst_sign_bit (op1
))
1646 bnd
= derive_constant_upper_bound (op0
, additional
);
1647 return double_int_udiv (bnd
, tree_to_double_int (op1
), FLOOR_DIV_EXPR
);
1650 op1
= TREE_OPERAND (val
, 1);
1651 if (TREE_CODE (op1
) != INTEGER_CST
1652 || tree_int_cst_sign_bit (op1
))
1654 return tree_to_double_int (op1
);
1657 stmt
= SSA_NAME_DEF_STMT (val
);
1658 if (TREE_CODE (stmt
) != GIMPLE_MODIFY_STMT
1659 || GIMPLE_STMT_OPERAND (stmt
, 0) != val
)
1661 return derive_constant_upper_bound (GIMPLE_STMT_OPERAND (stmt
, 1),
1669 /* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. The
1670 additional condition ADDITIONAL is recorded with the bound. IS_EXIT
1671 is true if the loop is exited immediately after STMT, and this exit
1672 is taken at last when the STMT is executed BOUND + 1 times.
1673 REALISTIC is true if the estimate comes from a reliable source
1674 (number of iterations analysis, or size of data accessed in the loop). */
1677 record_estimate (struct loop
*loop
, tree bound
, tree additional
, tree at_stmt
,
1678 bool is_exit
, bool realistic
)
1680 struct nb_iter_bound
*elt
= xmalloc (sizeof (struct nb_iter_bound
));
1681 double_int i_bound
= derive_constant_upper_bound (bound
, additional
);
1683 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1685 fprintf (dump_file
, "Statement %s", is_exit
? "(exit)" : "");
1686 print_generic_expr (dump_file
, at_stmt
, TDF_SLIM
);
1687 fprintf (dump_file
, " is executed at most ");
1688 print_generic_expr (dump_file
, bound
, TDF_SLIM
);
1689 fprintf (dump_file
, " (bounded by ");
1690 dump_double_int (dump_file
, i_bound
, true);
1691 fprintf (dump_file
, ") + 1 times in loop %d.\n", loop
->num
);
1694 elt
->bound
= i_bound
;
1695 elt
->stmt
= at_stmt
;
1696 elt
->is_exit
= is_exit
;
1697 elt
->realistic
= realistic
&& TREE_CODE (bound
) == INTEGER_CST
;
1698 elt
->next
= loop
->bounds
;
1702 /* Record the estimate on number of iterations of LOOP based on the fact that
1703 the induction variable BASE + STEP * i evaluated in STMT does not wrap and
1704 its values belong to the range <LOW, HIGH>. DATA_SIZE_BOUNDS_P is true if
1705 LOW and HIGH are derived from the size of data. */
1708 record_nonwrapping_iv (struct loop
*loop
, tree base
, tree step
, tree stmt
,
1709 tree low
, tree high
, bool data_size_bounds_p
)
1711 tree niter_bound
, extreme
, delta
;
1712 tree type
= TREE_TYPE (base
), unsigned_type
;
1714 if (TREE_CODE (step
) != INTEGER_CST
|| zero_p (step
))
1717 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1719 fprintf (dump_file
, "Induction variable (");
1720 print_generic_expr (dump_file
, TREE_TYPE (base
), TDF_SLIM
);
1721 fprintf (dump_file
, ") ");
1722 print_generic_expr (dump_file
, base
, TDF_SLIM
);
1723 fprintf (dump_file
, " + ");
1724 print_generic_expr (dump_file
, step
, TDF_SLIM
);
1725 fprintf (dump_file
, " * iteration does not wrap in statement ");
1726 print_generic_expr (dump_file
, stmt
, TDF_SLIM
);
1727 fprintf (dump_file
, " in loop %d.\n", loop
->num
);
1730 unsigned_type
= unsigned_type_for (type
);
1731 base
= fold_convert (unsigned_type
, base
);
1732 step
= fold_convert (unsigned_type
, step
);
1734 if (tree_int_cst_sign_bit (step
))
1736 extreme
= fold_convert (unsigned_type
, low
);
1737 if (TREE_CODE (base
) != INTEGER_CST
)
1738 base
= fold_convert (unsigned_type
, high
);
1739 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
1740 step
= fold_build1 (NEGATE_EXPR
, unsigned_type
, step
);
1744 extreme
= fold_convert (unsigned_type
, high
);
1745 if (TREE_CODE (base
) != INTEGER_CST
)
1746 base
= fold_convert (unsigned_type
, low
);
1747 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
1750 /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
1751 would get out of the range. */
1752 niter_bound
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step
);
1753 record_estimate (loop
, niter_bound
, boolean_true_node
, stmt
,
1754 false, data_size_bounds_p
);
1757 /* Initialize LOOP->ESTIMATED_NB_ITERATIONS with the lowest safe
1758 approximation of the number of iterations for LOOP. */
1761 compute_estimated_nb_iterations (struct loop
*loop
)
1763 struct nb_iter_bound
*bound
;
1765 gcc_assert (loop
->estimate_state
== EST_NOT_AVAILABLE
);
1767 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
1769 if (!bound
->realistic
)
1772 /* Update only when there is no previous estimation, or when the current
1773 estimation is smaller. */
1774 if (loop
->estimate_state
== EST_NOT_AVAILABLE
1775 || double_int_ucmp (bound
->bound
, loop
->estimated_nb_iterations
) < 0)
1777 loop
->estimate_state
= EST_AVAILABLE
;
1778 loop
->estimated_nb_iterations
= bound
->bound
;
1783 /* Determine information about number of iterations a LOOP from the index
1784 IDX of a data reference accessed in STMT. Callback for for_each_index. */
1793 idx_infer_loop_bounds (tree base
, tree
*idx
, void *dta
)
1795 struct ilb_data
*data
= dta
;
1796 tree ev
, init
, step
;
1797 tree low
, high
, type
, next
;
1799 struct loop
*loop
= data
->loop
;
1801 if (TREE_CODE (base
) != ARRAY_REF
)
1804 ev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, *idx
));
1805 init
= initial_condition (ev
);
1806 step
= evolution_part_in_loop_num (ev
, loop
->num
);
1810 || TREE_CODE (step
) != INTEGER_CST
1812 || tree_contains_chrecs (init
, NULL
)
1813 || chrec_contains_symbols_defined_in_loop (init
, loop
->num
))
1816 low
= array_ref_low_bound (base
);
1817 high
= array_ref_up_bound (base
);
1819 /* The case of nonconstant bounds could be handled, but it would be
1821 if (TREE_CODE (low
) != INTEGER_CST
1823 || TREE_CODE (high
) != INTEGER_CST
)
1825 sign
= tree_int_cst_sign_bit (step
);
1826 type
= TREE_TYPE (step
);
1828 /* In case the relevant bound of the array does not fit in type, or
1829 it does, but bound + step (in type) still belongs into the range of the
1830 array, the index may wrap and still stay within the range of the array
1831 (consider e.g. if the array is indexed by the full range of
1834 To make things simpler, we require both bounds to fit into type, although
1835 there are cases where this would not be strictly necessary. */
1836 if (!int_fits_type_p (high
, type
)
1837 || !int_fits_type_p (low
, type
))
1839 low
= fold_convert (type
, low
);
1840 high
= fold_convert (type
, high
);
1843 next
= fold_binary (PLUS_EXPR
, type
, low
, step
);
1845 next
= fold_binary (PLUS_EXPR
, type
, high
, step
);
1847 if (tree_int_cst_compare (low
, next
) <= 0
1848 && tree_int_cst_compare (next
, high
) <= 0)
1851 record_nonwrapping_iv (loop
, init
, step
, data
->stmt
, low
, high
, true);
1855 /* Determine information about number of iterations a LOOP from the bounds
1856 of arrays in the data reference REF accessed in STMT. */
1859 infer_loop_bounds_from_ref (struct loop
*loop
, tree stmt
, tree ref
)
1861 struct ilb_data data
;
1865 for_each_index (&ref
, idx_infer_loop_bounds
, &data
);
1868 /* Determine information about number of iterations of a LOOP from the way
1869 arrays are used in STMT. */
1872 infer_loop_bounds_from_array (struct loop
*loop
, tree stmt
)
1876 if (TREE_CODE (stmt
) == GIMPLE_MODIFY_STMT
)
1878 tree op0
= GIMPLE_STMT_OPERAND (stmt
, 0);
1879 tree op1
= GIMPLE_STMT_OPERAND (stmt
, 1);
1881 /* For each memory access, analyze its access function
1882 and record a bound on the loop iteration domain. */
1883 if (REFERENCE_CLASS_P (op0
))
1884 infer_loop_bounds_from_ref (loop
, stmt
, op0
);
1886 if (REFERENCE_CLASS_P (op1
))
1887 infer_loop_bounds_from_ref (loop
, stmt
, op1
);
1891 call
= get_call_expr_in (stmt
);
1896 for (args
= TREE_OPERAND (call
, 1); args
; args
= TREE_CHAIN (args
))
1897 if (REFERENCE_CLASS_P (TREE_VALUE (args
)))
1898 infer_loop_bounds_from_ref (loop
, stmt
, TREE_VALUE (args
));
1902 /* Determine information about number of iterations of a LOOP from the fact
1903 that signed arithmetics in STMT does not overflow. */
1906 infer_loop_bounds_from_signedness (struct loop
*loop
, tree stmt
)
1908 tree def
, base
, step
, scev
, type
, low
, high
;
1910 if (flag_wrapv
|| TREE_CODE (stmt
) != GIMPLE_MODIFY_STMT
)
1913 def
= GIMPLE_STMT_OPERAND (stmt
, 0);
1915 if (TREE_CODE (def
) != SSA_NAME
)
1918 type
= TREE_TYPE (def
);
1919 if (!INTEGRAL_TYPE_P (type
)
1920 || TYPE_UNSIGNED (type
))
1923 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
1924 if (chrec_contains_undetermined (scev
))
1927 base
= initial_condition_in_loop_num (scev
, loop
->num
);
1928 step
= evolution_part_in_loop_num (scev
, loop
->num
);
1931 || TREE_CODE (step
) != INTEGER_CST
1932 || tree_contains_chrecs (base
, NULL
)
1933 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
1936 low
= lower_bound_in_type (type
, type
);
1937 high
= upper_bound_in_type (type
, type
);
1939 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false);
1942 /* The following analyzers are extracting informations on the bounds
1943 of LOOP from the following undefined behaviors:
1945 - data references should not access elements over the statically
1948 - signed variables should not overflow when flag_wrapv is not set.
1952 infer_loop_bounds_from_undefined (struct loop
*loop
)
1956 block_stmt_iterator bsi
;
1959 bbs
= get_loop_body (loop
);
1961 for (i
= 0; i
< loop
->num_nodes
; i
++)
1965 /* If BB is not executed in each iteration of the loop, we cannot
1966 use it to infer any information about # of iterations of the loop. */
1967 if (!dominated_by_p (CDI_DOMINATORS
, loop
->latch
, bb
))
1970 for (bsi
= bsi_start (bb
); !bsi_end_p (bsi
); bsi_next (&bsi
))
1972 tree stmt
= bsi_stmt (bsi
);
1974 infer_loop_bounds_from_array (loop
, stmt
);
1975 infer_loop_bounds_from_signedness (loop
, stmt
);
1983 /* Records estimates on numbers of iterations of LOOP. */
1986 estimate_numbers_of_iterations_loop (struct loop
*loop
)
1988 VEC (edge
, heap
) *exits
;
1991 struct tree_niter_desc niter_desc
;
1994 /* Give up if we already have tried to compute an estimation. */
1995 if (loop
->estimate_state
!= EST_NOT_COMPUTED
)
1997 loop
->estimate_state
= EST_NOT_AVAILABLE
;
1999 exits
= get_loop_exit_edges (loop
);
2000 for (i
= 0; VEC_iterate (edge
, exits
, i
, ex
); i
++)
2002 if (!number_of_iterations_exit (loop
, ex
, &niter_desc
, false))
2005 niter
= niter_desc
.niter
;
2006 type
= TREE_TYPE (niter
);
2007 if (TREE_CODE (niter_desc
.may_be_zero
) != INTEGER_CST
)
2008 niter
= build3 (COND_EXPR
, type
, niter_desc
.may_be_zero
,
2009 build_int_cst (type
, 0),
2011 record_estimate (loop
, niter
,
2012 niter_desc
.additional_info
,
2013 last_stmt (ex
->src
),
2016 VEC_free (edge
, heap
, exits
);
2018 infer_loop_bounds_from_undefined (loop
);
2019 compute_estimated_nb_iterations (loop
);
2022 /* Records estimates on numbers of iterations of loops. */
2025 estimate_numbers_of_iterations (void)
2030 FOR_EACH_LOOP (li
, loop
, 0)
2032 estimate_numbers_of_iterations_loop (loop
);
2036 /* Returns true if statement S1 dominates statement S2. */
2039 stmt_dominates_stmt_p (tree s1
, tree s2
)
2041 basic_block bb1
= bb_for_stmt (s1
), bb2
= bb_for_stmt (s2
);
2049 block_stmt_iterator bsi
;
2051 for (bsi
= bsi_start (bb1
); bsi_stmt (bsi
) != s2
; bsi_next (&bsi
))
2052 if (bsi_stmt (bsi
) == s1
)
2058 return dominated_by_p (CDI_DOMINATORS
, bb2
, bb1
);
2061 /* Returns true when we can prove that the number of executions of
2062 STMT in the loop is at most NITER, according to the bound on
2063 the number of executions of the statement NITER_BOUND->stmt recorded in
2064 NITER_BOUND. If STMT is NULL, we must prove this bound for all
2065 statements in the loop. */
2068 n_of_executions_at_most (tree stmt
,
2069 struct nb_iter_bound
*niter_bound
,
2072 double_int bound
= niter_bound
->bound
;
2073 tree nit_type
= TREE_TYPE (niter
);
2076 gcc_assert (TYPE_UNSIGNED (nit_type
));
2078 /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
2079 the number of iterations is small. */
2080 if (!double_int_fits_to_tree_p (nit_type
, bound
))
2083 /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
2084 times. This means that:
2086 -- if NITER_BOUND->is_exit is true, then everything before
2087 NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
2088 times, and everything after it at most NITER_BOUND->bound times.
2090 -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
2091 is executed, then NITER_BOUND->stmt is executed as well in the same
2092 iteration (we conclude that if both statements belong to the same
2093 basic block, or if STMT is after NITER_BOUND->stmt), then STMT
2094 is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
2095 executed at most NITER_BOUND->bound + 2 times. */
2097 if (niter_bound
->is_exit
)
2100 && stmt
!= niter_bound
->stmt
2101 && stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
))
2109 || (bb_for_stmt (stmt
) != bb_for_stmt (niter_bound
->stmt
)
2110 && !stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
)))
2112 bound
= double_int_add (bound
, double_int_one
);
2113 if (double_int_zero_p (bound
)
2114 || !double_int_fits_to_tree_p (nit_type
, bound
))
2120 return nonzero_p (fold_binary (cmp
, boolean_type_node
,
2122 double_int_to_tree (nit_type
, bound
)));
2125 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
2128 nowrap_type_p (tree type
)
2131 && INTEGRAL_TYPE_P (type
)
2132 && !TYPE_UNSIGNED (type
))
2135 if (POINTER_TYPE_P (type
))
2141 /* Return false only when the induction variable BASE + STEP * I is
2142 known to not overflow: i.e. when the number of iterations is small
2143 enough with respect to the step and initial condition in order to
2144 keep the evolution confined in TYPEs bounds. Return true when the
2145 iv is known to overflow or when the property is not computable.
2147 USE_OVERFLOW_SEMANTICS is true if this function should assume that
2148 the rules for overflow of the given language apply (e.g., that signed
2149 arithmetics in C does not overflow). */
2152 scev_probably_wraps_p (tree base
, tree step
,
2153 tree at_stmt
, struct loop
*loop
,
2154 bool use_overflow_semantics
)
2156 struct nb_iter_bound
*bound
;
2157 tree delta
, step_abs
;
2158 tree unsigned_type
, valid_niter
;
2159 tree type
= TREE_TYPE (step
);
2161 /* FIXME: We really need something like
2162 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
2164 We used to test for the following situation that frequently appears
2165 during address arithmetics:
2167 D.1621_13 = (long unsigned intD.4) D.1620_12;
2168 D.1622_14 = D.1621_13 * 8;
2169 D.1623_15 = (doubleD.29 *) D.1622_14;
2171 And derived that the sequence corresponding to D_14
2172 can be proved to not wrap because it is used for computing a
2173 memory access; however, this is not really the case -- for example,
2174 if D_12 = (unsigned char) [254,+,1], then D_14 has values
2175 2032, 2040, 0, 8, ..., but the code is still legal. */
2177 if (chrec_contains_undetermined (base
)
2178 || chrec_contains_undetermined (step
)
2179 || TREE_CODE (step
) != INTEGER_CST
)
2185 /* If we can use the fact that signed and pointer arithmetics does not
2186 wrap, we are done. */
2187 if (use_overflow_semantics
&& nowrap_type_p (type
))
2190 /* Otherwise, compute the number of iterations before we reach the
2191 bound of the type, and verify that the loop is exited before this
2193 unsigned_type
= unsigned_type_for (type
);
2194 base
= fold_convert (unsigned_type
, base
);
2196 if (tree_int_cst_sign_bit (step
))
2198 tree extreme
= fold_convert (unsigned_type
,
2199 lower_bound_in_type (type
, type
));
2200 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
2201 step_abs
= fold_build1 (NEGATE_EXPR
, unsigned_type
,
2202 fold_convert (unsigned_type
, step
));
2206 tree extreme
= fold_convert (unsigned_type
,
2207 upper_bound_in_type (type
, type
));
2208 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
2209 step_abs
= fold_convert (unsigned_type
, step
);
2212 valid_niter
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step_abs
);
2214 estimate_numbers_of_iterations_loop (loop
);
2215 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
2216 if (n_of_executions_at_most (at_stmt
, bound
, valid_niter
))
2219 /* At this point we still don't have a proof that the iv does not
2220 overflow: give up. */
2224 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
2227 free_numbers_of_iterations_estimates_loop (struct loop
*loop
)
2229 struct nb_iter_bound
*bound
, *next
;
2231 loop
->nb_iterations
= NULL
;
2232 loop
->estimate_state
= EST_NOT_COMPUTED
;
2233 for (bound
= loop
->bounds
; bound
; bound
= next
)
2239 loop
->bounds
= NULL
;
2242 /* Frees the information on upper bounds on numbers of iterations of loops. */
2245 free_numbers_of_iterations_estimates (void)
2250 FOR_EACH_LOOP (li
, loop
, 0)
2252 free_numbers_of_iterations_estimates_loop (loop
);
2256 /* Substitute value VAL for ssa name NAME inside expressions held
2260 substitute_in_loop_info (struct loop
*loop
, tree name
, tree val
)
2262 loop
->nb_iterations
= simplify_replace_tree (loop
->nb_iterations
, name
, val
);