1 /* Functions to determine/estimate number of iterations of a loop.
2 Copyright (C) 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012
3 Free Software Foundation, Inc.
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it
8 under the terms of the GNU General Public License as published by the
9 Free Software Foundation; either version 3, or (at your option) any
12 GCC is distributed in the hope that it will be useful, but WITHOUT
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING3. If not see
19 <http://www.gnu.org/licenses/>. */
23 #include "coretypes.h"
27 #include "basic-block.h"
28 #include "gimple-pretty-print.h"
30 #include "tree-flow.h"
34 #include "tree-chrec.h"
35 #include "tree-scalar-evolution.h"
36 #include "tree-data-ref.h"
39 #include "diagnostic-core.h"
40 #include "tree-inline.h"
43 #define SWAP(X, Y) do { affine_iv *tmp = (X); (X) = (Y); (Y) = tmp; } while (0)
45 /* The maximum number of dominator BBs we search for conditions
46 of loop header copies we use for simplifying a conditional
48 #define MAX_DOMINATORS_TO_WALK 8
52 Analysis of number of iterations of an affine exit test.
56 /* Bounds on some value, BELOW <= X <= UP. */
64 /* Splits expression EXPR to a variable part VAR and constant OFFSET. */
67 split_to_var_and_offset (tree expr
, tree
*var
, mpz_t offset
)
69 tree type
= TREE_TYPE (expr
);
75 mpz_set_ui (offset
, 0);
77 switch (TREE_CODE (expr
))
84 case POINTER_PLUS_EXPR
:
85 op0
= TREE_OPERAND (expr
, 0);
86 op1
= TREE_OPERAND (expr
, 1);
88 if (TREE_CODE (op1
) != INTEGER_CST
)
92 /* Always sign extend the offset. */
93 off
= tree_to_double_int (op1
);
94 off
= off
.sext (TYPE_PRECISION (type
));
95 mpz_set_double_int (offset
, off
, false);
97 mpz_neg (offset
, offset
);
101 *var
= build_int_cst_type (type
, 0);
102 off
= tree_to_double_int (expr
);
103 mpz_set_double_int (offset
, off
, TYPE_UNSIGNED (type
));
111 /* Stores estimate on the minimum/maximum value of the expression VAR + OFF
112 in TYPE to MIN and MAX. */
115 determine_value_range (tree type
, tree var
, mpz_t off
,
116 mpz_t min
, mpz_t max
)
118 /* If the expression is a constant, we know its value exactly. */
119 if (integer_zerop (var
))
126 /* If the computation may wrap, we know nothing about the value, except for
127 the range of the type. */
128 get_type_static_bounds (type
, min
, max
);
129 if (!nowrap_type_p (type
))
132 /* Since the addition of OFF does not wrap, if OFF is positive, then we may
133 add it to MIN, otherwise to MAX. */
134 if (mpz_sgn (off
) < 0)
135 mpz_add (max
, max
, off
);
137 mpz_add (min
, min
, off
);
140 /* Stores the bounds on the difference of the values of the expressions
141 (var + X) and (var + Y), computed in TYPE, to BNDS. */
144 bound_difference_of_offsetted_base (tree type
, mpz_t x
, mpz_t y
,
147 int rel
= mpz_cmp (x
, y
);
148 bool may_wrap
= !nowrap_type_p (type
);
151 /* If X == Y, then the expressions are always equal.
152 If X > Y, there are the following possibilities:
153 a) neither of var + X and var + Y overflow or underflow, or both of
154 them do. Then their difference is X - Y.
155 b) var + X overflows, and var + Y does not. Then the values of the
156 expressions are var + X - M and var + Y, where M is the range of
157 the type, and their difference is X - Y - M.
158 c) var + Y underflows and var + X does not. Their difference again
160 Therefore, if the arithmetics in type does not overflow, then the
161 bounds are (X - Y, X - Y), otherwise they are (X - Y - M, X - Y)
162 Similarly, if X < Y, the bounds are either (X - Y, X - Y) or
163 (X - Y, X - Y + M). */
167 mpz_set_ui (bnds
->below
, 0);
168 mpz_set_ui (bnds
->up
, 0);
173 mpz_set_double_int (m
, double_int::mask (TYPE_PRECISION (type
)), true);
174 mpz_add_ui (m
, m
, 1);
175 mpz_sub (bnds
->up
, x
, y
);
176 mpz_set (bnds
->below
, bnds
->up
);
181 mpz_sub (bnds
->below
, bnds
->below
, m
);
183 mpz_add (bnds
->up
, bnds
->up
, m
);
189 /* From condition C0 CMP C1 derives information regarding the
190 difference of values of VARX + OFFX and VARY + OFFY, computed in TYPE,
191 and stores it to BNDS. */
194 refine_bounds_using_guard (tree type
, tree varx
, mpz_t offx
,
195 tree vary
, mpz_t offy
,
196 tree c0
, enum tree_code cmp
, tree c1
,
199 tree varc0
, varc1
, tmp
, ctype
;
200 mpz_t offc0
, offc1
, loffx
, loffy
, bnd
;
202 bool no_wrap
= nowrap_type_p (type
);
211 STRIP_SIGN_NOPS (c0
);
212 STRIP_SIGN_NOPS (c1
);
213 ctype
= TREE_TYPE (c0
);
214 if (!useless_type_conversion_p (ctype
, type
))
220 /* We could derive quite precise information from EQ_EXPR, however, such
221 a guard is unlikely to appear, so we do not bother with handling
226 /* NE_EXPR comparisons do not contain much of useful information, except for
227 special case of comparing with the bounds of the type. */
228 if (TREE_CODE (c1
) != INTEGER_CST
229 || !INTEGRAL_TYPE_P (type
))
232 /* Ensure that the condition speaks about an expression in the same type
234 ctype
= TREE_TYPE (c0
);
235 if (TYPE_PRECISION (ctype
) != TYPE_PRECISION (type
))
237 c0
= fold_convert (type
, c0
);
238 c1
= fold_convert (type
, c1
);
240 if (TYPE_MIN_VALUE (type
)
241 && operand_equal_p (c1
, TYPE_MIN_VALUE (type
), 0))
246 if (TYPE_MAX_VALUE (type
)
247 && operand_equal_p (c1
, TYPE_MAX_VALUE (type
), 0))
260 split_to_var_and_offset (expand_simple_operations (c0
), &varc0
, offc0
);
261 split_to_var_and_offset (expand_simple_operations (c1
), &varc1
, offc1
);
263 /* We are only interested in comparisons of expressions based on VARX and
264 VARY. TODO -- we might also be able to derive some bounds from
265 expressions containing just one of the variables. */
267 if (operand_equal_p (varx
, varc1
, 0))
269 tmp
= varc0
; varc0
= varc1
; varc1
= tmp
;
270 mpz_swap (offc0
, offc1
);
271 cmp
= swap_tree_comparison (cmp
);
274 if (!operand_equal_p (varx
, varc0
, 0)
275 || !operand_equal_p (vary
, varc1
, 0))
278 mpz_init_set (loffx
, offx
);
279 mpz_init_set (loffy
, offy
);
281 if (cmp
== GT_EXPR
|| cmp
== GE_EXPR
)
283 tmp
= varx
; varx
= vary
; vary
= tmp
;
284 mpz_swap (offc0
, offc1
);
285 mpz_swap (loffx
, loffy
);
286 cmp
= swap_tree_comparison (cmp
);
290 /* If there is no overflow, the condition implies that
292 (VARX + OFFX) cmp (VARY + OFFY) + (OFFX - OFFY + OFFC1 - OFFC0).
294 The overflows and underflows may complicate things a bit; each
295 overflow decreases the appropriate offset by M, and underflow
296 increases it by M. The above inequality would not necessarily be
299 -- VARX + OFFX underflows and VARX + OFFC0 does not, or
300 VARX + OFFC0 overflows, but VARX + OFFX does not.
301 This may only happen if OFFX < OFFC0.
302 -- VARY + OFFY overflows and VARY + OFFC1 does not, or
303 VARY + OFFC1 underflows and VARY + OFFY does not.
304 This may only happen if OFFY > OFFC1. */
313 x_ok
= (integer_zerop (varx
)
314 || mpz_cmp (loffx
, offc0
) >= 0);
315 y_ok
= (integer_zerop (vary
)
316 || mpz_cmp (loffy
, offc1
) <= 0);
322 mpz_sub (bnd
, loffx
, loffy
);
323 mpz_add (bnd
, bnd
, offc1
);
324 mpz_sub (bnd
, bnd
, offc0
);
327 mpz_sub_ui (bnd
, bnd
, 1);
332 if (mpz_cmp (bnds
->below
, bnd
) < 0)
333 mpz_set (bnds
->below
, bnd
);
337 if (mpz_cmp (bnd
, bnds
->up
) < 0)
338 mpz_set (bnds
->up
, bnd
);
350 /* Stores the bounds on the value of the expression X - Y in LOOP to BNDS.
351 The subtraction is considered to be performed in arbitrary precision,
354 We do not attempt to be too clever regarding the value ranges of X and
355 Y; most of the time, they are just integers or ssa names offsetted by
356 integer. However, we try to use the information contained in the
357 comparisons before the loop (usually created by loop header copying). */
360 bound_difference (struct loop
*loop
, tree x
, tree y
, bounds
*bnds
)
362 tree type
= TREE_TYPE (x
);
365 mpz_t minx
, maxx
, miny
, maxy
;
373 /* Get rid of unnecessary casts, but preserve the value of
378 mpz_init (bnds
->below
);
382 split_to_var_and_offset (x
, &varx
, offx
);
383 split_to_var_and_offset (y
, &vary
, offy
);
385 if (!integer_zerop (varx
)
386 && operand_equal_p (varx
, vary
, 0))
388 /* Special case VARX == VARY -- we just need to compare the
389 offsets. The matters are a bit more complicated in the
390 case addition of offsets may wrap. */
391 bound_difference_of_offsetted_base (type
, offx
, offy
, bnds
);
395 /* Otherwise, use the value ranges to determine the initial
396 estimates on below and up. */
401 determine_value_range (type
, varx
, offx
, minx
, maxx
);
402 determine_value_range (type
, vary
, offy
, miny
, maxy
);
404 mpz_sub (bnds
->below
, minx
, maxy
);
405 mpz_sub (bnds
->up
, maxx
, miny
);
412 /* If both X and Y are constants, we cannot get any more precise. */
413 if (integer_zerop (varx
) && integer_zerop (vary
))
416 /* Now walk the dominators of the loop header and use the entry
417 guards to refine the estimates. */
418 for (bb
= loop
->header
;
419 bb
!= ENTRY_BLOCK_PTR
&& cnt
< MAX_DOMINATORS_TO_WALK
;
420 bb
= get_immediate_dominator (CDI_DOMINATORS
, bb
))
422 if (!single_pred_p (bb
))
424 e
= single_pred_edge (bb
);
426 if (!(e
->flags
& (EDGE_TRUE_VALUE
| EDGE_FALSE_VALUE
)))
429 cond
= last_stmt (e
->src
);
430 c0
= gimple_cond_lhs (cond
);
431 cmp
= gimple_cond_code (cond
);
432 c1
= gimple_cond_rhs (cond
);
434 if (e
->flags
& EDGE_FALSE_VALUE
)
435 cmp
= invert_tree_comparison (cmp
, false);
437 refine_bounds_using_guard (type
, varx
, offx
, vary
, offy
,
447 /* Update the bounds in BNDS that restrict the value of X to the bounds
448 that restrict the value of X + DELTA. X can be obtained as a
449 difference of two values in TYPE. */
452 bounds_add (bounds
*bnds
, double_int delta
, tree type
)
457 mpz_set_double_int (mdelta
, delta
, false);
460 mpz_set_double_int (max
, double_int::mask (TYPE_PRECISION (type
)), true);
462 mpz_add (bnds
->up
, bnds
->up
, mdelta
);
463 mpz_add (bnds
->below
, bnds
->below
, mdelta
);
465 if (mpz_cmp (bnds
->up
, max
) > 0)
466 mpz_set (bnds
->up
, max
);
469 if (mpz_cmp (bnds
->below
, max
) < 0)
470 mpz_set (bnds
->below
, max
);
476 /* Update the bounds in BNDS that restrict the value of X to the bounds
477 that restrict the value of -X. */
480 bounds_negate (bounds
*bnds
)
484 mpz_init_set (tmp
, bnds
->up
);
485 mpz_neg (bnds
->up
, bnds
->below
);
486 mpz_neg (bnds
->below
, tmp
);
490 /* Returns inverse of X modulo 2^s, where MASK = 2^s-1. */
493 inverse (tree x
, tree mask
)
495 tree type
= TREE_TYPE (x
);
497 unsigned ctr
= tree_floor_log2 (mask
);
499 if (TYPE_PRECISION (type
) <= HOST_BITS_PER_WIDE_INT
)
501 unsigned HOST_WIDE_INT ix
;
502 unsigned HOST_WIDE_INT imask
;
503 unsigned HOST_WIDE_INT irslt
= 1;
505 gcc_assert (cst_and_fits_in_hwi (x
));
506 gcc_assert (cst_and_fits_in_hwi (mask
));
508 ix
= int_cst_value (x
);
509 imask
= int_cst_value (mask
);
518 rslt
= build_int_cst_type (type
, irslt
);
522 rslt
= build_int_cst (type
, 1);
525 rslt
= int_const_binop (MULT_EXPR
, rslt
, x
);
526 x
= int_const_binop (MULT_EXPR
, x
, x
);
528 rslt
= int_const_binop (BIT_AND_EXPR
, rslt
, mask
);
534 /* Derives the upper bound BND on the number of executions of loop with exit
535 condition S * i <> C. If NO_OVERFLOW is true, then the control variable of
536 the loop does not overflow. EXIT_MUST_BE_TAKEN is true if we are guaranteed
537 that the loop ends through this exit, i.e., the induction variable ever
538 reaches the value of C.
540 The value C is equal to final - base, where final and base are the final and
541 initial value of the actual induction variable in the analysed loop. BNDS
542 bounds the value of this difference when computed in signed type with
543 unbounded range, while the computation of C is performed in an unsigned
544 type with the range matching the range of the type of the induction variable.
545 In particular, BNDS.up contains an upper bound on C in the following cases:
546 -- if the iv must reach its final value without overflow, i.e., if
547 NO_OVERFLOW && EXIT_MUST_BE_TAKEN is true, or
548 -- if final >= base, which we know to hold when BNDS.below >= 0. */
551 number_of_iterations_ne_max (mpz_t bnd
, bool no_overflow
, tree c
, tree s
,
552 bounds
*bnds
, bool exit_must_be_taken
)
556 bool bnds_u_valid
= ((no_overflow
&& exit_must_be_taken
)
557 || mpz_sgn (bnds
->below
) >= 0);
559 if (multiple_of_p (TREE_TYPE (c
), c
, s
))
561 /* If C is an exact multiple of S, then its value will be reached before
562 the induction variable overflows (unless the loop is exited in some
563 other way before). Note that the actual induction variable in the
564 loop (which ranges from base to final instead of from 0 to C) may
565 overflow, in which case BNDS.up will not be giving a correct upper
566 bound on C; thus, BNDS_U_VALID had to be computed in advance. */
568 exit_must_be_taken
= true;
571 /* If the induction variable can overflow, the number of iterations is at
572 most the period of the control variable (or infinite, but in that case
573 the whole # of iterations analysis will fail). */
576 max
= double_int::mask (TYPE_PRECISION (TREE_TYPE (c
))
577 - tree_low_cst (num_ending_zeros (s
), 1));
578 mpz_set_double_int (bnd
, max
, true);
582 /* Now we know that the induction variable does not overflow, so the loop
583 iterates at most (range of type / S) times. */
584 mpz_set_double_int (bnd
, double_int::mask (TYPE_PRECISION (TREE_TYPE (c
))),
587 /* If the induction variable is guaranteed to reach the value of C before
589 if (exit_must_be_taken
)
591 /* ... then we can strengthen this to C / S, and possibly we can use
592 the upper bound on C given by BNDS. */
593 if (TREE_CODE (c
) == INTEGER_CST
)
594 mpz_set_double_int (bnd
, tree_to_double_int (c
), true);
595 else if (bnds_u_valid
)
596 mpz_set (bnd
, bnds
->up
);
600 mpz_set_double_int (d
, tree_to_double_int (s
), true);
601 mpz_fdiv_q (bnd
, bnd
, d
);
605 /* Determines number of iterations of loop whose ending condition
606 is IV <> FINAL. TYPE is the type of the iv. The number of
607 iterations is stored to NITER. EXIT_MUST_BE_TAKEN is true if
608 we know that the exit must be taken eventually, i.e., that the IV
609 ever reaches the value FINAL (we derived this earlier, and possibly set
610 NITER->assumptions to make sure this is the case). BNDS contains the
611 bounds on the difference FINAL - IV->base. */
614 number_of_iterations_ne (tree type
, affine_iv
*iv
, tree final
,
615 struct tree_niter_desc
*niter
, bool exit_must_be_taken
,
618 tree niter_type
= unsigned_type_for (type
);
619 tree s
, c
, d
, bits
, assumption
, tmp
, bound
;
622 niter
->control
= *iv
;
623 niter
->bound
= final
;
624 niter
->cmp
= NE_EXPR
;
626 /* Rearrange the terms so that we get inequality S * i <> C, with S
627 positive. Also cast everything to the unsigned type. If IV does
628 not overflow, BNDS bounds the value of C. Also, this is the
629 case if the computation |FINAL - IV->base| does not overflow, i.e.,
630 if BNDS->below in the result is nonnegative. */
631 if (tree_int_cst_sign_bit (iv
->step
))
633 s
= fold_convert (niter_type
,
634 fold_build1 (NEGATE_EXPR
, type
, iv
->step
));
635 c
= fold_build2 (MINUS_EXPR
, niter_type
,
636 fold_convert (niter_type
, iv
->base
),
637 fold_convert (niter_type
, final
));
638 bounds_negate (bnds
);
642 s
= fold_convert (niter_type
, iv
->step
);
643 c
= fold_build2 (MINUS_EXPR
, niter_type
,
644 fold_convert (niter_type
, final
),
645 fold_convert (niter_type
, iv
->base
));
649 number_of_iterations_ne_max (max
, iv
->no_overflow
, c
, s
, bnds
,
651 niter
->max
= mpz_get_double_int (niter_type
, max
, false);
654 /* First the trivial cases -- when the step is 1. */
655 if (integer_onep (s
))
661 /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
662 is infinite. Otherwise, the number of iterations is
663 (inverse(s/d) * (c/d)) mod (size of mode/d). */
664 bits
= num_ending_zeros (s
);
665 bound
= build_low_bits_mask (niter_type
,
666 (TYPE_PRECISION (niter_type
)
667 - tree_low_cst (bits
, 1)));
669 d
= fold_binary_to_constant (LSHIFT_EXPR
, niter_type
,
670 build_int_cst (niter_type
, 1), bits
);
671 s
= fold_binary_to_constant (RSHIFT_EXPR
, niter_type
, s
, bits
);
673 if (!exit_must_be_taken
)
675 /* If we cannot assume that the exit is taken eventually, record the
676 assumptions for divisibility of c. */
677 assumption
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, c
, d
);
678 assumption
= fold_build2 (EQ_EXPR
, boolean_type_node
,
679 assumption
, build_int_cst (niter_type
, 0));
680 if (!integer_nonzerop (assumption
))
681 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
682 niter
->assumptions
, assumption
);
685 c
= fold_build2 (EXACT_DIV_EXPR
, niter_type
, c
, d
);
686 tmp
= fold_build2 (MULT_EXPR
, niter_type
, c
, inverse (s
, bound
));
687 niter
->niter
= fold_build2 (BIT_AND_EXPR
, niter_type
, tmp
, bound
);
691 /* Checks whether we can determine the final value of the control variable
692 of the loop with ending condition IV0 < IV1 (computed in TYPE).
693 DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
694 of the step. The assumptions necessary to ensure that the computation
695 of the final value does not overflow are recorded in NITER. If we
696 find the final value, we adjust DELTA and return TRUE. Otherwise
697 we return false. BNDS bounds the value of IV1->base - IV0->base,
698 and will be updated by the same amount as DELTA. EXIT_MUST_BE_TAKEN is
699 true if we know that the exit must be taken eventually. */
702 number_of_iterations_lt_to_ne (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
703 struct tree_niter_desc
*niter
,
704 tree
*delta
, tree step
,
705 bool exit_must_be_taken
, bounds
*bnds
)
707 tree niter_type
= TREE_TYPE (step
);
708 tree mod
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, *delta
, step
);
711 tree assumption
= boolean_true_node
, bound
, noloop
;
712 bool ret
= false, fv_comp_no_overflow
;
714 if (POINTER_TYPE_P (type
))
717 if (TREE_CODE (mod
) != INTEGER_CST
)
719 if (integer_nonzerop (mod
))
720 mod
= fold_build2 (MINUS_EXPR
, niter_type
, step
, mod
);
721 tmod
= fold_convert (type1
, mod
);
724 mpz_set_double_int (mmod
, tree_to_double_int (mod
), true);
725 mpz_neg (mmod
, mmod
);
727 /* If the induction variable does not overflow and the exit is taken,
728 then the computation of the final value does not overflow. This is
729 also obviously the case if the new final value is equal to the
730 current one. Finally, we postulate this for pointer type variables,
731 as the code cannot rely on the object to that the pointer points being
732 placed at the end of the address space (and more pragmatically,
733 TYPE_{MIN,MAX}_VALUE is not defined for pointers). */
734 if (integer_zerop (mod
) || POINTER_TYPE_P (type
))
735 fv_comp_no_overflow
= true;
736 else if (!exit_must_be_taken
)
737 fv_comp_no_overflow
= false;
739 fv_comp_no_overflow
=
740 (iv0
->no_overflow
&& integer_nonzerop (iv0
->step
))
741 || (iv1
->no_overflow
&& integer_nonzerop (iv1
->step
));
743 if (integer_nonzerop (iv0
->step
))
745 /* The final value of the iv is iv1->base + MOD, assuming that this
746 computation does not overflow, and that
747 iv0->base <= iv1->base + MOD. */
748 if (!fv_comp_no_overflow
)
750 bound
= fold_build2 (MINUS_EXPR
, type1
,
751 TYPE_MAX_VALUE (type1
), tmod
);
752 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
754 if (integer_zerop (assumption
))
757 if (mpz_cmp (mmod
, bnds
->below
) < 0)
758 noloop
= boolean_false_node
;
759 else if (POINTER_TYPE_P (type
))
760 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
762 fold_build_pointer_plus (iv1
->base
, tmod
));
764 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
766 fold_build2 (PLUS_EXPR
, type1
,
771 /* The final value of the iv is iv0->base - MOD, assuming that this
772 computation does not overflow, and that
773 iv0->base - MOD <= iv1->base. */
774 if (!fv_comp_no_overflow
)
776 bound
= fold_build2 (PLUS_EXPR
, type1
,
777 TYPE_MIN_VALUE (type1
), tmod
);
778 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
780 if (integer_zerop (assumption
))
783 if (mpz_cmp (mmod
, bnds
->below
) < 0)
784 noloop
= boolean_false_node
;
785 else if (POINTER_TYPE_P (type
))
786 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
787 fold_build_pointer_plus (iv0
->base
,
788 fold_build1 (NEGATE_EXPR
,
792 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
793 fold_build2 (MINUS_EXPR
, type1
,
798 if (!integer_nonzerop (assumption
))
799 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
802 if (!integer_zerop (noloop
))
803 niter
->may_be_zero
= fold_build2 (TRUTH_OR_EXPR
, boolean_type_node
,
806 bounds_add (bnds
, tree_to_double_int (mod
), type
);
807 *delta
= fold_build2 (PLUS_EXPR
, niter_type
, *delta
, mod
);
815 /* Add assertions to NITER that ensure that the control variable of the loop
816 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
817 are TYPE. Returns false if we can prove that there is an overflow, true
818 otherwise. STEP is the absolute value of the step. */
821 assert_no_overflow_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
822 struct tree_niter_desc
*niter
, tree step
)
824 tree bound
, d
, assumption
, diff
;
825 tree niter_type
= TREE_TYPE (step
);
827 if (integer_nonzerop (iv0
->step
))
829 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
830 if (iv0
->no_overflow
)
833 /* If iv0->base is a constant, we can determine the last value before
834 overflow precisely; otherwise we conservatively assume
837 if (TREE_CODE (iv0
->base
) == INTEGER_CST
)
839 d
= fold_build2 (MINUS_EXPR
, niter_type
,
840 fold_convert (niter_type
, TYPE_MAX_VALUE (type
)),
841 fold_convert (niter_type
, iv0
->base
));
842 diff
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, d
, step
);
845 diff
= fold_build2 (MINUS_EXPR
, niter_type
, step
,
846 build_int_cst (niter_type
, 1));
847 bound
= fold_build2 (MINUS_EXPR
, type
,
848 TYPE_MAX_VALUE (type
), fold_convert (type
, diff
));
849 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
854 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
855 if (iv1
->no_overflow
)
858 if (TREE_CODE (iv1
->base
) == INTEGER_CST
)
860 d
= fold_build2 (MINUS_EXPR
, niter_type
,
861 fold_convert (niter_type
, iv1
->base
),
862 fold_convert (niter_type
, TYPE_MIN_VALUE (type
)));
863 diff
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, d
, step
);
866 diff
= fold_build2 (MINUS_EXPR
, niter_type
, step
,
867 build_int_cst (niter_type
, 1));
868 bound
= fold_build2 (PLUS_EXPR
, type
,
869 TYPE_MIN_VALUE (type
), fold_convert (type
, diff
));
870 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
874 if (integer_zerop (assumption
))
876 if (!integer_nonzerop (assumption
))
877 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
878 niter
->assumptions
, assumption
);
880 iv0
->no_overflow
= true;
881 iv1
->no_overflow
= true;
885 /* Add an assumption to NITER that a loop whose ending condition
886 is IV0 < IV1 rolls. TYPE is the type of the control iv. BNDS
887 bounds the value of IV1->base - IV0->base. */
890 assert_loop_rolls_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
891 struct tree_niter_desc
*niter
, bounds
*bnds
)
893 tree assumption
= boolean_true_node
, bound
, diff
;
894 tree mbz
, mbzl
, mbzr
, type1
;
895 bool rolls_p
, no_overflow_p
;
899 /* We are going to compute the number of iterations as
900 (iv1->base - iv0->base + step - 1) / step, computed in the unsigned
901 variant of TYPE. This formula only works if
903 -step + 1 <= (iv1->base - iv0->base) <= MAX - step + 1
905 (where MAX is the maximum value of the unsigned variant of TYPE, and
906 the computations in this formula are performed in full precision,
907 i.e., without overflows).
909 Usually, for loops with exit condition iv0->base + step * i < iv1->base,
910 we have a condition of the form iv0->base - step < iv1->base before the loop,
911 and for loops iv0->base < iv1->base - step * i the condition
912 iv0->base < iv1->base + step, due to loop header copying, which enable us
913 to prove the lower bound.
915 The upper bound is more complicated. Unless the expressions for initial
916 and final value themselves contain enough information, we usually cannot
917 derive it from the context. */
919 /* First check whether the answer does not follow from the bounds we gathered
921 if (integer_nonzerop (iv0
->step
))
922 dstep
= tree_to_double_int (iv0
->step
);
925 dstep
= tree_to_double_int (iv1
->step
).sext (TYPE_PRECISION (type
));
930 mpz_set_double_int (mstep
, dstep
, true);
931 mpz_neg (mstep
, mstep
);
932 mpz_add_ui (mstep
, mstep
, 1);
934 rolls_p
= mpz_cmp (mstep
, bnds
->below
) <= 0;
937 mpz_set_double_int (max
, double_int::mask (TYPE_PRECISION (type
)), true);
938 mpz_add (max
, max
, mstep
);
939 no_overflow_p
= (mpz_cmp (bnds
->up
, max
) <= 0
940 /* For pointers, only values lying inside a single object
941 can be compared or manipulated by pointer arithmetics.
942 Gcc in general does not allow or handle objects larger
943 than half of the address space, hence the upper bound
944 is satisfied for pointers. */
945 || POINTER_TYPE_P (type
));
949 if (rolls_p
&& no_overflow_p
)
953 if (POINTER_TYPE_P (type
))
956 /* Now the hard part; we must formulate the assumption(s) as expressions, and
957 we must be careful not to introduce overflow. */
959 if (integer_nonzerop (iv0
->step
))
961 diff
= fold_build2 (MINUS_EXPR
, type1
,
962 iv0
->step
, build_int_cst (type1
, 1));
964 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
965 0 address never belongs to any object, we can assume this for
967 if (!POINTER_TYPE_P (type
))
969 bound
= fold_build2 (PLUS_EXPR
, type1
,
970 TYPE_MIN_VALUE (type
), diff
);
971 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
975 /* And then we can compute iv0->base - diff, and compare it with
977 mbzl
= fold_build2 (MINUS_EXPR
, type1
,
978 fold_convert (type1
, iv0
->base
), diff
);
979 mbzr
= fold_convert (type1
, iv1
->base
);
983 diff
= fold_build2 (PLUS_EXPR
, type1
,
984 iv1
->step
, build_int_cst (type1
, 1));
986 if (!POINTER_TYPE_P (type
))
988 bound
= fold_build2 (PLUS_EXPR
, type1
,
989 TYPE_MAX_VALUE (type
), diff
);
990 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
994 mbzl
= fold_convert (type1
, iv0
->base
);
995 mbzr
= fold_build2 (MINUS_EXPR
, type1
,
996 fold_convert (type1
, iv1
->base
), diff
);
999 if (!integer_nonzerop (assumption
))
1000 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
1001 niter
->assumptions
, assumption
);
1004 mbz
= fold_build2 (GT_EXPR
, boolean_type_node
, mbzl
, mbzr
);
1005 niter
->may_be_zero
= fold_build2 (TRUTH_OR_EXPR
, boolean_type_node
,
1006 niter
->may_be_zero
, mbz
);
1010 /* Determines number of iterations of loop whose ending condition
1011 is IV0 < IV1. TYPE is the type of the iv. The number of
1012 iterations is stored to NITER. BNDS bounds the difference
1013 IV1->base - IV0->base. EXIT_MUST_BE_TAKEN is true if we know
1014 that the exit must be taken eventually. */
1017 number_of_iterations_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
1018 struct tree_niter_desc
*niter
,
1019 bool exit_must_be_taken
, bounds
*bnds
)
1021 tree niter_type
= unsigned_type_for (type
);
1022 tree delta
, step
, s
;
1025 if (integer_nonzerop (iv0
->step
))
1027 niter
->control
= *iv0
;
1028 niter
->cmp
= LT_EXPR
;
1029 niter
->bound
= iv1
->base
;
1033 niter
->control
= *iv1
;
1034 niter
->cmp
= GT_EXPR
;
1035 niter
->bound
= iv0
->base
;
1038 delta
= fold_build2 (MINUS_EXPR
, niter_type
,
1039 fold_convert (niter_type
, iv1
->base
),
1040 fold_convert (niter_type
, iv0
->base
));
1042 /* First handle the special case that the step is +-1. */
1043 if ((integer_onep (iv0
->step
) && integer_zerop (iv1
->step
))
1044 || (integer_all_onesp (iv1
->step
) && integer_zerop (iv0
->step
)))
1046 /* for (i = iv0->base; i < iv1->base; i++)
1050 for (i = iv1->base; i > iv0->base; i--).
1052 In both cases # of iterations is iv1->base - iv0->base, assuming that
1053 iv1->base >= iv0->base.
1055 First try to derive a lower bound on the value of
1056 iv1->base - iv0->base, computed in full precision. If the difference
1057 is nonnegative, we are done, otherwise we must record the
1060 if (mpz_sgn (bnds
->below
) < 0)
1061 niter
->may_be_zero
= fold_build2 (LT_EXPR
, boolean_type_node
,
1062 iv1
->base
, iv0
->base
);
1063 niter
->niter
= delta
;
1064 niter
->max
= mpz_get_double_int (niter_type
, bnds
->up
, false);
1068 if (integer_nonzerop (iv0
->step
))
1069 step
= fold_convert (niter_type
, iv0
->step
);
1071 step
= fold_convert (niter_type
,
1072 fold_build1 (NEGATE_EXPR
, type
, iv1
->step
));
1074 /* If we can determine the final value of the control iv exactly, we can
1075 transform the condition to != comparison. In particular, this will be
1076 the case if DELTA is constant. */
1077 if (number_of_iterations_lt_to_ne (type
, iv0
, iv1
, niter
, &delta
, step
,
1078 exit_must_be_taken
, bnds
))
1082 zps
.base
= build_int_cst (niter_type
, 0);
1084 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
1085 zps does not overflow. */
1086 zps
.no_overflow
= true;
1088 return number_of_iterations_ne (type
, &zps
, delta
, niter
, true, bnds
);
1091 /* Make sure that the control iv does not overflow. */
1092 if (!assert_no_overflow_lt (type
, iv0
, iv1
, niter
, step
))
1095 /* We determine the number of iterations as (delta + step - 1) / step. For
1096 this to work, we must know that iv1->base >= iv0->base - step + 1,
1097 otherwise the loop does not roll. */
1098 assert_loop_rolls_lt (type
, iv0
, iv1
, niter
, bnds
);
1100 s
= fold_build2 (MINUS_EXPR
, niter_type
,
1101 step
, build_int_cst (niter_type
, 1));
1102 delta
= fold_build2 (PLUS_EXPR
, niter_type
, delta
, s
);
1103 niter
->niter
= fold_build2 (FLOOR_DIV_EXPR
, niter_type
, delta
, step
);
1107 mpz_set_double_int (mstep
, tree_to_double_int (step
), true);
1108 mpz_add (tmp
, bnds
->up
, mstep
);
1109 mpz_sub_ui (tmp
, tmp
, 1);
1110 mpz_fdiv_q (tmp
, tmp
, mstep
);
1111 niter
->max
= mpz_get_double_int (niter_type
, tmp
, false);
1118 /* Determines number of iterations of loop whose ending condition
1119 is IV0 <= IV1. TYPE is the type of the iv. The number of
1120 iterations is stored to NITER. EXIT_MUST_BE_TAKEN is true if
1121 we know that this condition must eventually become false (we derived this
1122 earlier, and possibly set NITER->assumptions to make sure this
1123 is the case). BNDS bounds the difference IV1->base - IV0->base. */
1126 number_of_iterations_le (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
1127 struct tree_niter_desc
*niter
, bool exit_must_be_taken
,
1132 if (POINTER_TYPE_P (type
))
1135 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
1136 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
1137 value of the type. This we must know anyway, since if it is
1138 equal to this value, the loop rolls forever. We do not check
1139 this condition for pointer type ivs, as the code cannot rely on
1140 the object to that the pointer points being placed at the end of
1141 the address space (and more pragmatically, TYPE_{MIN,MAX}_VALUE is
1142 not defined for pointers). */
1144 if (!exit_must_be_taken
&& !POINTER_TYPE_P (type
))
1146 if (integer_nonzerop (iv0
->step
))
1147 assumption
= fold_build2 (NE_EXPR
, boolean_type_node
,
1148 iv1
->base
, TYPE_MAX_VALUE (type
));
1150 assumption
= fold_build2 (NE_EXPR
, boolean_type_node
,
1151 iv0
->base
, TYPE_MIN_VALUE (type
));
1153 if (integer_zerop (assumption
))
1155 if (!integer_nonzerop (assumption
))
1156 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
1157 niter
->assumptions
, assumption
);
1160 if (integer_nonzerop (iv0
->step
))
1162 if (POINTER_TYPE_P (type
))
1163 iv1
->base
= fold_build_pointer_plus_hwi (iv1
->base
, 1);
1165 iv1
->base
= fold_build2 (PLUS_EXPR
, type1
, iv1
->base
,
1166 build_int_cst (type1
, 1));
1168 else if (POINTER_TYPE_P (type
))
1169 iv0
->base
= fold_build_pointer_plus_hwi (iv0
->base
, -1);
1171 iv0
->base
= fold_build2 (MINUS_EXPR
, type1
,
1172 iv0
->base
, build_int_cst (type1
, 1));
1174 bounds_add (bnds
, double_int_one
, type1
);
1176 return number_of_iterations_lt (type
, iv0
, iv1
, niter
, exit_must_be_taken
,
1180 /* Dumps description of affine induction variable IV to FILE. */
1183 dump_affine_iv (FILE *file
, affine_iv
*iv
)
1185 if (!integer_zerop (iv
->step
))
1186 fprintf (file
, "[");
1188 print_generic_expr (dump_file
, iv
->base
, TDF_SLIM
);
1190 if (!integer_zerop (iv
->step
))
1192 fprintf (file
, ", + , ");
1193 print_generic_expr (dump_file
, iv
->step
, TDF_SLIM
);
1194 fprintf (file
, "]%s", iv
->no_overflow
? "(no_overflow)" : "");
1198 /* Determine the number of iterations according to condition (for staying
1199 inside loop) which compares two induction variables using comparison
1200 operator CODE. The induction variable on left side of the comparison
1201 is IV0, the right-hand side is IV1. Both induction variables must have
1202 type TYPE, which must be an integer or pointer type. The steps of the
1203 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
1205 LOOP is the loop whose number of iterations we are determining.
1207 ONLY_EXIT is true if we are sure this is the only way the loop could be
1208 exited (including possibly non-returning function calls, exceptions, etc.)
1209 -- in this case we can use the information whether the control induction
1210 variables can overflow or not in a more efficient way.
1212 The results (number of iterations and assumptions as described in
1213 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
1214 Returns false if it fails to determine number of iterations, true if it
1215 was determined (possibly with some assumptions). */
1218 number_of_iterations_cond (struct loop
*loop
,
1219 tree type
, affine_iv
*iv0
, enum tree_code code
,
1220 affine_iv
*iv1
, struct tree_niter_desc
*niter
,
1223 bool exit_must_be_taken
= false, ret
;
1226 /* The meaning of these assumptions is this:
1228 then the rest of information does not have to be valid
1229 if may_be_zero then the loop does not roll, even if
1231 niter
->assumptions
= boolean_true_node
;
1232 niter
->may_be_zero
= boolean_false_node
;
1233 niter
->niter
= NULL_TREE
;
1234 niter
->max
= double_int_zero
;
1236 niter
->bound
= NULL_TREE
;
1237 niter
->cmp
= ERROR_MARK
;
1239 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
1240 the control variable is on lhs. */
1241 if (code
== GE_EXPR
|| code
== GT_EXPR
1242 || (code
== NE_EXPR
&& integer_zerop (iv0
->step
)))
1245 code
= swap_tree_comparison (code
);
1248 if (POINTER_TYPE_P (type
))
1250 /* Comparison of pointers is undefined unless both iv0 and iv1 point
1251 to the same object. If they do, the control variable cannot wrap
1252 (as wrap around the bounds of memory will never return a pointer
1253 that would be guaranteed to point to the same object, even if we
1254 avoid undefined behavior by casting to size_t and back). */
1255 iv0
->no_overflow
= true;
1256 iv1
->no_overflow
= true;
1259 /* If the control induction variable does not overflow and the only exit
1260 from the loop is the one that we analyze, we know it must be taken
1264 if (!integer_zerop (iv0
->step
) && iv0
->no_overflow
)
1265 exit_must_be_taken
= true;
1266 else if (!integer_zerop (iv1
->step
) && iv1
->no_overflow
)
1267 exit_must_be_taken
= true;
1270 /* We can handle the case when neither of the sides of the comparison is
1271 invariant, provided that the test is NE_EXPR. This rarely occurs in
1272 practice, but it is simple enough to manage. */
1273 if (!integer_zerop (iv0
->step
) && !integer_zerop (iv1
->step
))
1275 tree step_type
= POINTER_TYPE_P (type
) ? sizetype
: type
;
1276 if (code
!= NE_EXPR
)
1279 iv0
->step
= fold_binary_to_constant (MINUS_EXPR
, step_type
,
1280 iv0
->step
, iv1
->step
);
1281 iv0
->no_overflow
= false;
1282 iv1
->step
= build_int_cst (step_type
, 0);
1283 iv1
->no_overflow
= true;
1286 /* If the result of the comparison is a constant, the loop is weird. More
1287 precise handling would be possible, but the situation is not common enough
1288 to waste time on it. */
1289 if (integer_zerop (iv0
->step
) && integer_zerop (iv1
->step
))
1292 /* Ignore loops of while (i-- < 10) type. */
1293 if (code
!= NE_EXPR
)
1295 if (iv0
->step
&& tree_int_cst_sign_bit (iv0
->step
))
1298 if (!integer_zerop (iv1
->step
) && !tree_int_cst_sign_bit (iv1
->step
))
1302 /* If the loop exits immediately, there is nothing to do. */
1303 if (integer_zerop (fold_build2 (code
, boolean_type_node
, iv0
->base
, iv1
->base
)))
1305 niter
->niter
= build_int_cst (unsigned_type_for (type
), 0);
1306 niter
->max
= double_int_zero
;
1310 /* OK, now we know we have a senseful loop. Handle several cases, depending
1311 on what comparison operator is used. */
1312 bound_difference (loop
, iv1
->base
, iv0
->base
, &bnds
);
1314 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1317 "Analyzing # of iterations of loop %d\n", loop
->num
);
1319 fprintf (dump_file
, " exit condition ");
1320 dump_affine_iv (dump_file
, iv0
);
1321 fprintf (dump_file
, " %s ",
1322 code
== NE_EXPR
? "!="
1323 : code
== LT_EXPR
? "<"
1325 dump_affine_iv (dump_file
, iv1
);
1326 fprintf (dump_file
, "\n");
1328 fprintf (dump_file
, " bounds on difference of bases: ");
1329 mpz_out_str (dump_file
, 10, bnds
.below
);
1330 fprintf (dump_file
, " ... ");
1331 mpz_out_str (dump_file
, 10, bnds
.up
);
1332 fprintf (dump_file
, "\n");
1338 gcc_assert (integer_zerop (iv1
->step
));
1339 ret
= number_of_iterations_ne (type
, iv0
, iv1
->base
, niter
,
1340 exit_must_be_taken
, &bnds
);
1344 ret
= number_of_iterations_lt (type
, iv0
, iv1
, niter
, exit_must_be_taken
,
1349 ret
= number_of_iterations_le (type
, iv0
, iv1
, niter
, exit_must_be_taken
,
1357 mpz_clear (bnds
.up
);
1358 mpz_clear (bnds
.below
);
1360 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1364 fprintf (dump_file
, " result:\n");
1365 if (!integer_nonzerop (niter
->assumptions
))
1367 fprintf (dump_file
, " under assumptions ");
1368 print_generic_expr (dump_file
, niter
->assumptions
, TDF_SLIM
);
1369 fprintf (dump_file
, "\n");
1372 if (!integer_zerop (niter
->may_be_zero
))
1374 fprintf (dump_file
, " zero if ");
1375 print_generic_expr (dump_file
, niter
->may_be_zero
, TDF_SLIM
);
1376 fprintf (dump_file
, "\n");
1379 fprintf (dump_file
, " # of iterations ");
1380 print_generic_expr (dump_file
, niter
->niter
, TDF_SLIM
);
1381 fprintf (dump_file
, ", bounded by ");
1382 dump_double_int (dump_file
, niter
->max
, true);
1383 fprintf (dump_file
, "\n");
1386 fprintf (dump_file
, " failed\n\n");
1391 /* Substitute NEW for OLD in EXPR and fold the result. */
1394 simplify_replace_tree (tree expr
, tree old
, tree new_tree
)
1397 tree ret
= NULL_TREE
, e
, se
;
1402 /* Do not bother to replace constants. */
1403 if (CONSTANT_CLASS_P (old
))
1407 || operand_equal_p (expr
, old
, 0))
1408 return unshare_expr (new_tree
);
1413 n
= TREE_OPERAND_LENGTH (expr
);
1414 for (i
= 0; i
< n
; i
++)
1416 e
= TREE_OPERAND (expr
, i
);
1417 se
= simplify_replace_tree (e
, old
, new_tree
);
1422 ret
= copy_node (expr
);
1424 TREE_OPERAND (ret
, i
) = se
;
1427 return (ret
? fold (ret
) : expr
);
1430 /* Expand definitions of ssa names in EXPR as long as they are simple
1431 enough, and return the new expression. */
1434 expand_simple_operations (tree expr
)
1437 tree ret
= NULL_TREE
, e
, ee
, e1
;
1438 enum tree_code code
;
1441 if (expr
== NULL_TREE
)
1444 if (is_gimple_min_invariant (expr
))
1447 code
= TREE_CODE (expr
);
1448 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code
)))
1450 n
= TREE_OPERAND_LENGTH (expr
);
1451 for (i
= 0; i
< n
; i
++)
1453 e
= TREE_OPERAND (expr
, i
);
1454 ee
= expand_simple_operations (e
);
1459 ret
= copy_node (expr
);
1461 TREE_OPERAND (ret
, i
) = ee
;
1467 fold_defer_overflow_warnings ();
1469 fold_undefer_and_ignore_overflow_warnings ();
1473 if (TREE_CODE (expr
) != SSA_NAME
)
1476 stmt
= SSA_NAME_DEF_STMT (expr
);
1477 if (gimple_code (stmt
) == GIMPLE_PHI
)
1479 basic_block src
, dest
;
1481 if (gimple_phi_num_args (stmt
) != 1)
1483 e
= PHI_ARG_DEF (stmt
, 0);
1485 /* Avoid propagating through loop exit phi nodes, which
1486 could break loop-closed SSA form restrictions. */
1487 dest
= gimple_bb (stmt
);
1488 src
= single_pred (dest
);
1489 if (TREE_CODE (e
) == SSA_NAME
1490 && src
->loop_father
!= dest
->loop_father
)
1493 return expand_simple_operations (e
);
1495 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
1498 e
= gimple_assign_rhs1 (stmt
);
1499 code
= gimple_assign_rhs_code (stmt
);
1500 if (get_gimple_rhs_class (code
) == GIMPLE_SINGLE_RHS
)
1502 if (is_gimple_min_invariant (e
))
1505 if (code
== SSA_NAME
)
1506 return expand_simple_operations (e
);
1514 /* Casts are simple. */
1515 ee
= expand_simple_operations (e
);
1516 return fold_build1 (code
, TREE_TYPE (expr
), ee
);
1520 case POINTER_PLUS_EXPR
:
1521 /* And increments and decrements by a constant are simple. */
1522 e1
= gimple_assign_rhs2 (stmt
);
1523 if (!is_gimple_min_invariant (e1
))
1526 ee
= expand_simple_operations (e
);
1527 return fold_build2 (code
, TREE_TYPE (expr
), ee
, e1
);
1534 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1535 expression (or EXPR unchanged, if no simplification was possible). */
1538 tree_simplify_using_condition_1 (tree cond
, tree expr
)
1541 tree e
, te
, e0
, e1
, e2
, notcond
;
1542 enum tree_code code
= TREE_CODE (expr
);
1544 if (code
== INTEGER_CST
)
1547 if (code
== TRUTH_OR_EXPR
1548 || code
== TRUTH_AND_EXPR
1549 || code
== COND_EXPR
)
1553 e0
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 0));
1554 if (TREE_OPERAND (expr
, 0) != e0
)
1557 e1
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 1));
1558 if (TREE_OPERAND (expr
, 1) != e1
)
1561 if (code
== COND_EXPR
)
1563 e2
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 2));
1564 if (TREE_OPERAND (expr
, 2) != e2
)
1572 if (code
== COND_EXPR
)
1573 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
1575 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
1581 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
1582 propagation, and vice versa. Fold does not handle this, since it is
1583 considered too expensive. */
1584 if (TREE_CODE (cond
) == EQ_EXPR
)
1586 e0
= TREE_OPERAND (cond
, 0);
1587 e1
= TREE_OPERAND (cond
, 1);
1589 /* We know that e0 == e1. Check whether we cannot simplify expr
1591 e
= simplify_replace_tree (expr
, e0
, e1
);
1592 if (integer_zerop (e
) || integer_nonzerop (e
))
1595 e
= simplify_replace_tree (expr
, e1
, e0
);
1596 if (integer_zerop (e
) || integer_nonzerop (e
))
1599 if (TREE_CODE (expr
) == EQ_EXPR
)
1601 e0
= TREE_OPERAND (expr
, 0);
1602 e1
= TREE_OPERAND (expr
, 1);
1604 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
1605 e
= simplify_replace_tree (cond
, e0
, e1
);
1606 if (integer_zerop (e
))
1608 e
= simplify_replace_tree (cond
, e1
, e0
);
1609 if (integer_zerop (e
))
1612 if (TREE_CODE (expr
) == NE_EXPR
)
1614 e0
= TREE_OPERAND (expr
, 0);
1615 e1
= TREE_OPERAND (expr
, 1);
1617 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
1618 e
= simplify_replace_tree (cond
, e0
, e1
);
1619 if (integer_zerop (e
))
1620 return boolean_true_node
;
1621 e
= simplify_replace_tree (cond
, e1
, e0
);
1622 if (integer_zerop (e
))
1623 return boolean_true_node
;
1626 te
= expand_simple_operations (expr
);
1628 /* Check whether COND ==> EXPR. */
1629 notcond
= invert_truthvalue (cond
);
1630 e
= fold_binary (TRUTH_OR_EXPR
, boolean_type_node
, notcond
, te
);
1631 if (e
&& integer_nonzerop (e
))
1634 /* Check whether COND ==> not EXPR. */
1635 e
= fold_binary (TRUTH_AND_EXPR
, boolean_type_node
, cond
, te
);
1636 if (e
&& integer_zerop (e
))
1642 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1643 expression (or EXPR unchanged, if no simplification was possible).
1644 Wrapper around tree_simplify_using_condition_1 that ensures that chains
1645 of simple operations in definitions of ssa names in COND are expanded,
1646 so that things like casts or incrementing the value of the bound before
1647 the loop do not cause us to fail. */
1650 tree_simplify_using_condition (tree cond
, tree expr
)
1652 cond
= expand_simple_operations (cond
);
1654 return tree_simplify_using_condition_1 (cond
, expr
);
1657 /* Tries to simplify EXPR using the conditions on entry to LOOP.
1658 Returns the simplified expression (or EXPR unchanged, if no
1659 simplification was possible).*/
1662 simplify_using_initial_conditions (struct loop
*loop
, tree expr
)
1670 if (TREE_CODE (expr
) == INTEGER_CST
)
1673 /* Limit walking the dominators to avoid quadraticness in
1674 the number of BBs times the number of loops in degenerate
1676 for (bb
= loop
->header
;
1677 bb
!= ENTRY_BLOCK_PTR
&& cnt
< MAX_DOMINATORS_TO_WALK
;
1678 bb
= get_immediate_dominator (CDI_DOMINATORS
, bb
))
1680 if (!single_pred_p (bb
))
1682 e
= single_pred_edge (bb
);
1684 if (!(e
->flags
& (EDGE_TRUE_VALUE
| EDGE_FALSE_VALUE
)))
1687 stmt
= last_stmt (e
->src
);
1688 cond
= fold_build2 (gimple_cond_code (stmt
),
1690 gimple_cond_lhs (stmt
),
1691 gimple_cond_rhs (stmt
));
1692 if (e
->flags
& EDGE_FALSE_VALUE
)
1693 cond
= invert_truthvalue (cond
);
1694 expr
= tree_simplify_using_condition (cond
, expr
);
1701 /* Tries to simplify EXPR using the evolutions of the loop invariants
1702 in the superloops of LOOP. Returns the simplified expression
1703 (or EXPR unchanged, if no simplification was possible). */
1706 simplify_using_outer_evolutions (struct loop
*loop
, tree expr
)
1708 enum tree_code code
= TREE_CODE (expr
);
1712 if (is_gimple_min_invariant (expr
))
1715 if (code
== TRUTH_OR_EXPR
1716 || code
== TRUTH_AND_EXPR
1717 || code
== COND_EXPR
)
1721 e0
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 0));
1722 if (TREE_OPERAND (expr
, 0) != e0
)
1725 e1
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 1));
1726 if (TREE_OPERAND (expr
, 1) != e1
)
1729 if (code
== COND_EXPR
)
1731 e2
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 2));
1732 if (TREE_OPERAND (expr
, 2) != e2
)
1740 if (code
== COND_EXPR
)
1741 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
1743 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
1749 e
= instantiate_parameters (loop
, expr
);
1750 if (is_gimple_min_invariant (e
))
1756 /* Returns true if EXIT is the only possible exit from LOOP. */
1759 loop_only_exit_p (const struct loop
*loop
, const_edge exit
)
1762 gimple_stmt_iterator bsi
;
1766 if (exit
!= single_exit (loop
))
1769 body
= get_loop_body (loop
);
1770 for (i
= 0; i
< loop
->num_nodes
; i
++)
1772 for (bsi
= gsi_start_bb (body
[i
]); !gsi_end_p (bsi
); gsi_next (&bsi
))
1774 call
= gsi_stmt (bsi
);
1775 if (gimple_code (call
) != GIMPLE_CALL
)
1778 if (gimple_has_side_effects (call
))
1790 /* Stores description of number of iterations of LOOP derived from
1791 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1792 useful information could be derived (and fields of NITER has
1793 meaning described in comments at struct tree_niter_desc
1794 declaration), false otherwise. If WARN is true and
1795 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1796 potentially unsafe assumptions. */
1799 number_of_iterations_exit (struct loop
*loop
, edge exit
,
1800 struct tree_niter_desc
*niter
,
1806 enum tree_code code
;
1809 if (!dominated_by_p (CDI_DOMINATORS
, loop
->latch
, exit
->src
))
1812 niter
->assumptions
= boolean_false_node
;
1813 stmt
= last_stmt (exit
->src
);
1814 if (!stmt
|| gimple_code (stmt
) != GIMPLE_COND
)
1817 /* We want the condition for staying inside loop. */
1818 code
= gimple_cond_code (stmt
);
1819 if (exit
->flags
& EDGE_TRUE_VALUE
)
1820 code
= invert_tree_comparison (code
, false);
1835 op0
= gimple_cond_lhs (stmt
);
1836 op1
= gimple_cond_rhs (stmt
);
1837 type
= TREE_TYPE (op0
);
1839 if (TREE_CODE (type
) != INTEGER_TYPE
1840 && !POINTER_TYPE_P (type
))
1843 if (!simple_iv (loop
, loop_containing_stmt (stmt
), op0
, &iv0
, false))
1845 if (!simple_iv (loop
, loop_containing_stmt (stmt
), op1
, &iv1
, false))
1848 /* We don't want to see undefined signed overflow warnings while
1849 computing the number of iterations. */
1850 fold_defer_overflow_warnings ();
1852 iv0
.base
= expand_simple_operations (iv0
.base
);
1853 iv1
.base
= expand_simple_operations (iv1
.base
);
1854 if (!number_of_iterations_cond (loop
, type
, &iv0
, code
, &iv1
, niter
,
1855 loop_only_exit_p (loop
, exit
)))
1857 fold_undefer_and_ignore_overflow_warnings ();
1863 niter
->assumptions
= simplify_using_outer_evolutions (loop
,
1864 niter
->assumptions
);
1865 niter
->may_be_zero
= simplify_using_outer_evolutions (loop
,
1866 niter
->may_be_zero
);
1867 niter
->niter
= simplify_using_outer_evolutions (loop
, niter
->niter
);
1871 = simplify_using_initial_conditions (loop
,
1872 niter
->assumptions
);
1874 = simplify_using_initial_conditions (loop
,
1875 niter
->may_be_zero
);
1877 fold_undefer_and_ignore_overflow_warnings ();
1879 if (integer_onep (niter
->assumptions
))
1882 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1883 But if we can prove that there is overflow or some other source of weird
1884 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1885 if (integer_zerop (niter
->assumptions
) || !single_exit (loop
))
1888 if (flag_unsafe_loop_optimizations
)
1889 niter
->assumptions
= boolean_true_node
;
1893 const char *wording
;
1894 location_t loc
= gimple_location (stmt
);
1896 /* We can provide a more specific warning if one of the operator is
1897 constant and the other advances by +1 or -1. */
1898 if (!integer_zerop (iv1
.step
)
1899 ? (integer_zerop (iv0
.step
)
1900 && (integer_onep (iv1
.step
) || integer_all_onesp (iv1
.step
)))
1901 : (integer_onep (iv0
.step
) || integer_all_onesp (iv0
.step
)))
1903 flag_unsafe_loop_optimizations
1904 ? N_("assuming that the loop is not infinite")
1905 : N_("cannot optimize possibly infinite loops");
1908 flag_unsafe_loop_optimizations
1909 ? N_("assuming that the loop counter does not overflow")
1910 : N_("cannot optimize loop, the loop counter may overflow");
1912 warning_at ((LOCATION_LINE (loc
) > 0) ? loc
: input_location
,
1913 OPT_Wunsafe_loop_optimizations
, "%s", gettext (wording
));
1916 return flag_unsafe_loop_optimizations
;
1919 /* Try to determine the number of iterations of LOOP. If we succeed,
1920 expression giving number of iterations is returned and *EXIT is
1921 set to the edge from that the information is obtained. Otherwise
1922 chrec_dont_know is returned. */
1925 find_loop_niter (struct loop
*loop
, edge
*exit
)
1928 VEC (edge
, heap
) *exits
= get_loop_exit_edges (loop
);
1930 tree niter
= NULL_TREE
, aniter
;
1931 struct tree_niter_desc desc
;
1934 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
1936 if (!just_once_each_iteration_p (loop
, ex
->src
))
1939 if (!number_of_iterations_exit (loop
, ex
, &desc
, false))
1942 if (integer_nonzerop (desc
.may_be_zero
))
1944 /* We exit in the first iteration through this exit.
1945 We won't find anything better. */
1946 niter
= build_int_cst (unsigned_type_node
, 0);
1951 if (!integer_zerop (desc
.may_be_zero
))
1954 aniter
= desc
.niter
;
1958 /* Nothing recorded yet. */
1964 /* Prefer constants, the lower the better. */
1965 if (TREE_CODE (aniter
) != INTEGER_CST
)
1968 if (TREE_CODE (niter
) != INTEGER_CST
)
1975 if (tree_int_cst_lt (aniter
, niter
))
1982 VEC_free (edge
, heap
, exits
);
1984 return niter
? niter
: chrec_dont_know
;
1987 /* Return true if loop is known to have bounded number of iterations. */
1990 finite_loop_p (struct loop
*loop
)
1993 VEC (edge
, heap
) *exits
;
1995 struct tree_niter_desc desc
;
1996 bool finite
= false;
1999 if (flag_unsafe_loop_optimizations
)
2001 flags
= flags_from_decl_or_type (current_function_decl
);
2002 if ((flags
& (ECF_CONST
|ECF_PURE
)) && !(flags
& ECF_LOOPING_CONST_OR_PURE
))
2004 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2005 fprintf (dump_file
, "Found loop %i to be finite: it is within pure or const function.\n",
2010 exits
= get_loop_exit_edges (loop
);
2011 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
2013 if (!just_once_each_iteration_p (loop
, ex
->src
))
2016 if (number_of_iterations_exit (loop
, ex
, &desc
, false))
2018 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2020 fprintf (dump_file
, "Found loop %i to be finite: iterating ", loop
->num
);
2021 print_generic_expr (dump_file
, desc
.niter
, TDF_SLIM
);
2022 fprintf (dump_file
, " times\n");
2028 VEC_free (edge
, heap
, exits
);
2034 Analysis of a number of iterations of a loop by a brute-force evaluation.
2038 /* Bound on the number of iterations we try to evaluate. */
2040 #define MAX_ITERATIONS_TO_TRACK \
2041 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
2043 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
2044 result by a chain of operations such that all but exactly one of their
2045 operands are constants. */
2048 chain_of_csts_start (struct loop
*loop
, tree x
)
2050 gimple stmt
= SSA_NAME_DEF_STMT (x
);
2052 basic_block bb
= gimple_bb (stmt
);
2053 enum tree_code code
;
2056 || !flow_bb_inside_loop_p (loop
, bb
))
2059 if (gimple_code (stmt
) == GIMPLE_PHI
)
2061 if (bb
== loop
->header
)
2067 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
2070 code
= gimple_assign_rhs_code (stmt
);
2071 if (gimple_references_memory_p (stmt
)
2072 || TREE_CODE_CLASS (code
) == tcc_reference
2073 || (code
== ADDR_EXPR
2074 && !is_gimple_min_invariant (gimple_assign_rhs1 (stmt
))))
2077 use
= SINGLE_SSA_TREE_OPERAND (stmt
, SSA_OP_USE
);
2078 if (use
== NULL_TREE
)
2081 return chain_of_csts_start (loop
, use
);
2084 /* Determines whether the expression X is derived from a result of a phi node
2085 in header of LOOP such that
2087 * the derivation of X consists only from operations with constants
2088 * the initial value of the phi node is constant
2089 * the value of the phi node in the next iteration can be derived from the
2090 value in the current iteration by a chain of operations with constants.
2092 If such phi node exists, it is returned, otherwise NULL is returned. */
2095 get_base_for (struct loop
*loop
, tree x
)
2100 if (is_gimple_min_invariant (x
))
2103 phi
= chain_of_csts_start (loop
, x
);
2107 init
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
2108 next
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
2110 if (TREE_CODE (next
) != SSA_NAME
)
2113 if (!is_gimple_min_invariant (init
))
2116 if (chain_of_csts_start (loop
, next
) != phi
)
2122 /* Given an expression X, then
2124 * if X is NULL_TREE, we return the constant BASE.
2125 * otherwise X is a SSA name, whose value in the considered loop is derived
2126 by a chain of operations with constant from a result of a phi node in
2127 the header of the loop. Then we return value of X when the value of the
2128 result of this phi node is given by the constant BASE. */
2131 get_val_for (tree x
, tree base
)
2135 gcc_assert (is_gimple_min_invariant (base
));
2140 stmt
= SSA_NAME_DEF_STMT (x
);
2141 if (gimple_code (stmt
) == GIMPLE_PHI
)
2144 gcc_assert (is_gimple_assign (stmt
));
2146 /* STMT must be either an assignment of a single SSA name or an
2147 expression involving an SSA name and a constant. Try to fold that
2148 expression using the value for the SSA name. */
2149 if (gimple_assign_ssa_name_copy_p (stmt
))
2150 return get_val_for (gimple_assign_rhs1 (stmt
), base
);
2151 else if (gimple_assign_rhs_class (stmt
) == GIMPLE_UNARY_RHS
2152 && TREE_CODE (gimple_assign_rhs1 (stmt
)) == SSA_NAME
)
2154 return fold_build1 (gimple_assign_rhs_code (stmt
),
2155 gimple_expr_type (stmt
),
2156 get_val_for (gimple_assign_rhs1 (stmt
), base
));
2158 else if (gimple_assign_rhs_class (stmt
) == GIMPLE_BINARY_RHS
)
2160 tree rhs1
= gimple_assign_rhs1 (stmt
);
2161 tree rhs2
= gimple_assign_rhs2 (stmt
);
2162 if (TREE_CODE (rhs1
) == SSA_NAME
)
2163 rhs1
= get_val_for (rhs1
, base
);
2164 else if (TREE_CODE (rhs2
) == SSA_NAME
)
2165 rhs2
= get_val_for (rhs2
, base
);
2168 return fold_build2 (gimple_assign_rhs_code (stmt
),
2169 gimple_expr_type (stmt
), rhs1
, rhs2
);
2176 /* Tries to count the number of iterations of LOOP till it exits by EXIT
2177 by brute force -- i.e. by determining the value of the operands of the
2178 condition at EXIT in first few iterations of the loop (assuming that
2179 these values are constant) and determining the first one in that the
2180 condition is not satisfied. Returns the constant giving the number
2181 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
2184 loop_niter_by_eval (struct loop
*loop
, edge exit
)
2187 tree op
[2], val
[2], next
[2], aval
[2];
2192 cond
= last_stmt (exit
->src
);
2193 if (!cond
|| gimple_code (cond
) != GIMPLE_COND
)
2194 return chrec_dont_know
;
2196 cmp
= gimple_cond_code (cond
);
2197 if (exit
->flags
& EDGE_TRUE_VALUE
)
2198 cmp
= invert_tree_comparison (cmp
, false);
2208 op
[0] = gimple_cond_lhs (cond
);
2209 op
[1] = gimple_cond_rhs (cond
);
2213 return chrec_dont_know
;
2216 for (j
= 0; j
< 2; j
++)
2218 if (is_gimple_min_invariant (op
[j
]))
2221 next
[j
] = NULL_TREE
;
2226 phi
= get_base_for (loop
, op
[j
]);
2228 return chrec_dont_know
;
2229 val
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
2230 next
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
2234 /* Don't issue signed overflow warnings. */
2235 fold_defer_overflow_warnings ();
2237 for (i
= 0; i
< MAX_ITERATIONS_TO_TRACK
; i
++)
2239 for (j
= 0; j
< 2; j
++)
2240 aval
[j
] = get_val_for (op
[j
], val
[j
]);
2242 acnd
= fold_binary (cmp
, boolean_type_node
, aval
[0], aval
[1]);
2243 if (acnd
&& integer_zerop (acnd
))
2245 fold_undefer_and_ignore_overflow_warnings ();
2246 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2248 "Proved that loop %d iterates %d times using brute force.\n",
2250 return build_int_cst (unsigned_type_node
, i
);
2253 for (j
= 0; j
< 2; j
++)
2255 val
[j
] = get_val_for (next
[j
], val
[j
]);
2256 if (!is_gimple_min_invariant (val
[j
]))
2258 fold_undefer_and_ignore_overflow_warnings ();
2259 return chrec_dont_know
;
2264 fold_undefer_and_ignore_overflow_warnings ();
2266 return chrec_dont_know
;
2269 /* Finds the exit of the LOOP by that the loop exits after a constant
2270 number of iterations and stores the exit edge to *EXIT. The constant
2271 giving the number of iterations of LOOP is returned. The number of
2272 iterations is determined using loop_niter_by_eval (i.e. by brute force
2273 evaluation). If we are unable to find the exit for that loop_niter_by_eval
2274 determines the number of iterations, chrec_dont_know is returned. */
2277 find_loop_niter_by_eval (struct loop
*loop
, edge
*exit
)
2280 VEC (edge
, heap
) *exits
= get_loop_exit_edges (loop
);
2282 tree niter
= NULL_TREE
, aniter
;
2286 /* Loops with multiple exits are expensive to handle and less important. */
2287 if (!flag_expensive_optimizations
2288 && VEC_length (edge
, exits
) > 1)
2290 VEC_free (edge
, heap
, exits
);
2291 return chrec_dont_know
;
2294 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
2296 if (!just_once_each_iteration_p (loop
, ex
->src
))
2299 aniter
= loop_niter_by_eval (loop
, ex
);
2300 if (chrec_contains_undetermined (aniter
))
2304 && !tree_int_cst_lt (aniter
, niter
))
2310 VEC_free (edge
, heap
, exits
);
2312 return niter
? niter
: chrec_dont_know
;
2317 Analysis of upper bounds on number of iterations of a loop.
2321 static double_int
derive_constant_upper_bound_ops (tree
, tree
,
2322 enum tree_code
, tree
);
2324 /* Returns a constant upper bound on the value of the right-hand side of
2325 an assignment statement STMT. */
2328 derive_constant_upper_bound_assign (gimple stmt
)
2330 enum tree_code code
= gimple_assign_rhs_code (stmt
);
2331 tree op0
= gimple_assign_rhs1 (stmt
);
2332 tree op1
= gimple_assign_rhs2 (stmt
);
2334 return derive_constant_upper_bound_ops (TREE_TYPE (gimple_assign_lhs (stmt
)),
2338 /* Returns a constant upper bound on the value of expression VAL. VAL
2339 is considered to be unsigned. If its type is signed, its value must
2343 derive_constant_upper_bound (tree val
)
2345 enum tree_code code
;
2348 extract_ops_from_tree (val
, &code
, &op0
, &op1
);
2349 return derive_constant_upper_bound_ops (TREE_TYPE (val
), op0
, code
, op1
);
2352 /* Returns a constant upper bound on the value of expression OP0 CODE OP1,
2353 whose type is TYPE. The expression is considered to be unsigned. If
2354 its type is signed, its value must be nonnegative. */
2357 derive_constant_upper_bound_ops (tree type
, tree op0
,
2358 enum tree_code code
, tree op1
)
2361 double_int bnd
, max
, mmax
, cst
;
2364 if (INTEGRAL_TYPE_P (type
))
2365 maxt
= TYPE_MAX_VALUE (type
);
2367 maxt
= upper_bound_in_type (type
, type
);
2369 max
= tree_to_double_int (maxt
);
2374 return tree_to_double_int (op0
);
2377 subtype
= TREE_TYPE (op0
);
2378 if (!TYPE_UNSIGNED (subtype
)
2379 /* If TYPE is also signed, the fact that VAL is nonnegative implies
2380 that OP0 is nonnegative. */
2381 && TYPE_UNSIGNED (type
)
2382 && !tree_expr_nonnegative_p (op0
))
2384 /* If we cannot prove that the casted expression is nonnegative,
2385 we cannot establish more useful upper bound than the precision
2386 of the type gives us. */
2390 /* We now know that op0 is an nonnegative value. Try deriving an upper
2392 bnd
= derive_constant_upper_bound (op0
);
2394 /* If the bound does not fit in TYPE, max. value of TYPE could be
2402 case POINTER_PLUS_EXPR
:
2404 if (TREE_CODE (op1
) != INTEGER_CST
2405 || !tree_expr_nonnegative_p (op0
))
2408 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
2409 choose the most logical way how to treat this constant regardless
2410 of the signedness of the type. */
2411 cst
= tree_to_double_int (op1
);
2412 cst
= cst
.sext (TYPE_PRECISION (type
));
2413 if (code
!= MINUS_EXPR
)
2416 bnd
= derive_constant_upper_bound (op0
);
2418 if (cst
.is_negative ())
2421 /* Avoid CST == 0x80000... */
2422 if (cst
.is_negative ())
2425 /* OP0 + CST. We need to check that
2426 BND <= MAX (type) - CST. */
2436 /* OP0 - CST, where CST >= 0.
2438 If TYPE is signed, we have already verified that OP0 >= 0, and we
2439 know that the result is nonnegative. This implies that
2442 If TYPE is unsigned, we must additionally know that OP0 >= CST,
2443 otherwise the operation underflows.
2446 /* This should only happen if the type is unsigned; however, for
2447 buggy programs that use overflowing signed arithmetics even with
2448 -fno-wrapv, this condition may also be true for signed values. */
2452 if (TYPE_UNSIGNED (type
))
2454 tree tem
= fold_binary (GE_EXPR
, boolean_type_node
, op0
,
2455 double_int_to_tree (type
, cst
));
2456 if (!tem
|| integer_nonzerop (tem
))
2465 case FLOOR_DIV_EXPR
:
2466 case EXACT_DIV_EXPR
:
2467 if (TREE_CODE (op1
) != INTEGER_CST
2468 || tree_int_cst_sign_bit (op1
))
2471 bnd
= derive_constant_upper_bound (op0
);
2472 return bnd
.udiv (tree_to_double_int (op1
), FLOOR_DIV_EXPR
);
2475 if (TREE_CODE (op1
) != INTEGER_CST
2476 || tree_int_cst_sign_bit (op1
))
2478 return tree_to_double_int (op1
);
2481 stmt
= SSA_NAME_DEF_STMT (op0
);
2482 if (gimple_code (stmt
) != GIMPLE_ASSIGN
2483 || gimple_assign_lhs (stmt
) != op0
)
2485 return derive_constant_upper_bound_assign (stmt
);
2492 /* Records that every statement in LOOP is executed I_BOUND times.
2493 REALISTIC is true if I_BOUND is expected to be close to the real number
2494 of iterations. UPPER is true if we are sure the loop iterates at most
2498 record_niter_bound (struct loop
*loop
, double_int i_bound
, bool realistic
,
2501 /* Update the bounds only when there is no previous estimation, or when the
2502 current estimation is smaller. */
2504 && (!loop
->any_upper_bound
2505 || i_bound
.ult (loop
->nb_iterations_upper_bound
)))
2507 loop
->any_upper_bound
= true;
2508 loop
->nb_iterations_upper_bound
= i_bound
;
2511 && (!loop
->any_estimate
2512 || i_bound
.ult (loop
->nb_iterations_estimate
)))
2514 loop
->any_estimate
= true;
2515 loop
->nb_iterations_estimate
= i_bound
;
2518 /* If an upper bound is smaller than the realistic estimate of the
2519 number of iterations, use the upper bound instead. */
2520 if (loop
->any_upper_bound
2521 && loop
->any_estimate
2522 && loop
->nb_iterations_upper_bound
.ult (loop
->nb_iterations_estimate
))
2523 loop
->nb_iterations_estimate
= loop
->nb_iterations_upper_bound
;
2526 /* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. IS_EXIT
2527 is true if the loop is exited immediately after STMT, and this exit
2528 is taken at last when the STMT is executed BOUND + 1 times.
2529 REALISTIC is true if BOUND is expected to be close to the real number
2530 of iterations. UPPER is true if we are sure the loop iterates at most
2531 BOUND times. I_BOUND is an unsigned double_int upper estimate on BOUND. */
2534 record_estimate (struct loop
*loop
, tree bound
, double_int i_bound
,
2535 gimple at_stmt
, bool is_exit
, bool realistic
, bool upper
)
2540 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2542 fprintf (dump_file
, "Statement %s", is_exit
? "(exit)" : "");
2543 print_gimple_stmt (dump_file
, at_stmt
, 0, TDF_SLIM
);
2544 fprintf (dump_file
, " is %sexecuted at most ",
2545 upper
? "" : "probably ");
2546 print_generic_expr (dump_file
, bound
, TDF_SLIM
);
2547 fprintf (dump_file
, " (bounded by ");
2548 dump_double_int (dump_file
, i_bound
, true);
2549 fprintf (dump_file
, ") + 1 times in loop %d.\n", loop
->num
);
2552 /* If the I_BOUND is just an estimate of BOUND, it rarely is close to the
2553 real number of iterations. */
2554 if (TREE_CODE (bound
) != INTEGER_CST
)
2556 if (!upper
&& !realistic
)
2559 /* If we have a guaranteed upper bound, record it in the appropriate
2563 struct nb_iter_bound
*elt
= ggc_alloc_nb_iter_bound ();
2565 elt
->bound
= i_bound
;
2566 elt
->stmt
= at_stmt
;
2567 elt
->is_exit
= is_exit
;
2568 elt
->next
= loop
->bounds
;
2572 /* Update the number of iteration estimates according to the bound.
2573 If at_stmt is an exit or dominates the single exit from the loop,
2574 then the loop latch is executed at most BOUND times, otherwise
2575 it can be executed BOUND + 1 times. */
2576 exit
= single_exit (loop
);
2579 && dominated_by_p (CDI_DOMINATORS
,
2580 exit
->src
, gimple_bb (at_stmt
))))
2581 delta
= double_int_zero
;
2583 delta
= double_int_one
;
2586 /* If an overflow occurred, ignore the result. */
2587 if (i_bound
.ult (delta
))
2590 record_niter_bound (loop
, i_bound
, realistic
, upper
);
2593 /* Record the estimate on number of iterations of LOOP based on the fact that
2594 the induction variable BASE + STEP * i evaluated in STMT does not wrap and
2595 its values belong to the range <LOW, HIGH>. REALISTIC is true if the
2596 estimated number of iterations is expected to be close to the real one.
2597 UPPER is true if we are sure the induction variable does not wrap. */
2600 record_nonwrapping_iv (struct loop
*loop
, tree base
, tree step
, gimple stmt
,
2601 tree low
, tree high
, bool realistic
, bool upper
)
2603 tree niter_bound
, extreme
, delta
;
2604 tree type
= TREE_TYPE (base
), unsigned_type
;
2607 if (TREE_CODE (step
) != INTEGER_CST
|| integer_zerop (step
))
2610 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2612 fprintf (dump_file
, "Induction variable (");
2613 print_generic_expr (dump_file
, TREE_TYPE (base
), TDF_SLIM
);
2614 fprintf (dump_file
, ") ");
2615 print_generic_expr (dump_file
, base
, TDF_SLIM
);
2616 fprintf (dump_file
, " + ");
2617 print_generic_expr (dump_file
, step
, TDF_SLIM
);
2618 fprintf (dump_file
, " * iteration does not wrap in statement ");
2619 print_gimple_stmt (dump_file
, stmt
, 0, TDF_SLIM
);
2620 fprintf (dump_file
, " in loop %d.\n", loop
->num
);
2623 unsigned_type
= unsigned_type_for (type
);
2624 base
= fold_convert (unsigned_type
, base
);
2625 step
= fold_convert (unsigned_type
, step
);
2627 if (tree_int_cst_sign_bit (step
))
2629 extreme
= fold_convert (unsigned_type
, low
);
2630 if (TREE_CODE (base
) != INTEGER_CST
)
2631 base
= fold_convert (unsigned_type
, high
);
2632 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
2633 step
= fold_build1 (NEGATE_EXPR
, unsigned_type
, step
);
2637 extreme
= fold_convert (unsigned_type
, high
);
2638 if (TREE_CODE (base
) != INTEGER_CST
)
2639 base
= fold_convert (unsigned_type
, low
);
2640 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
2643 /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
2644 would get out of the range. */
2645 niter_bound
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step
);
2646 max
= derive_constant_upper_bound (niter_bound
);
2647 record_estimate (loop
, niter_bound
, max
, stmt
, false, realistic
, upper
);
2650 /* Determine information about number of iterations a LOOP from the index
2651 IDX of a data reference accessed in STMT. RELIABLE is true if STMT is
2652 guaranteed to be executed in every iteration of LOOP. Callback for
2663 idx_infer_loop_bounds (tree base
, tree
*idx
, void *dta
)
2665 struct ilb_data
*data
= (struct ilb_data
*) dta
;
2666 tree ev
, init
, step
;
2667 tree low
, high
, type
, next
;
2668 bool sign
, upper
= data
->reliable
, at_end
= false;
2669 struct loop
*loop
= data
->loop
;
2671 if (TREE_CODE (base
) != ARRAY_REF
)
2674 /* For arrays at the end of the structure, we are not guaranteed that they
2675 do not really extend over their declared size. However, for arrays of
2676 size greater than one, this is unlikely to be intended. */
2677 if (array_at_struct_end_p (base
))
2683 ev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, *idx
));
2684 init
= initial_condition (ev
);
2685 step
= evolution_part_in_loop_num (ev
, loop
->num
);
2689 || TREE_CODE (step
) != INTEGER_CST
2690 || integer_zerop (step
)
2691 || tree_contains_chrecs (init
, NULL
)
2692 || chrec_contains_symbols_defined_in_loop (init
, loop
->num
))
2695 low
= array_ref_low_bound (base
);
2696 high
= array_ref_up_bound (base
);
2698 /* The case of nonconstant bounds could be handled, but it would be
2700 if (TREE_CODE (low
) != INTEGER_CST
2702 || TREE_CODE (high
) != INTEGER_CST
)
2704 sign
= tree_int_cst_sign_bit (step
);
2705 type
= TREE_TYPE (step
);
2707 /* The array of length 1 at the end of a structure most likely extends
2708 beyond its bounds. */
2710 && operand_equal_p (low
, high
, 0))
2713 /* In case the relevant bound of the array does not fit in type, or
2714 it does, but bound + step (in type) still belongs into the range of the
2715 array, the index may wrap and still stay within the range of the array
2716 (consider e.g. if the array is indexed by the full range of
2719 To make things simpler, we require both bounds to fit into type, although
2720 there are cases where this would not be strictly necessary. */
2721 if (!int_fits_type_p (high
, type
)
2722 || !int_fits_type_p (low
, type
))
2724 low
= fold_convert (type
, low
);
2725 high
= fold_convert (type
, high
);
2728 next
= fold_binary (PLUS_EXPR
, type
, low
, step
);
2730 next
= fold_binary (PLUS_EXPR
, type
, high
, step
);
2732 if (tree_int_cst_compare (low
, next
) <= 0
2733 && tree_int_cst_compare (next
, high
) <= 0)
2736 record_nonwrapping_iv (loop
, init
, step
, data
->stmt
, low
, high
, true, upper
);
2740 /* Determine information about number of iterations a LOOP from the bounds
2741 of arrays in the data reference REF accessed in STMT. RELIABLE is true if
2742 STMT is guaranteed to be executed in every iteration of LOOP.*/
2745 infer_loop_bounds_from_ref (struct loop
*loop
, gimple stmt
, tree ref
,
2748 struct ilb_data data
;
2752 data
.reliable
= reliable
;
2753 for_each_index (&ref
, idx_infer_loop_bounds
, &data
);
2756 /* Determine information about number of iterations of a LOOP from the way
2757 arrays are used in STMT. RELIABLE is true if STMT is guaranteed to be
2758 executed in every iteration of LOOP. */
2761 infer_loop_bounds_from_array (struct loop
*loop
, gimple stmt
, bool reliable
)
2763 if (is_gimple_assign (stmt
))
2765 tree op0
= gimple_assign_lhs (stmt
);
2766 tree op1
= gimple_assign_rhs1 (stmt
);
2768 /* For each memory access, analyze its access function
2769 and record a bound on the loop iteration domain. */
2770 if (REFERENCE_CLASS_P (op0
))
2771 infer_loop_bounds_from_ref (loop
, stmt
, op0
, reliable
);
2773 if (REFERENCE_CLASS_P (op1
))
2774 infer_loop_bounds_from_ref (loop
, stmt
, op1
, reliable
);
2776 else if (is_gimple_call (stmt
))
2779 unsigned i
, n
= gimple_call_num_args (stmt
);
2781 lhs
= gimple_call_lhs (stmt
);
2782 if (lhs
&& REFERENCE_CLASS_P (lhs
))
2783 infer_loop_bounds_from_ref (loop
, stmt
, lhs
, reliable
);
2785 for (i
= 0; i
< n
; i
++)
2787 arg
= gimple_call_arg (stmt
, i
);
2788 if (REFERENCE_CLASS_P (arg
))
2789 infer_loop_bounds_from_ref (loop
, stmt
, arg
, reliable
);
2794 /* Determine information about number of iterations of a LOOP from the fact
2795 that pointer arithmetics in STMT does not overflow. */
2798 infer_loop_bounds_from_pointer_arith (struct loop
*loop
, gimple stmt
)
2800 tree def
, base
, step
, scev
, type
, low
, high
;
2803 if (!is_gimple_assign (stmt
)
2804 || gimple_assign_rhs_code (stmt
) != POINTER_PLUS_EXPR
)
2807 def
= gimple_assign_lhs (stmt
);
2808 if (TREE_CODE (def
) != SSA_NAME
)
2811 type
= TREE_TYPE (def
);
2812 if (!nowrap_type_p (type
))
2815 ptr
= gimple_assign_rhs1 (stmt
);
2816 if (!expr_invariant_in_loop_p (loop
, ptr
))
2819 var
= gimple_assign_rhs2 (stmt
);
2820 if (TYPE_PRECISION (type
) != TYPE_PRECISION (TREE_TYPE (var
)))
2823 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
2824 if (chrec_contains_undetermined (scev
))
2827 base
= initial_condition_in_loop_num (scev
, loop
->num
);
2828 step
= evolution_part_in_loop_num (scev
, loop
->num
);
2831 || TREE_CODE (step
) != INTEGER_CST
2832 || tree_contains_chrecs (base
, NULL
)
2833 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
2836 low
= lower_bound_in_type (type
, type
);
2837 high
= upper_bound_in_type (type
, type
);
2839 /* In C, pointer arithmetic p + 1 cannot use a NULL pointer, and p - 1 cannot
2840 produce a NULL pointer. The contrary would mean NULL points to an object,
2841 while NULL is supposed to compare unequal with the address of all objects.
2842 Furthermore, p + 1 cannot produce a NULL pointer and p - 1 cannot use a
2843 NULL pointer since that would mean wrapping, which we assume here not to
2844 happen. So, we can exclude NULL from the valid range of pointer
2846 if (flag_delete_null_pointer_checks
&& int_cst_value (low
) == 0)
2847 low
= build_int_cstu (TREE_TYPE (low
), TYPE_ALIGN_UNIT (TREE_TYPE (type
)));
2849 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false, true);
2852 /* Determine information about number of iterations of a LOOP from the fact
2853 that signed arithmetics in STMT does not overflow. */
2856 infer_loop_bounds_from_signedness (struct loop
*loop
, gimple stmt
)
2858 tree def
, base
, step
, scev
, type
, low
, high
;
2860 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
2863 def
= gimple_assign_lhs (stmt
);
2865 if (TREE_CODE (def
) != SSA_NAME
)
2868 type
= TREE_TYPE (def
);
2869 if (!INTEGRAL_TYPE_P (type
)
2870 || !TYPE_OVERFLOW_UNDEFINED (type
))
2873 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
2874 if (chrec_contains_undetermined (scev
))
2877 base
= initial_condition_in_loop_num (scev
, loop
->num
);
2878 step
= evolution_part_in_loop_num (scev
, loop
->num
);
2881 || TREE_CODE (step
) != INTEGER_CST
2882 || tree_contains_chrecs (base
, NULL
)
2883 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
2886 low
= lower_bound_in_type (type
, type
);
2887 high
= upper_bound_in_type (type
, type
);
2889 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false, true);
2892 /* The following analyzers are extracting informations on the bounds
2893 of LOOP from the following undefined behaviors:
2895 - data references should not access elements over the statically
2898 - signed variables should not overflow when flag_wrapv is not set.
2902 infer_loop_bounds_from_undefined (struct loop
*loop
)
2906 gimple_stmt_iterator bsi
;
2910 bbs
= get_loop_body (loop
);
2912 for (i
= 0; i
< loop
->num_nodes
; i
++)
2916 /* If BB is not executed in each iteration of the loop, we cannot
2917 use the operations in it to infer reliable upper bound on the
2918 # of iterations of the loop. However, we can use it as a guess. */
2919 reliable
= dominated_by_p (CDI_DOMINATORS
, loop
->latch
, bb
);
2921 for (bsi
= gsi_start_bb (bb
); !gsi_end_p (bsi
); gsi_next (&bsi
))
2923 gimple stmt
= gsi_stmt (bsi
);
2925 infer_loop_bounds_from_array (loop
, stmt
, reliable
);
2929 infer_loop_bounds_from_signedness (loop
, stmt
);
2930 infer_loop_bounds_from_pointer_arith (loop
, stmt
);
2939 /* Converts VAL to double_int. */
2942 gcov_type_to_double_int (gcov_type val
)
2946 ret
.low
= (unsigned HOST_WIDE_INT
) val
;
2947 /* If HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_WIDEST_INT, avoid shifting by
2948 the size of type. */
2949 val
>>= HOST_BITS_PER_WIDE_INT
- 1;
2951 ret
.high
= (unsigned HOST_WIDE_INT
) val
;
2956 /* Records estimates on numbers of iterations of LOOP. If USE_UNDEFINED_P
2957 is true also use estimates derived from undefined behavior. */
2960 estimate_numbers_of_iterations_loop (struct loop
*loop
)
2962 VEC (edge
, heap
) *exits
;
2965 struct tree_niter_desc niter_desc
;
2969 /* Give up if we already have tried to compute an estimation. */
2970 if (loop
->estimate_state
!= EST_NOT_COMPUTED
)
2973 loop
->estimate_state
= EST_AVAILABLE
;
2974 /* Force estimate compuation but leave any existing upper bound in place. */
2975 loop
->any_estimate
= false;
2977 exits
= get_loop_exit_edges (loop
);
2978 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
2980 if (!number_of_iterations_exit (loop
, ex
, &niter_desc
, false))
2983 niter
= niter_desc
.niter
;
2984 type
= TREE_TYPE (niter
);
2985 if (TREE_CODE (niter_desc
.may_be_zero
) != INTEGER_CST
)
2986 niter
= build3 (COND_EXPR
, type
, niter_desc
.may_be_zero
,
2987 build_int_cst (type
, 0),
2989 record_estimate (loop
, niter
, niter_desc
.max
,
2990 last_stmt (ex
->src
),
2993 VEC_free (edge
, heap
, exits
);
2995 infer_loop_bounds_from_undefined (loop
);
2997 /* If we have a measured profile, use it to estimate the number of
2999 if (loop
->header
->count
!= 0)
3001 gcov_type nit
= expected_loop_iterations_unbounded (loop
) + 1;
3002 bound
= gcov_type_to_double_int (nit
);
3003 record_niter_bound (loop
, bound
, true, false);
3007 /* Sets NIT to the estimated number of executions of the latch of the
3008 LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as
3009 large as the number of iterations. If we have no reliable estimate,
3010 the function returns false, otherwise returns true. */
3013 estimated_loop_iterations (struct loop
*loop
, double_int
*nit
)
3015 estimate_numbers_of_iterations_loop (loop
);
3016 if (!loop
->any_estimate
)
3019 *nit
= loop
->nb_iterations_estimate
;
3023 /* Sets NIT to an upper bound for the maximum number of executions of the
3024 latch of the LOOP. If we have no reliable estimate, the function returns
3025 false, otherwise returns true. */
3028 max_loop_iterations (struct loop
*loop
, double_int
*nit
)
3030 estimate_numbers_of_iterations_loop (loop
);
3031 if (!loop
->any_upper_bound
)
3034 *nit
= loop
->nb_iterations_upper_bound
;
3038 /* Similar to estimated_loop_iterations, but returns the estimate only
3039 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
3040 on the number of iterations of LOOP could not be derived, returns -1. */
3043 estimated_loop_iterations_int (struct loop
*loop
)
3046 HOST_WIDE_INT hwi_nit
;
3048 if (!estimated_loop_iterations (loop
, &nit
))
3051 if (!nit
.fits_shwi ())
3053 hwi_nit
= nit
.to_shwi ();
3055 return hwi_nit
< 0 ? -1 : hwi_nit
;
3058 /* Similar to max_loop_iterations, but returns the estimate only
3059 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
3060 on the number of iterations of LOOP could not be derived, returns -1. */
3063 max_loop_iterations_int (struct loop
*loop
)
3066 HOST_WIDE_INT hwi_nit
;
3068 if (!max_loop_iterations (loop
, &nit
))
3071 if (!nit
.fits_shwi ())
3073 hwi_nit
= nit
.to_shwi ();
3075 return hwi_nit
< 0 ? -1 : hwi_nit
;
3078 /* Returns an upper bound on the number of executions of statements
3079 in the LOOP. For statements before the loop exit, this exceeds
3080 the number of execution of the latch by one. */
3083 max_stmt_executions_int (struct loop
*loop
)
3085 HOST_WIDE_INT nit
= max_loop_iterations_int (loop
);
3091 snit
= (HOST_WIDE_INT
) ((unsigned HOST_WIDE_INT
) nit
+ 1);
3093 /* If the computation overflows, return -1. */
3094 return snit
< 0 ? -1 : snit
;
3097 /* Returns an estimate for the number of executions of statements
3098 in the LOOP. For statements before the loop exit, this exceeds
3099 the number of execution of the latch by one. */
3102 estimated_stmt_executions_int (struct loop
*loop
)
3104 HOST_WIDE_INT nit
= estimated_loop_iterations_int (loop
);
3110 snit
= (HOST_WIDE_INT
) ((unsigned HOST_WIDE_INT
) nit
+ 1);
3112 /* If the computation overflows, return -1. */
3113 return snit
< 0 ? -1 : snit
;
3116 /* Sets NIT to the estimated maximum number of executions of the latch of the
3117 LOOP, plus one. If we have no reliable estimate, the function returns
3118 false, otherwise returns true. */
3121 max_stmt_executions (struct loop
*loop
, double_int
*nit
)
3123 double_int nit_minus_one
;
3125 if (!max_loop_iterations (loop
, nit
))
3128 nit_minus_one
= *nit
;
3130 *nit
+= double_int_one
;
3132 return (*nit
).ugt (nit_minus_one
);
3135 /* Sets NIT to the estimated number of executions of the latch of the
3136 LOOP, plus one. If we have no reliable estimate, the function returns
3137 false, otherwise returns true. */
3140 estimated_stmt_executions (struct loop
*loop
, double_int
*nit
)
3142 double_int nit_minus_one
;
3144 if (!estimated_loop_iterations (loop
, nit
))
3147 nit_minus_one
= *nit
;
3149 *nit
+= double_int_one
;
3151 return (*nit
).ugt (nit_minus_one
);
3154 /* Records estimates on numbers of iterations of loops. */
3157 estimate_numbers_of_iterations (void)
3162 /* We don't want to issue signed overflow warnings while getting
3163 loop iteration estimates. */
3164 fold_defer_overflow_warnings ();
3166 FOR_EACH_LOOP (li
, loop
, 0)
3168 estimate_numbers_of_iterations_loop (loop
);
3171 fold_undefer_and_ignore_overflow_warnings ();
3174 /* Returns true if statement S1 dominates statement S2. */
3177 stmt_dominates_stmt_p (gimple s1
, gimple s2
)
3179 basic_block bb1
= gimple_bb (s1
), bb2
= gimple_bb (s2
);
3187 gimple_stmt_iterator bsi
;
3189 if (gimple_code (s2
) == GIMPLE_PHI
)
3192 if (gimple_code (s1
) == GIMPLE_PHI
)
3195 for (bsi
= gsi_start_bb (bb1
); gsi_stmt (bsi
) != s2
; gsi_next (&bsi
))
3196 if (gsi_stmt (bsi
) == s1
)
3202 return dominated_by_p (CDI_DOMINATORS
, bb2
, bb1
);
3205 /* Returns true when we can prove that the number of executions of
3206 STMT in the loop is at most NITER, according to the bound on
3207 the number of executions of the statement NITER_BOUND->stmt recorded in
3208 NITER_BOUND. If STMT is NULL, we must prove this bound for all
3209 statements in the loop. */
3212 n_of_executions_at_most (gimple stmt
,
3213 struct nb_iter_bound
*niter_bound
,
3216 double_int bound
= niter_bound
->bound
;
3217 tree nit_type
= TREE_TYPE (niter
), e
;
3220 gcc_assert (TYPE_UNSIGNED (nit_type
));
3222 /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
3223 the number of iterations is small. */
3224 if (!double_int_fits_to_tree_p (nit_type
, bound
))
3227 /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
3228 times. This means that:
3230 -- if NITER_BOUND->is_exit is true, then everything before
3231 NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
3232 times, and everything after it at most NITER_BOUND->bound times.
3234 -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
3235 is executed, then NITER_BOUND->stmt is executed as well in the same
3236 iteration (we conclude that if both statements belong to the same
3237 basic block, or if STMT is after NITER_BOUND->stmt), then STMT
3238 is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
3239 executed at most NITER_BOUND->bound + 2 times. */
3241 if (niter_bound
->is_exit
)
3244 && stmt
!= niter_bound
->stmt
3245 && stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
))
3253 || (gimple_bb (stmt
) != gimple_bb (niter_bound
->stmt
)
3254 && !stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
)))
3256 bound
+= double_int_one
;
3257 if (bound
.is_zero ()
3258 || !double_int_fits_to_tree_p (nit_type
, bound
))
3264 e
= fold_binary (cmp
, boolean_type_node
,
3265 niter
, double_int_to_tree (nit_type
, bound
));
3266 return e
&& integer_nonzerop (e
);
3269 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
3272 nowrap_type_p (tree type
)
3274 if (INTEGRAL_TYPE_P (type
)
3275 && TYPE_OVERFLOW_UNDEFINED (type
))
3278 if (POINTER_TYPE_P (type
))
3284 /* Return false only when the induction variable BASE + STEP * I is
3285 known to not overflow: i.e. when the number of iterations is small
3286 enough with respect to the step and initial condition in order to
3287 keep the evolution confined in TYPEs bounds. Return true when the
3288 iv is known to overflow or when the property is not computable.
3290 USE_OVERFLOW_SEMANTICS is true if this function should assume that
3291 the rules for overflow of the given language apply (e.g., that signed
3292 arithmetics in C does not overflow). */
3295 scev_probably_wraps_p (tree base
, tree step
,
3296 gimple at_stmt
, struct loop
*loop
,
3297 bool use_overflow_semantics
)
3299 struct nb_iter_bound
*bound
;
3300 tree delta
, step_abs
;
3301 tree unsigned_type
, valid_niter
;
3302 tree type
= TREE_TYPE (step
);
3304 /* FIXME: We really need something like
3305 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
3307 We used to test for the following situation that frequently appears
3308 during address arithmetics:
3310 D.1621_13 = (long unsigned intD.4) D.1620_12;
3311 D.1622_14 = D.1621_13 * 8;
3312 D.1623_15 = (doubleD.29 *) D.1622_14;
3314 And derived that the sequence corresponding to D_14
3315 can be proved to not wrap because it is used for computing a
3316 memory access; however, this is not really the case -- for example,
3317 if D_12 = (unsigned char) [254,+,1], then D_14 has values
3318 2032, 2040, 0, 8, ..., but the code is still legal. */
3320 if (chrec_contains_undetermined (base
)
3321 || chrec_contains_undetermined (step
))
3324 if (integer_zerop (step
))
3327 /* If we can use the fact that signed and pointer arithmetics does not
3328 wrap, we are done. */
3329 if (use_overflow_semantics
&& nowrap_type_p (TREE_TYPE (base
)))
3332 /* To be able to use estimates on number of iterations of the loop,
3333 we must have an upper bound on the absolute value of the step. */
3334 if (TREE_CODE (step
) != INTEGER_CST
)
3337 /* Don't issue signed overflow warnings. */
3338 fold_defer_overflow_warnings ();
3340 /* Otherwise, compute the number of iterations before we reach the
3341 bound of the type, and verify that the loop is exited before this
3343 unsigned_type
= unsigned_type_for (type
);
3344 base
= fold_convert (unsigned_type
, base
);
3346 if (tree_int_cst_sign_bit (step
))
3348 tree extreme
= fold_convert (unsigned_type
,
3349 lower_bound_in_type (type
, type
));
3350 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
3351 step_abs
= fold_build1 (NEGATE_EXPR
, unsigned_type
,
3352 fold_convert (unsigned_type
, step
));
3356 tree extreme
= fold_convert (unsigned_type
,
3357 upper_bound_in_type (type
, type
));
3358 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
3359 step_abs
= fold_convert (unsigned_type
, step
);
3362 valid_niter
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step_abs
);
3364 estimate_numbers_of_iterations_loop (loop
);
3365 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
3367 if (n_of_executions_at_most (at_stmt
, bound
, valid_niter
))
3369 fold_undefer_and_ignore_overflow_warnings ();
3374 fold_undefer_and_ignore_overflow_warnings ();
3376 /* At this point we still don't have a proof that the iv does not
3377 overflow: give up. */
3381 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
3384 free_numbers_of_iterations_estimates_loop (struct loop
*loop
)
3386 struct nb_iter_bound
*bound
, *next
;
3388 loop
->nb_iterations
= NULL
;
3389 loop
->estimate_state
= EST_NOT_COMPUTED
;
3390 for (bound
= loop
->bounds
; bound
; bound
= next
)
3396 loop
->bounds
= NULL
;
3399 /* Frees the information on upper bounds on numbers of iterations of loops. */
3402 free_numbers_of_iterations_estimates (void)
3407 FOR_EACH_LOOP (li
, loop
, 0)
3409 free_numbers_of_iterations_estimates_loop (loop
);
3413 /* Substitute value VAL for ssa name NAME inside expressions held
3417 substitute_in_loop_info (struct loop
*loop
, tree name
, tree val
)
3419 loop
->nb_iterations
= simplify_replace_tree (loop
->nb_iterations
, name
, val
);