1 /* Functions to determine/estimate number of iterations of a loop.
2 Copyright (C) 2004, 2005, 2006, 2007, 2008, 2009, 2010
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"
29 #include "tree-pretty-print.h"
30 #include "gimple-pretty-print.h"
32 #include "tree-flow.h"
33 #include "tree-dump.h"
35 #include "tree-pass.h"
37 #include "tree-chrec.h"
38 #include "tree-scalar-evolution.h"
39 #include "tree-data-ref.h"
42 #include "diagnostic-core.h"
43 #include "tree-inline.h"
46 #define SWAP(X, Y) do { affine_iv *tmp = (X); (X) = (Y); (Y) = tmp; } while (0)
48 /* The maximum number of dominator BBs we search for conditions
49 of loop header copies we use for simplifying a conditional
51 #define MAX_DOMINATORS_TO_WALK 8
55 Analysis of number of iterations of an affine exit test.
59 /* Bounds on some value, BELOW <= X <= UP. */
67 /* Splits expression EXPR to a variable part VAR and constant OFFSET. */
70 split_to_var_and_offset (tree expr
, tree
*var
, mpz_t offset
)
72 tree type
= TREE_TYPE (expr
);
78 mpz_set_ui (offset
, 0);
80 switch (TREE_CODE (expr
))
87 case POINTER_PLUS_EXPR
:
88 op0
= TREE_OPERAND (expr
, 0);
89 op1
= TREE_OPERAND (expr
, 1);
91 if (TREE_CODE (op1
) != INTEGER_CST
)
95 /* Always sign extend the offset. */
96 off
= tree_to_double_int (op1
);
97 off
= double_int_sext (off
, TYPE_PRECISION (type
));
98 mpz_set_double_int (offset
, off
, false);
100 mpz_neg (offset
, offset
);
104 *var
= build_int_cst_type (type
, 0);
105 off
= tree_to_double_int (expr
);
106 mpz_set_double_int (offset
, off
, TYPE_UNSIGNED (type
));
114 /* Stores estimate on the minimum/maximum value of the expression VAR + OFF
115 in TYPE to MIN and MAX. */
118 determine_value_range (tree type
, tree var
, mpz_t off
,
119 mpz_t min
, mpz_t max
)
121 /* If the expression is a constant, we know its value exactly. */
122 if (integer_zerop (var
))
129 /* If the computation may wrap, we know nothing about the value, except for
130 the range of the type. */
131 get_type_static_bounds (type
, min
, max
);
132 if (!nowrap_type_p (type
))
135 /* Since the addition of OFF does not wrap, if OFF is positive, then we may
136 add it to MIN, otherwise to MAX. */
137 if (mpz_sgn (off
) < 0)
138 mpz_add (max
, max
, off
);
140 mpz_add (min
, min
, off
);
143 /* Stores the bounds on the difference of the values of the expressions
144 (var + X) and (var + Y), computed in TYPE, to BNDS. */
147 bound_difference_of_offsetted_base (tree type
, mpz_t x
, mpz_t y
,
150 int rel
= mpz_cmp (x
, y
);
151 bool may_wrap
= !nowrap_type_p (type
);
154 /* If X == Y, then the expressions are always equal.
155 If X > Y, there are the following possibilities:
156 a) neither of var + X and var + Y overflow or underflow, or both of
157 them do. Then their difference is X - Y.
158 b) var + X overflows, and var + Y does not. Then the values of the
159 expressions are var + X - M and var + Y, where M is the range of
160 the type, and their difference is X - Y - M.
161 c) var + Y underflows and var + X does not. Their difference again
163 Therefore, if the arithmetics in type does not overflow, then the
164 bounds are (X - Y, X - Y), otherwise they are (X - Y - M, X - Y)
165 Similarly, if X < Y, the bounds are either (X - Y, X - Y) or
166 (X - Y, X - Y + M). */
170 mpz_set_ui (bnds
->below
, 0);
171 mpz_set_ui (bnds
->up
, 0);
176 mpz_set_double_int (m
, double_int_mask (TYPE_PRECISION (type
)), true);
177 mpz_add_ui (m
, m
, 1);
178 mpz_sub (bnds
->up
, x
, y
);
179 mpz_set (bnds
->below
, bnds
->up
);
184 mpz_sub (bnds
->below
, bnds
->below
, m
);
186 mpz_add (bnds
->up
, bnds
->up
, m
);
192 /* From condition C0 CMP C1 derives information regarding the
193 difference of values of VARX + OFFX and VARY + OFFY, computed in TYPE,
194 and stores it to BNDS. */
197 refine_bounds_using_guard (tree type
, tree varx
, mpz_t offx
,
198 tree vary
, mpz_t offy
,
199 tree c0
, enum tree_code cmp
, tree c1
,
202 tree varc0
, varc1
, tmp
, ctype
;
203 mpz_t offc0
, offc1
, loffx
, loffy
, bnd
;
205 bool no_wrap
= nowrap_type_p (type
);
214 STRIP_SIGN_NOPS (c0
);
215 STRIP_SIGN_NOPS (c1
);
216 ctype
= TREE_TYPE (c0
);
217 if (!useless_type_conversion_p (ctype
, type
))
223 /* We could derive quite precise information from EQ_EXPR, however, such
224 a guard is unlikely to appear, so we do not bother with handling
229 /* NE_EXPR comparisons do not contain much of useful information, except for
230 special case of comparing with the bounds of the type. */
231 if (TREE_CODE (c1
) != INTEGER_CST
232 || !INTEGRAL_TYPE_P (type
))
235 /* Ensure that the condition speaks about an expression in the same type
237 ctype
= TREE_TYPE (c0
);
238 if (TYPE_PRECISION (ctype
) != TYPE_PRECISION (type
))
240 c0
= fold_convert (type
, c0
);
241 c1
= fold_convert (type
, c1
);
243 if (TYPE_MIN_VALUE (type
)
244 && operand_equal_p (c1
, TYPE_MIN_VALUE (type
), 0))
249 if (TYPE_MAX_VALUE (type
)
250 && operand_equal_p (c1
, TYPE_MAX_VALUE (type
), 0))
263 split_to_var_and_offset (expand_simple_operations (c0
), &varc0
, offc0
);
264 split_to_var_and_offset (expand_simple_operations (c1
), &varc1
, offc1
);
266 /* We are only interested in comparisons of expressions based on VARX and
267 VARY. TODO -- we might also be able to derive some bounds from
268 expressions containing just one of the variables. */
270 if (operand_equal_p (varx
, varc1
, 0))
272 tmp
= varc0
; varc0
= varc1
; varc1
= tmp
;
273 mpz_swap (offc0
, offc1
);
274 cmp
= swap_tree_comparison (cmp
);
277 if (!operand_equal_p (varx
, varc0
, 0)
278 || !operand_equal_p (vary
, varc1
, 0))
281 mpz_init_set (loffx
, offx
);
282 mpz_init_set (loffy
, offy
);
284 if (cmp
== GT_EXPR
|| cmp
== GE_EXPR
)
286 tmp
= varx
; varx
= vary
; vary
= tmp
;
287 mpz_swap (offc0
, offc1
);
288 mpz_swap (loffx
, loffy
);
289 cmp
= swap_tree_comparison (cmp
);
293 /* If there is no overflow, the condition implies that
295 (VARX + OFFX) cmp (VARY + OFFY) + (OFFX - OFFY + OFFC1 - OFFC0).
297 The overflows and underflows may complicate things a bit; each
298 overflow decreases the appropriate offset by M, and underflow
299 increases it by M. The above inequality would not necessarily be
302 -- VARX + OFFX underflows and VARX + OFFC0 does not, or
303 VARX + OFFC0 overflows, but VARX + OFFX does not.
304 This may only happen if OFFX < OFFC0.
305 -- VARY + OFFY overflows and VARY + OFFC1 does not, or
306 VARY + OFFC1 underflows and VARY + OFFY does not.
307 This may only happen if OFFY > OFFC1. */
316 x_ok
= (integer_zerop (varx
)
317 || mpz_cmp (loffx
, offc0
) >= 0);
318 y_ok
= (integer_zerop (vary
)
319 || mpz_cmp (loffy
, offc1
) <= 0);
325 mpz_sub (bnd
, loffx
, loffy
);
326 mpz_add (bnd
, bnd
, offc1
);
327 mpz_sub (bnd
, bnd
, offc0
);
330 mpz_sub_ui (bnd
, bnd
, 1);
335 if (mpz_cmp (bnds
->below
, bnd
) < 0)
336 mpz_set (bnds
->below
, bnd
);
340 if (mpz_cmp (bnd
, bnds
->up
) < 0)
341 mpz_set (bnds
->up
, bnd
);
353 /* Stores the bounds on the value of the expression X - Y in LOOP to BNDS.
354 The subtraction is considered to be performed in arbitrary precision,
357 We do not attempt to be too clever regarding the value ranges of X and
358 Y; most of the time, they are just integers or ssa names offsetted by
359 integer. However, we try to use the information contained in the
360 comparisons before the loop (usually created by loop header copying). */
363 bound_difference (struct loop
*loop
, tree x
, tree y
, bounds
*bnds
)
365 tree type
= TREE_TYPE (x
);
368 mpz_t minx
, maxx
, miny
, maxy
;
376 /* Get rid of unnecessary casts, but preserve the value of
381 mpz_init (bnds
->below
);
385 split_to_var_and_offset (x
, &varx
, offx
);
386 split_to_var_and_offset (y
, &vary
, offy
);
388 if (!integer_zerop (varx
)
389 && operand_equal_p (varx
, vary
, 0))
391 /* Special case VARX == VARY -- we just need to compare the
392 offsets. The matters are a bit more complicated in the
393 case addition of offsets may wrap. */
394 bound_difference_of_offsetted_base (type
, offx
, offy
, bnds
);
398 /* Otherwise, use the value ranges to determine the initial
399 estimates on below and up. */
404 determine_value_range (type
, varx
, offx
, minx
, maxx
);
405 determine_value_range (type
, vary
, offy
, miny
, maxy
);
407 mpz_sub (bnds
->below
, minx
, maxy
);
408 mpz_sub (bnds
->up
, maxx
, miny
);
415 /* If both X and Y are constants, we cannot get any more precise. */
416 if (integer_zerop (varx
) && integer_zerop (vary
))
419 /* Now walk the dominators of the loop header and use the entry
420 guards to refine the estimates. */
421 for (bb
= loop
->header
;
422 bb
!= ENTRY_BLOCK_PTR
&& cnt
< MAX_DOMINATORS_TO_WALK
;
423 bb
= get_immediate_dominator (CDI_DOMINATORS
, bb
))
425 if (!single_pred_p (bb
))
427 e
= single_pred_edge (bb
);
429 if (!(e
->flags
& (EDGE_TRUE_VALUE
| EDGE_FALSE_VALUE
)))
432 cond
= last_stmt (e
->src
);
433 c0
= gimple_cond_lhs (cond
);
434 cmp
= gimple_cond_code (cond
);
435 c1
= gimple_cond_rhs (cond
);
437 if (e
->flags
& EDGE_FALSE_VALUE
)
438 cmp
= invert_tree_comparison (cmp
, false);
440 refine_bounds_using_guard (type
, varx
, offx
, vary
, offy
,
450 /* Update the bounds in BNDS that restrict the value of X to the bounds
451 that restrict the value of X + DELTA. X can be obtained as a
452 difference of two values in TYPE. */
455 bounds_add (bounds
*bnds
, double_int delta
, tree type
)
460 mpz_set_double_int (mdelta
, delta
, false);
463 mpz_set_double_int (max
, double_int_mask (TYPE_PRECISION (type
)), true);
465 mpz_add (bnds
->up
, bnds
->up
, mdelta
);
466 mpz_add (bnds
->below
, bnds
->below
, mdelta
);
468 if (mpz_cmp (bnds
->up
, max
) > 0)
469 mpz_set (bnds
->up
, max
);
472 if (mpz_cmp (bnds
->below
, max
) < 0)
473 mpz_set (bnds
->below
, max
);
479 /* Update the bounds in BNDS that restrict the value of X to the bounds
480 that restrict the value of -X. */
483 bounds_negate (bounds
*bnds
)
487 mpz_init_set (tmp
, bnds
->up
);
488 mpz_neg (bnds
->up
, bnds
->below
);
489 mpz_neg (bnds
->below
, tmp
);
493 /* Returns inverse of X modulo 2^s, where MASK = 2^s-1. */
496 inverse (tree x
, tree mask
)
498 tree type
= TREE_TYPE (x
);
500 unsigned ctr
= tree_floor_log2 (mask
);
502 if (TYPE_PRECISION (type
) <= HOST_BITS_PER_WIDE_INT
)
504 unsigned HOST_WIDE_INT ix
;
505 unsigned HOST_WIDE_INT imask
;
506 unsigned HOST_WIDE_INT irslt
= 1;
508 gcc_assert (cst_and_fits_in_hwi (x
));
509 gcc_assert (cst_and_fits_in_hwi (mask
));
511 ix
= int_cst_value (x
);
512 imask
= int_cst_value (mask
);
521 rslt
= build_int_cst_type (type
, irslt
);
525 rslt
= build_int_cst (type
, 1);
528 rslt
= int_const_binop (MULT_EXPR
, rslt
, x
);
529 x
= int_const_binop (MULT_EXPR
, x
, x
);
531 rslt
= int_const_binop (BIT_AND_EXPR
, rslt
, mask
);
537 /* Derives the upper bound BND on the number of executions of loop with exit
538 condition S * i <> C. If NO_OVERFLOW is true, then the control variable of
539 the loop does not overflow. EXIT_MUST_BE_TAKEN is true if we are guaranteed
540 that the loop ends through this exit, i.e., the induction variable ever
541 reaches the value of C.
543 The value C is equal to final - base, where final and base are the final and
544 initial value of the actual induction variable in the analysed loop. BNDS
545 bounds the value of this difference when computed in signed type with
546 unbounded range, while the computation of C is performed in an unsigned
547 type with the range matching the range of the type of the induction variable.
548 In particular, BNDS.up contains an upper bound on C in the following cases:
549 -- if the iv must reach its final value without overflow, i.e., if
550 NO_OVERFLOW && EXIT_MUST_BE_TAKEN is true, or
551 -- if final >= base, which we know to hold when BNDS.below >= 0. */
554 number_of_iterations_ne_max (mpz_t bnd
, bool no_overflow
, tree c
, tree s
,
555 bounds
*bnds
, bool exit_must_be_taken
)
559 bool bnds_u_valid
= ((no_overflow
&& exit_must_be_taken
)
560 || mpz_sgn (bnds
->below
) >= 0);
562 if (multiple_of_p (TREE_TYPE (c
), c
, s
))
564 /* If C is an exact multiple of S, then its value will be reached before
565 the induction variable overflows (unless the loop is exited in some
566 other way before). Note that the actual induction variable in the
567 loop (which ranges from base to final instead of from 0 to C) may
568 overflow, in which case BNDS.up will not be giving a correct upper
569 bound on C; thus, BNDS_U_VALID had to be computed in advance. */
571 exit_must_be_taken
= true;
574 /* If the induction variable can overflow, the number of iterations is at
575 most the period of the control variable (or infinite, but in that case
576 the whole # of iterations analysis will fail). */
579 max
= double_int_mask (TYPE_PRECISION (TREE_TYPE (c
))
580 - tree_low_cst (num_ending_zeros (s
), 1));
581 mpz_set_double_int (bnd
, max
, true);
585 /* Now we know that the induction variable does not overflow, so the loop
586 iterates at most (range of type / S) times. */
587 mpz_set_double_int (bnd
, double_int_mask (TYPE_PRECISION (TREE_TYPE (c
))),
590 /* If the induction variable is guaranteed to reach the value of C before
592 if (exit_must_be_taken
)
594 /* ... then we can strenghten this to C / S, and possibly we can use
595 the upper bound on C given by BNDS. */
596 if (TREE_CODE (c
) == INTEGER_CST
)
597 mpz_set_double_int (bnd
, tree_to_double_int (c
), true);
598 else if (bnds_u_valid
)
599 mpz_set (bnd
, bnds
->up
);
603 mpz_set_double_int (d
, tree_to_double_int (s
), true);
604 mpz_fdiv_q (bnd
, bnd
, d
);
608 /* Determines number of iterations of loop whose ending condition
609 is IV <> FINAL. TYPE is the type of the iv. The number of
610 iterations is stored to NITER. EXIT_MUST_BE_TAKEN is true if
611 we know that the exit must be taken eventually, i.e., that the IV
612 ever reaches the value FINAL (we derived this earlier, and possibly set
613 NITER->assumptions to make sure this is the case). BNDS contains the
614 bounds on the difference FINAL - IV->base. */
617 number_of_iterations_ne (tree type
, affine_iv
*iv
, tree final
,
618 struct tree_niter_desc
*niter
, bool exit_must_be_taken
,
621 tree niter_type
= unsigned_type_for (type
);
622 tree s
, c
, d
, bits
, assumption
, tmp
, bound
;
625 niter
->control
= *iv
;
626 niter
->bound
= final
;
627 niter
->cmp
= NE_EXPR
;
629 /* Rearrange the terms so that we get inequality S * i <> C, with S
630 positive. Also cast everything to the unsigned type. If IV does
631 not overflow, BNDS bounds the value of C. Also, this is the
632 case if the computation |FINAL - IV->base| does not overflow, i.e.,
633 if BNDS->below in the result is nonnegative. */
634 if (tree_int_cst_sign_bit (iv
->step
))
636 s
= fold_convert (niter_type
,
637 fold_build1 (NEGATE_EXPR
, type
, iv
->step
));
638 c
= fold_build2 (MINUS_EXPR
, niter_type
,
639 fold_convert (niter_type
, iv
->base
),
640 fold_convert (niter_type
, final
));
641 bounds_negate (bnds
);
645 s
= fold_convert (niter_type
, iv
->step
);
646 c
= fold_build2 (MINUS_EXPR
, niter_type
,
647 fold_convert (niter_type
, final
),
648 fold_convert (niter_type
, iv
->base
));
652 number_of_iterations_ne_max (max
, iv
->no_overflow
, c
, s
, bnds
,
654 niter
->max
= mpz_get_double_int (niter_type
, max
, false);
657 /* First the trivial cases -- when the step is 1. */
658 if (integer_onep (s
))
664 /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
665 is infinite. Otherwise, the number of iterations is
666 (inverse(s/d) * (c/d)) mod (size of mode/d). */
667 bits
= num_ending_zeros (s
);
668 bound
= build_low_bits_mask (niter_type
,
669 (TYPE_PRECISION (niter_type
)
670 - tree_low_cst (bits
, 1)));
672 d
= fold_binary_to_constant (LSHIFT_EXPR
, niter_type
,
673 build_int_cst (niter_type
, 1), bits
);
674 s
= fold_binary_to_constant (RSHIFT_EXPR
, niter_type
, s
, bits
);
676 if (!exit_must_be_taken
)
678 /* If we cannot assume that the exit is taken eventually, record the
679 assumptions for divisibility of c. */
680 assumption
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, c
, d
);
681 assumption
= fold_build2 (EQ_EXPR
, boolean_type_node
,
682 assumption
, build_int_cst (niter_type
, 0));
683 if (!integer_nonzerop (assumption
))
684 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
685 niter
->assumptions
, assumption
);
688 c
= fold_build2 (EXACT_DIV_EXPR
, niter_type
, c
, d
);
689 tmp
= fold_build2 (MULT_EXPR
, niter_type
, c
, inverse (s
, bound
));
690 niter
->niter
= fold_build2 (BIT_AND_EXPR
, niter_type
, tmp
, bound
);
694 /* Checks whether we can determine the final value of the control variable
695 of the loop with ending condition IV0 < IV1 (computed in TYPE).
696 DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
697 of the step. The assumptions necessary to ensure that the computation
698 of the final value does not overflow are recorded in NITER. If we
699 find the final value, we adjust DELTA and return TRUE. Otherwise
700 we return false. BNDS bounds the value of IV1->base - IV0->base,
701 and will be updated by the same amount as DELTA. EXIT_MUST_BE_TAKEN is
702 true if we know that the exit must be taken eventually. */
705 number_of_iterations_lt_to_ne (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
706 struct tree_niter_desc
*niter
,
707 tree
*delta
, tree step
,
708 bool exit_must_be_taken
, bounds
*bnds
)
710 tree niter_type
= TREE_TYPE (step
);
711 tree mod
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, *delta
, step
);
714 tree assumption
= boolean_true_node
, bound
, noloop
;
715 bool ret
= false, fv_comp_no_overflow
;
717 if (POINTER_TYPE_P (type
))
720 if (TREE_CODE (mod
) != INTEGER_CST
)
722 if (integer_nonzerop (mod
))
723 mod
= fold_build2 (MINUS_EXPR
, niter_type
, step
, mod
);
724 tmod
= fold_convert (type1
, mod
);
727 mpz_set_double_int (mmod
, tree_to_double_int (mod
), true);
728 mpz_neg (mmod
, mmod
);
730 /* If the induction variable does not overflow and the exit is taken,
731 then the computation of the final value does not overflow. This is
732 also obviously the case if the new final value is equal to the
733 current one. Finally, we postulate this for pointer type variables,
734 as the code cannot rely on the object to that the pointer points being
735 placed at the end of the address space (and more pragmatically,
736 TYPE_{MIN,MAX}_VALUE is not defined for pointers). */
737 if (integer_zerop (mod
) || POINTER_TYPE_P (type
))
738 fv_comp_no_overflow
= true;
739 else if (!exit_must_be_taken
)
740 fv_comp_no_overflow
= false;
742 fv_comp_no_overflow
=
743 (iv0
->no_overflow
&& integer_nonzerop (iv0
->step
))
744 || (iv1
->no_overflow
&& integer_nonzerop (iv1
->step
));
746 if (integer_nonzerop (iv0
->step
))
748 /* The final value of the iv is iv1->base + MOD, assuming that this
749 computation does not overflow, and that
750 iv0->base <= iv1->base + MOD. */
751 if (!fv_comp_no_overflow
)
753 bound
= fold_build2 (MINUS_EXPR
, type1
,
754 TYPE_MAX_VALUE (type1
), tmod
);
755 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
757 if (integer_zerop (assumption
))
760 if (mpz_cmp (mmod
, bnds
->below
) < 0)
761 noloop
= boolean_false_node
;
762 else if (POINTER_TYPE_P (type
))
763 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
765 fold_build_pointer_plus (iv1
->base
, tmod
));
767 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
769 fold_build2 (PLUS_EXPR
, type1
,
774 /* The final value of the iv is iv0->base - MOD, assuming that this
775 computation does not overflow, and that
776 iv0->base - MOD <= iv1->base. */
777 if (!fv_comp_no_overflow
)
779 bound
= fold_build2 (PLUS_EXPR
, type1
,
780 TYPE_MIN_VALUE (type1
), tmod
);
781 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
783 if (integer_zerop (assumption
))
786 if (mpz_cmp (mmod
, bnds
->below
) < 0)
787 noloop
= boolean_false_node
;
788 else if (POINTER_TYPE_P (type
))
789 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
790 fold_build_pointer_plus (iv0
->base
,
791 fold_build1 (NEGATE_EXPR
,
795 noloop
= fold_build2 (GT_EXPR
, boolean_type_node
,
796 fold_build2 (MINUS_EXPR
, type1
,
801 if (!integer_nonzerop (assumption
))
802 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
805 if (!integer_zerop (noloop
))
806 niter
->may_be_zero
= fold_build2 (TRUTH_OR_EXPR
, boolean_type_node
,
809 bounds_add (bnds
, tree_to_double_int (mod
), type
);
810 *delta
= fold_build2 (PLUS_EXPR
, niter_type
, *delta
, mod
);
818 /* Add assertions to NITER that ensure that the control variable of the loop
819 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
820 are TYPE. Returns false if we can prove that there is an overflow, true
821 otherwise. STEP is the absolute value of the step. */
824 assert_no_overflow_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
825 struct tree_niter_desc
*niter
, tree step
)
827 tree bound
, d
, assumption
, diff
;
828 tree niter_type
= TREE_TYPE (step
);
830 if (integer_nonzerop (iv0
->step
))
832 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
833 if (iv0
->no_overflow
)
836 /* If iv0->base is a constant, we can determine the last value before
837 overflow precisely; otherwise we conservatively assume
840 if (TREE_CODE (iv0
->base
) == INTEGER_CST
)
842 d
= fold_build2 (MINUS_EXPR
, niter_type
,
843 fold_convert (niter_type
, TYPE_MAX_VALUE (type
)),
844 fold_convert (niter_type
, iv0
->base
));
845 diff
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, d
, step
);
848 diff
= fold_build2 (MINUS_EXPR
, niter_type
, step
,
849 build_int_cst (niter_type
, 1));
850 bound
= fold_build2 (MINUS_EXPR
, type
,
851 TYPE_MAX_VALUE (type
), fold_convert (type
, diff
));
852 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
857 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
858 if (iv1
->no_overflow
)
861 if (TREE_CODE (iv1
->base
) == INTEGER_CST
)
863 d
= fold_build2 (MINUS_EXPR
, niter_type
,
864 fold_convert (niter_type
, iv1
->base
),
865 fold_convert (niter_type
, TYPE_MIN_VALUE (type
)));
866 diff
= fold_build2 (FLOOR_MOD_EXPR
, niter_type
, d
, step
);
869 diff
= fold_build2 (MINUS_EXPR
, niter_type
, step
,
870 build_int_cst (niter_type
, 1));
871 bound
= fold_build2 (PLUS_EXPR
, type
,
872 TYPE_MIN_VALUE (type
), fold_convert (type
, diff
));
873 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
877 if (integer_zerop (assumption
))
879 if (!integer_nonzerop (assumption
))
880 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
881 niter
->assumptions
, assumption
);
883 iv0
->no_overflow
= true;
884 iv1
->no_overflow
= true;
888 /* Add an assumption to NITER that a loop whose ending condition
889 is IV0 < IV1 rolls. TYPE is the type of the control iv. BNDS
890 bounds the value of IV1->base - IV0->base. */
893 assert_loop_rolls_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
894 struct tree_niter_desc
*niter
, bounds
*bnds
)
896 tree assumption
= boolean_true_node
, bound
, diff
;
897 tree mbz
, mbzl
, mbzr
, type1
;
898 bool rolls_p
, no_overflow_p
;
902 /* We are going to compute the number of iterations as
903 (iv1->base - iv0->base + step - 1) / step, computed in the unsigned
904 variant of TYPE. This formula only works if
906 -step + 1 <= (iv1->base - iv0->base) <= MAX - step + 1
908 (where MAX is the maximum value of the unsigned variant of TYPE, and
909 the computations in this formula are performed in full precision,
910 i.e., without overflows).
912 Usually, for loops with exit condition iv0->base + step * i < iv1->base,
913 we have a condition of the form iv0->base - step < iv1->base before the loop,
914 and for loops iv0->base < iv1->base - step * i the condition
915 iv0->base < iv1->base + step, due to loop header copying, which enable us
916 to prove the lower bound.
918 The upper bound is more complicated. Unless the expressions for initial
919 and final value themselves contain enough information, we usually cannot
920 derive it from the context. */
922 /* First check whether the answer does not follow from the bounds we gathered
924 if (integer_nonzerop (iv0
->step
))
925 dstep
= tree_to_double_int (iv0
->step
);
928 dstep
= double_int_sext (tree_to_double_int (iv1
->step
),
929 TYPE_PRECISION (type
));
930 dstep
= double_int_neg (dstep
);
934 mpz_set_double_int (mstep
, dstep
, true);
935 mpz_neg (mstep
, mstep
);
936 mpz_add_ui (mstep
, mstep
, 1);
938 rolls_p
= mpz_cmp (mstep
, bnds
->below
) <= 0;
941 mpz_set_double_int (max
, double_int_mask (TYPE_PRECISION (type
)), true);
942 mpz_add (max
, max
, mstep
);
943 no_overflow_p
= (mpz_cmp (bnds
->up
, max
) <= 0
944 /* For pointers, only values lying inside a single object
945 can be compared or manipulated by pointer arithmetics.
946 Gcc in general does not allow or handle objects larger
947 than half of the address space, hence the upper bound
948 is satisfied for pointers. */
949 || POINTER_TYPE_P (type
));
953 if (rolls_p
&& no_overflow_p
)
957 if (POINTER_TYPE_P (type
))
960 /* Now the hard part; we must formulate the assumption(s) as expressions, and
961 we must be careful not to introduce overflow. */
963 if (integer_nonzerop (iv0
->step
))
965 diff
= fold_build2 (MINUS_EXPR
, type1
,
966 iv0
->step
, build_int_cst (type1
, 1));
968 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
969 0 address never belongs to any object, we can assume this for
971 if (!POINTER_TYPE_P (type
))
973 bound
= fold_build2 (PLUS_EXPR
, type1
,
974 TYPE_MIN_VALUE (type
), diff
);
975 assumption
= fold_build2 (GE_EXPR
, boolean_type_node
,
979 /* And then we can compute iv0->base - diff, and compare it with
981 mbzl
= fold_build2 (MINUS_EXPR
, type1
,
982 fold_convert (type1
, iv0
->base
), diff
);
983 mbzr
= fold_convert (type1
, iv1
->base
);
987 diff
= fold_build2 (PLUS_EXPR
, type1
,
988 iv1
->step
, build_int_cst (type1
, 1));
990 if (!POINTER_TYPE_P (type
))
992 bound
= fold_build2 (PLUS_EXPR
, type1
,
993 TYPE_MAX_VALUE (type
), diff
);
994 assumption
= fold_build2 (LE_EXPR
, boolean_type_node
,
998 mbzl
= fold_convert (type1
, iv0
->base
);
999 mbzr
= fold_build2 (MINUS_EXPR
, type1
,
1000 fold_convert (type1
, iv1
->base
), diff
);
1003 if (!integer_nonzerop (assumption
))
1004 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
1005 niter
->assumptions
, assumption
);
1008 mbz
= fold_build2 (GT_EXPR
, boolean_type_node
, mbzl
, mbzr
);
1009 niter
->may_be_zero
= fold_build2 (TRUTH_OR_EXPR
, boolean_type_node
,
1010 niter
->may_be_zero
, mbz
);
1014 /* Determines number of iterations of loop whose ending condition
1015 is IV0 < IV1. TYPE is the type of the iv. The number of
1016 iterations is stored to NITER. BNDS bounds the difference
1017 IV1->base - IV0->base. EXIT_MUST_BE_TAKEN is true if we know
1018 that the exit must be taken eventually. */
1021 number_of_iterations_lt (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
1022 struct tree_niter_desc
*niter
,
1023 bool exit_must_be_taken
, bounds
*bnds
)
1025 tree niter_type
= unsigned_type_for (type
);
1026 tree delta
, step
, s
;
1029 if (integer_nonzerop (iv0
->step
))
1031 niter
->control
= *iv0
;
1032 niter
->cmp
= LT_EXPR
;
1033 niter
->bound
= iv1
->base
;
1037 niter
->control
= *iv1
;
1038 niter
->cmp
= GT_EXPR
;
1039 niter
->bound
= iv0
->base
;
1042 delta
= fold_build2 (MINUS_EXPR
, niter_type
,
1043 fold_convert (niter_type
, iv1
->base
),
1044 fold_convert (niter_type
, iv0
->base
));
1046 /* First handle the special case that the step is +-1. */
1047 if ((integer_onep (iv0
->step
) && integer_zerop (iv1
->step
))
1048 || (integer_all_onesp (iv1
->step
) && integer_zerop (iv0
->step
)))
1050 /* for (i = iv0->base; i < iv1->base; i++)
1054 for (i = iv1->base; i > iv0->base; i--).
1056 In both cases # of iterations is iv1->base - iv0->base, assuming that
1057 iv1->base >= iv0->base.
1059 First try to derive a lower bound on the value of
1060 iv1->base - iv0->base, computed in full precision. If the difference
1061 is nonnegative, we are done, otherwise we must record the
1064 if (mpz_sgn (bnds
->below
) < 0)
1065 niter
->may_be_zero
= fold_build2 (LT_EXPR
, boolean_type_node
,
1066 iv1
->base
, iv0
->base
);
1067 niter
->niter
= delta
;
1068 niter
->max
= mpz_get_double_int (niter_type
, bnds
->up
, false);
1072 if (integer_nonzerop (iv0
->step
))
1073 step
= fold_convert (niter_type
, iv0
->step
);
1075 step
= fold_convert (niter_type
,
1076 fold_build1 (NEGATE_EXPR
, type
, iv1
->step
));
1078 /* If we can determine the final value of the control iv exactly, we can
1079 transform the condition to != comparison. In particular, this will be
1080 the case if DELTA is constant. */
1081 if (number_of_iterations_lt_to_ne (type
, iv0
, iv1
, niter
, &delta
, step
,
1082 exit_must_be_taken
, bnds
))
1086 zps
.base
= build_int_cst (niter_type
, 0);
1088 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
1089 zps does not overflow. */
1090 zps
.no_overflow
= true;
1092 return number_of_iterations_ne (type
, &zps
, delta
, niter
, true, bnds
);
1095 /* Make sure that the control iv does not overflow. */
1096 if (!assert_no_overflow_lt (type
, iv0
, iv1
, niter
, step
))
1099 /* We determine the number of iterations as (delta + step - 1) / step. For
1100 this to work, we must know that iv1->base >= iv0->base - step + 1,
1101 otherwise the loop does not roll. */
1102 assert_loop_rolls_lt (type
, iv0
, iv1
, niter
, bnds
);
1104 s
= fold_build2 (MINUS_EXPR
, niter_type
,
1105 step
, build_int_cst (niter_type
, 1));
1106 delta
= fold_build2 (PLUS_EXPR
, niter_type
, delta
, s
);
1107 niter
->niter
= fold_build2 (FLOOR_DIV_EXPR
, niter_type
, delta
, step
);
1111 mpz_set_double_int (mstep
, tree_to_double_int (step
), true);
1112 mpz_add (tmp
, bnds
->up
, mstep
);
1113 mpz_sub_ui (tmp
, tmp
, 1);
1114 mpz_fdiv_q (tmp
, tmp
, mstep
);
1115 niter
->max
= mpz_get_double_int (niter_type
, tmp
, false);
1122 /* Determines number of iterations of loop whose ending condition
1123 is IV0 <= IV1. TYPE is the type of the iv. The number of
1124 iterations is stored to NITER. EXIT_MUST_BE_TAKEN is true if
1125 we know that this condition must eventually become false (we derived this
1126 earlier, and possibly set NITER->assumptions to make sure this
1127 is the case). BNDS bounds the difference IV1->base - IV0->base. */
1130 number_of_iterations_le (tree type
, affine_iv
*iv0
, affine_iv
*iv1
,
1131 struct tree_niter_desc
*niter
, bool exit_must_be_taken
,
1136 if (POINTER_TYPE_P (type
))
1139 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
1140 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
1141 value of the type. This we must know anyway, since if it is
1142 equal to this value, the loop rolls forever. We do not check
1143 this condition for pointer type ivs, as the code cannot rely on
1144 the object to that the pointer points being placed at the end of
1145 the address space (and more pragmatically, TYPE_{MIN,MAX}_VALUE is
1146 not defined for pointers). */
1148 if (!exit_must_be_taken
&& !POINTER_TYPE_P (type
))
1150 if (integer_nonzerop (iv0
->step
))
1151 assumption
= fold_build2 (NE_EXPR
, boolean_type_node
,
1152 iv1
->base
, TYPE_MAX_VALUE (type
));
1154 assumption
= fold_build2 (NE_EXPR
, boolean_type_node
,
1155 iv0
->base
, TYPE_MIN_VALUE (type
));
1157 if (integer_zerop (assumption
))
1159 if (!integer_nonzerop (assumption
))
1160 niter
->assumptions
= fold_build2 (TRUTH_AND_EXPR
, boolean_type_node
,
1161 niter
->assumptions
, assumption
);
1164 if (integer_nonzerop (iv0
->step
))
1166 if (POINTER_TYPE_P (type
))
1167 iv1
->base
= fold_build_pointer_plus_hwi (iv1
->base
, 1);
1169 iv1
->base
= fold_build2 (PLUS_EXPR
, type1
, iv1
->base
,
1170 build_int_cst (type1
, 1));
1172 else if (POINTER_TYPE_P (type
))
1173 iv0
->base
= fold_build_pointer_plus_hwi (iv0
->base
, -1);
1175 iv0
->base
= fold_build2 (MINUS_EXPR
, type1
,
1176 iv0
->base
, build_int_cst (type1
, 1));
1178 bounds_add (bnds
, double_int_one
, type1
);
1180 return number_of_iterations_lt (type
, iv0
, iv1
, niter
, exit_must_be_taken
,
1184 /* Dumps description of affine induction variable IV to FILE. */
1187 dump_affine_iv (FILE *file
, affine_iv
*iv
)
1189 if (!integer_zerop (iv
->step
))
1190 fprintf (file
, "[");
1192 print_generic_expr (dump_file
, iv
->base
, TDF_SLIM
);
1194 if (!integer_zerop (iv
->step
))
1196 fprintf (file
, ", + , ");
1197 print_generic_expr (dump_file
, iv
->step
, TDF_SLIM
);
1198 fprintf (file
, "]%s", iv
->no_overflow
? "(no_overflow)" : "");
1202 /* Determine the number of iterations according to condition (for staying
1203 inside loop) which compares two induction variables using comparison
1204 operator CODE. The induction variable on left side of the comparison
1205 is IV0, the right-hand side is IV1. Both induction variables must have
1206 type TYPE, which must be an integer or pointer type. The steps of the
1207 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
1209 LOOP is the loop whose number of iterations we are determining.
1211 ONLY_EXIT is true if we are sure this is the only way the loop could be
1212 exited (including possibly non-returning function calls, exceptions, etc.)
1213 -- in this case we can use the information whether the control induction
1214 variables can overflow or not in a more efficient way.
1216 The results (number of iterations and assumptions as described in
1217 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
1218 Returns false if it fails to determine number of iterations, true if it
1219 was determined (possibly with some assumptions). */
1222 number_of_iterations_cond (struct loop
*loop
,
1223 tree type
, affine_iv
*iv0
, enum tree_code code
,
1224 affine_iv
*iv1
, struct tree_niter_desc
*niter
,
1227 bool exit_must_be_taken
= false, ret
;
1230 /* The meaning of these assumptions is this:
1232 then the rest of information does not have to be valid
1233 if may_be_zero then the loop does not roll, even if
1235 niter
->assumptions
= boolean_true_node
;
1236 niter
->may_be_zero
= boolean_false_node
;
1237 niter
->niter
= NULL_TREE
;
1238 niter
->max
= double_int_zero
;
1240 niter
->bound
= NULL_TREE
;
1241 niter
->cmp
= ERROR_MARK
;
1243 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
1244 the control variable is on lhs. */
1245 if (code
== GE_EXPR
|| code
== GT_EXPR
1246 || (code
== NE_EXPR
&& integer_zerop (iv0
->step
)))
1249 code
= swap_tree_comparison (code
);
1252 if (POINTER_TYPE_P (type
))
1254 /* Comparison of pointers is undefined unless both iv0 and iv1 point
1255 to the same object. If they do, the control variable cannot wrap
1256 (as wrap around the bounds of memory will never return a pointer
1257 that would be guaranteed to point to the same object, even if we
1258 avoid undefined behavior by casting to size_t and back). */
1259 iv0
->no_overflow
= true;
1260 iv1
->no_overflow
= true;
1263 /* If the control induction variable does not overflow and the only exit
1264 from the loop is the one that we analyze, we know it must be taken
1268 if (!integer_zerop (iv0
->step
) && iv0
->no_overflow
)
1269 exit_must_be_taken
= true;
1270 else if (!integer_zerop (iv1
->step
) && iv1
->no_overflow
)
1271 exit_must_be_taken
= true;
1274 /* We can handle the case when neither of the sides of the comparison is
1275 invariant, provided that the test is NE_EXPR. This rarely occurs in
1276 practice, but it is simple enough to manage. */
1277 if (!integer_zerop (iv0
->step
) && !integer_zerop (iv1
->step
))
1279 if (code
!= NE_EXPR
)
1282 iv0
->step
= fold_binary_to_constant (MINUS_EXPR
, type
,
1283 iv0
->step
, iv1
->step
);
1284 iv0
->no_overflow
= false;
1285 iv1
->step
= build_int_cst (type
, 0);
1286 iv1
->no_overflow
= true;
1289 /* If the result of the comparison is a constant, the loop is weird. More
1290 precise handling would be possible, but the situation is not common enough
1291 to waste time on it. */
1292 if (integer_zerop (iv0
->step
) && integer_zerop (iv1
->step
))
1295 /* Ignore loops of while (i-- < 10) type. */
1296 if (code
!= NE_EXPR
)
1298 if (iv0
->step
&& tree_int_cst_sign_bit (iv0
->step
))
1301 if (!integer_zerop (iv1
->step
) && !tree_int_cst_sign_bit (iv1
->step
))
1305 /* If the loop exits immediately, there is nothing to do. */
1306 if (integer_zerop (fold_build2 (code
, boolean_type_node
, iv0
->base
, iv1
->base
)))
1308 niter
->niter
= build_int_cst (unsigned_type_for (type
), 0);
1309 niter
->max
= double_int_zero
;
1313 /* OK, now we know we have a senseful loop. Handle several cases, depending
1314 on what comparison operator is used. */
1315 bound_difference (loop
, iv1
->base
, iv0
->base
, &bnds
);
1317 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1320 "Analyzing # of iterations of loop %d\n", loop
->num
);
1322 fprintf (dump_file
, " exit condition ");
1323 dump_affine_iv (dump_file
, iv0
);
1324 fprintf (dump_file
, " %s ",
1325 code
== NE_EXPR
? "!="
1326 : code
== LT_EXPR
? "<"
1328 dump_affine_iv (dump_file
, iv1
);
1329 fprintf (dump_file
, "\n");
1331 fprintf (dump_file
, " bounds on difference of bases: ");
1332 mpz_out_str (dump_file
, 10, bnds
.below
);
1333 fprintf (dump_file
, " ... ");
1334 mpz_out_str (dump_file
, 10, bnds
.up
);
1335 fprintf (dump_file
, "\n");
1341 gcc_assert (integer_zerop (iv1
->step
));
1342 ret
= number_of_iterations_ne (type
, iv0
, iv1
->base
, niter
,
1343 exit_must_be_taken
, &bnds
);
1347 ret
= number_of_iterations_lt (type
, iv0
, iv1
, niter
, exit_must_be_taken
,
1352 ret
= number_of_iterations_le (type
, iv0
, iv1
, niter
, exit_must_be_taken
,
1360 mpz_clear (bnds
.up
);
1361 mpz_clear (bnds
.below
);
1363 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
1367 fprintf (dump_file
, " result:\n");
1368 if (!integer_nonzerop (niter
->assumptions
))
1370 fprintf (dump_file
, " under assumptions ");
1371 print_generic_expr (dump_file
, niter
->assumptions
, TDF_SLIM
);
1372 fprintf (dump_file
, "\n");
1375 if (!integer_zerop (niter
->may_be_zero
))
1377 fprintf (dump_file
, " zero if ");
1378 print_generic_expr (dump_file
, niter
->may_be_zero
, TDF_SLIM
);
1379 fprintf (dump_file
, "\n");
1382 fprintf (dump_file
, " # of iterations ");
1383 print_generic_expr (dump_file
, niter
->niter
, TDF_SLIM
);
1384 fprintf (dump_file
, ", bounded by ");
1385 dump_double_int (dump_file
, niter
->max
, true);
1386 fprintf (dump_file
, "\n");
1389 fprintf (dump_file
, " failed\n\n");
1394 /* Substitute NEW for OLD in EXPR and fold the result. */
1397 simplify_replace_tree (tree expr
, tree old
, tree new_tree
)
1400 tree ret
= NULL_TREE
, e
, se
;
1405 /* Do not bother to replace constants. */
1406 if (CONSTANT_CLASS_P (old
))
1410 || operand_equal_p (expr
, old
, 0))
1411 return unshare_expr (new_tree
);
1416 n
= TREE_OPERAND_LENGTH (expr
);
1417 for (i
= 0; i
< n
; i
++)
1419 e
= TREE_OPERAND (expr
, i
);
1420 se
= simplify_replace_tree (e
, old
, new_tree
);
1425 ret
= copy_node (expr
);
1427 TREE_OPERAND (ret
, i
) = se
;
1430 return (ret
? fold (ret
) : expr
);
1433 /* Expand definitions of ssa names in EXPR as long as they are simple
1434 enough, and return the new expression. */
1437 expand_simple_operations (tree expr
)
1440 tree ret
= NULL_TREE
, e
, ee
, e1
;
1441 enum tree_code code
;
1444 if (expr
== NULL_TREE
)
1447 if (is_gimple_min_invariant (expr
))
1450 code
= TREE_CODE (expr
);
1451 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code
)))
1453 n
= TREE_OPERAND_LENGTH (expr
);
1454 for (i
= 0; i
< n
; i
++)
1456 e
= TREE_OPERAND (expr
, i
);
1457 ee
= expand_simple_operations (e
);
1462 ret
= copy_node (expr
);
1464 TREE_OPERAND (ret
, i
) = ee
;
1470 fold_defer_overflow_warnings ();
1472 fold_undefer_and_ignore_overflow_warnings ();
1476 if (TREE_CODE (expr
) != SSA_NAME
)
1479 stmt
= SSA_NAME_DEF_STMT (expr
);
1480 if (gimple_code (stmt
) == GIMPLE_PHI
)
1482 basic_block src
, dest
;
1484 if (gimple_phi_num_args (stmt
) != 1)
1486 e
= PHI_ARG_DEF (stmt
, 0);
1488 /* Avoid propagating through loop exit phi nodes, which
1489 could break loop-closed SSA form restrictions. */
1490 dest
= gimple_bb (stmt
);
1491 src
= single_pred (dest
);
1492 if (TREE_CODE (e
) == SSA_NAME
1493 && src
->loop_father
!= dest
->loop_father
)
1496 return expand_simple_operations (e
);
1498 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
1501 e
= gimple_assign_rhs1 (stmt
);
1502 code
= gimple_assign_rhs_code (stmt
);
1503 if (get_gimple_rhs_class (code
) == GIMPLE_SINGLE_RHS
)
1505 if (is_gimple_min_invariant (e
))
1508 if (code
== SSA_NAME
)
1509 return expand_simple_operations (e
);
1517 /* Casts are simple. */
1518 ee
= expand_simple_operations (e
);
1519 return fold_build1 (code
, TREE_TYPE (expr
), ee
);
1523 case POINTER_PLUS_EXPR
:
1524 /* And increments and decrements by a constant are simple. */
1525 e1
= gimple_assign_rhs2 (stmt
);
1526 if (!is_gimple_min_invariant (e1
))
1529 ee
= expand_simple_operations (e
);
1530 return fold_build2 (code
, TREE_TYPE (expr
), ee
, e1
);
1537 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1538 expression (or EXPR unchanged, if no simplification was possible). */
1541 tree_simplify_using_condition_1 (tree cond
, tree expr
)
1544 tree e
, te
, e0
, e1
, e2
, notcond
;
1545 enum tree_code code
= TREE_CODE (expr
);
1547 if (code
== INTEGER_CST
)
1550 if (code
== TRUTH_OR_EXPR
1551 || code
== TRUTH_AND_EXPR
1552 || code
== COND_EXPR
)
1556 e0
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 0));
1557 if (TREE_OPERAND (expr
, 0) != e0
)
1560 e1
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 1));
1561 if (TREE_OPERAND (expr
, 1) != e1
)
1564 if (code
== COND_EXPR
)
1566 e2
= tree_simplify_using_condition_1 (cond
, TREE_OPERAND (expr
, 2));
1567 if (TREE_OPERAND (expr
, 2) != e2
)
1575 if (code
== COND_EXPR
)
1576 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
1578 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
1584 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
1585 propagation, and vice versa. Fold does not handle this, since it is
1586 considered too expensive. */
1587 if (TREE_CODE (cond
) == EQ_EXPR
)
1589 e0
= TREE_OPERAND (cond
, 0);
1590 e1
= TREE_OPERAND (cond
, 1);
1592 /* We know that e0 == e1. Check whether we cannot simplify expr
1594 e
= simplify_replace_tree (expr
, e0
, e1
);
1595 if (integer_zerop (e
) || integer_nonzerop (e
))
1598 e
= simplify_replace_tree (expr
, e1
, e0
);
1599 if (integer_zerop (e
) || integer_nonzerop (e
))
1602 if (TREE_CODE (expr
) == EQ_EXPR
)
1604 e0
= TREE_OPERAND (expr
, 0);
1605 e1
= TREE_OPERAND (expr
, 1);
1607 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
1608 e
= simplify_replace_tree (cond
, e0
, e1
);
1609 if (integer_zerop (e
))
1611 e
= simplify_replace_tree (cond
, e1
, e0
);
1612 if (integer_zerop (e
))
1615 if (TREE_CODE (expr
) == NE_EXPR
)
1617 e0
= TREE_OPERAND (expr
, 0);
1618 e1
= TREE_OPERAND (expr
, 1);
1620 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
1621 e
= simplify_replace_tree (cond
, e0
, e1
);
1622 if (integer_zerop (e
))
1623 return boolean_true_node
;
1624 e
= simplify_replace_tree (cond
, e1
, e0
);
1625 if (integer_zerop (e
))
1626 return boolean_true_node
;
1629 te
= expand_simple_operations (expr
);
1631 /* Check whether COND ==> EXPR. */
1632 notcond
= invert_truthvalue (cond
);
1633 e
= fold_binary (TRUTH_OR_EXPR
, boolean_type_node
, notcond
, te
);
1634 if (e
&& integer_nonzerop (e
))
1637 /* Check whether COND ==> not EXPR. */
1638 e
= fold_binary (TRUTH_AND_EXPR
, boolean_type_node
, cond
, te
);
1639 if (e
&& integer_zerop (e
))
1645 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1646 expression (or EXPR unchanged, if no simplification was possible).
1647 Wrapper around tree_simplify_using_condition_1 that ensures that chains
1648 of simple operations in definitions of ssa names in COND are expanded,
1649 so that things like casts or incrementing the value of the bound before
1650 the loop do not cause us to fail. */
1653 tree_simplify_using_condition (tree cond
, tree expr
)
1655 cond
= expand_simple_operations (cond
);
1657 return tree_simplify_using_condition_1 (cond
, expr
);
1660 /* Tries to simplify EXPR using the conditions on entry to LOOP.
1661 Returns the simplified expression (or EXPR unchanged, if no
1662 simplification was possible).*/
1665 simplify_using_initial_conditions (struct loop
*loop
, tree expr
)
1673 if (TREE_CODE (expr
) == INTEGER_CST
)
1676 /* Limit walking the dominators to avoid quadraticness in
1677 the number of BBs times the number of loops in degenerate
1679 for (bb
= loop
->header
;
1680 bb
!= ENTRY_BLOCK_PTR
&& cnt
< MAX_DOMINATORS_TO_WALK
;
1681 bb
= get_immediate_dominator (CDI_DOMINATORS
, bb
))
1683 if (!single_pred_p (bb
))
1685 e
= single_pred_edge (bb
);
1687 if (!(e
->flags
& (EDGE_TRUE_VALUE
| EDGE_FALSE_VALUE
)))
1690 stmt
= last_stmt (e
->src
);
1691 cond
= fold_build2 (gimple_cond_code (stmt
),
1693 gimple_cond_lhs (stmt
),
1694 gimple_cond_rhs (stmt
));
1695 if (e
->flags
& EDGE_FALSE_VALUE
)
1696 cond
= invert_truthvalue (cond
);
1697 expr
= tree_simplify_using_condition (cond
, expr
);
1704 /* Tries to simplify EXPR using the evolutions of the loop invariants
1705 in the superloops of LOOP. Returns the simplified expression
1706 (or EXPR unchanged, if no simplification was possible). */
1709 simplify_using_outer_evolutions (struct loop
*loop
, tree expr
)
1711 enum tree_code code
= TREE_CODE (expr
);
1715 if (is_gimple_min_invariant (expr
))
1718 if (code
== TRUTH_OR_EXPR
1719 || code
== TRUTH_AND_EXPR
1720 || code
== COND_EXPR
)
1724 e0
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 0));
1725 if (TREE_OPERAND (expr
, 0) != e0
)
1728 e1
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 1));
1729 if (TREE_OPERAND (expr
, 1) != e1
)
1732 if (code
== COND_EXPR
)
1734 e2
= simplify_using_outer_evolutions (loop
, TREE_OPERAND (expr
, 2));
1735 if (TREE_OPERAND (expr
, 2) != e2
)
1743 if (code
== COND_EXPR
)
1744 expr
= fold_build3 (code
, boolean_type_node
, e0
, e1
, e2
);
1746 expr
= fold_build2 (code
, boolean_type_node
, e0
, e1
);
1752 e
= instantiate_parameters (loop
, expr
);
1753 if (is_gimple_min_invariant (e
))
1759 /* Returns true if EXIT is the only possible exit from LOOP. */
1762 loop_only_exit_p (const struct loop
*loop
, const_edge exit
)
1765 gimple_stmt_iterator bsi
;
1769 if (exit
!= single_exit (loop
))
1772 body
= get_loop_body (loop
);
1773 for (i
= 0; i
< loop
->num_nodes
; i
++)
1775 for (bsi
= gsi_start_bb (body
[i
]); !gsi_end_p (bsi
); gsi_next (&bsi
))
1777 call
= gsi_stmt (bsi
);
1778 if (gimple_code (call
) != GIMPLE_CALL
)
1781 if (gimple_has_side_effects (call
))
1793 /* Stores description of number of iterations of LOOP derived from
1794 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1795 useful information could be derived (and fields of NITER has
1796 meaning described in comments at struct tree_niter_desc
1797 declaration), false otherwise. If WARN is true and
1798 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1799 potentially unsafe assumptions. */
1802 number_of_iterations_exit (struct loop
*loop
, edge exit
,
1803 struct tree_niter_desc
*niter
,
1809 enum tree_code code
;
1812 if (!dominated_by_p (CDI_DOMINATORS
, loop
->latch
, exit
->src
))
1815 niter
->assumptions
= boolean_false_node
;
1816 stmt
= last_stmt (exit
->src
);
1817 if (!stmt
|| gimple_code (stmt
) != GIMPLE_COND
)
1820 /* We want the condition for staying inside loop. */
1821 code
= gimple_cond_code (stmt
);
1822 if (exit
->flags
& EDGE_TRUE_VALUE
)
1823 code
= invert_tree_comparison (code
, false);
1838 op0
= gimple_cond_lhs (stmt
);
1839 op1
= gimple_cond_rhs (stmt
);
1840 type
= TREE_TYPE (op0
);
1842 if (TREE_CODE (type
) != INTEGER_TYPE
1843 && !POINTER_TYPE_P (type
))
1846 if (!simple_iv (loop
, loop_containing_stmt (stmt
), op0
, &iv0
, false))
1848 if (!simple_iv (loop
, loop_containing_stmt (stmt
), op1
, &iv1
, false))
1851 /* We don't want to see undefined signed overflow warnings while
1852 computing the number of iterations. */
1853 fold_defer_overflow_warnings ();
1855 iv0
.base
= expand_simple_operations (iv0
.base
);
1856 iv1
.base
= expand_simple_operations (iv1
.base
);
1857 if (!number_of_iterations_cond (loop
, type
, &iv0
, code
, &iv1
, niter
,
1858 loop_only_exit_p (loop
, exit
)))
1860 fold_undefer_and_ignore_overflow_warnings ();
1866 niter
->assumptions
= simplify_using_outer_evolutions (loop
,
1867 niter
->assumptions
);
1868 niter
->may_be_zero
= simplify_using_outer_evolutions (loop
,
1869 niter
->may_be_zero
);
1870 niter
->niter
= simplify_using_outer_evolutions (loop
, niter
->niter
);
1874 = simplify_using_initial_conditions (loop
,
1875 niter
->assumptions
);
1877 = simplify_using_initial_conditions (loop
,
1878 niter
->may_be_zero
);
1880 fold_undefer_and_ignore_overflow_warnings ();
1882 if (integer_onep (niter
->assumptions
))
1885 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1886 But if we can prove that there is overflow or some other source of weird
1887 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1888 if (integer_zerop (niter
->assumptions
) || !single_exit (loop
))
1891 if (flag_unsafe_loop_optimizations
)
1892 niter
->assumptions
= boolean_true_node
;
1896 const char *wording
;
1897 location_t loc
= gimple_location (stmt
);
1899 /* We can provide a more specific warning if one of the operator is
1900 constant and the other advances by +1 or -1. */
1901 if (!integer_zerop (iv1
.step
)
1902 ? (integer_zerop (iv0
.step
)
1903 && (integer_onep (iv1
.step
) || integer_all_onesp (iv1
.step
)))
1904 : (integer_onep (iv0
.step
) || integer_all_onesp (iv0
.step
)))
1906 flag_unsafe_loop_optimizations
1907 ? N_("assuming that the loop is not infinite")
1908 : N_("cannot optimize possibly infinite loops");
1911 flag_unsafe_loop_optimizations
1912 ? N_("assuming that the loop counter does not overflow")
1913 : N_("cannot optimize loop, the loop counter may overflow");
1915 warning_at ((LOCATION_LINE (loc
) > 0) ? loc
: input_location
,
1916 OPT_Wunsafe_loop_optimizations
, "%s", gettext (wording
));
1919 return flag_unsafe_loop_optimizations
;
1922 /* Try to determine the number of iterations of LOOP. If we succeed,
1923 expression giving number of iterations is returned and *EXIT is
1924 set to the edge from that the information is obtained. Otherwise
1925 chrec_dont_know is returned. */
1928 find_loop_niter (struct loop
*loop
, edge
*exit
)
1931 VEC (edge
, heap
) *exits
= get_loop_exit_edges (loop
);
1933 tree niter
= NULL_TREE
, aniter
;
1934 struct tree_niter_desc desc
;
1937 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
1939 if (!just_once_each_iteration_p (loop
, ex
->src
))
1942 if (!number_of_iterations_exit (loop
, ex
, &desc
, false))
1945 if (integer_nonzerop (desc
.may_be_zero
))
1947 /* We exit in the first iteration through this exit.
1948 We won't find anything better. */
1949 niter
= build_int_cst (unsigned_type_node
, 0);
1954 if (!integer_zerop (desc
.may_be_zero
))
1957 aniter
= desc
.niter
;
1961 /* Nothing recorded yet. */
1967 /* Prefer constants, the lower the better. */
1968 if (TREE_CODE (aniter
) != INTEGER_CST
)
1971 if (TREE_CODE (niter
) != INTEGER_CST
)
1978 if (tree_int_cst_lt (aniter
, niter
))
1985 VEC_free (edge
, heap
, exits
);
1987 return niter
? niter
: chrec_dont_know
;
1990 /* Return true if loop is known to have bounded number of iterations. */
1993 finite_loop_p (struct loop
*loop
)
1996 VEC (edge
, heap
) *exits
;
1998 struct tree_niter_desc desc
;
1999 bool finite
= false;
2002 if (flag_unsafe_loop_optimizations
)
2004 flags
= flags_from_decl_or_type (current_function_decl
);
2005 if ((flags
& (ECF_CONST
|ECF_PURE
)) && !(flags
& ECF_LOOPING_CONST_OR_PURE
))
2007 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2008 fprintf (dump_file
, "Found loop %i to be finite: it is within pure or const function.\n",
2013 exits
= get_loop_exit_edges (loop
);
2014 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
2016 if (!just_once_each_iteration_p (loop
, ex
->src
))
2019 if (number_of_iterations_exit (loop
, ex
, &desc
, false))
2021 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2023 fprintf (dump_file
, "Found loop %i to be finite: iterating ", loop
->num
);
2024 print_generic_expr (dump_file
, desc
.niter
, TDF_SLIM
);
2025 fprintf (dump_file
, " times\n");
2031 VEC_free (edge
, heap
, exits
);
2037 Analysis of a number of iterations of a loop by a brute-force evaluation.
2041 /* Bound on the number of iterations we try to evaluate. */
2043 #define MAX_ITERATIONS_TO_TRACK \
2044 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
2046 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
2047 result by a chain of operations such that all but exactly one of their
2048 operands are constants. */
2051 chain_of_csts_start (struct loop
*loop
, tree x
)
2053 gimple stmt
= SSA_NAME_DEF_STMT (x
);
2055 basic_block bb
= gimple_bb (stmt
);
2056 enum tree_code code
;
2059 || !flow_bb_inside_loop_p (loop
, bb
))
2062 if (gimple_code (stmt
) == GIMPLE_PHI
)
2064 if (bb
== loop
->header
)
2070 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
2073 code
= gimple_assign_rhs_code (stmt
);
2074 if (gimple_references_memory_p (stmt
)
2075 || TREE_CODE_CLASS (code
) == tcc_reference
2076 || (code
== ADDR_EXPR
2077 && !is_gimple_min_invariant (gimple_assign_rhs1 (stmt
))))
2080 use
= SINGLE_SSA_TREE_OPERAND (stmt
, SSA_OP_USE
);
2081 if (use
== NULL_TREE
)
2084 return chain_of_csts_start (loop
, use
);
2087 /* Determines whether the expression X is derived from a result of a phi node
2088 in header of LOOP such that
2090 * the derivation of X consists only from operations with constants
2091 * the initial value of the phi node is constant
2092 * the value of the phi node in the next iteration can be derived from the
2093 value in the current iteration by a chain of operations with constants.
2095 If such phi node exists, it is returned, otherwise NULL is returned. */
2098 get_base_for (struct loop
*loop
, tree x
)
2103 if (is_gimple_min_invariant (x
))
2106 phi
= chain_of_csts_start (loop
, x
);
2110 init
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
2111 next
= PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
2113 if (TREE_CODE (next
) != SSA_NAME
)
2116 if (!is_gimple_min_invariant (init
))
2119 if (chain_of_csts_start (loop
, next
) != phi
)
2125 /* Given an expression X, then
2127 * if X is NULL_TREE, we return the constant BASE.
2128 * otherwise X is a SSA name, whose value in the considered loop is derived
2129 by a chain of operations with constant from a result of a phi node in
2130 the header of the loop. Then we return value of X when the value of the
2131 result of this phi node is given by the constant BASE. */
2134 get_val_for (tree x
, tree base
)
2138 gcc_assert (is_gimple_min_invariant (base
));
2143 stmt
= SSA_NAME_DEF_STMT (x
);
2144 if (gimple_code (stmt
) == GIMPLE_PHI
)
2147 gcc_assert (is_gimple_assign (stmt
));
2149 /* STMT must be either an assignment of a single SSA name or an
2150 expression involving an SSA name and a constant. Try to fold that
2151 expression using the value for the SSA name. */
2152 if (gimple_assign_ssa_name_copy_p (stmt
))
2153 return get_val_for (gimple_assign_rhs1 (stmt
), base
);
2154 else if (gimple_assign_rhs_class (stmt
) == GIMPLE_UNARY_RHS
2155 && TREE_CODE (gimple_assign_rhs1 (stmt
)) == SSA_NAME
)
2157 return fold_build1 (gimple_assign_rhs_code (stmt
),
2158 gimple_expr_type (stmt
),
2159 get_val_for (gimple_assign_rhs1 (stmt
), base
));
2161 else if (gimple_assign_rhs_class (stmt
) == GIMPLE_BINARY_RHS
)
2163 tree rhs1
= gimple_assign_rhs1 (stmt
);
2164 tree rhs2
= gimple_assign_rhs2 (stmt
);
2165 if (TREE_CODE (rhs1
) == SSA_NAME
)
2166 rhs1
= get_val_for (rhs1
, base
);
2167 else if (TREE_CODE (rhs2
) == SSA_NAME
)
2168 rhs2
= get_val_for (rhs2
, base
);
2171 return fold_build2 (gimple_assign_rhs_code (stmt
),
2172 gimple_expr_type (stmt
), rhs1
, rhs2
);
2179 /* Tries to count the number of iterations of LOOP till it exits by EXIT
2180 by brute force -- i.e. by determining the value of the operands of the
2181 condition at EXIT in first few iterations of the loop (assuming that
2182 these values are constant) and determining the first one in that the
2183 condition is not satisfied. Returns the constant giving the number
2184 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
2187 loop_niter_by_eval (struct loop
*loop
, edge exit
)
2190 tree op
[2], val
[2], next
[2], aval
[2];
2195 cond
= last_stmt (exit
->src
);
2196 if (!cond
|| gimple_code (cond
) != GIMPLE_COND
)
2197 return chrec_dont_know
;
2199 cmp
= gimple_cond_code (cond
);
2200 if (exit
->flags
& EDGE_TRUE_VALUE
)
2201 cmp
= invert_tree_comparison (cmp
, false);
2211 op
[0] = gimple_cond_lhs (cond
);
2212 op
[1] = gimple_cond_rhs (cond
);
2216 return chrec_dont_know
;
2219 for (j
= 0; j
< 2; j
++)
2221 if (is_gimple_min_invariant (op
[j
]))
2224 next
[j
] = NULL_TREE
;
2229 phi
= get_base_for (loop
, op
[j
]);
2231 return chrec_dont_know
;
2232 val
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
, loop_preheader_edge (loop
));
2233 next
[j
] = PHI_ARG_DEF_FROM_EDGE (phi
, loop_latch_edge (loop
));
2237 /* Don't issue signed overflow warnings. */
2238 fold_defer_overflow_warnings ();
2240 for (i
= 0; i
< MAX_ITERATIONS_TO_TRACK
; i
++)
2242 for (j
= 0; j
< 2; j
++)
2243 aval
[j
] = get_val_for (op
[j
], val
[j
]);
2245 acnd
= fold_binary (cmp
, boolean_type_node
, aval
[0], aval
[1]);
2246 if (acnd
&& integer_zerop (acnd
))
2248 fold_undefer_and_ignore_overflow_warnings ();
2249 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2251 "Proved that loop %d iterates %d times using brute force.\n",
2253 return build_int_cst (unsigned_type_node
, i
);
2256 for (j
= 0; j
< 2; j
++)
2258 val
[j
] = get_val_for (next
[j
], val
[j
]);
2259 if (!is_gimple_min_invariant (val
[j
]))
2261 fold_undefer_and_ignore_overflow_warnings ();
2262 return chrec_dont_know
;
2267 fold_undefer_and_ignore_overflow_warnings ();
2269 return chrec_dont_know
;
2272 /* Finds the exit of the LOOP by that the loop exits after a constant
2273 number of iterations and stores the exit edge to *EXIT. The constant
2274 giving the number of iterations of LOOP is returned. The number of
2275 iterations is determined using loop_niter_by_eval (i.e. by brute force
2276 evaluation). If we are unable to find the exit for that loop_niter_by_eval
2277 determines the number of iterations, chrec_dont_know is returned. */
2280 find_loop_niter_by_eval (struct loop
*loop
, edge
*exit
)
2283 VEC (edge
, heap
) *exits
= get_loop_exit_edges (loop
);
2285 tree niter
= NULL_TREE
, aniter
;
2289 /* Loops with multiple exits are expensive to handle and less important. */
2290 if (!flag_expensive_optimizations
2291 && VEC_length (edge
, exits
) > 1)
2292 return chrec_dont_know
;
2294 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
2296 if (!just_once_each_iteration_p (loop
, ex
->src
))
2299 aniter
= loop_niter_by_eval (loop
, ex
);
2300 if (chrec_contains_undetermined (aniter
))
2304 && !tree_int_cst_lt (aniter
, niter
))
2310 VEC_free (edge
, heap
, exits
);
2312 return niter
? niter
: chrec_dont_know
;
2317 Analysis of upper bounds on number of iterations of a loop.
2321 static double_int
derive_constant_upper_bound_ops (tree
, tree
,
2322 enum tree_code
, tree
);
2324 /* Returns a constant upper bound on the value of the right-hand side of
2325 an assignment statement STMT. */
2328 derive_constant_upper_bound_assign (gimple stmt
)
2330 enum tree_code code
= gimple_assign_rhs_code (stmt
);
2331 tree op0
= gimple_assign_rhs1 (stmt
);
2332 tree op1
= gimple_assign_rhs2 (stmt
);
2334 return derive_constant_upper_bound_ops (TREE_TYPE (gimple_assign_lhs (stmt
)),
2338 /* Returns a constant upper bound on the value of expression VAL. VAL
2339 is considered to be unsigned. If its type is signed, its value must
2343 derive_constant_upper_bound (tree val
)
2345 enum tree_code code
;
2348 extract_ops_from_tree (val
, &code
, &op0
, &op1
);
2349 return derive_constant_upper_bound_ops (TREE_TYPE (val
), op0
, code
, op1
);
2352 /* Returns a constant upper bound on the value of expression OP0 CODE OP1,
2353 whose type is TYPE. The expression is considered to be unsigned. If
2354 its type is signed, its value must be nonnegative. */
2357 derive_constant_upper_bound_ops (tree type
, tree op0
,
2358 enum tree_code code
, tree op1
)
2361 double_int bnd
, max
, mmax
, cst
;
2364 if (INTEGRAL_TYPE_P (type
))
2365 maxt
= TYPE_MAX_VALUE (type
);
2367 maxt
= upper_bound_in_type (type
, type
);
2369 max
= tree_to_double_int (maxt
);
2374 return tree_to_double_int (op0
);
2377 subtype
= TREE_TYPE (op0
);
2378 if (!TYPE_UNSIGNED (subtype
)
2379 /* If TYPE is also signed, the fact that VAL is nonnegative implies
2380 that OP0 is nonnegative. */
2381 && TYPE_UNSIGNED (type
)
2382 && !tree_expr_nonnegative_p (op0
))
2384 /* If we cannot prove that the casted expression is nonnegative,
2385 we cannot establish more useful upper bound than the precision
2386 of the type gives us. */
2390 /* We now know that op0 is an nonnegative value. Try deriving an upper
2392 bnd
= derive_constant_upper_bound (op0
);
2394 /* If the bound does not fit in TYPE, max. value of TYPE could be
2396 if (double_int_ucmp (max
, bnd
) < 0)
2402 case POINTER_PLUS_EXPR
:
2404 if (TREE_CODE (op1
) != INTEGER_CST
2405 || !tree_expr_nonnegative_p (op0
))
2408 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
2409 choose the most logical way how to treat this constant regardless
2410 of the signedness of the type. */
2411 cst
= tree_to_double_int (op1
);
2412 cst
= double_int_sext (cst
, TYPE_PRECISION (type
));
2413 if (code
!= MINUS_EXPR
)
2414 cst
= double_int_neg (cst
);
2416 bnd
= derive_constant_upper_bound (op0
);
2418 if (double_int_negative_p (cst
))
2420 cst
= double_int_neg (cst
);
2421 /* Avoid CST == 0x80000... */
2422 if (double_int_negative_p (cst
))
2425 /* OP0 + CST. We need to check that
2426 BND <= MAX (type) - CST. */
2428 mmax
= double_int_sub (max
, cst
);
2429 if (double_int_ucmp (bnd
, mmax
) > 0)
2432 return double_int_add (bnd
, cst
);
2436 /* OP0 - CST, where CST >= 0.
2438 If TYPE is signed, we have already verified that OP0 >= 0, and we
2439 know that the result is nonnegative. This implies that
2442 If TYPE is unsigned, we must additionally know that OP0 >= CST,
2443 otherwise the operation underflows.
2446 /* This should only happen if the type is unsigned; however, for
2447 buggy programs that use overflowing signed arithmetics even with
2448 -fno-wrapv, this condition may also be true for signed values. */
2449 if (double_int_ucmp (bnd
, cst
) < 0)
2452 if (TYPE_UNSIGNED (type
))
2454 tree tem
= fold_binary (GE_EXPR
, boolean_type_node
, op0
,
2455 double_int_to_tree (type
, cst
));
2456 if (!tem
|| integer_nonzerop (tem
))
2460 bnd
= double_int_sub (bnd
, cst
);
2465 case FLOOR_DIV_EXPR
:
2466 case EXACT_DIV_EXPR
:
2467 if (TREE_CODE (op1
) != INTEGER_CST
2468 || tree_int_cst_sign_bit (op1
))
2471 bnd
= derive_constant_upper_bound (op0
);
2472 return double_int_udiv (bnd
, tree_to_double_int (op1
), FLOOR_DIV_EXPR
);
2475 if (TREE_CODE (op1
) != INTEGER_CST
2476 || tree_int_cst_sign_bit (op1
))
2478 return tree_to_double_int (op1
);
2481 stmt
= SSA_NAME_DEF_STMT (op0
);
2482 if (gimple_code (stmt
) != GIMPLE_ASSIGN
2483 || gimple_assign_lhs (stmt
) != op0
)
2485 return derive_constant_upper_bound_assign (stmt
);
2492 /* Records that every statement in LOOP is executed I_BOUND times.
2493 REALISTIC is true if I_BOUND is expected to be close to the real number
2494 of iterations. UPPER is true if we are sure the loop iterates at most
2498 record_niter_bound (struct loop
*loop
, double_int i_bound
, bool realistic
,
2501 /* Update the bounds only when there is no previous estimation, or when the current
2502 estimation is smaller. */
2504 && (!loop
->any_upper_bound
2505 || double_int_ucmp (i_bound
, loop
->nb_iterations_upper_bound
) < 0))
2507 loop
->any_upper_bound
= true;
2508 loop
->nb_iterations_upper_bound
= i_bound
;
2511 && (!loop
->any_estimate
2512 || double_int_ucmp (i_bound
, loop
->nb_iterations_estimate
) < 0))
2514 loop
->any_estimate
= true;
2515 loop
->nb_iterations_estimate
= i_bound
;
2519 /* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. IS_EXIT
2520 is true if the loop is exited immediately after STMT, and this exit
2521 is taken at last when the STMT is executed BOUND + 1 times.
2522 REALISTIC is true if BOUND is expected to be close to the real number
2523 of iterations. UPPER is true if we are sure the loop iterates at most
2524 BOUND times. I_BOUND is an unsigned double_int upper estimate on BOUND. */
2527 record_estimate (struct loop
*loop
, tree bound
, double_int i_bound
,
2528 gimple at_stmt
, bool is_exit
, bool realistic
, bool upper
)
2533 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2535 fprintf (dump_file
, "Statement %s", is_exit
? "(exit)" : "");
2536 print_gimple_stmt (dump_file
, at_stmt
, 0, TDF_SLIM
);
2537 fprintf (dump_file
, " is %sexecuted at most ",
2538 upper
? "" : "probably ");
2539 print_generic_expr (dump_file
, bound
, TDF_SLIM
);
2540 fprintf (dump_file
, " (bounded by ");
2541 dump_double_int (dump_file
, i_bound
, true);
2542 fprintf (dump_file
, ") + 1 times in loop %d.\n", loop
->num
);
2545 /* If the I_BOUND is just an estimate of BOUND, it rarely is close to the
2546 real number of iterations. */
2547 if (TREE_CODE (bound
) != INTEGER_CST
)
2549 if (!upper
&& !realistic
)
2552 /* If we have a guaranteed upper bound, record it in the appropriate
2556 struct nb_iter_bound
*elt
= ggc_alloc_nb_iter_bound ();
2558 elt
->bound
= i_bound
;
2559 elt
->stmt
= at_stmt
;
2560 elt
->is_exit
= is_exit
;
2561 elt
->next
= loop
->bounds
;
2565 /* Update the number of iteration estimates according to the bound.
2566 If at_stmt is an exit or dominates the single exit from the loop,
2567 then the loop latch is executed at most BOUND times, otherwise
2568 it can be executed BOUND + 1 times. */
2569 exit
= single_exit (loop
);
2572 && dominated_by_p (CDI_DOMINATORS
,
2573 exit
->src
, gimple_bb (at_stmt
))))
2574 delta
= double_int_zero
;
2576 delta
= double_int_one
;
2577 i_bound
= double_int_add (i_bound
, delta
);
2579 /* If an overflow occurred, ignore the result. */
2580 if (double_int_ucmp (i_bound
, delta
) < 0)
2583 record_niter_bound (loop
, i_bound
, realistic
, upper
);
2586 /* Record the estimate on number of iterations of LOOP based on the fact that
2587 the induction variable BASE + STEP * i evaluated in STMT does not wrap and
2588 its values belong to the range <LOW, HIGH>. REALISTIC is true if the
2589 estimated number of iterations is expected to be close to the real one.
2590 UPPER is true if we are sure the induction variable does not wrap. */
2593 record_nonwrapping_iv (struct loop
*loop
, tree base
, tree step
, gimple stmt
,
2594 tree low
, tree high
, bool realistic
, bool upper
)
2596 tree niter_bound
, extreme
, delta
;
2597 tree type
= TREE_TYPE (base
), unsigned_type
;
2600 if (TREE_CODE (step
) != INTEGER_CST
|| integer_zerop (step
))
2603 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
2605 fprintf (dump_file
, "Induction variable (");
2606 print_generic_expr (dump_file
, TREE_TYPE (base
), TDF_SLIM
);
2607 fprintf (dump_file
, ") ");
2608 print_generic_expr (dump_file
, base
, TDF_SLIM
);
2609 fprintf (dump_file
, " + ");
2610 print_generic_expr (dump_file
, step
, TDF_SLIM
);
2611 fprintf (dump_file
, " * iteration does not wrap in statement ");
2612 print_gimple_stmt (dump_file
, stmt
, 0, TDF_SLIM
);
2613 fprintf (dump_file
, " in loop %d.\n", loop
->num
);
2616 unsigned_type
= unsigned_type_for (type
);
2617 base
= fold_convert (unsigned_type
, base
);
2618 step
= fold_convert (unsigned_type
, step
);
2620 if (tree_int_cst_sign_bit (step
))
2622 extreme
= fold_convert (unsigned_type
, low
);
2623 if (TREE_CODE (base
) != INTEGER_CST
)
2624 base
= fold_convert (unsigned_type
, high
);
2625 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
2626 step
= fold_build1 (NEGATE_EXPR
, unsigned_type
, step
);
2630 extreme
= fold_convert (unsigned_type
, high
);
2631 if (TREE_CODE (base
) != INTEGER_CST
)
2632 base
= fold_convert (unsigned_type
, low
);
2633 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
2636 /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
2637 would get out of the range. */
2638 niter_bound
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step
);
2639 max
= derive_constant_upper_bound (niter_bound
);
2640 record_estimate (loop
, niter_bound
, max
, stmt
, false, realistic
, upper
);
2643 /* Returns true if REF is a reference to an array at the end of a dynamically
2644 allocated structure. If this is the case, the array may be allocated larger
2645 than its upper bound implies. */
2648 array_at_struct_end_p (tree ref
)
2650 tree base
= get_base_address (ref
);
2653 /* Unless the reference is through a pointer, the size of the array matches
2655 if (!base
|| (!INDIRECT_REF_P (base
) && TREE_CODE (base
) != MEM_REF
))
2658 for (;handled_component_p (ref
); ref
= parent
)
2660 parent
= TREE_OPERAND (ref
, 0);
2662 if (TREE_CODE (ref
) == COMPONENT_REF
)
2664 /* All fields of a union are at its end. */
2665 if (TREE_CODE (TREE_TYPE (parent
)) == UNION_TYPE
)
2668 /* Unless the field is at the end of the struct, we are done. */
2669 field
= TREE_OPERAND (ref
, 1);
2670 if (DECL_CHAIN (field
))
2674 /* The other options are ARRAY_REF, ARRAY_RANGE_REF, VIEW_CONVERT_EXPR.
2675 In all these cases, we might be accessing the last element, and
2676 although in practice this will probably never happen, it is legal for
2677 the indices of this last element to exceed the bounds of the array.
2678 Therefore, continue checking. */
2684 /* Determine information about number of iterations a LOOP from the index
2685 IDX of a data reference accessed in STMT. RELIABLE is true if STMT is
2686 guaranteed to be executed in every iteration of LOOP. Callback for
2697 idx_infer_loop_bounds (tree base
, tree
*idx
, void *dta
)
2699 struct ilb_data
*data
= (struct ilb_data
*) dta
;
2700 tree ev
, init
, step
;
2701 tree low
, high
, type
, next
;
2702 bool sign
, upper
= data
->reliable
, at_end
= false;
2703 struct loop
*loop
= data
->loop
;
2705 if (TREE_CODE (base
) != ARRAY_REF
)
2708 /* For arrays at the end of the structure, we are not guaranteed that they
2709 do not really extend over their declared size. However, for arrays of
2710 size greater than one, this is unlikely to be intended. */
2711 if (array_at_struct_end_p (base
))
2717 ev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, *idx
));
2718 init
= initial_condition (ev
);
2719 step
= evolution_part_in_loop_num (ev
, loop
->num
);
2723 || TREE_CODE (step
) != INTEGER_CST
2724 || integer_zerop (step
)
2725 || tree_contains_chrecs (init
, NULL
)
2726 || chrec_contains_symbols_defined_in_loop (init
, loop
->num
))
2729 low
= array_ref_low_bound (base
);
2730 high
= array_ref_up_bound (base
);
2732 /* The case of nonconstant bounds could be handled, but it would be
2734 if (TREE_CODE (low
) != INTEGER_CST
2736 || TREE_CODE (high
) != INTEGER_CST
)
2738 sign
= tree_int_cst_sign_bit (step
);
2739 type
= TREE_TYPE (step
);
2741 /* The array of length 1 at the end of a structure most likely extends
2742 beyond its bounds. */
2744 && operand_equal_p (low
, high
, 0))
2747 /* In case the relevant bound of the array does not fit in type, or
2748 it does, but bound + step (in type) still belongs into the range of the
2749 array, the index may wrap and still stay within the range of the array
2750 (consider e.g. if the array is indexed by the full range of
2753 To make things simpler, we require both bounds to fit into type, although
2754 there are cases where this would not be strictly necessary. */
2755 if (!int_fits_type_p (high
, type
)
2756 || !int_fits_type_p (low
, type
))
2758 low
= fold_convert (type
, low
);
2759 high
= fold_convert (type
, high
);
2762 next
= fold_binary (PLUS_EXPR
, type
, low
, step
);
2764 next
= fold_binary (PLUS_EXPR
, type
, high
, step
);
2766 if (tree_int_cst_compare (low
, next
) <= 0
2767 && tree_int_cst_compare (next
, high
) <= 0)
2770 record_nonwrapping_iv (loop
, init
, step
, data
->stmt
, low
, high
, true, upper
);
2774 /* Determine information about number of iterations a LOOP from the bounds
2775 of arrays in the data reference REF accessed in STMT. RELIABLE is true if
2776 STMT is guaranteed to be executed in every iteration of LOOP.*/
2779 infer_loop_bounds_from_ref (struct loop
*loop
, gimple stmt
, tree ref
,
2782 struct ilb_data data
;
2786 data
.reliable
= reliable
;
2787 for_each_index (&ref
, idx_infer_loop_bounds
, &data
);
2790 /* Determine information about number of iterations of a LOOP from the way
2791 arrays are used in STMT. RELIABLE is true if STMT is guaranteed to be
2792 executed in every iteration of LOOP. */
2795 infer_loop_bounds_from_array (struct loop
*loop
, gimple stmt
, bool reliable
)
2797 if (is_gimple_assign (stmt
))
2799 tree op0
= gimple_assign_lhs (stmt
);
2800 tree op1
= gimple_assign_rhs1 (stmt
);
2802 /* For each memory access, analyze its access function
2803 and record a bound on the loop iteration domain. */
2804 if (REFERENCE_CLASS_P (op0
))
2805 infer_loop_bounds_from_ref (loop
, stmt
, op0
, reliable
);
2807 if (REFERENCE_CLASS_P (op1
))
2808 infer_loop_bounds_from_ref (loop
, stmt
, op1
, reliable
);
2810 else if (is_gimple_call (stmt
))
2813 unsigned i
, n
= gimple_call_num_args (stmt
);
2815 lhs
= gimple_call_lhs (stmt
);
2816 if (lhs
&& REFERENCE_CLASS_P (lhs
))
2817 infer_loop_bounds_from_ref (loop
, stmt
, lhs
, reliable
);
2819 for (i
= 0; i
< n
; i
++)
2821 arg
= gimple_call_arg (stmt
, i
);
2822 if (REFERENCE_CLASS_P (arg
))
2823 infer_loop_bounds_from_ref (loop
, stmt
, arg
, reliable
);
2828 /* Determine information about number of iterations of a LOOP from the fact
2829 that pointer arithmetics in STMT does not overflow. */
2832 infer_loop_bounds_from_pointer_arith (struct loop
*loop
, gimple stmt
)
2834 tree def
, base
, step
, scev
, type
, low
, high
;
2837 if (!is_gimple_assign (stmt
)
2838 || gimple_assign_rhs_code (stmt
) != POINTER_PLUS_EXPR
)
2841 def
= gimple_assign_lhs (stmt
);
2842 if (TREE_CODE (def
) != SSA_NAME
)
2845 type
= TREE_TYPE (def
);
2846 if (!nowrap_type_p (type
))
2849 ptr
= gimple_assign_rhs1 (stmt
);
2850 if (!expr_invariant_in_loop_p (loop
, ptr
))
2853 var
= gimple_assign_rhs2 (stmt
);
2854 if (TYPE_PRECISION (type
) != TYPE_PRECISION (TREE_TYPE (var
)))
2857 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
2858 if (chrec_contains_undetermined (scev
))
2861 base
= initial_condition_in_loop_num (scev
, loop
->num
);
2862 step
= evolution_part_in_loop_num (scev
, loop
->num
);
2865 || TREE_CODE (step
) != INTEGER_CST
2866 || tree_contains_chrecs (base
, NULL
)
2867 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
2870 low
= lower_bound_in_type (type
, type
);
2871 high
= upper_bound_in_type (type
, type
);
2873 /* In C, pointer arithmetic p + 1 cannot use a NULL pointer, and p - 1 cannot
2874 produce a NULL pointer. The contrary would mean NULL points to an object,
2875 while NULL is supposed to compare unequal with the address of all objects.
2876 Furthermore, p + 1 cannot produce a NULL pointer and p - 1 cannot use a
2877 NULL pointer since that would mean wrapping, which we assume here not to
2878 happen. So, we can exclude NULL from the valid range of pointer
2880 if (flag_delete_null_pointer_checks
&& int_cst_value (low
) == 0)
2881 low
= build_int_cstu (TREE_TYPE (low
), TYPE_ALIGN_UNIT (TREE_TYPE (type
)));
2883 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false, true);
2886 /* Determine information about number of iterations of a LOOP from the fact
2887 that signed arithmetics in STMT does not overflow. */
2890 infer_loop_bounds_from_signedness (struct loop
*loop
, gimple stmt
)
2892 tree def
, base
, step
, scev
, type
, low
, high
;
2894 if (gimple_code (stmt
) != GIMPLE_ASSIGN
)
2897 def
= gimple_assign_lhs (stmt
);
2899 if (TREE_CODE (def
) != SSA_NAME
)
2902 type
= TREE_TYPE (def
);
2903 if (!INTEGRAL_TYPE_P (type
)
2904 || !TYPE_OVERFLOW_UNDEFINED (type
))
2907 scev
= instantiate_parameters (loop
, analyze_scalar_evolution (loop
, def
));
2908 if (chrec_contains_undetermined (scev
))
2911 base
= initial_condition_in_loop_num (scev
, loop
->num
);
2912 step
= evolution_part_in_loop_num (scev
, loop
->num
);
2915 || TREE_CODE (step
) != INTEGER_CST
2916 || tree_contains_chrecs (base
, NULL
)
2917 || chrec_contains_symbols_defined_in_loop (base
, loop
->num
))
2920 low
= lower_bound_in_type (type
, type
);
2921 high
= upper_bound_in_type (type
, type
);
2923 record_nonwrapping_iv (loop
, base
, step
, stmt
, low
, high
, false, true);
2926 /* The following analyzers are extracting informations on the bounds
2927 of LOOP from the following undefined behaviors:
2929 - data references should not access elements over the statically
2932 - signed variables should not overflow when flag_wrapv is not set.
2936 infer_loop_bounds_from_undefined (struct loop
*loop
)
2940 gimple_stmt_iterator bsi
;
2944 bbs
= get_loop_body (loop
);
2946 for (i
= 0; i
< loop
->num_nodes
; i
++)
2950 /* If BB is not executed in each iteration of the loop, we cannot
2951 use the operations in it to infer reliable upper bound on the
2952 # of iterations of the loop. However, we can use it as a guess. */
2953 reliable
= dominated_by_p (CDI_DOMINATORS
, loop
->latch
, bb
);
2955 for (bsi
= gsi_start_bb (bb
); !gsi_end_p (bsi
); gsi_next (&bsi
))
2957 gimple stmt
= gsi_stmt (bsi
);
2959 infer_loop_bounds_from_array (loop
, stmt
, reliable
);
2963 infer_loop_bounds_from_signedness (loop
, stmt
);
2964 infer_loop_bounds_from_pointer_arith (loop
, stmt
);
2973 /* Converts VAL to double_int. */
2976 gcov_type_to_double_int (gcov_type val
)
2980 ret
.low
= (unsigned HOST_WIDE_INT
) val
;
2981 /* If HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_WIDEST_INT, avoid shifting by
2982 the size of type. */
2983 val
>>= HOST_BITS_PER_WIDE_INT
- 1;
2985 ret
.high
= (unsigned HOST_WIDE_INT
) val
;
2990 /* Records estimates on numbers of iterations of LOOP. If USE_UNDEFINED_P
2991 is true also use estimates derived from undefined behavior. */
2994 estimate_numbers_of_iterations_loop (struct loop
*loop
, bool use_undefined_p
)
2996 VEC (edge
, heap
) *exits
;
2999 struct tree_niter_desc niter_desc
;
3003 /* Give up if we already have tried to compute an estimation. */
3004 if (loop
->estimate_state
!= EST_NOT_COMPUTED
)
3006 loop
->estimate_state
= EST_AVAILABLE
;
3007 loop
->any_upper_bound
= false;
3008 loop
->any_estimate
= false;
3010 exits
= get_loop_exit_edges (loop
);
3011 FOR_EACH_VEC_ELT (edge
, exits
, i
, ex
)
3013 if (!number_of_iterations_exit (loop
, ex
, &niter_desc
, false))
3016 niter
= niter_desc
.niter
;
3017 type
= TREE_TYPE (niter
);
3018 if (TREE_CODE (niter_desc
.may_be_zero
) != INTEGER_CST
)
3019 niter
= build3 (COND_EXPR
, type
, niter_desc
.may_be_zero
,
3020 build_int_cst (type
, 0),
3022 record_estimate (loop
, niter
, niter_desc
.max
,
3023 last_stmt (ex
->src
),
3026 VEC_free (edge
, heap
, exits
);
3028 if (use_undefined_p
)
3029 infer_loop_bounds_from_undefined (loop
);
3031 /* If we have a measured profile, use it to estimate the number of
3033 if (loop
->header
->count
!= 0)
3035 gcov_type nit
= expected_loop_iterations_unbounded (loop
) + 1;
3036 bound
= gcov_type_to_double_int (nit
);
3037 record_niter_bound (loop
, bound
, true, false);
3040 /* If an upper bound is smaller than the realistic estimate of the
3041 number of iterations, use the upper bound instead. */
3042 if (loop
->any_upper_bound
3043 && loop
->any_estimate
3044 && double_int_ucmp (loop
->nb_iterations_upper_bound
,
3045 loop
->nb_iterations_estimate
) < 0)
3046 loop
->nb_iterations_estimate
= loop
->nb_iterations_upper_bound
;
3049 /* Sets NIT to the estimated number of executions of the latch of the
3050 LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as
3051 large as the number of iterations. If we have no reliable estimate,
3052 the function returns false, otherwise returns true. */
3055 estimated_loop_iterations (struct loop
*loop
, double_int
*nit
)
3057 estimate_numbers_of_iterations_loop (loop
, true);
3058 if (!loop
->any_estimate
)
3061 *nit
= loop
->nb_iterations_estimate
;
3065 /* Sets NIT to an upper bound for the maximum number of executions of the
3066 latch of the LOOP. If we have no reliable estimate, the function returns
3067 false, otherwise returns true. */
3070 max_loop_iterations (struct loop
*loop
, double_int
*nit
)
3072 estimate_numbers_of_iterations_loop (loop
, true);
3073 if (!loop
->any_upper_bound
)
3076 *nit
= loop
->nb_iterations_upper_bound
;
3080 /* Similar to estimated_loop_iterations, but returns the estimate only
3081 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
3082 on the number of iterations of LOOP could not be derived, returns -1. */
3085 estimated_loop_iterations_int (struct loop
*loop
)
3088 HOST_WIDE_INT hwi_nit
;
3090 if (!estimated_loop_iterations (loop
, &nit
))
3093 if (!double_int_fits_in_shwi_p (nit
))
3095 hwi_nit
= double_int_to_shwi (nit
);
3097 return hwi_nit
< 0 ? -1 : hwi_nit
;
3100 /* Similar to max_loop_iterations, but returns the estimate only
3101 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
3102 on the number of iterations of LOOP could not be derived, returns -1. */
3105 max_loop_iterations_int (struct loop
*loop
)
3108 HOST_WIDE_INT hwi_nit
;
3110 if (!max_loop_iterations (loop
, &nit
))
3113 if (!double_int_fits_in_shwi_p (nit
))
3115 hwi_nit
= double_int_to_shwi (nit
);
3117 return hwi_nit
< 0 ? -1 : hwi_nit
;
3120 /* Returns an upper bound on the number of executions of statements
3121 in the LOOP. For statements before the loop exit, this exceeds
3122 the number of execution of the latch by one. */
3125 max_stmt_executions_int (struct loop
*loop
)
3127 HOST_WIDE_INT nit
= max_loop_iterations_int (loop
);
3133 snit
= (HOST_WIDE_INT
) ((unsigned HOST_WIDE_INT
) nit
+ 1);
3135 /* If the computation overflows, return -1. */
3136 return snit
< 0 ? -1 : snit
;
3139 /* Returns an estimate for the number of executions of statements
3140 in the LOOP. For statements before the loop exit, this exceeds
3141 the number of execution of the latch by one. */
3144 estimated_stmt_executions_int (struct loop
*loop
)
3146 HOST_WIDE_INT nit
= estimated_loop_iterations_int (loop
);
3152 snit
= (HOST_WIDE_INT
) ((unsigned HOST_WIDE_INT
) nit
+ 1);
3154 /* If the computation overflows, return -1. */
3155 return snit
< 0 ? -1 : snit
;
3158 /* Sets NIT to the estimated maximum number of executions of the latch of the
3159 LOOP, plus one. If we have no reliable estimate, the function returns
3160 false, otherwise returns true. */
3163 max_stmt_executions (struct loop
*loop
, double_int
*nit
)
3165 double_int nit_minus_one
;
3167 if (!max_loop_iterations (loop
, nit
))
3170 nit_minus_one
= *nit
;
3172 *nit
= double_int_add (*nit
, double_int_one
);
3174 return double_int_ucmp (*nit
, nit_minus_one
) > 0;
3177 /* Sets NIT to the estimated number of executions of the latch of the
3178 LOOP, plus one. If we have no reliable estimate, the function returns
3179 false, otherwise returns true. */
3182 estimated_stmt_executions (struct loop
*loop
, double_int
*nit
)
3184 double_int nit_minus_one
;
3186 if (!estimated_loop_iterations (loop
, nit
))
3189 nit_minus_one
= *nit
;
3191 *nit
= double_int_add (*nit
, double_int_one
);
3193 return double_int_ucmp (*nit
, nit_minus_one
) > 0;
3196 /* Records estimates on numbers of iterations of loops. */
3199 estimate_numbers_of_iterations (bool use_undefined_p
)
3204 /* We don't want to issue signed overflow warnings while getting
3205 loop iteration estimates. */
3206 fold_defer_overflow_warnings ();
3208 FOR_EACH_LOOP (li
, loop
, 0)
3210 estimate_numbers_of_iterations_loop (loop
, use_undefined_p
);
3213 fold_undefer_and_ignore_overflow_warnings ();
3216 /* Returns true if statement S1 dominates statement S2. */
3219 stmt_dominates_stmt_p (gimple s1
, gimple s2
)
3221 basic_block bb1
= gimple_bb (s1
), bb2
= gimple_bb (s2
);
3229 gimple_stmt_iterator bsi
;
3231 if (gimple_code (s2
) == GIMPLE_PHI
)
3234 if (gimple_code (s1
) == GIMPLE_PHI
)
3237 for (bsi
= gsi_start_bb (bb1
); gsi_stmt (bsi
) != s2
; gsi_next (&bsi
))
3238 if (gsi_stmt (bsi
) == s1
)
3244 return dominated_by_p (CDI_DOMINATORS
, bb2
, bb1
);
3247 /* Returns true when we can prove that the number of executions of
3248 STMT in the loop is at most NITER, according to the bound on
3249 the number of executions of the statement NITER_BOUND->stmt recorded in
3250 NITER_BOUND. If STMT is NULL, we must prove this bound for all
3251 statements in the loop. */
3254 n_of_executions_at_most (gimple stmt
,
3255 struct nb_iter_bound
*niter_bound
,
3258 double_int bound
= niter_bound
->bound
;
3259 tree nit_type
= TREE_TYPE (niter
), e
;
3262 gcc_assert (TYPE_UNSIGNED (nit_type
));
3264 /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
3265 the number of iterations is small. */
3266 if (!double_int_fits_to_tree_p (nit_type
, bound
))
3269 /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
3270 times. This means that:
3272 -- if NITER_BOUND->is_exit is true, then everything before
3273 NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
3274 times, and everything after it at most NITER_BOUND->bound times.
3276 -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
3277 is executed, then NITER_BOUND->stmt is executed as well in the same
3278 iteration (we conclude that if both statements belong to the same
3279 basic block, or if STMT is after NITER_BOUND->stmt), then STMT
3280 is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
3281 executed at most NITER_BOUND->bound + 2 times. */
3283 if (niter_bound
->is_exit
)
3286 && stmt
!= niter_bound
->stmt
3287 && stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
))
3295 || (gimple_bb (stmt
) != gimple_bb (niter_bound
->stmt
)
3296 && !stmt_dominates_stmt_p (niter_bound
->stmt
, stmt
)))
3298 bound
= double_int_add (bound
, double_int_one
);
3299 if (double_int_zero_p (bound
)
3300 || !double_int_fits_to_tree_p (nit_type
, bound
))
3306 e
= fold_binary (cmp
, boolean_type_node
,
3307 niter
, double_int_to_tree (nit_type
, bound
));
3308 return e
&& integer_nonzerop (e
);
3311 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
3314 nowrap_type_p (tree type
)
3316 if (INTEGRAL_TYPE_P (type
)
3317 && TYPE_OVERFLOW_UNDEFINED (type
))
3320 if (POINTER_TYPE_P (type
))
3326 /* Return false only when the induction variable BASE + STEP * I is
3327 known to not overflow: i.e. when the number of iterations is small
3328 enough with respect to the step and initial condition in order to
3329 keep the evolution confined in TYPEs bounds. Return true when the
3330 iv is known to overflow or when the property is not computable.
3332 USE_OVERFLOW_SEMANTICS is true if this function should assume that
3333 the rules for overflow of the given language apply (e.g., that signed
3334 arithmetics in C does not overflow). */
3337 scev_probably_wraps_p (tree base
, tree step
,
3338 gimple at_stmt
, struct loop
*loop
,
3339 bool use_overflow_semantics
)
3341 struct nb_iter_bound
*bound
;
3342 tree delta
, step_abs
;
3343 tree unsigned_type
, valid_niter
;
3344 tree type
= TREE_TYPE (step
);
3346 /* FIXME: We really need something like
3347 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
3349 We used to test for the following situation that frequently appears
3350 during address arithmetics:
3352 D.1621_13 = (long unsigned intD.4) D.1620_12;
3353 D.1622_14 = D.1621_13 * 8;
3354 D.1623_15 = (doubleD.29 *) D.1622_14;
3356 And derived that the sequence corresponding to D_14
3357 can be proved to not wrap because it is used for computing a
3358 memory access; however, this is not really the case -- for example,
3359 if D_12 = (unsigned char) [254,+,1], then D_14 has values
3360 2032, 2040, 0, 8, ..., but the code is still legal. */
3362 if (chrec_contains_undetermined (base
)
3363 || chrec_contains_undetermined (step
))
3366 if (integer_zerop (step
))
3369 /* If we can use the fact that signed and pointer arithmetics does not
3370 wrap, we are done. */
3371 if (use_overflow_semantics
&& nowrap_type_p (TREE_TYPE (base
)))
3374 /* To be able to use estimates on number of iterations of the loop,
3375 we must have an upper bound on the absolute value of the step. */
3376 if (TREE_CODE (step
) != INTEGER_CST
)
3379 /* Don't issue signed overflow warnings. */
3380 fold_defer_overflow_warnings ();
3382 /* Otherwise, compute the number of iterations before we reach the
3383 bound of the type, and verify that the loop is exited before this
3385 unsigned_type
= unsigned_type_for (type
);
3386 base
= fold_convert (unsigned_type
, base
);
3388 if (tree_int_cst_sign_bit (step
))
3390 tree extreme
= fold_convert (unsigned_type
,
3391 lower_bound_in_type (type
, type
));
3392 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, base
, extreme
);
3393 step_abs
= fold_build1 (NEGATE_EXPR
, unsigned_type
,
3394 fold_convert (unsigned_type
, step
));
3398 tree extreme
= fold_convert (unsigned_type
,
3399 upper_bound_in_type (type
, type
));
3400 delta
= fold_build2 (MINUS_EXPR
, unsigned_type
, extreme
, base
);
3401 step_abs
= fold_convert (unsigned_type
, step
);
3404 valid_niter
= fold_build2 (FLOOR_DIV_EXPR
, unsigned_type
, delta
, step_abs
);
3406 estimate_numbers_of_iterations_loop (loop
, true);
3407 for (bound
= loop
->bounds
; bound
; bound
= bound
->next
)
3409 if (n_of_executions_at_most (at_stmt
, bound
, valid_niter
))
3411 fold_undefer_and_ignore_overflow_warnings ();
3416 fold_undefer_and_ignore_overflow_warnings ();
3418 /* At this point we still don't have a proof that the iv does not
3419 overflow: give up. */
3423 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
3426 free_numbers_of_iterations_estimates_loop (struct loop
*loop
)
3428 struct nb_iter_bound
*bound
, *next
;
3430 loop
->nb_iterations
= NULL
;
3431 loop
->estimate_state
= EST_NOT_COMPUTED
;
3432 for (bound
= loop
->bounds
; bound
; bound
= next
)
3438 loop
->bounds
= NULL
;
3441 /* Frees the information on upper bounds on numbers of iterations of loops. */
3444 free_numbers_of_iterations_estimates (void)
3449 FOR_EACH_LOOP (li
, loop
, 0)
3451 free_numbers_of_iterations_estimates_loop (loop
);
3455 /* Substitute value VAL for ssa name NAME inside expressions held
3459 substitute_in_loop_info (struct loop
*loop
, tree name
, tree val
)
3461 loop
->nb_iterations
= simplify_replace_tree (loop
->nb_iterations
, name
, val
);