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.
1797 When EVERY_ITERATION is true, only tests that are known to be executed
1798 every iteration are considered (i.e. only test that alone bounds the loop).
1802 number_of_iterations_exit (struct loop
*loop
, edge exit
,
1803 struct tree_niter_desc
*niter
,
1804 bool warn
, bool every_iteration
)
1809 enum tree_code code
;
1813 && !dominated_by_p (CDI_DOMINATORS
, loop
->latch
, exit
->src
))
1816 niter
->assumptions
= boolean_false_node
;
1817 stmt
= last_stmt (exit
->src
);
1818 if (!stmt
|| gimple_code (stmt
) != GIMPLE_COND
)
1821 /* We want the condition for staying inside loop. */
1822 code
= gimple_cond_code (stmt
);
1823 if (exit
->flags
& EDGE_TRUE_VALUE
)
1824 code
= invert_tree_comparison (code
, false);
1839 op0
= gimple_cond_lhs (stmt
);
1840 op1
= gimple_cond_rhs (stmt
);
1841 type
= TREE_TYPE (op0
);
1843 if (TREE_CODE (type
) != INTEGER_TYPE
1844 && !POINTER_TYPE_P (type
))
1847 if (!simple_iv (loop
, loop_containing_stmt (stmt
), op0
, &iv0
, false))
1849 if (!simple_iv (loop
, loop_containing_stmt (stmt
), op1
, &iv1
, false))
1852 /* We don't want to see undefined signed overflow warnings while
1853 computing the number of iterations. */
1854 fold_defer_overflow_warnings ();
1856 iv0
.base
= expand_simple_operations (iv0
.base
);
1857 iv1
.base
= expand_simple_operations (iv1
.base
);
1858 if (!number_of_iterations_cond (loop
, type
, &iv0
, code
, &iv1
, niter
,
1859 loop_only_exit_p (loop
, exit
)))
1861 fold_undefer_and_ignore_overflow_warnings ();
1867 niter
->assumptions
= simplify_using_outer_evolutions (loop
,
1868 niter
->assumptions
);
1869 niter
->may_be_zero
= simplify_using_outer_evolutions (loop
,
1870 niter
->may_be_zero
);
1871 niter
->niter
= simplify_using_outer_evolutions (loop
, niter
->niter
);
1875 = simplify_using_initial_conditions (loop
,
1876 niter
->assumptions
);
1878 = simplify_using_initial_conditions (loop
,
1879 niter
->may_be_zero
);
1881 fold_undefer_and_ignore_overflow_warnings ();
1883 /* If NITER has simplified into a constant, update MAX. */
1884 if (TREE_CODE (niter
->niter
) == INTEGER_CST
)
1885 niter
->max
= tree_to_double_int (niter
->niter
);
1887 if (integer_onep (niter
->assumptions
))
1890 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1891 But if we can prove that there is overflow or some other source of weird
1892 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1893 if (integer_zerop (niter
->assumptions
) || !single_exit (loop
))
1896 if (flag_unsafe_loop_optimizations
)
1897 niter
->assumptions
= boolean_true_node
;
1901 const char *wording
;
1902 location_t loc
= gimple_location (stmt
);
1904 /* We can provide a more specific warning if one of the operator is
1905 constant and the other advances by +1 or -1. */
1906 if (!integer_zerop (iv1
.step
)
1907 ? (integer_zerop (iv0
.step
)
1908 && (integer_onep (iv1
.step
) || integer_all_onesp (iv1
.step
)))
1909 : (integer_onep (iv0
.step
) || integer_all_onesp (iv0
.step
)))
1911 flag_unsafe_loop_optimizations
1912 ? N_("assuming that the loop is not infinite")
1913 : N_("cannot optimize possibly infinite loops");
1916 flag_unsafe_loop_optimizations
1917 ? N_("assuming that the loop counter does not overflow")
1918 : N_("cannot optimize loop, the loop counter may overflow");
1920 warning_at ((LOCATION_LINE (loc
) > 0) ? loc
: input_location
,
1921 OPT_Wunsafe_loop_optimizations
, "%s", gettext (wording
));
1924 return flag_unsafe_loop_optimizations
;
1927 /* Try to determine the number of iterations of LOOP. If we succeed,
1928 expression giving number of iterations is returned and *EXIT is
1929 set to the edge from that the information is obtained. Otherwise
1930 chrec_dont_know is returned. */
1933 find_loop_niter (struct loop
*loop
, edge
*exit
)
1936 vec
<edge
> exits
= get_loop_exit_edges (loop
);
1938 tree niter
= NULL_TREE
, aniter
;
1939 struct tree_niter_desc desc
;
1942 FOR_EACH_VEC_ELT (exits
, i
, ex
)
1944 if (!number_of_iterations_exit (loop
, ex
, &desc
, false))
1947 if (integer_nonzerop (desc
.may_be_zero
))
1949 /* We exit in the first iteration through this exit.
1950 We won't find anything better. */
1951 niter
= build_int_cst (unsigned_type_node
, 0);
1956 if (!integer_zerop (desc
.may_be_zero
))
1959 aniter
= desc
.niter
;
1963 /* Nothing recorded yet. */
1969 /* Prefer constants, the lower the better. */
1970 if (TREE_CODE (aniter
) != INTEGER_CST
)
1973 if (TREE_CODE (niter
) != INTEGER_CST
)
1980 if (tree_int_cst_lt (aniter
, niter
))
1989 return niter
? niter
: chrec_dont_know
;
1992 /* Return true if loop is known to have bounded number of iterations. */
1995 finite_loop_p (struct loop
*loop
)
2000 if (flag_unsafe_loop_optimizations
)
2002 flags
= flags_from_decl_or_type (current_function_decl
);
2003 if ((flags
& (ECF_CONST
|ECF_PURE
)) && !(flags
& ECF_LOOPING_CONST_OR_PURE
))
2005 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2006 fprintf (dump_file
, "Found loop %i to be finite: it is within pure or const function.\n",
2011 if (loop
->any_upper_bound
2012 || max_loop_iterations (loop
, &nit
))
2014 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2015 fprintf (dump_file
, "Found loop %i to be finite: upper bound found.\n",
2024 Analysis of a number of iterations of a loop by a brute-force evaluation.
2028 /* Bound on the number of iterations we try to evaluate. */
2030 #define MAX_ITERATIONS_TO_TRACK \
2031 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
2033 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
2034 result by a chain of operations such that all but exactly one of their
2035 operands are constants. */
2038 chain_of_csts_start (struct loop
*loop
, tree x
)
2040 gimple stmt
= SSA_NAME_DEF_STMT (x
);
2042 basic_block bb
= gimple_bb (stmt
);
2043 enum tree_code code
;
2046 || !flow_bb_inside_loop_p (loop
, bb
))
2049 if (gimple_code (stmt
) == GIMPLE_PHI
)
2051 if (bb
== loop
->header
)
2057 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
2060 code
= gimple_assign_rhs_code (stmt
);
2061 if (gimple_references_memory_p (stmt
)
2062 || TREE_CODE_CLASS (code
) == tcc_reference
2063 || (code
== ADDR_EXPR
2064 && !is_gimple_min_invariant (gimple_assign_rhs1 (stmt
))))
2067 use
= SINGLE_SSA_TREE_OPERAND (stmt
, SSA_OP_USE
);
2068 if (use
== NULL_TREE
)
2071 return chain_of_csts_start (loop
, use
);
2074 /* Determines whether the expression X is derived from a result of a phi node
2075 in header of LOOP such that
2077 * the derivation of X consists only from operations with constants
2078 * the initial value of the phi node is constant
2079 * the value of the phi node in the next iteration can be derived from the
2080 value in the current iteration by a chain of operations with constants.
2082 If such phi node exists, it is returned, otherwise NULL is returned. */
2085 get_base_for (struct loop
*loop
, tree x
)
2090 if (is_gimple_min_invariant (x
))
2093 phi
= chain_of_csts_start (loop
, x
);
2097 init
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
2098 next
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
2100 if (TREE_CODE (next
) != SSA_NAME
)
2103 if (!is_gimple_min_invariant (init
))
2106 if (chain_of_csts_start (loop
, next
) != phi
)
2112 /* Given an expression X, then
2114 * if X is NULL_TREE, we return the constant BASE.
2115 * otherwise X is a SSA name, whose value in the considered loop is derived
2116 by a chain of operations with constant from a result of a phi node in
2117 the header of the loop. Then we return value of X when the value of the
2118 result of this phi node is given by the constant BASE. */
2121 get_val_for (tree x
, tree base
)
2125 gcc_assert (is_gimple_min_invariant (base
));
2130 stmt
= SSA_NAME_DEF_STMT (x
);
2131 if (gimple_code (stmt
) == GIMPLE_PHI
)
2134 gcc_assert (is_gimple_assign (stmt
));
2136 /* STMT must be either an assignment of a single SSA name or an
2137 expression involving an SSA name and a constant. Try to fold that
2138 expression using the value for the SSA name. */
2139 if (gimple_assign_ssa_name_copy_p (stmt
))
2140 return get_val_for (gimple_assign_rhs1 (stmt
), base
);
2141 else if (gimple_assign_rhs_class (stmt
) == GIMPLE_UNARY_RHS
2142 && TREE_CODE (gimple_assign_rhs1 (stmt
)) == SSA_NAME
)
2144 return fold_build1 (gimple_assign_rhs_code (stmt
),
2145 gimple_expr_type (stmt
),
2146 get_val_for (gimple_assign_rhs1 (stmt
), base
));
2148 else if (gimple_assign_rhs_class (stmt
) == GIMPLE_BINARY_RHS
)
2150 tree rhs1
= gimple_assign_rhs1 (stmt
);
2151 tree rhs2
= gimple_assign_rhs2 (stmt
);
2152 if (TREE_CODE (rhs1
) == SSA_NAME
)
2153 rhs1
= get_val_for (rhs1
, base
);
2154 else if (TREE_CODE (rhs2
) == SSA_NAME
)
2155 rhs2
= get_val_for (rhs2
, base
);
2158 return fold_build2 (gimple_assign_rhs_code (stmt
),
2159 gimple_expr_type (stmt
), rhs1
, rhs2
);
2166 /* Tries to count the number of iterations of LOOP till it exits by EXIT
2167 by brute force -- i.e. by determining the value of the operands of the
2168 condition at EXIT in first few iterations of the loop (assuming that
2169 these values are constant) and determining the first one in that the
2170 condition is not satisfied. Returns the constant giving the number
2171 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
2174 loop_niter_by_eval (struct loop
*loop
, edge exit
)
2177 tree op
[2], val
[2], next
[2], aval
[2];
2182 cond
= last_stmt (exit
->src
);
2183 if (!cond
|| gimple_code (cond
) != GIMPLE_COND
)
2184 return chrec_dont_know
;
2186 cmp
= gimple_cond_code (cond
);
2187 if (exit
->flags
& EDGE_TRUE_VALUE
)
2188 cmp
= invert_tree_comparison (cmp
, false);
2198 op
[0] = gimple_cond_lhs (cond
);
2199 op
[1] = gimple_cond_rhs (cond
);
2203 return chrec_dont_know
;
2206 for (j
= 0; j
< 2; j
++)
2208 if (is_gimple_min_invariant (op
[j
]))
2211 next
[j
] = NULL_TREE
;
2216 phi
= get_base_for (loop
, op
[j
]);
2218 return chrec_dont_know
;
2219 val
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
2220 next
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
2224 /* Don't issue signed overflow warnings. */
2225 fold_defer_overflow_warnings ();
2227 for (i
= 0; i
< MAX_ITERATIONS_TO_TRACK
; i
++)
2229 for (j
= 0; j
< 2; j
++)
2230 aval
[j
] = get_val_for (op
[j
], val
[j
]);
2232 acnd
= fold_binary (cmp
, boolean_type_node
, aval
[0], aval
[1]);
2233 if (acnd
&& integer_zerop (acnd
))
2235 fold_undefer_and_ignore_overflow_warnings ();
2236 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2238 "Proved that loop %d iterates %d times using brute force.\n",
2240 return build_int_cst (unsigned_type_node
, i
);
2243 for (j
= 0; j
< 2; j
++)
2245 val
[j
] = get_val_for (next
[j
], val
[j
]);
2246 if (!is_gimple_min_invariant (val
[j
]))
2248 fold_undefer_and_ignore_overflow_warnings ();
2249 return chrec_dont_know
;
2254 fold_undefer_and_ignore_overflow_warnings ();
2256 return chrec_dont_know
;
2259 /* Finds the exit of the LOOP by that the loop exits after a constant
2260 number of iterations and stores the exit edge to *EXIT. The constant
2261 giving the number of iterations of LOOP is returned. The number of
2262 iterations is determined using loop_niter_by_eval (i.e. by brute force
2263 evaluation). If we are unable to find the exit for that loop_niter_by_eval
2264 determines the number of iterations, chrec_dont_know is returned. */
2267 find_loop_niter_by_eval (struct loop
*loop
, edge
*exit
)
2270 vec
<edge
> exits
= get_loop_exit_edges (loop
);
2272 tree niter
= NULL_TREE
, aniter
;
2276 /* Loops with multiple exits are expensive to handle and less important. */
2277 if (!flag_expensive_optimizations
2278 && exits
.length () > 1)
2281 return chrec_dont_know
;
2284 FOR_EACH_VEC_ELT (exits
, i
, ex
)
2286 if (!just_once_each_iteration_p (loop
, ex
->src
))
2289 aniter
= loop_niter_by_eval (loop
, ex
);
2290 if (chrec_contains_undetermined (aniter
))
2294 && !tree_int_cst_lt (aniter
, niter
))
2302 return niter
? niter
: chrec_dont_know
;
2307 Analysis of upper bounds on number of iterations of a loop.
2311 static double_int
derive_constant_upper_bound_ops (tree
, tree
,
2312 enum tree_code
, tree
);
2314 /* Returns a constant upper bound on the value of the right-hand side of
2315 an assignment statement STMT. */
2318 derive_constant_upper_bound_assign (gimple stmt
)
2320 enum tree_code code
= gimple_assign_rhs_code (stmt
);
2321 tree op0
= gimple_assign_rhs1 (stmt
);
2322 tree op1
= gimple_assign_rhs2 (stmt
);
2324 return derive_constant_upper_bound_ops (TREE_TYPE (gimple_assign_lhs (stmt
)),
2328 /* Returns a constant upper bound on the value of expression VAL. VAL
2329 is considered to be unsigned. If its type is signed, its value must
2333 derive_constant_upper_bound (tree val
)
2335 enum tree_code code
;
2338 extract_ops_from_tree (val
, &code
, &op0
, &op1
);
2339 return derive_constant_upper_bound_ops (TREE_TYPE (val
), op0
, code
, op1
);
2342 /* Returns a constant upper bound on the value of expression OP0 CODE OP1,
2343 whose type is TYPE. The expression is considered to be unsigned. If
2344 its type is signed, its value must be nonnegative. */
2347 derive_constant_upper_bound_ops (tree type
, tree op0
,
2348 enum tree_code code
, tree op1
)
2351 double_int bnd
, max
, mmax
, cst
;
2354 if (INTEGRAL_TYPE_P (type
))
2355 maxt
= TYPE_MAX_VALUE (type
);
2357 maxt
= upper_bound_in_type (type
, type
);
2359 max
= tree_to_double_int (maxt
);
2364 return tree_to_double_int (op0
);
2367 subtype
= TREE_TYPE (op0
);
2368 if (!TYPE_UNSIGNED (subtype
)
2369 /* If TYPE is also signed, the fact that VAL is nonnegative implies
2370 that OP0 is nonnegative. */
2371 && TYPE_UNSIGNED (type
)
2372 && !tree_expr_nonnegative_p (op0
))
2374 /* If we cannot prove that the casted expression is nonnegative,
2375 we cannot establish more useful upper bound than the precision
2376 of the type gives us. */
2380 /* We now know that op0 is an nonnegative value. Try deriving an upper
2382 bnd
= derive_constant_upper_bound (op0
);
2384 /* If the bound does not fit in TYPE, max. value of TYPE could be
2392 case POINTER_PLUS_EXPR
:
2394 if (TREE_CODE (op1
) != INTEGER_CST
2395 || !tree_expr_nonnegative_p (op0
))
2398 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
2399 choose the most logical way how to treat this constant regardless
2400 of the signedness of the type. */
2401 cst
= tree_to_double_int (op1
);
2402 cst
= cst
.sext (TYPE_PRECISION (type
));
2403 if (code
!= MINUS_EXPR
)
2406 bnd
= derive_constant_upper_bound (op0
);
2408 if (cst
.is_negative ())
2411 /* Avoid CST == 0x80000... */
2412 if (cst
.is_negative ())
2415 /* OP0 + CST. We need to check that
2416 BND <= MAX (type) - CST. */
2426 /* OP0 - CST, where CST >= 0.
2428 If TYPE is signed, we have already verified that OP0 >= 0, and we
2429 know that the result is nonnegative. This implies that
2432 If TYPE is unsigned, we must additionally know that OP0 >= CST,
2433 otherwise the operation underflows.
2436 /* This should only happen if the type is unsigned; however, for
2437 buggy programs that use overflowing signed arithmetics even with
2438 -fno-wrapv, this condition may also be true for signed values. */
2442 if (TYPE_UNSIGNED (type
))
2444 tree tem
= fold_binary (GE_EXPR
, boolean_type_node
, op0
,
2445 double_int_to_tree (type
, cst
));
2446 if (!tem
|| integer_nonzerop (tem
))
2455 case FLOOR_DIV_EXPR
:
2456 case EXACT_DIV_EXPR
:
2457 if (TREE_CODE (op1
) != INTEGER_CST
2458 || tree_int_cst_sign_bit (op1
))
2461 bnd
= derive_constant_upper_bound (op0
);
2462 return bnd
.udiv (tree_to_double_int (op1
), FLOOR_DIV_EXPR
);
2465 if (TREE_CODE (op1
) != INTEGER_CST
2466 || tree_int_cst_sign_bit (op1
))
2468 return tree_to_double_int (op1
);
2471 stmt
= SSA_NAME_DEF_STMT (op0
);
2472 if (gimple_code (stmt
) != GIMPLE_ASSIGN
2473 || gimple_assign_lhs (stmt
) != op0
)
2475 return derive_constant_upper_bound_assign (stmt
);
2482 /* Records that every statement in LOOP is executed I_BOUND times.
2483 REALISTIC is true if I_BOUND is expected to be close to the real number
2484 of iterations. UPPER is true if we are sure the loop iterates at most
2488 record_niter_bound (struct loop
*loop
, double_int i_bound
, bool realistic
,
2491 /* Update the bounds only when there is no previous estimation, or when the
2492 current estimation is smaller. */
2494 && (!loop
->any_upper_bound
2495 || i_bound
.ult (loop
->nb_iterations_upper_bound
)))
2497 loop
->any_upper_bound
= true;
2498 loop
->nb_iterations_upper_bound
= i_bound
;
2501 && (!loop
->any_estimate
2502 || i_bound
.ult (loop
->nb_iterations_estimate
)))
2504 loop
->any_estimate
= true;
2505 loop
->nb_iterations_estimate
= i_bound
;
2508 /* If an upper bound is smaller than the realistic estimate of the
2509 number of iterations, use the upper bound instead. */
2510 if (loop
->any_upper_bound
2511 && loop
->any_estimate
2512 && loop
->nb_iterations_upper_bound
.ult (loop
->nb_iterations_estimate
))
2513 loop
->nb_iterations_estimate
= loop
->nb_iterations_upper_bound
;
2516 /* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. IS_EXIT
2517 is true if the loop is exited immediately after STMT, and this exit
2518 is taken at last when the STMT is executed BOUND + 1 times.
2519 REALISTIC is true if BOUND is expected to be close to the real number
2520 of iterations. UPPER is true if we are sure the loop iterates at most
2521 BOUND times. I_BOUND is an unsigned double_int upper estimate on BOUND. */
2524 record_estimate (struct loop
*loop
, tree bound
, double_int i_bound
,
2525 gimple at_stmt
, bool is_exit
, bool realistic
, bool upper
)
2529 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2531 fprintf (dump_file
, "Statement %s", is_exit
? "(exit)" : "");
2532 print_gimple_stmt (dump_file
, at_stmt
, 0, TDF_SLIM
);
2533 fprintf (dump_file
, " is %sexecuted at most ",
2534 upper
? "" : "probably ");
2535 print_generic_expr (dump_file
, bound
, TDF_SLIM
);
2536 fprintf (dump_file
, " (bounded by ");
2537 dump_double_int (dump_file
, i_bound
, true);
2538 fprintf (dump_file
, ") + 1 times in loop %d.\n", loop
->num
);
2541 /* If the I_BOUND is just an estimate of BOUND, it rarely is close to the
2542 real number of iterations. */
2543 if (TREE_CODE (bound
) != INTEGER_CST
)
2546 gcc_checking_assert (i_bound
== tree_to_double_int (bound
));
2547 if (!upper
&& !realistic
)
2550 /* If we have a guaranteed upper bound, record it in the appropriate
2554 struct nb_iter_bound
*elt
= ggc_alloc_nb_iter_bound ();
2556 elt
->bound
= i_bound
;
2557 elt
->stmt
= at_stmt
;
2558 elt
->is_exit
= is_exit
;
2559 elt
->next
= loop
->bounds
;
2563 /* If statement is executed on every path to the loop latch, we can directly
2564 infer the upper bound on the # of iterations of the loop. */
2565 if (!dominated_by_p (CDI_DOMINATORS
, loop
->latch
, gimple_bb (at_stmt
)))
2568 /* Update the number of iteration estimates according to the bound.
2569 If at_stmt is an exit then the loop latch is executed at most BOUND times,
2570 otherwise it can be executed BOUND + 1 times. We will lower the estimate
2571 later if such statement must be executed on last iteration */
2573 delta
= double_int_zero
;
2575 delta
= double_int_one
;
2578 /* If an overflow occurred, ignore the result. */
2579 if (i_bound
.ult (delta
))
2582 record_niter_bound (loop
, i_bound
, realistic
, upper
);
2585 /* Record the estimate on number of iterations of LOOP based on the fact that
2586 the induction variable BASE + STEP * i evaluated in STMT does not wrap and
2587 its values belong to the range <LOW, HIGH>. REALISTIC is true if the
2588 estimated number of iterations is expected to be close to the real one.
2589 UPPER is true if we are sure the induction variable does not wrap. */
2592 record_nonwrapping_iv (struct loop
*loop
, tree base
, tree step
, gimple stmt
,
2593 tree low
, tree high
, bool realistic
, bool upper
)
2595 tree niter_bound
, extreme
, delta
;
2596 tree type
= TREE_TYPE (base
), unsigned_type
;
2599 if (TREE_CODE (step
) != INTEGER_CST
|| integer_zerop (step
))
2602 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2604 fprintf (dump_file
, "Induction variable (");
2605 print_generic_expr (dump_file
, TREE_TYPE (base
), TDF_SLIM
);
2606 fprintf (dump_file
, ") ");
2607 print_generic_expr (dump_file
, base
, TDF_SLIM
);
2608 fprintf (dump_file
, " + ");
2609 print_generic_expr (dump_file
, step
, TDF_SLIM
);
2610 fprintf (dump_file
, " * iteration does not wrap in statement ");
2611 print_gimple_stmt (dump_file
, stmt
, 0, TDF_SLIM
);
2612 fprintf (dump_file
, " in loop %d.\n", loop
->num
);
2615 unsigned_type
= unsigned_type_for (type
);
2616 base
= fold_convert (unsigned_type
, base
);
2617 step
= fold_convert (unsigned_type
, step
);
2619 if (tree_int_cst_sign_bit (step
))
2621 extreme
= fold_convert (unsigned_type
, low
);
2622 if (TREE_CODE (base
) != INTEGER_CST
)
2623 base
= fold_convert (unsigned_type
, high
);
2624 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
2625 step
= fold_build1 (NEGATE_EXPR
, unsigned_type
, step
);
2629 extreme
= fold_convert (unsigned_type
, high
);
2630 if (TREE_CODE (base
) != INTEGER_CST
)
2631 base
= fold_convert (unsigned_type
, low
);
2632 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
2635 /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
2636 would get out of the range. */
2637 niter_bound
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step
);
2638 max
= derive_constant_upper_bound (niter_bound
);
2639 record_estimate (loop
, niter_bound
, max
, stmt
, false, realistic
, upper
);
2642 /* Determine information about number of iterations a LOOP from the index
2643 IDX of a data reference accessed in STMT. RELIABLE is true if STMT is
2644 guaranteed to be executed in every iteration of LOOP. Callback for
2654 idx_infer_loop_bounds (tree base
, tree
*idx
, void *dta
)
2656 struct ilb_data
*data
= (struct ilb_data
*) dta
;
2657 tree ev
, init
, step
;
2658 tree low
, high
, type
, next
;
2659 bool sign
, upper
= true, at_end
= false;
2660 struct loop
*loop
= data
->loop
;
2662 if (TREE_CODE (base
) != ARRAY_REF
)
2665 /* For arrays at the end of the structure, we are not guaranteed that they
2666 do not really extend over their declared size. However, for arrays of
2667 size greater than one, this is unlikely to be intended. */
2668 if (array_at_struct_end_p (base
))
2674 struct loop
*dloop
= loop_containing_stmt (data
->stmt
);
2678 ev
= analyze_scalar_evolution (dloop
, *idx
);
2679 ev
= instantiate_parameters (loop
, ev
);
2680 init
= initial_condition (ev
);
2681 step
= evolution_part_in_loop_num (ev
, loop
->num
);
2685 || TREE_CODE (step
) != INTEGER_CST
2686 || integer_zerop (step
)
2687 || tree_contains_chrecs (init
, NULL
)
2688 || chrec_contains_symbols_defined_in_loop (init
, loop
->num
))
2691 low
= array_ref_low_bound (base
);
2692 high
= array_ref_up_bound (base
);
2694 /* The case of nonconstant bounds could be handled, but it would be
2696 if (TREE_CODE (low
) != INTEGER_CST
2698 || TREE_CODE (high
) != INTEGER_CST
)
2700 sign
= tree_int_cst_sign_bit (step
);
2701 type
= TREE_TYPE (step
);
2703 /* The array of length 1 at the end of a structure most likely extends
2704 beyond its bounds. */
2706 && operand_equal_p (low
, high
, 0))
2709 /* In case the relevant bound of the array does not fit in type, or
2710 it does, but bound + step (in type) still belongs into the range of the
2711 array, the index may wrap and still stay within the range of the array
2712 (consider e.g. if the array is indexed by the full range of
2715 To make things simpler, we require both bounds to fit into type, although
2716 there are cases where this would not be strictly necessary. */
2717 if (!int_fits_type_p (high
, type
)
2718 || !int_fits_type_p (low
, type
))
2720 low
= fold_convert (type
, low
);
2721 high
= fold_convert (type
, high
);
2724 next
= fold_binary (PLUS_EXPR
, type
, low
, step
);
2726 next
= fold_binary (PLUS_EXPR
, type
, high
, step
);
2728 if (tree_int_cst_compare (low
, next
) <= 0
2729 && tree_int_cst_compare (next
, high
) <= 0)
2732 record_nonwrapping_iv (loop
, init
, step
, data
->stmt
, low
, high
, true, upper
);
2736 /* Determine information about number of iterations a LOOP from the bounds
2737 of arrays in the data reference REF accessed in STMT. RELIABLE is true if
2738 STMT is guaranteed to be executed in every iteration of LOOP.*/
2741 infer_loop_bounds_from_ref (struct loop
*loop
, gimple stmt
, tree ref
)
2743 struct ilb_data data
;
2747 for_each_index (&ref
, idx_infer_loop_bounds
, &data
);
2750 /* Determine information about number of iterations of a LOOP from the way
2751 arrays are used in STMT. RELIABLE is true if STMT is guaranteed to be
2752 executed in every iteration of LOOP. */
2755 infer_loop_bounds_from_array (struct loop
*loop
, gimple stmt
)
2757 if (is_gimple_assign (stmt
))
2759 tree op0
= gimple_assign_lhs (stmt
);
2760 tree op1
= gimple_assign_rhs1 (stmt
);
2762 /* For each memory access, analyze its access function
2763 and record a bound on the loop iteration domain. */
2764 if (REFERENCE_CLASS_P (op0
))
2765 infer_loop_bounds_from_ref (loop
, stmt
, op0
);
2767 if (REFERENCE_CLASS_P (op1
))
2768 infer_loop_bounds_from_ref (loop
, stmt
, op1
);
2770 else if (is_gimple_call (stmt
))
2773 unsigned i
, n
= gimple_call_num_args (stmt
);
2775 lhs
= gimple_call_lhs (stmt
);
2776 if (lhs
&& REFERENCE_CLASS_P (lhs
))
2777 infer_loop_bounds_from_ref (loop
, stmt
, lhs
);
2779 for (i
= 0; i
< n
; i
++)
2781 arg
= gimple_call_arg (stmt
, i
);
2782 if (REFERENCE_CLASS_P (arg
))
2783 infer_loop_bounds_from_ref (loop
, stmt
, arg
);
2788 /* Determine information about number of iterations of a LOOP from the fact
2789 that pointer arithmetics in STMT does not overflow. */
2792 infer_loop_bounds_from_pointer_arith (struct loop
*loop
, gimple stmt
)
2794 tree def
, base
, step
, scev
, type
, low
, high
;
2797 if (!is_gimple_assign (stmt
)
2798 || gimple_assign_rhs_code (stmt
) != POINTER_PLUS_EXPR
)
2801 def
= gimple_assign_lhs (stmt
);
2802 if (TREE_CODE (def
) != SSA_NAME
)
2805 type
= TREE_TYPE (def
);
2806 if (!nowrap_type_p (type
))
2809 ptr
= gimple_assign_rhs1 (stmt
);
2810 if (!expr_invariant_in_loop_p (loop
, ptr
))
2813 var
= gimple_assign_rhs2 (stmt
);
2814 if (TYPE_PRECISION (type
) != TYPE_PRECISION (TREE_TYPE (var
)))
2817 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
2818 if (chrec_contains_undetermined (scev
))
2821 base
= initial_condition_in_loop_num (scev
, loop
->num
);
2822 step
= evolution_part_in_loop_num (scev
, loop
->num
);
2825 || TREE_CODE (step
) != INTEGER_CST
2826 || tree_contains_chrecs (base
, NULL
)
2827 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
2830 low
= lower_bound_in_type (type
, type
);
2831 high
= upper_bound_in_type (type
, type
);
2833 /* In C, pointer arithmetic p + 1 cannot use a NULL pointer, and p - 1 cannot
2834 produce a NULL pointer. The contrary would mean NULL points to an object,
2835 while NULL is supposed to compare unequal with the address of all objects.
2836 Furthermore, p + 1 cannot produce a NULL pointer and p - 1 cannot use a
2837 NULL pointer since that would mean wrapping, which we assume here not to
2838 happen. So, we can exclude NULL from the valid range of pointer
2840 if (flag_delete_null_pointer_checks
&& int_cst_value (low
) == 0)
2841 low
= build_int_cstu (TREE_TYPE (low
), TYPE_ALIGN_UNIT (TREE_TYPE (type
)));
2843 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false, true);
2846 /* Determine information about number of iterations of a LOOP from the fact
2847 that signed arithmetics in STMT does not overflow. */
2850 infer_loop_bounds_from_signedness (struct loop
*loop
, gimple stmt
)
2852 tree def
, base
, step
, scev
, type
, low
, high
;
2854 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
2857 def
= gimple_assign_lhs (stmt
);
2859 if (TREE_CODE (def
) != SSA_NAME
)
2862 type
= TREE_TYPE (def
);
2863 if (!INTEGRAL_TYPE_P (type
)
2864 || !TYPE_OVERFLOW_UNDEFINED (type
))
2867 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
2868 if (chrec_contains_undetermined (scev
))
2871 base
= initial_condition_in_loop_num (scev
, loop
->num
);
2872 step
= evolution_part_in_loop_num (scev
, loop
->num
);
2875 || TREE_CODE (step
) != INTEGER_CST
2876 || tree_contains_chrecs (base
, NULL
)
2877 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
2880 low
= lower_bound_in_type (type
, type
);
2881 high
= upper_bound_in_type (type
, type
);
2883 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false, true);
2886 /* The following analyzers are extracting informations on the bounds
2887 of LOOP from the following undefined behaviors:
2889 - data references should not access elements over the statically
2892 - signed variables should not overflow when flag_wrapv is not set.
2896 infer_loop_bounds_from_undefined (struct loop
*loop
)
2900 gimple_stmt_iterator bsi
;
2904 bbs
= get_loop_body (loop
);
2906 for (i
= 0; i
< loop
->num_nodes
; i
++)
2910 /* If BB is not executed in each iteration of the loop, we cannot
2911 use the operations in it to infer reliable upper bound on the
2912 # of iterations of the loop. However, we can use it as a guess.
2913 Reliable guesses come only from array bounds. */
2914 reliable
= dominated_by_p (CDI_DOMINATORS
, loop
->latch
, bb
);
2916 for (bsi
= gsi_start_bb (bb
); !gsi_end_p (bsi
); gsi_next (&bsi
))
2918 gimple stmt
= gsi_stmt (bsi
);
2920 infer_loop_bounds_from_array (loop
, stmt
);
2924 infer_loop_bounds_from_signedness (loop
, stmt
);
2925 infer_loop_bounds_from_pointer_arith (loop
, stmt
);
2934 /* Converts VAL to double_int. */
2937 gcov_type_to_double_int (gcov_type val
)
2941 ret
.low
= (unsigned HOST_WIDE_INT
) val
;
2942 /* If HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_WIDEST_INT, avoid shifting by
2943 the size of type. */
2944 val
>>= HOST_BITS_PER_WIDE_INT
- 1;
2946 ret
.high
= (unsigned HOST_WIDE_INT
) val
;
2951 /* Compare double ints, callback for qsort. */
2954 double_int_cmp (const void *p1
, const void *p2
)
2956 const double_int
*d1
= (const double_int
*)p1
;
2957 const double_int
*d2
= (const double_int
*)p2
;
2965 /* Return index of BOUND in BOUNDS array sorted in increasing order.
2966 Lookup by binary search. */
2969 bound_index (vec
<double_int
> bounds
, double_int bound
)
2971 unsigned int end
= bounds
.length ();
2972 unsigned int begin
= 0;
2974 /* Find a matching index by means of a binary search. */
2975 while (begin
!= end
)
2977 unsigned int middle
= (begin
+ end
) / 2;
2978 double_int index
= bounds
[middle
];
2982 else if (index
.ult (bound
))
2990 /* Used to hold vector of queues of basic blocks bellow. */
2991 typedef vec
<basic_block
> bb_queue
;
2993 /* We recorded loop bounds only for statements dominating loop latch (and thus
2994 executed each loop iteration). If there are any bounds on statements not
2995 dominating the loop latch we can improve the estimate by walking the loop
2996 body and seeing if every path from loop header to loop latch contains
2997 some bounded statement. */
3000 discover_iteration_bound_by_body_walk (struct loop
*loop
)
3002 pointer_map_t
*bb_bounds
;
3003 struct nb_iter_bound
*elt
;
3004 vec
<double_int
> bounds
= vNULL
;
3005 vec
<bb_queue
> queues
= vNULL
;
3006 bb_queue queue
= bb_queue();
3007 ptrdiff_t queue_index
;
3008 ptrdiff_t latch_index
= 0;
3009 pointer_map_t
*block_priority
;
3011 /* Discover what bounds may interest us. */
3012 for (elt
= loop
->bounds
; elt
; elt
= elt
->next
)
3014 double_int bound
= elt
->bound
;
3016 /* Exit terminates loop at given iteration, while non-exits produce undefined
3017 effect on the next iteration. */
3020 bound
+= double_int_one
;
3021 /* If an overflow occurred, ignore the result. */
3022 if (bound
.is_zero ())
3026 if (!loop
->any_upper_bound
3027 || bound
.ult (loop
->nb_iterations_upper_bound
))
3028 bounds
.safe_push (bound
);
3031 /* Exit early if there is nothing to do. */
3032 if (!bounds
.exists ())
3035 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
3036 fprintf (dump_file
, " Trying to walk loop body to reduce the bound.\n");
3038 /* Sort the bounds in decreasing order. */
3039 qsort (bounds
.address (), bounds
.length (),
3040 sizeof (double_int
), double_int_cmp
);
3042 /* For every basic block record the lowest bound that is guaranteed to
3043 terminate the loop. */
3045 bb_bounds
= pointer_map_create ();
3046 for (elt
= loop
->bounds
; elt
; elt
= elt
->next
)
3048 double_int bound
= elt
->bound
;
3051 bound
+= double_int_one
;
3052 /* If an overflow occurred, ignore the result. */
3053 if (bound
.is_zero ())
3057 if (!loop
->any_upper_bound
3058 || bound
.ult (loop
->nb_iterations_upper_bound
))
3060 ptrdiff_t index
= bound_index (bounds
, bound
);
3061 void **entry
= pointer_map_contains (bb_bounds
,
3062 gimple_bb (elt
->stmt
));
3064 *pointer_map_insert (bb_bounds
,
3065 gimple_bb (elt
->stmt
)) = (void *)index
;
3066 else if ((ptrdiff_t)*entry
> index
)
3067 *entry
= (void *)index
;
3071 block_priority
= pointer_map_create ();
3073 /* Perform shortest path discovery loop->header ... loop->latch.
3075 The "distance" is given by the smallest loop bound of basic block
3076 present in the path and we look for path with largest smallest bound
3079 To avoid the need for fibonaci heap on double ints we simply compress
3080 double ints into indexes to BOUNDS array and then represent the queue
3081 as arrays of queues for every index.
3082 Index of BOUNDS.length() means that the execution of given BB has
3083 no bounds determined.
3085 VISITED is a pointer map translating basic block into smallest index
3086 it was inserted into the priority queue with. */
3089 /* Start walk in loop header with index set to infinite bound. */
3090 queue_index
= bounds
.length ();
3091 queues
.safe_grow_cleared (queue_index
+ 1);
3092 queue
.safe_push (loop
->header
);
3093 queues
[queue_index
] = queue
;
3094 *pointer_map_insert (block_priority
, loop
->header
) = (void *)queue_index
;
3096 for (; queue_index
>= 0; queue_index
--)
3098 if (latch_index
< queue_index
)
3100 while (queues
[queue_index
].length ())
3103 ptrdiff_t bound_index
= queue_index
;
3108 queue
= queues
[queue_index
];
3111 /* OK, we later inserted the BB with lower priority, skip it. */
3112 if ((ptrdiff_t)*pointer_map_contains (block_priority
, bb
) > queue_index
)
3115 /* See if we can improve the bound. */
3116 entry
= pointer_map_contains (bb_bounds
, bb
);
3117 if (entry
&& (ptrdiff_t)*entry
< bound_index
)
3118 bound_index
= (ptrdiff_t)*entry
;
3120 /* Insert succesors into the queue, watch for latch edge
3121 and record greatest index we saw. */
3122 FOR_EACH_EDGE (e
, ei
, bb
->succs
)
3124 bool insert
= false;
3127 if (loop_exit_edge_p (loop
, e
))
3130 if (e
== loop_latch_edge (loop
)
3131 && latch_index
< bound_index
)
3132 latch_index
= bound_index
;
3133 else if (!(entry
= pointer_map_contains (block_priority
, e
->dest
)))
3136 *pointer_map_insert (block_priority
, e
->dest
) = (void *)bound_index
;
3138 else if ((ptrdiff_t)*entry
< bound_index
)
3141 *entry
= (void *)bound_index
;
3146 bb_queue queue2
= queues
[bound_index
];
3147 queue2
.safe_push (e
->dest
);
3148 queues
[bound_index
] = queue2
;
3154 queues
[queue_index
].release ();
3157 gcc_assert (latch_index
>= 0);
3158 if ((unsigned)latch_index
< bounds
.length ())
3160 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
3162 fprintf (dump_file
, "Found better loop bound ");
3163 dump_double_int (dump_file
, bounds
[latch_index
], true);
3164 fprintf (dump_file
, "\n");
3166 record_niter_bound (loop
, bounds
[latch_index
], false, true);
3170 pointer_map_destroy (bb_bounds
);
3171 pointer_map_destroy (block_priority
);
3174 /* See if every path cross the loop goes through a statement that is known
3175 to not execute at the last iteration. In that case we can decrese iteration
3179 maybe_lower_iteration_bound (struct loop
*loop
)
3181 pointer_set_t
*not_executed_last_iteration
= NULL
;
3182 struct nb_iter_bound
*elt
;
3183 bool found_exit
= false;
3184 vec
<basic_block
> queue
= vNULL
;
3187 /* Collect all statements with interesting (i.e. lower than
3188 nb_iterations_upper_bound) bound on them.
3190 TODO: Due to the way record_estimate choose estimates to store, the bounds
3191 will be always nb_iterations_upper_bound-1. We can change this to record
3192 also statements not dominating the loop latch and update the walk bellow
3193 to the shortest path algorthm. */
3194 for (elt
= loop
->bounds
; elt
; elt
= elt
->next
)
3197 && elt
->bound
.ult (loop
->nb_iterations_upper_bound
))
3199 if (!not_executed_last_iteration
)
3200 not_executed_last_iteration
= pointer_set_create ();
3201 pointer_set_insert (not_executed_last_iteration
, elt
->stmt
);
3204 if (!not_executed_last_iteration
)
3207 /* Start DFS walk in the loop header and see if we can reach the
3208 loop latch or any of the exits (including statements with side
3209 effects that may terminate the loop otherwise) without visiting
3210 any of the statements known to have undefined effect on the last
3212 queue
.safe_push (loop
->header
);
3213 visited
= BITMAP_ALLOC (NULL
);
3214 bitmap_set_bit (visited
, loop
->header
->index
);
3219 basic_block bb
= queue
.pop ();
3220 gimple_stmt_iterator gsi
;
3221 bool stmt_found
= false;
3223 /* Loop for possible exits and statements bounding the execution. */
3224 for (gsi
= gsi_start_bb (bb
); !gsi_end_p (gsi
); gsi_next (&gsi
))
3226 gimple stmt
= gsi_stmt (gsi
);
3227 if (pointer_set_contains (not_executed_last_iteration
, stmt
))
3232 if (gimple_has_side_effects (stmt
))
3241 /* If no bounding statement is found, continue the walk. */
3247 FOR_EACH_EDGE (e
, ei
, bb
->succs
)
3249 if (loop_exit_edge_p (loop
, e
)
3250 || e
== loop_latch_edge (loop
))
3255 if (bitmap_set_bit (visited
, e
->dest
->index
))
3256 queue
.safe_push (e
->dest
);
3260 while (queue
.length () && !found_exit
);
3262 /* If every path through the loop reach bounding statement before exit,
3263 then we know the last iteration of the loop will have undefined effect
3264 and we can decrease number of iterations. */
3268 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
3269 fprintf (dump_file
, "Reducing loop iteration estimate by 1; "
3270 "undefined statement must be executed at the last iteration.\n");
3271 record_niter_bound (loop
, loop
->nb_iterations_upper_bound
- double_int_one
,
3274 BITMAP_FREE (visited
);
3278 /* Records estimates on numbers of iterations of LOOP. If USE_UNDEFINED_P
3279 is true also use estimates derived from undefined behavior. */
3282 estimate_numbers_of_iterations_loop (struct loop
*loop
)
3287 struct tree_niter_desc niter_desc
;
3292 /* Give up if we already have tried to compute an estimation. */
3293 if (loop
->estimate_state
!= EST_NOT_COMPUTED
)
3296 loop
->estimate_state
= EST_AVAILABLE
;
3297 /* Force estimate compuation but leave any existing upper bound in place. */
3298 loop
->any_estimate
= false;
3300 exits
= get_loop_exit_edges (loop
);
3301 likely_exit
= single_likely_exit (loop
);
3302 FOR_EACH_VEC_ELT (exits
, i
, ex
)
3304 if (!number_of_iterations_exit (loop
, ex
, &niter_desc
, false, false))
3307 niter
= niter_desc
.niter
;
3308 type
= TREE_TYPE (niter
);
3309 if (TREE_CODE (niter_desc
.may_be_zero
) != INTEGER_CST
)
3310 niter
= build3 (COND_EXPR
, type
, niter_desc
.may_be_zero
,
3311 build_int_cst (type
, 0),
3313 record_estimate (loop
, niter
, niter_desc
.max
,
3314 last_stmt (ex
->src
),
3315 true, ex
== likely_exit
, true);
3319 infer_loop_bounds_from_undefined (loop
);
3321 discover_iteration_bound_by_body_walk (loop
);
3323 maybe_lower_iteration_bound (loop
);
3325 /* If we have a measured profile, use it to estimate the number of
3327 if (loop
->header
->count
!= 0)
3329 gcov_type nit
= expected_loop_iterations_unbounded (loop
) + 1;
3330 bound
= gcov_type_to_double_int (nit
);
3331 record_niter_bound (loop
, bound
, true, false);
3335 /* Sets NIT to the estimated number of executions of the latch of the
3336 LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as
3337 large as the number of iterations. If we have no reliable estimate,
3338 the function returns false, otherwise returns true. */
3341 estimated_loop_iterations (struct loop
*loop
, double_int
*nit
)
3343 /* When SCEV information is available, try to update loop iterations
3344 estimate. Otherwise just return whatever we recorded earlier. */
3345 if (scev_initialized_p ())
3346 estimate_numbers_of_iterations_loop (loop
);
3348 /* Even if the bound is not recorded, possibly we can derrive one from
3350 if (!loop
->any_estimate
)
3352 if (loop
->header
->count
)
3354 *nit
= gcov_type_to_double_int
3355 (expected_loop_iterations_unbounded (loop
) + 1);
3361 *nit
= loop
->nb_iterations_estimate
;
3365 /* Sets NIT to an upper bound for the maximum number of executions of the
3366 latch of the LOOP. If we have no reliable estimate, the function returns
3367 false, otherwise returns true. */
3370 max_loop_iterations (struct loop
*loop
, double_int
*nit
)
3372 /* When SCEV information is available, try to update loop iterations
3373 estimate. Otherwise just return whatever we recorded earlier. */
3374 if (scev_initialized_p ())
3375 estimate_numbers_of_iterations_loop (loop
);
3376 if (!loop
->any_upper_bound
)
3379 *nit
= loop
->nb_iterations_upper_bound
;
3383 /* Similar to estimated_loop_iterations, but returns the estimate only
3384 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
3385 on the number of iterations of LOOP could not be derived, returns -1. */
3388 estimated_loop_iterations_int (struct loop
*loop
)
3391 HOST_WIDE_INT hwi_nit
;
3393 if (!estimated_loop_iterations (loop
, &nit
))
3396 if (!nit
.fits_shwi ())
3398 hwi_nit
= nit
.to_shwi ();
3400 return hwi_nit
< 0 ? -1 : hwi_nit
;
3403 /* Similar to max_loop_iterations, but returns the estimate only
3404 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
3405 on the number of iterations of LOOP could not be derived, returns -1. */
3408 max_loop_iterations_int (struct loop
*loop
)
3411 HOST_WIDE_INT hwi_nit
;
3413 if (!max_loop_iterations (loop
, &nit
))
3416 if (!nit
.fits_shwi ())
3418 hwi_nit
= nit
.to_shwi ();
3420 return hwi_nit
< 0 ? -1 : hwi_nit
;
3423 /* Returns an upper bound on the number of executions of statements
3424 in the LOOP. For statements before the loop exit, this exceeds
3425 the number of execution of the latch by one. */
3428 max_stmt_executions_int (struct loop
*loop
)
3430 HOST_WIDE_INT nit
= max_loop_iterations_int (loop
);
3436 snit
= (HOST_WIDE_INT
) ((unsigned HOST_WIDE_INT
) nit
+ 1);
3438 /* If the computation overflows, return -1. */
3439 return snit
< 0 ? -1 : snit
;
3442 /* Returns an estimate for the number of executions of statements
3443 in the LOOP. For statements before the loop exit, this exceeds
3444 the number of execution of the latch by one. */
3447 estimated_stmt_executions_int (struct loop
*loop
)
3449 HOST_WIDE_INT nit
= estimated_loop_iterations_int (loop
);
3455 snit
= (HOST_WIDE_INT
) ((unsigned HOST_WIDE_INT
) nit
+ 1);
3457 /* If the computation overflows, return -1. */
3458 return snit
< 0 ? -1 : snit
;
3461 /* Sets NIT to the estimated maximum number of executions of the latch of the
3462 LOOP, plus one. If we have no reliable estimate, the function returns
3463 false, otherwise returns true. */
3466 max_stmt_executions (struct loop
*loop
, double_int
*nit
)
3468 double_int nit_minus_one
;
3470 if (!max_loop_iterations (loop
, nit
))
3473 nit_minus_one
= *nit
;
3475 *nit
+= double_int_one
;
3477 return (*nit
).ugt (nit_minus_one
);
3480 /* Sets NIT to the estimated number of executions of the latch of the
3481 LOOP, plus one. If we have no reliable estimate, the function returns
3482 false, otherwise returns true. */
3485 estimated_stmt_executions (struct loop
*loop
, double_int
*nit
)
3487 double_int nit_minus_one
;
3489 if (!estimated_loop_iterations (loop
, nit
))
3492 nit_minus_one
= *nit
;
3494 *nit
+= double_int_one
;
3496 return (*nit
).ugt (nit_minus_one
);
3499 /* Records estimates on numbers of iterations of loops. */
3502 estimate_numbers_of_iterations (void)
3507 /* We don't want to issue signed overflow warnings while getting
3508 loop iteration estimates. */
3509 fold_defer_overflow_warnings ();
3511 FOR_EACH_LOOP (li
, loop
, 0)
3513 estimate_numbers_of_iterations_loop (loop
);
3516 fold_undefer_and_ignore_overflow_warnings ();
3519 /* Returns true if statement S1 dominates statement S2. */
3522 stmt_dominates_stmt_p (gimple s1
, gimple s2
)
3524 basic_block bb1
= gimple_bb (s1
), bb2
= gimple_bb (s2
);
3532 gimple_stmt_iterator bsi
;
3534 if (gimple_code (s2
) == GIMPLE_PHI
)
3537 if (gimple_code (s1
) == GIMPLE_PHI
)
3540 for (bsi
= gsi_start_bb (bb1
); gsi_stmt (bsi
) != s2
; gsi_next (&bsi
))
3541 if (gsi_stmt (bsi
) == s1
)
3547 return dominated_by_p (CDI_DOMINATORS
, bb2
, bb1
);
3550 /* Returns true when we can prove that the number of executions of
3551 STMT in the loop is at most NITER, according to the bound on
3552 the number of executions of the statement NITER_BOUND->stmt recorded in
3553 NITER_BOUND. If STMT is NULL, we must prove this bound for all
3554 statements in the loop. */
3557 n_of_executions_at_most (gimple stmt
,
3558 struct nb_iter_bound
*niter_bound
,
3561 double_int bound
= niter_bound
->bound
;
3562 tree nit_type
= TREE_TYPE (niter
), e
;
3565 gcc_assert (TYPE_UNSIGNED (nit_type
));
3567 /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
3568 the number of iterations is small. */
3569 if (!double_int_fits_to_tree_p (nit_type
, bound
))
3572 /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
3573 times. This means that:
3575 -- if NITER_BOUND->is_exit is true, then everything before
3576 NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
3577 times, and everything after it at most NITER_BOUND->bound times.
3579 -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
3580 is executed, then NITER_BOUND->stmt is executed as well in the same
3581 iteration (we conclude that if both statements belong to the same
3582 basic block, or if STMT is after NITER_BOUND->stmt), then STMT
3583 is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
3584 executed at most NITER_BOUND->bound + 2 times. */
3586 if (niter_bound
->is_exit
)
3589 && stmt
!= niter_bound
->stmt
3590 && stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
))
3598 || (gimple_bb (stmt
) != gimple_bb (niter_bound
->stmt
)
3599 && !stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
)))
3601 bound
+= double_int_one
;
3602 if (bound
.is_zero ()
3603 || !double_int_fits_to_tree_p (nit_type
, bound
))
3609 e
= fold_binary (cmp
, boolean_type_node
,
3610 niter
, double_int_to_tree (nit_type
, bound
));
3611 return e
&& integer_nonzerop (e
);
3614 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
3617 nowrap_type_p (tree type
)
3619 if (INTEGRAL_TYPE_P (type
)
3620 && TYPE_OVERFLOW_UNDEFINED (type
))
3623 if (POINTER_TYPE_P (type
))
3629 /* Return false only when the induction variable BASE + STEP * I is
3630 known to not overflow: i.e. when the number of iterations is small
3631 enough with respect to the step and initial condition in order to
3632 keep the evolution confined in TYPEs bounds. Return true when the
3633 iv is known to overflow or when the property is not computable.
3635 USE_OVERFLOW_SEMANTICS is true if this function should assume that
3636 the rules for overflow of the given language apply (e.g., that signed
3637 arithmetics in C does not overflow). */
3640 scev_probably_wraps_p (tree base
, tree step
,
3641 gimple at_stmt
, struct loop
*loop
,
3642 bool use_overflow_semantics
)
3644 struct nb_iter_bound
*bound
;
3645 tree delta
, step_abs
;
3646 tree unsigned_type
, valid_niter
;
3647 tree type
= TREE_TYPE (step
);
3649 /* FIXME: We really need something like
3650 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
3652 We used to test for the following situation that frequently appears
3653 during address arithmetics:
3655 D.1621_13 = (long unsigned intD.4) D.1620_12;
3656 D.1622_14 = D.1621_13 * 8;
3657 D.1623_15 = (doubleD.29 *) D.1622_14;
3659 And derived that the sequence corresponding to D_14
3660 can be proved to not wrap because it is used for computing a
3661 memory access; however, this is not really the case -- for example,
3662 if D_12 = (unsigned char) [254,+,1], then D_14 has values
3663 2032, 2040, 0, 8, ..., but the code is still legal. */
3665 if (chrec_contains_undetermined (base
)
3666 || chrec_contains_undetermined (step
))
3669 if (integer_zerop (step
))
3672 /* If we can use the fact that signed and pointer arithmetics does not
3673 wrap, we are done. */
3674 if (use_overflow_semantics
&& nowrap_type_p (TREE_TYPE (base
)))
3677 /* To be able to use estimates on number of iterations of the loop,
3678 we must have an upper bound on the absolute value of the step. */
3679 if (TREE_CODE (step
) != INTEGER_CST
)
3682 /* Don't issue signed overflow warnings. */
3683 fold_defer_overflow_warnings ();
3685 /* Otherwise, compute the number of iterations before we reach the
3686 bound of the type, and verify that the loop is exited before this
3688 unsigned_type
= unsigned_type_for (type
);
3689 base
= fold_convert (unsigned_type
, base
);
3691 if (tree_int_cst_sign_bit (step
))
3693 tree extreme
= fold_convert (unsigned_type
,
3694 lower_bound_in_type (type
, type
));
3695 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
3696 step_abs
= fold_build1 (NEGATE_EXPR
, unsigned_type
,
3697 fold_convert (unsigned_type
, step
));
3701 tree extreme
= fold_convert (unsigned_type
,
3702 upper_bound_in_type (type
, type
));
3703 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
3704 step_abs
= fold_convert (unsigned_type
, step
);
3707 valid_niter
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step_abs
);
3709 estimate_numbers_of_iterations_loop (loop
);
3710 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
3712 if (n_of_executions_at_most (at_stmt
, bound
, valid_niter
))
3714 fold_undefer_and_ignore_overflow_warnings ();
3719 fold_undefer_and_ignore_overflow_warnings ();
3721 /* At this point we still don't have a proof that the iv does not
3722 overflow: give up. */
3726 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
3729 free_numbers_of_iterations_estimates_loop (struct loop
*loop
)
3731 struct nb_iter_bound
*bound
, *next
;
3733 loop
->nb_iterations
= NULL
;
3734 loop
->estimate_state
= EST_NOT_COMPUTED
;
3735 for (bound
= loop
->bounds
; bound
; bound
= next
)
3741 loop
->bounds
= NULL
;
3744 /* Frees the information on upper bounds on numbers of iterations of loops. */
3747 free_numbers_of_iterations_estimates (void)
3752 FOR_EACH_LOOP (li
, loop
, 0)
3754 free_numbers_of_iterations_estimates_loop (loop
);
3758 /* Substitute value VAL for ssa name NAME inside expressions held
3762 substitute_in_loop_info (struct loop
*loop
, tree name
, tree val
)
3764 loop
->nb_iterations
= simplify_replace_tree (loop
->nb_iterations
, name
, val
);