1 /* Functions to determine/estimate number of iterations of a loop.
2 Copyright (C) 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
4 This file is part of GCC.
6 GCC is free software; you can redistribute it and/or modify it
7 under the terms of the GNU General Public License as published by the
8 Free Software Foundation; either version 3, or (at your option) any
11 GCC is distributed in the hope that it will be useful, but WITHOUT
12 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
16 You should have received a copy of the GNU General Public License
17 along with GCC; see the file COPYING3. If not see
18 <http://www.gnu.org/licenses/>. */
22 #include "coretypes.h"
27 #include "hard-reg-set.h"
28 #include "basic-block.h"
30 #include "diagnostic.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"
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 = double_int_sext (tree_to_double_int (op1),
97 TYPE_PRECISION (type));
98 mpz_set_double_int (offset, off, false);
102 *var = build_int_cst_type (type, 0);
103 off = tree_to_double_int (expr);
104 mpz_set_double_int (offset, off, TYPE_UNSIGNED (type));
112 /* Stores estimate on the minimum/maximum value of the expression VAR + OFF
113 in TYPE to MIN and MAX. */
116 determine_value_range (tree type, tree var, mpz_t off,
117 mpz_t min, mpz_t max)
119 /* If the expression is a constant, we know its value exactly. */
120 if (integer_zerop (var))
127 /* If the computation may wrap, we know nothing about the value, except for
128 the range of the type. */
129 get_type_static_bounds (type, min, max);
130 if (!nowrap_type_p (type))
133 /* Since the addition of OFF does not wrap, if OFF is positive, then we may
134 add it to MIN, otherwise to MAX. */
135 if (mpz_sgn (off) < 0)
136 mpz_add (max, max, off);
138 mpz_add (min, min, off);
141 /* Stores the bounds on the difference of the values of the expressions
142 (var + X) and (var + Y), computed in TYPE, to BNDS. */
145 bound_difference_of_offsetted_base (tree type, mpz_t x, mpz_t y,
148 int rel = mpz_cmp (x, y);
149 bool may_wrap = !nowrap_type_p (type);
152 /* If X == Y, then the expressions are always equal.
153 If X > Y, there are the following possibilities:
154 a) neither of var + X and var + Y overflow or underflow, or both of
155 them do. Then their difference is X - Y.
156 b) var + X overflows, and var + Y does not. Then the values of the
157 expressions are var + X - M and var + Y, where M is the range of
158 the type, and their difference is X - Y - M.
159 c) var + Y underflows and var + X does not. Their difference again
161 Therefore, if the arithmetics in type does not overflow, then the
162 bounds are (X - Y, X - Y), otherwise they are (X - Y - M, X - Y)
163 Similarly, if X < Y, the bounds are either (X - Y, X - Y) or
164 (X - Y, X - Y + M). */
168 mpz_set_ui (bnds->below, 0);
169 mpz_set_ui (bnds->up, 0);
174 mpz_set_double_int (m, double_int_mask (TYPE_PRECISION (type)), true);
175 mpz_add_ui (m, m, 1);
176 mpz_sub (bnds->up, x, y);
177 mpz_set (bnds->below, bnds->up);
182 mpz_sub (bnds->below, bnds->below, m);
184 mpz_add (bnds->up, bnds->up, m);
190 /* From condition C0 CMP C1 derives information regarding the
191 difference of values of VARX + OFFX and VARY + OFFY, computed in TYPE,
192 and stores it to BNDS. */
195 refine_bounds_using_guard (tree type, tree varx, mpz_t offx,
196 tree vary, mpz_t offy,
197 tree c0, enum tree_code cmp, tree c1,
200 tree varc0, varc1, tmp, ctype;
201 mpz_t offc0, offc1, loffx, loffy, bnd;
203 bool no_wrap = nowrap_type_p (type);
212 STRIP_SIGN_NOPS (c0);
213 STRIP_SIGN_NOPS (c1);
214 ctype = TREE_TYPE (c0);
215 if (!useless_type_conversion_p (ctype, type))
221 /* We could derive quite precise information from EQ_EXPR, however, such
222 a guard is unlikely to appear, so we do not bother with handling
227 /* NE_EXPR comparisons do not contain much of useful information, except for
228 special case of comparing with the bounds of the type. */
229 if (TREE_CODE (c1) != INTEGER_CST
230 || !INTEGRAL_TYPE_P (type))
233 /* Ensure that the condition speaks about an expression in the same type
235 ctype = TREE_TYPE (c0);
236 if (TYPE_PRECISION (ctype) != TYPE_PRECISION (type))
238 c0 = fold_convert (type, c0);
239 c1 = fold_convert (type, c1);
241 if (TYPE_MIN_VALUE (type)
242 && operand_equal_p (c1, TYPE_MIN_VALUE (type), 0))
247 if (TYPE_MAX_VALUE (type)
248 && operand_equal_p (c1, TYPE_MAX_VALUE (type), 0))
261 split_to_var_and_offset (expand_simple_operations (c0), &varc0, offc0);
262 split_to_var_and_offset (expand_simple_operations (c1), &varc1, offc1);
264 /* We are only interested in comparisons of expressions based on VARX and
265 VARY. TODO -- we might also be able to derive some bounds from
266 expressions containing just one of the variables. */
268 if (operand_equal_p (varx, varc1, 0))
270 tmp = varc0; varc0 = varc1; varc1 = tmp;
271 mpz_swap (offc0, offc1);
272 cmp = swap_tree_comparison (cmp);
275 if (!operand_equal_p (varx, varc0, 0)
276 || !operand_equal_p (vary, varc1, 0))
279 mpz_init_set (loffx, offx);
280 mpz_init_set (loffy, offy);
282 if (cmp == GT_EXPR || cmp == GE_EXPR)
284 tmp = varx; varx = vary; vary = tmp;
285 mpz_swap (offc0, offc1);
286 mpz_swap (loffx, loffy);
287 cmp = swap_tree_comparison (cmp);
291 /* If there is no overflow, the condition implies that
293 (VARX + OFFX) cmp (VARY + OFFY) + (OFFX - OFFY + OFFC1 - OFFC0).
295 The overflows and underflows may complicate things a bit; each
296 overflow decreases the appropriate offset by M, and underflow
297 increases it by M. The above inequality would not necessarily be
300 -- VARX + OFFX underflows and VARX + OFFC0 does not, or
301 VARX + OFFC0 overflows, but VARX + OFFX does not.
302 This may only happen if OFFX < OFFC0.
303 -- VARY + OFFY overflows and VARY + OFFC1 does not, or
304 VARY + OFFC1 underflows and VARY + OFFY does not.
305 This may only happen if OFFY > OFFC1. */
314 x_ok = (integer_zerop (varx)
315 || mpz_cmp (loffx, offc0) >= 0);
316 y_ok = (integer_zerop (vary)
317 || mpz_cmp (loffy, offc1) <= 0);
323 mpz_sub (bnd, loffx, loffy);
324 mpz_add (bnd, bnd, offc1);
325 mpz_sub (bnd, bnd, offc0);
328 mpz_sub_ui (bnd, bnd, 1);
333 if (mpz_cmp (bnds->below, bnd) < 0)
334 mpz_set (bnds->below, bnd);
338 if (mpz_cmp (bnd, bnds->up) < 0)
339 mpz_set (bnds->up, bnd);
351 /* Stores the bounds on the value of the expression X - Y in LOOP to BNDS.
352 The subtraction is considered to be performed in arbitrary precision,
355 We do not attempt to be too clever regarding the value ranges of X and
356 Y; most of the time, they are just integers or ssa names offsetted by
357 integer. However, we try to use the information contained in the
358 comparisons before the loop (usually created by loop header copying). */
361 bound_difference (struct loop *loop, tree x, tree y, bounds *bnds)
363 tree type = TREE_TYPE (x);
366 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 = COND_EXPR_COND (last_stmt (e->src));
430 if (!COMPARISON_CLASS_P (cond))
432 c0 = TREE_OPERAND (cond, 0);
433 cmp = TREE_CODE (cond);
434 c1 = TREE_OPERAND (cond, 1);
436 if (e->flags & EDGE_FALSE_VALUE)
437 cmp = invert_tree_comparison (cmp, false);
439 refine_bounds_using_guard (type, varx, offx, vary, offy,
449 /* Update the bounds in BNDS that restrict the value of X to the bounds
450 that restrict the value of X + DELTA. X can be obtained as a
451 difference of two values in TYPE. */
454 bounds_add (bounds *bnds, double_int delta, tree type)
459 mpz_set_double_int (mdelta, delta, false);
462 mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
464 mpz_add (bnds->up, bnds->up, mdelta);
465 mpz_add (bnds->below, bnds->below, mdelta);
467 if (mpz_cmp (bnds->up, max) > 0)
468 mpz_set (bnds->up, max);
471 if (mpz_cmp (bnds->below, max) < 0)
472 mpz_set (bnds->below, max);
478 /* Update the bounds in BNDS that restrict the value of X to the bounds
479 that restrict the value of -X. */
482 bounds_negate (bounds *bnds)
486 mpz_init_set (tmp, bnds->up);
487 mpz_neg (bnds->up, bnds->below);
488 mpz_neg (bnds->below, tmp);
492 /* Returns inverse of X modulo 2^s, where MASK = 2^s-1. */
495 inverse (tree x, tree mask)
497 tree type = TREE_TYPE (x);
499 unsigned ctr = tree_floor_log2 (mask);
501 if (TYPE_PRECISION (type) <= HOST_BITS_PER_WIDE_INT)
503 unsigned HOST_WIDE_INT ix;
504 unsigned HOST_WIDE_INT imask;
505 unsigned HOST_WIDE_INT irslt = 1;
507 gcc_assert (cst_and_fits_in_hwi (x));
508 gcc_assert (cst_and_fits_in_hwi (mask));
510 ix = int_cst_value (x);
511 imask = int_cst_value (mask);
520 rslt = build_int_cst_type (type, irslt);
524 rslt = build_int_cst (type, 1);
527 rslt = int_const_binop (MULT_EXPR, rslt, x, 0);
528 x = int_const_binop (MULT_EXPR, x, x, 0);
530 rslt = int_const_binop (BIT_AND_EXPR, rslt, mask, 0);
536 /* Derives the upper bound BND on the number of executions of loop with exit
537 condition S * i <> C, assuming that the loop is not infinite. If
538 NO_OVERFLOW is true, then the control variable of the loop does not
539 overflow. If NO_OVERFLOW is true or BNDS.below >= 0, then BNDS.up
540 contains the upper bound on the value of C. */
543 number_of_iterations_ne_max (mpz_t bnd, bool no_overflow, tree c, tree s,
549 /* If the control variable does not overflow, the number of iterations is
550 at most c / s. Otherwise it is at most the period of the control
552 if (!no_overflow && !multiple_of_p (TREE_TYPE (c), c, s))
554 max = double_int_mask (TYPE_PRECISION (TREE_TYPE (c))
555 - tree_low_cst (num_ending_zeros (s), 1));
556 mpz_set_double_int (bnd, max, true);
560 /* Determine the upper bound on C. */
561 if (no_overflow || mpz_sgn (bnds->below) >= 0)
562 mpz_set (bnd, bnds->up);
563 else if (TREE_CODE (c) == INTEGER_CST)
564 mpz_set_double_int (bnd, tree_to_double_int (c), true);
566 mpz_set_double_int (bnd, double_int_mask (TYPE_PRECISION (TREE_TYPE (c))),
570 mpz_set_double_int (d, tree_to_double_int (s), true);
571 mpz_fdiv_q (bnd, bnd, d);
575 /* Determines number of iterations of loop whose ending condition
576 is IV <> FINAL. TYPE is the type of the iv. The number of
577 iterations is stored to NITER. NEVER_INFINITE is true if
578 we know that the exit must be taken eventually, i.e., that the IV
579 ever reaches the value FINAL (we derived this earlier, and possibly set
580 NITER->assumptions to make sure this is the case). BNDS contains the
581 bounds on the difference FINAL - IV->base. */
584 number_of_iterations_ne (tree type, affine_iv *iv, tree final,
585 struct tree_niter_desc *niter, bool never_infinite,
588 tree niter_type = unsigned_type_for (type);
589 tree s, c, d, bits, assumption, tmp, bound;
592 niter->control = *iv;
593 niter->bound = final;
594 niter->cmp = NE_EXPR;
596 /* Rearrange the terms so that we get inequality S * i <> C, with S
597 positive. Also cast everything to the unsigned type. If IV does
598 not overflow, BNDS bounds the value of C. Also, this is the
599 case if the computation |FINAL - IV->base| does not overflow, i.e.,
600 if BNDS->below in the result is nonnegative. */
601 if (tree_int_cst_sign_bit (iv->step))
603 s = fold_convert (niter_type,
604 fold_build1 (NEGATE_EXPR, type, iv->step));
605 c = fold_build2 (MINUS_EXPR, niter_type,
606 fold_convert (niter_type, iv->base),
607 fold_convert (niter_type, final));
608 bounds_negate (bnds);
612 s = fold_convert (niter_type, iv->step);
613 c = fold_build2 (MINUS_EXPR, niter_type,
614 fold_convert (niter_type, final),
615 fold_convert (niter_type, iv->base));
619 number_of_iterations_ne_max (max, iv->no_overflow, c, s, bnds);
620 niter->max = mpz_get_double_int (niter_type, max, false);
623 /* First the trivial cases -- when the step is 1. */
624 if (integer_onep (s))
630 /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
631 is infinite. Otherwise, the number of iterations is
632 (inverse(s/d) * (c/d)) mod (size of mode/d). */
633 bits = num_ending_zeros (s);
634 bound = build_low_bits_mask (niter_type,
635 (TYPE_PRECISION (niter_type)
636 - tree_low_cst (bits, 1)));
638 d = fold_binary_to_constant (LSHIFT_EXPR, niter_type,
639 build_int_cst (niter_type, 1), bits);
640 s = fold_binary_to_constant (RSHIFT_EXPR, niter_type, s, bits);
644 /* If we cannot assume that the loop is not infinite, record the
645 assumptions for divisibility of c. */
646 assumption = fold_build2 (FLOOR_MOD_EXPR, niter_type, c, d);
647 assumption = fold_build2 (EQ_EXPR, boolean_type_node,
648 assumption, build_int_cst (niter_type, 0));
649 if (!integer_nonzerop (assumption))
650 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
651 niter->assumptions, assumption);
654 c = fold_build2 (EXACT_DIV_EXPR, niter_type, c, d);
655 tmp = fold_build2 (MULT_EXPR, niter_type, c, inverse (s, bound));
656 niter->niter = fold_build2 (BIT_AND_EXPR, niter_type, tmp, bound);
660 /* Checks whether we can determine the final value of the control variable
661 of the loop with ending condition IV0 < IV1 (computed in TYPE).
662 DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
663 of the step. The assumptions necessary to ensure that the computation
664 of the final value does not overflow are recorded in NITER. If we
665 find the final value, we adjust DELTA and return TRUE. Otherwise
666 we return false. BNDS bounds the value of IV1->base - IV0->base,
667 and will be updated by the same amount as DELTA. */
670 number_of_iterations_lt_to_ne (tree type, affine_iv *iv0, affine_iv *iv1,
671 struct tree_niter_desc *niter,
672 tree *delta, tree step,
675 tree niter_type = TREE_TYPE (step);
676 tree mod = fold_build2 (FLOOR_MOD_EXPR, niter_type, *delta, step);
679 tree assumption = boolean_true_node, bound, noloop;
682 if (POINTER_TYPE_P (type))
685 if (TREE_CODE (mod) != INTEGER_CST)
687 if (integer_nonzerop (mod))
688 mod = fold_build2 (MINUS_EXPR, niter_type, step, mod);
689 tmod = fold_convert (type1, mod);
692 mpz_set_double_int (mmod, tree_to_double_int (mod), true);
693 mpz_neg (mmod, mmod);
695 if (integer_nonzerop (iv0->step))
697 /* The final value of the iv is iv1->base + MOD, assuming that this
698 computation does not overflow, and that
699 iv0->base <= iv1->base + MOD. */
700 if (!iv1->no_overflow && !integer_zerop (mod))
702 bound = fold_build2 (MINUS_EXPR, type,
703 TYPE_MAX_VALUE (type1), tmod);
704 assumption = fold_build2 (LE_EXPR, boolean_type_node,
706 if (integer_zerop (assumption))
709 if (mpz_cmp (mmod, bnds->below) < 0)
710 noloop = boolean_false_node;
712 noloop = fold_build2 (GT_EXPR, boolean_type_node,
714 fold_build2 (PLUS_EXPR, type1,
719 /* The final value of the iv is iv0->base - MOD, assuming that this
720 computation does not overflow, and that
721 iv0->base - MOD <= iv1->base. */
722 if (!iv0->no_overflow && !integer_zerop (mod))
724 bound = fold_build2 (PLUS_EXPR, type1,
725 TYPE_MIN_VALUE (type1), tmod);
726 assumption = fold_build2 (GE_EXPR, boolean_type_node,
728 if (integer_zerop (assumption))
731 if (mpz_cmp (mmod, bnds->below) < 0)
732 noloop = boolean_false_node;
734 noloop = fold_build2 (GT_EXPR, boolean_type_node,
735 fold_build2 (MINUS_EXPR, type1,
740 if (!integer_nonzerop (assumption))
741 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
744 if (!integer_zerop (noloop))
745 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
748 bounds_add (bnds, tree_to_double_int (mod), type);
749 *delta = fold_build2 (PLUS_EXPR, niter_type, *delta, mod);
757 /* Add assertions to NITER that ensure that the control variable of the loop
758 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
759 are TYPE. Returns false if we can prove that there is an overflow, true
760 otherwise. STEP is the absolute value of the step. */
763 assert_no_overflow_lt (tree type, affine_iv *iv0, affine_iv *iv1,
764 struct tree_niter_desc *niter, tree step)
766 tree bound, d, assumption, diff;
767 tree niter_type = TREE_TYPE (step);
769 if (integer_nonzerop (iv0->step))
771 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
772 if (iv0->no_overflow)
775 /* If iv0->base is a constant, we can determine the last value before
776 overflow precisely; otherwise we conservatively assume
779 if (TREE_CODE (iv0->base) == INTEGER_CST)
781 d = fold_build2 (MINUS_EXPR, niter_type,
782 fold_convert (niter_type, TYPE_MAX_VALUE (type)),
783 fold_convert (niter_type, iv0->base));
784 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
787 diff = fold_build2 (MINUS_EXPR, niter_type, step,
788 build_int_cst (niter_type, 1));
789 bound = fold_build2 (MINUS_EXPR, type,
790 TYPE_MAX_VALUE (type), fold_convert (type, diff));
791 assumption = fold_build2 (LE_EXPR, boolean_type_node,
796 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
797 if (iv1->no_overflow)
800 if (TREE_CODE (iv1->base) == INTEGER_CST)
802 d = fold_build2 (MINUS_EXPR, niter_type,
803 fold_convert (niter_type, iv1->base),
804 fold_convert (niter_type, TYPE_MIN_VALUE (type)));
805 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
808 diff = fold_build2 (MINUS_EXPR, niter_type, step,
809 build_int_cst (niter_type, 1));
810 bound = fold_build2 (PLUS_EXPR, type,
811 TYPE_MIN_VALUE (type), fold_convert (type, diff));
812 assumption = fold_build2 (GE_EXPR, boolean_type_node,
816 if (integer_zerop (assumption))
818 if (!integer_nonzerop (assumption))
819 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
820 niter->assumptions, assumption);
822 iv0->no_overflow = true;
823 iv1->no_overflow = true;
827 /* Add an assumption to NITER that a loop whose ending condition
828 is IV0 < IV1 rolls. TYPE is the type of the control iv. BNDS
829 bounds the value of IV1->base - IV0->base. */
832 assert_loop_rolls_lt (tree type, affine_iv *iv0, affine_iv *iv1,
833 struct tree_niter_desc *niter, bounds *bnds)
835 tree assumption = boolean_true_node, bound, diff;
836 tree mbz, mbzl, mbzr, type1;
837 bool rolls_p, no_overflow_p;
841 /* We are going to compute the number of iterations as
842 (iv1->base - iv0->base + step - 1) / step, computed in the unsigned
843 variant of TYPE. This formula only works if
845 -step + 1 <= (iv1->base - iv0->base) <= MAX - step + 1
847 (where MAX is the maximum value of the unsigned variant of TYPE, and
848 the computations in this formula are performed in full precision
851 Usually, for loops with exit condition iv0->base + step * i < iv1->base,
852 we have a condition of form iv0->base - step < iv1->base before the loop,
853 and for loops iv0->base < iv1->base - step * i the condition
854 iv0->base < iv1->base + step, due to loop header copying, which enable us
855 to prove the lower bound.
857 The upper bound is more complicated. Unless the expressions for initial
858 and final value themselves contain enough information, we usually cannot
859 derive it from the context. */
861 /* First check whether the answer does not follow from the bounds we gathered
863 if (integer_nonzerop (iv0->step))
864 dstep = tree_to_double_int (iv0->step);
867 dstep = double_int_sext (tree_to_double_int (iv1->step),
868 TYPE_PRECISION (type));
869 dstep = double_int_neg (dstep);
873 mpz_set_double_int (mstep, dstep, true);
874 mpz_neg (mstep, mstep);
875 mpz_add_ui (mstep, mstep, 1);
877 rolls_p = mpz_cmp (mstep, bnds->below) <= 0;
880 mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
881 mpz_add (max, max, mstep);
882 no_overflow_p = (mpz_cmp (bnds->up, max) <= 0
883 /* For pointers, only values lying inside a single object
884 can be compared or manipulated by pointer arithmetics.
885 Gcc in general does not allow or handle objects larger
886 than half of the address space, hence the upper bound
887 is satisfied for pointers. */
888 || POINTER_TYPE_P (type));
892 if (rolls_p && no_overflow_p)
896 if (POINTER_TYPE_P (type))
899 /* Now the hard part; we must formulate the assumption(s) as expressions, and
900 we must be careful not to introduce overflow. */
902 if (integer_nonzerop (iv0->step))
904 diff = fold_build2 (MINUS_EXPR, type1,
905 iv0->step, build_int_cst (type1, 1));
907 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
908 0 address never belongs to any object, we can assume this for
910 if (!POINTER_TYPE_P (type))
912 bound = fold_build2 (PLUS_EXPR, type1,
913 TYPE_MIN_VALUE (type), diff);
914 assumption = fold_build2 (GE_EXPR, boolean_type_node,
918 /* And then we can compute iv0->base - diff, and compare it with
920 mbzl = fold_build2 (MINUS_EXPR, type1,
921 fold_convert (type1, iv0->base), diff);
922 mbzr = fold_convert (type1, iv1->base);
926 diff = fold_build2 (PLUS_EXPR, type1,
927 iv1->step, build_int_cst (type1, 1));
929 if (!POINTER_TYPE_P (type))
931 bound = fold_build2 (PLUS_EXPR, type1,
932 TYPE_MAX_VALUE (type), diff);
933 assumption = fold_build2 (LE_EXPR, boolean_type_node,
937 mbzl = fold_convert (type1, iv0->base);
938 mbzr = fold_build2 (MINUS_EXPR, type1,
939 fold_convert (type1, iv1->base), diff);
942 if (!integer_nonzerop (assumption))
943 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
944 niter->assumptions, assumption);
947 mbz = fold_build2 (GT_EXPR, boolean_type_node, mbzl, mbzr);
948 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
949 niter->may_be_zero, mbz);
953 /* Determines number of iterations of loop whose ending condition
954 is IV0 < IV1. TYPE is the type of the iv. The number of
955 iterations is stored to NITER. BNDS bounds the difference
956 IV1->base - IV0->base. */
959 number_of_iterations_lt (tree type, affine_iv *iv0, affine_iv *iv1,
960 struct tree_niter_desc *niter,
961 bool never_infinite ATTRIBUTE_UNUSED,
964 tree niter_type = unsigned_type_for (type);
968 if (integer_nonzerop (iv0->step))
970 niter->control = *iv0;
971 niter->cmp = LT_EXPR;
972 niter->bound = iv1->base;
976 niter->control = *iv1;
977 niter->cmp = GT_EXPR;
978 niter->bound = iv0->base;
981 delta = fold_build2 (MINUS_EXPR, niter_type,
982 fold_convert (niter_type, iv1->base),
983 fold_convert (niter_type, iv0->base));
985 /* First handle the special case that the step is +-1. */
986 if ((integer_onep (iv0->step) && integer_zerop (iv1->step))
987 || (integer_all_onesp (iv1->step) && integer_zerop (iv0->step)))
989 /* for (i = iv0->base; i < iv1->base; i++)
993 for (i = iv1->base; i > iv0->base; i--).
995 In both cases # of iterations is iv1->base - iv0->base, assuming that
996 iv1->base >= iv0->base.
998 First try to derive a lower bound on the value of
999 iv1->base - iv0->base, computed in full precision. If the difference
1000 is nonnegative, we are done, otherwise we must record the
1003 if (mpz_sgn (bnds->below) < 0)
1004 niter->may_be_zero = fold_build2 (LT_EXPR, boolean_type_node,
1005 iv1->base, iv0->base);
1006 niter->niter = delta;
1007 niter->max = mpz_get_double_int (niter_type, bnds->up, false);
1011 if (integer_nonzerop (iv0->step))
1012 step = fold_convert (niter_type, iv0->step);
1014 step = fold_convert (niter_type,
1015 fold_build1 (NEGATE_EXPR, type, iv1->step));
1017 /* If we can determine the final value of the control iv exactly, we can
1018 transform the condition to != comparison. In particular, this will be
1019 the case if DELTA is constant. */
1020 if (number_of_iterations_lt_to_ne (type, iv0, iv1, niter, &delta, step,
1025 zps.base = build_int_cst (niter_type, 0);
1027 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
1028 zps does not overflow. */
1029 zps.no_overflow = true;
1031 return number_of_iterations_ne (type, &zps, delta, niter, true, bnds);
1034 /* Make sure that the control iv does not overflow. */
1035 if (!assert_no_overflow_lt (type, iv0, iv1, niter, step))
1038 /* We determine the number of iterations as (delta + step - 1) / step. For
1039 this to work, we must know that iv1->base >= iv0->base - step + 1,
1040 otherwise the loop does not roll. */
1041 assert_loop_rolls_lt (type, iv0, iv1, niter, bnds);
1043 s = fold_build2 (MINUS_EXPR, niter_type,
1044 step, build_int_cst (niter_type, 1));
1045 delta = fold_build2 (PLUS_EXPR, niter_type, delta, s);
1046 niter->niter = fold_build2 (FLOOR_DIV_EXPR, niter_type, delta, step);
1050 mpz_set_double_int (mstep, tree_to_double_int (step), true);
1051 mpz_add (tmp, bnds->up, mstep);
1052 mpz_sub_ui (tmp, tmp, 1);
1053 mpz_fdiv_q (tmp, tmp, mstep);
1054 niter->max = mpz_get_double_int (niter_type, tmp, false);
1061 /* Determines number of iterations of loop whose ending condition
1062 is IV0 <= IV1. TYPE is the type of the iv. The number of
1063 iterations is stored to NITER. NEVER_INFINITE is true if
1064 we know that this condition must eventually become false (we derived this
1065 earlier, and possibly set NITER->assumptions to make sure this
1066 is the case). BNDS bounds the difference IV1->base - IV0->base. */
1069 number_of_iterations_le (tree type, affine_iv *iv0, affine_iv *iv1,
1070 struct tree_niter_desc *niter, bool never_infinite,
1075 if (POINTER_TYPE_P (type))
1078 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
1079 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
1080 value of the type. This we must know anyway, since if it is
1081 equal to this value, the loop rolls forever. */
1083 if (!never_infinite)
1085 if (integer_nonzerop (iv0->step))
1086 assumption = fold_build2 (NE_EXPR, boolean_type_node,
1087 iv1->base, TYPE_MAX_VALUE (type1));
1089 assumption = fold_build2 (NE_EXPR, boolean_type_node,
1090 iv0->base, TYPE_MIN_VALUE (type1));
1092 if (integer_zerop (assumption))
1094 if (!integer_nonzerop (assumption))
1095 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
1096 niter->assumptions, assumption);
1099 if (integer_nonzerop (iv0->step))
1100 iv1->base = fold_build2 (PLUS_EXPR, type1,
1101 iv1->base, build_int_cst (type1, 1));
1103 iv0->base = fold_build2 (MINUS_EXPR, type1,
1104 iv0->base, build_int_cst (type1, 1));
1106 bounds_add (bnds, double_int_one, type1);
1108 return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite, bnds);
1111 /* Dumps description of affine induction variable IV to FILE. */
1114 dump_affine_iv (FILE *file, affine_iv *iv)
1116 if (!integer_zerop (iv->step))
1117 fprintf (file, "[");
1119 print_generic_expr (dump_file, iv->base, TDF_SLIM);
1121 if (!integer_zerop (iv->step))
1123 fprintf (file, ", + , ");
1124 print_generic_expr (dump_file, iv->step, TDF_SLIM);
1125 fprintf (file, "]%s", iv->no_overflow ? "(no_overflow)" : "");
1129 /* Determine the number of iterations according to condition (for staying
1130 inside loop) which compares two induction variables using comparison
1131 operator CODE. The induction variable on left side of the comparison
1132 is IV0, the right-hand side is IV1. Both induction variables must have
1133 type TYPE, which must be an integer or pointer type. The steps of the
1134 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
1136 LOOP is the loop whose number of iterations we are determining.
1138 ONLY_EXIT is true if we are sure this is the only way the loop could be
1139 exited (including possibly non-returning function calls, exceptions, etc.)
1140 -- in this case we can use the information whether the control induction
1141 variables can overflow or not in a more efficient way.
1143 The results (number of iterations and assumptions as described in
1144 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
1145 Returns false if it fails to determine number of iterations, true if it
1146 was determined (possibly with some assumptions). */
1149 number_of_iterations_cond (struct loop *loop,
1150 tree type, affine_iv *iv0, enum tree_code code,
1151 affine_iv *iv1, struct tree_niter_desc *niter,
1154 bool never_infinite, ret;
1157 /* The meaning of these assumptions is this:
1159 then the rest of information does not have to be valid
1160 if may_be_zero then the loop does not roll, even if
1162 niter->assumptions = boolean_true_node;
1163 niter->may_be_zero = boolean_false_node;
1164 niter->niter = NULL_TREE;
1165 niter->max = double_int_zero;
1167 niter->bound = NULL_TREE;
1168 niter->cmp = ERROR_MARK;
1170 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
1171 the control variable is on lhs. */
1172 if (code == GE_EXPR || code == GT_EXPR
1173 || (code == NE_EXPR && integer_zerop (iv0->step)))
1176 code = swap_tree_comparison (code);
1181 /* If this is not the only possible exit from the loop, the information
1182 that the induction variables cannot overflow as derived from
1183 signedness analysis cannot be relied upon. We use them e.g. in the
1184 following way: given loop for (i = 0; i <= n; i++), if i is
1185 signed, it cannot overflow, thus this loop is equivalent to
1186 for (i = 0; i < n + 1; i++); however, if n == MAX, but the loop
1187 is exited in some other way before i overflows, this transformation
1188 is incorrect (the new loop exits immediately). */
1189 iv0->no_overflow = false;
1190 iv1->no_overflow = false;
1193 if (POINTER_TYPE_P (type))
1195 /* Comparison of pointers is undefined unless both iv0 and iv1 point
1196 to the same object. If they do, the control variable cannot wrap
1197 (as wrap around the bounds of memory will never return a pointer
1198 that would be guaranteed to point to the same object, even if we
1199 avoid undefined behavior by casting to size_t and back). The
1200 restrictions on pointer arithmetics and comparisons of pointers
1201 ensure that using the no-overflow assumptions is correct in this
1202 case even if ONLY_EXIT is false. */
1203 iv0->no_overflow = true;
1204 iv1->no_overflow = true;
1207 /* If the control induction variable does not overflow, the loop obviously
1208 cannot be infinite. */
1209 if (!integer_zerop (iv0->step) && iv0->no_overflow)
1210 never_infinite = true;
1211 else if (!integer_zerop (iv1->step) && iv1->no_overflow)
1212 never_infinite = true;
1214 never_infinite = false;
1216 /* We can handle the case when neither of the sides of the comparison is
1217 invariant, provided that the test is NE_EXPR. This rarely occurs in
1218 practice, but it is simple enough to manage. */
1219 if (!integer_zerop (iv0->step) && !integer_zerop (iv1->step))
1221 if (code != NE_EXPR)
1224 iv0->step = fold_binary_to_constant (MINUS_EXPR, type,
1225 iv0->step, iv1->step);
1226 iv0->no_overflow = false;
1227 iv1->step = build_int_cst (type, 0);
1228 iv1->no_overflow = true;
1231 /* If the result of the comparison is a constant, the loop is weird. More
1232 precise handling would be possible, but the situation is not common enough
1233 to waste time on it. */
1234 if (integer_zerop (iv0->step) && integer_zerop (iv1->step))
1237 /* Ignore loops of while (i-- < 10) type. */
1238 if (code != NE_EXPR)
1240 if (iv0->step && tree_int_cst_sign_bit (iv0->step))
1243 if (!integer_zerop (iv1->step) && !tree_int_cst_sign_bit (iv1->step))
1247 /* If the loop exits immediately, there is nothing to do. */
1248 if (integer_zerop (fold_build2 (code, boolean_type_node, iv0->base, iv1->base)))
1250 niter->niter = build_int_cst (unsigned_type_for (type), 0);
1251 niter->max = double_int_zero;
1255 /* OK, now we know we have a senseful loop. Handle several cases, depending
1256 on what comparison operator is used. */
1257 bound_difference (loop, iv1->base, iv0->base, &bnds);
1259 if (dump_file && (dump_flags & TDF_DETAILS))
1262 "Analyzing # of iterations of loop %d\n", loop->num);
1264 fprintf (dump_file, " exit condition ");
1265 dump_affine_iv (dump_file, iv0);
1266 fprintf (dump_file, " %s ",
1267 code == NE_EXPR ? "!="
1268 : code == LT_EXPR ? "<"
1270 dump_affine_iv (dump_file, iv1);
1271 fprintf (dump_file, "\n");
1273 fprintf (dump_file, " bounds on difference of bases: ");
1274 mpz_out_str (dump_file, 10, bnds.below);
1275 fprintf (dump_file, " ... ");
1276 mpz_out_str (dump_file, 10, bnds.up);
1277 fprintf (dump_file, "\n");
1283 gcc_assert (integer_zerop (iv1->step));
1284 ret = number_of_iterations_ne (type, iv0, iv1->base, niter,
1285 never_infinite, &bnds);
1289 ret = number_of_iterations_lt (type, iv0, iv1, niter, never_infinite,
1294 ret = number_of_iterations_le (type, iv0, iv1, niter, never_infinite,
1302 mpz_clear (bnds.up);
1303 mpz_clear (bnds.below);
1305 if (dump_file && (dump_flags & TDF_DETAILS))
1309 fprintf (dump_file, " result:\n");
1310 if (!integer_nonzerop (niter->assumptions))
1312 fprintf (dump_file, " under assumptions ");
1313 print_generic_expr (dump_file, niter->assumptions, TDF_SLIM);
1314 fprintf (dump_file, "\n");
1317 if (!integer_zerop (niter->may_be_zero))
1319 fprintf (dump_file, " zero if ");
1320 print_generic_expr (dump_file, niter->may_be_zero, TDF_SLIM);
1321 fprintf (dump_file, "\n");
1324 fprintf (dump_file, " # of iterations ");
1325 print_generic_expr (dump_file, niter->niter, TDF_SLIM);
1326 fprintf (dump_file, ", bounded by ");
1327 dump_double_int (dump_file, niter->max, true);
1328 fprintf (dump_file, "\n");
1331 fprintf (dump_file, " failed\n\n");
1336 /* Substitute NEW for OLD in EXPR and fold the result. */
1339 simplify_replace_tree (tree expr, tree old, tree new_tree)
1342 tree ret = NULL_TREE, e, se;
1348 || operand_equal_p (expr, old, 0))
1349 return unshare_expr (new_tree);
1351 if (!EXPR_P (expr) && !GIMPLE_STMT_P (expr))
1354 n = TREE_OPERAND_LENGTH (expr);
1355 for (i = 0; i < n; i++)
1357 e = TREE_OPERAND (expr, i);
1358 se = simplify_replace_tree (e, old, new_tree);
1363 ret = copy_node (expr);
1365 TREE_OPERAND (ret, i) = se;
1368 return (ret ? fold (ret) : expr);
1371 /* Expand definitions of ssa names in EXPR as long as they are simple
1372 enough, and return the new expression. */
1375 expand_simple_operations (tree expr)
1378 tree ret = NULL_TREE, e, ee, stmt;
1379 enum tree_code code;
1381 if (expr == NULL_TREE)
1384 if (is_gimple_min_invariant (expr))
1387 code = TREE_CODE (expr);
1388 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code)))
1390 n = TREE_OPERAND_LENGTH (expr);
1391 for (i = 0; i < n; i++)
1393 e = TREE_OPERAND (expr, i);
1394 ee = expand_simple_operations (e);
1399 ret = copy_node (expr);
1401 TREE_OPERAND (ret, i) = ee;
1407 fold_defer_overflow_warnings ();
1409 fold_undefer_and_ignore_overflow_warnings ();
1413 if (TREE_CODE (expr) != SSA_NAME)
1416 stmt = SSA_NAME_DEF_STMT (expr);
1417 if (TREE_CODE (stmt) == PHI_NODE)
1419 basic_block src, dest;
1421 if (PHI_NUM_ARGS (stmt) != 1)
1423 e = PHI_ARG_DEF (stmt, 0);
1425 /* Avoid propagating through loop exit phi nodes, which
1426 could break loop-closed SSA form restrictions. */
1427 dest = bb_for_stmt (stmt);
1428 src = single_pred (dest);
1429 if (TREE_CODE (e) == SSA_NAME
1430 && src->loop_father != dest->loop_father)
1433 return expand_simple_operations (e);
1435 if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
1438 e = GIMPLE_STMT_OPERAND (stmt, 1);
1439 if (/* Casts are simple. */
1441 /* Copies are simple. */
1442 && TREE_CODE (e) != SSA_NAME
1443 /* Assignments of invariants are simple. */
1444 && !is_gimple_min_invariant (e)
1445 /* And increments and decrements by a constant are simple. */
1446 && !((TREE_CODE (e) == PLUS_EXPR
1447 || TREE_CODE (e) == MINUS_EXPR
1448 || TREE_CODE (e) == POINTER_PLUS_EXPR)
1449 && is_gimple_min_invariant (TREE_OPERAND (e, 1))))
1452 return expand_simple_operations (e);
1455 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1456 expression (or EXPR unchanged, if no simplification was possible). */
1459 tree_simplify_using_condition_1 (tree cond, tree expr)
1462 tree e, te, e0, e1, e2, notcond;
1463 enum tree_code code = TREE_CODE (expr);
1465 if (code == INTEGER_CST)
1468 if (code == TRUTH_OR_EXPR
1469 || code == TRUTH_AND_EXPR
1470 || code == COND_EXPR)
1474 e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
1475 if (TREE_OPERAND (expr, 0) != e0)
1478 e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
1479 if (TREE_OPERAND (expr, 1) != e1)
1482 if (code == COND_EXPR)
1484 e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
1485 if (TREE_OPERAND (expr, 2) != e2)
1493 if (code == COND_EXPR)
1494 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
1496 expr = fold_build2 (code, boolean_type_node, e0, e1);
1502 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
1503 propagation, and vice versa. Fold does not handle this, since it is
1504 considered too expensive. */
1505 if (TREE_CODE (cond) == EQ_EXPR)
1507 e0 = TREE_OPERAND (cond, 0);
1508 e1 = TREE_OPERAND (cond, 1);
1510 /* We know that e0 == e1. Check whether we cannot simplify expr
1512 e = simplify_replace_tree (expr, e0, e1);
1513 if (integer_zerop (e) || integer_nonzerop (e))
1516 e = simplify_replace_tree (expr, e1, e0);
1517 if (integer_zerop (e) || integer_nonzerop (e))
1520 if (TREE_CODE (expr) == EQ_EXPR)
1522 e0 = TREE_OPERAND (expr, 0);
1523 e1 = TREE_OPERAND (expr, 1);
1525 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
1526 e = simplify_replace_tree (cond, e0, e1);
1527 if (integer_zerop (e))
1529 e = simplify_replace_tree (cond, e1, e0);
1530 if (integer_zerop (e))
1533 if (TREE_CODE (expr) == NE_EXPR)
1535 e0 = TREE_OPERAND (expr, 0);
1536 e1 = TREE_OPERAND (expr, 1);
1538 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
1539 e = simplify_replace_tree (cond, e0, e1);
1540 if (integer_zerop (e))
1541 return boolean_true_node;
1542 e = simplify_replace_tree (cond, e1, e0);
1543 if (integer_zerop (e))
1544 return boolean_true_node;
1547 te = expand_simple_operations (expr);
1549 /* Check whether COND ==> EXPR. */
1550 notcond = invert_truthvalue (cond);
1551 e = fold_binary (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
1552 if (e && integer_nonzerop (e))
1555 /* Check whether COND ==> not EXPR. */
1556 e = fold_binary (TRUTH_AND_EXPR, boolean_type_node, cond, te);
1557 if (e && integer_zerop (e))
1563 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1564 expression (or EXPR unchanged, if no simplification was possible).
1565 Wrapper around tree_simplify_using_condition_1 that ensures that chains
1566 of simple operations in definitions of ssa names in COND are expanded,
1567 so that things like casts or incrementing the value of the bound before
1568 the loop do not cause us to fail. */
1571 tree_simplify_using_condition (tree cond, tree expr)
1573 cond = expand_simple_operations (cond);
1575 return tree_simplify_using_condition_1 (cond, expr);
1578 /* Tries to simplify EXPR using the conditions on entry to LOOP.
1579 Returns the simplified expression (or EXPR unchanged, if no
1580 simplification was possible).*/
1583 simplify_using_initial_conditions (struct loop *loop, tree expr)
1590 if (TREE_CODE (expr) == INTEGER_CST)
1593 /* Limit walking the dominators to avoid quadraticness in
1594 the number of BBs times the number of loops in degenerate
1596 for (bb = loop->header;
1597 bb != ENTRY_BLOCK_PTR && cnt < MAX_DOMINATORS_TO_WALK;
1598 bb = get_immediate_dominator (CDI_DOMINATORS, bb))
1600 if (!single_pred_p (bb))
1602 e = single_pred_edge (bb);
1604 if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
1607 cond = COND_EXPR_COND (last_stmt (e->src));
1608 if (e->flags & EDGE_FALSE_VALUE)
1609 cond = invert_truthvalue (cond);
1610 expr = tree_simplify_using_condition (cond, expr);
1617 /* Tries to simplify EXPR using the evolutions of the loop invariants
1618 in the superloops of LOOP. Returns the simplified expression
1619 (or EXPR unchanged, if no simplification was possible). */
1622 simplify_using_outer_evolutions (struct loop *loop, tree expr)
1624 enum tree_code code = TREE_CODE (expr);
1628 if (is_gimple_min_invariant (expr))
1631 if (code == TRUTH_OR_EXPR
1632 || code == TRUTH_AND_EXPR
1633 || code == COND_EXPR)
1637 e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
1638 if (TREE_OPERAND (expr, 0) != e0)
1641 e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
1642 if (TREE_OPERAND (expr, 1) != e1)
1645 if (code == COND_EXPR)
1647 e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
1648 if (TREE_OPERAND (expr, 2) != e2)
1656 if (code == COND_EXPR)
1657 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
1659 expr = fold_build2 (code, boolean_type_node, e0, e1);
1665 e = instantiate_parameters (loop, expr);
1666 if (is_gimple_min_invariant (e))
1672 /* Returns true if EXIT is the only possible exit from LOOP. */
1675 loop_only_exit_p (const struct loop *loop, const_edge exit)
1678 block_stmt_iterator bsi;
1682 if (exit != single_exit (loop))
1685 body = get_loop_body (loop);
1686 for (i = 0; i < loop->num_nodes; i++)
1688 for (bsi = bsi_start (body[0]); !bsi_end_p (bsi); bsi_next (&bsi))
1690 call = get_call_expr_in (bsi_stmt (bsi));
1691 if (call && TREE_SIDE_EFFECTS (call))
1703 /* Stores description of number of iterations of LOOP derived from
1704 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1705 useful information could be derived (and fields of NITER has
1706 meaning described in comments at struct tree_niter_desc
1707 declaration), false otherwise. If WARN is true and
1708 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1709 potentially unsafe assumptions. */
1712 number_of_iterations_exit (struct loop *loop, edge exit,
1713 struct tree_niter_desc *niter,
1716 tree stmt, cond, type;
1718 enum tree_code code;
1721 if (!dominated_by_p (CDI_DOMINATORS, loop->latch, exit->src))
1724 niter->assumptions = boolean_false_node;
1725 stmt = last_stmt (exit->src);
1726 if (!stmt || TREE_CODE (stmt) != COND_EXPR)
1729 /* We want the condition for staying inside loop. */
1730 cond = COND_EXPR_COND (stmt);
1731 if (exit->flags & EDGE_TRUE_VALUE)
1732 cond = invert_truthvalue (cond);
1734 code = TREE_CODE (cond);
1748 op0 = TREE_OPERAND (cond, 0);
1749 op1 = TREE_OPERAND (cond, 1);
1750 type = TREE_TYPE (op0);
1752 if (TREE_CODE (type) != INTEGER_TYPE
1753 && !POINTER_TYPE_P (type))
1756 if (!simple_iv (loop, stmt, op0, &iv0, false))
1758 if (!simple_iv (loop, stmt, op1, &iv1, false))
1761 /* We don't want to see undefined signed overflow warnings while
1762 computing the number of iterations. */
1763 fold_defer_overflow_warnings ();
1765 iv0.base = expand_simple_operations (iv0.base);
1766 iv1.base = expand_simple_operations (iv1.base);
1767 if (!number_of_iterations_cond (loop, type, &iv0, code, &iv1, niter,
1768 loop_only_exit_p (loop, exit)))
1770 fold_undefer_and_ignore_overflow_warnings ();
1776 niter->assumptions = simplify_using_outer_evolutions (loop,
1777 niter->assumptions);
1778 niter->may_be_zero = simplify_using_outer_evolutions (loop,
1779 niter->may_be_zero);
1780 niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
1784 = simplify_using_initial_conditions (loop,
1785 niter->assumptions);
1787 = simplify_using_initial_conditions (loop,
1788 niter->may_be_zero);
1790 fold_undefer_and_ignore_overflow_warnings ();
1792 if (integer_onep (niter->assumptions))
1795 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1796 But if we can prove that there is overflow or some other source of weird
1797 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1798 if (integer_zerop (niter->assumptions))
1801 if (flag_unsafe_loop_optimizations)
1802 niter->assumptions = boolean_true_node;
1806 const char *wording;
1807 location_t loc = EXPR_LOCATION (stmt);
1809 /* We can provide a more specific warning if one of the operator is
1810 constant and the other advances by +1 or -1. */
1811 if (!integer_zerop (iv1.step)
1812 ? (integer_zerop (iv0.step)
1813 && (integer_onep (iv1.step) || integer_all_onesp (iv1.step)))
1814 : (integer_onep (iv0.step) || integer_all_onesp (iv0.step)))
1816 flag_unsafe_loop_optimizations
1817 ? N_("assuming that the loop is not infinite")
1818 : N_("cannot optimize possibly infinite loops");
1821 flag_unsafe_loop_optimizations
1822 ? N_("assuming that the loop counter does not overflow")
1823 : N_("cannot optimize loop, the loop counter may overflow");
1825 if (LOCATION_LINE (loc) > 0)
1826 warning (OPT_Wunsafe_loop_optimizations, "%H%s", &loc, gettext (wording));
1828 warning (OPT_Wunsafe_loop_optimizations, "%s", gettext (wording));
1831 return flag_unsafe_loop_optimizations;
1834 /* Try to determine the number of iterations of LOOP. If we succeed,
1835 expression giving number of iterations is returned and *EXIT is
1836 set to the edge from that the information is obtained. Otherwise
1837 chrec_dont_know is returned. */
1840 find_loop_niter (struct loop *loop, edge *exit)
1843 VEC (edge, heap) *exits = get_loop_exit_edges (loop);
1845 tree niter = NULL_TREE, aniter;
1846 struct tree_niter_desc desc;
1849 for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
1851 if (!just_once_each_iteration_p (loop, ex->src))
1854 if (!number_of_iterations_exit (loop, ex, &desc, false))
1857 if (integer_nonzerop (desc.may_be_zero))
1859 /* We exit in the first iteration through this exit.
1860 We won't find anything better. */
1861 niter = build_int_cst (unsigned_type_node, 0);
1866 if (!integer_zerop (desc.may_be_zero))
1869 aniter = desc.niter;
1873 /* Nothing recorded yet. */
1879 /* Prefer constants, the lower the better. */
1880 if (TREE_CODE (aniter) != INTEGER_CST)
1883 if (TREE_CODE (niter) != INTEGER_CST)
1890 if (tree_int_cst_lt (aniter, niter))
1897 VEC_free (edge, heap, exits);
1899 return niter ? niter : chrec_dont_know;
1904 Analysis of a number of iterations of a loop by a brute-force evaluation.
1908 /* Bound on the number of iterations we try to evaluate. */
1910 #define MAX_ITERATIONS_TO_TRACK \
1911 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1913 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1914 result by a chain of operations such that all but exactly one of their
1915 operands are constants. */
1918 chain_of_csts_start (struct loop *loop, tree x)
1920 tree stmt = SSA_NAME_DEF_STMT (x);
1922 basic_block bb = bb_for_stmt (stmt);
1925 || !flow_bb_inside_loop_p (loop, bb))
1928 if (TREE_CODE (stmt) == PHI_NODE)
1930 if (bb == loop->header)
1936 if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
1939 if (!ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
1941 if (SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_DEF) == NULL_DEF_OPERAND_P)
1944 use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
1945 if (use == NULL_USE_OPERAND_P)
1948 return chain_of_csts_start (loop, use);
1951 /* Determines whether the expression X is derived from a result of a phi node
1952 in header of LOOP such that
1954 * the derivation of X consists only from operations with constants
1955 * the initial value of the phi node is constant
1956 * the value of the phi node in the next iteration can be derived from the
1957 value in the current iteration by a chain of operations with constants.
1959 If such phi node exists, it is returned. If X is a constant, X is returned
1960 unchanged. Otherwise NULL_TREE is returned. */
1963 get_base_for (struct loop *loop, tree x)
1965 tree phi, init, next;
1967 if (is_gimple_min_invariant (x))
1970 phi = chain_of_csts_start (loop, x);
1974 init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
1975 next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
1977 if (TREE_CODE (next) != SSA_NAME)
1980 if (!is_gimple_min_invariant (init))
1983 if (chain_of_csts_start (loop, next) != phi)
1989 /* Given an expression X, then
1991 * if X is NULL_TREE, we return the constant BASE.
1992 * otherwise X is a SSA name, whose value in the considered loop is derived
1993 by a chain of operations with constant from a result of a phi node in
1994 the header of the loop. Then we return value of X when the value of the
1995 result of this phi node is given by the constant BASE. */
1998 get_val_for (tree x, tree base)
2004 gcc_assert (is_gimple_min_invariant (base));
2009 stmt = SSA_NAME_DEF_STMT (x);
2010 if (TREE_CODE (stmt) == PHI_NODE)
2013 FOR_EACH_SSA_USE_OPERAND (op, stmt, iter, SSA_OP_USE)
2015 nx = USE_FROM_PTR (op);
2016 val = get_val_for (nx, base);
2018 val = fold (GIMPLE_STMT_OPERAND (stmt, 1));
2020 /* only iterate loop once. */
2024 /* Should never reach here. */
2028 /* Tries to count the number of iterations of LOOP till it exits by EXIT
2029 by brute force -- i.e. by determining the value of the operands of the
2030 condition at EXIT in first few iterations of the loop (assuming that
2031 these values are constant) and determining the first one in that the
2032 condition is not satisfied. Returns the constant giving the number
2033 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
2036 loop_niter_by_eval (struct loop *loop, edge exit)
2038 tree cond, cnd, acnd;
2039 tree op[2], val[2], next[2], aval[2], phi[2];
2043 cond = last_stmt (exit->src);
2044 if (!cond || TREE_CODE (cond) != COND_EXPR)
2045 return chrec_dont_know;
2047 cnd = COND_EXPR_COND (cond);
2048 if (exit->flags & EDGE_TRUE_VALUE)
2049 cnd = invert_truthvalue (cnd);
2051 cmp = TREE_CODE (cnd);
2060 for (j = 0; j < 2; j++)
2061 op[j] = TREE_OPERAND (cnd, j);
2065 return chrec_dont_know;
2068 for (j = 0; j < 2; j++)
2070 phi[j] = get_base_for (loop, op[j]);
2072 return chrec_dont_know;
2075 for (j = 0; j < 2; j++)
2077 if (TREE_CODE (phi[j]) == PHI_NODE)
2079 val[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_preheader_edge (loop));
2080 next[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_latch_edge (loop));
2085 next[j] = NULL_TREE;
2090 /* Don't issue signed overflow warnings. */
2091 fold_defer_overflow_warnings ();
2093 for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
2095 for (j = 0; j < 2; j++)
2096 aval[j] = get_val_for (op[j], val[j]);
2098 acnd = fold_binary (cmp, boolean_type_node, aval[0], aval[1]);
2099 if (acnd && integer_zerop (acnd))
2101 fold_undefer_and_ignore_overflow_warnings ();
2102 if (dump_file && (dump_flags & TDF_DETAILS))
2104 "Proved that loop %d iterates %d times using brute force.\n",
2106 return build_int_cst (unsigned_type_node, i);
2109 for (j = 0; j < 2; j++)
2111 val[j] = get_val_for (next[j], val[j]);
2112 if (!is_gimple_min_invariant (val[j]))
2114 fold_undefer_and_ignore_overflow_warnings ();
2115 return chrec_dont_know;
2120 fold_undefer_and_ignore_overflow_warnings ();
2122 return chrec_dont_know;
2125 /* Finds the exit of the LOOP by that the loop exits after a constant
2126 number of iterations and stores the exit edge to *EXIT. The constant
2127 giving the number of iterations of LOOP is returned. The number of
2128 iterations is determined using loop_niter_by_eval (i.e. by brute force
2129 evaluation). If we are unable to find the exit for that loop_niter_by_eval
2130 determines the number of iterations, chrec_dont_know is returned. */
2133 find_loop_niter_by_eval (struct loop *loop, edge *exit)
2136 VEC (edge, heap) *exits = get_loop_exit_edges (loop);
2138 tree niter = NULL_TREE, aniter;
2141 for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
2143 if (!just_once_each_iteration_p (loop, ex->src))
2146 aniter = loop_niter_by_eval (loop, ex);
2147 if (chrec_contains_undetermined (aniter))
2151 && !tree_int_cst_lt (aniter, niter))
2157 VEC_free (edge, heap, exits);
2159 return niter ? niter : chrec_dont_know;
2164 Analysis of upper bounds on number of iterations of a loop.
2168 /* Returns a constant upper bound on the value of expression VAL. VAL
2169 is considered to be unsigned. If its type is signed, its value must
2173 derive_constant_upper_bound (const_tree val)
2175 tree type = TREE_TYPE (val);
2176 tree op0, op1, subtype, maxt;
2177 double_int bnd, max, mmax, cst;
2180 if (INTEGRAL_TYPE_P (type))
2181 maxt = TYPE_MAX_VALUE (type);
2183 maxt = upper_bound_in_type (type, type);
2185 max = tree_to_double_int (maxt);
2187 switch (TREE_CODE (val))
2190 return tree_to_double_int (val);
2193 op0 = TREE_OPERAND (val, 0);
2194 subtype = TREE_TYPE (op0);
2195 if (!TYPE_UNSIGNED (subtype)
2196 /* If TYPE is also signed, the fact that VAL is nonnegative implies
2197 that OP0 is nonnegative. */
2198 && TYPE_UNSIGNED (type)
2199 && !tree_expr_nonnegative_p (op0))
2201 /* If we cannot prove that the casted expression is nonnegative,
2202 we cannot establish more useful upper bound than the precision
2203 of the type gives us. */
2207 /* We now know that op0 is an nonnegative value. Try deriving an upper
2209 bnd = derive_constant_upper_bound (op0);
2211 /* If the bound does not fit in TYPE, max. value of TYPE could be
2213 if (double_int_ucmp (max, bnd) < 0)
2219 case POINTER_PLUS_EXPR:
2221 op0 = TREE_OPERAND (val, 0);
2222 op1 = TREE_OPERAND (val, 1);
2224 if (TREE_CODE (op1) != INTEGER_CST
2225 || !tree_expr_nonnegative_p (op0))
2228 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
2229 choose the most logical way how to treat this constant regardless
2230 of the signedness of the type. */
2231 cst = tree_to_double_int (op1);
2232 cst = double_int_sext (cst, TYPE_PRECISION (type));
2233 if (TREE_CODE (val) == PLUS_EXPR)
2234 cst = double_int_neg (cst);
2236 bnd = derive_constant_upper_bound (op0);
2238 if (double_int_negative_p (cst))
2240 cst = double_int_neg (cst);
2241 /* Avoid CST == 0x80000... */
2242 if (double_int_negative_p (cst))
2245 /* OP0 + CST. We need to check that
2246 BND <= MAX (type) - CST. */
2248 mmax = double_int_add (max, double_int_neg (cst));
2249 if (double_int_ucmp (bnd, mmax) > 0)
2252 return double_int_add (bnd, cst);
2256 /* OP0 - CST, where CST >= 0.
2258 If TYPE is signed, we have already verified that OP0 >= 0, and we
2259 know that the result is nonnegative. This implies that
2262 If TYPE is unsigned, we must additionally know that OP0 >= CST,
2263 otherwise the operation underflows.
2266 /* This should only happen if the type is unsigned; however, for
2267 buggy programs that use overflowing signed arithmetics even with
2268 -fno-wrapv, this condition may also be true for signed values. */
2269 if (double_int_ucmp (bnd, cst) < 0)
2272 if (TYPE_UNSIGNED (type))
2274 tree tem = fold_binary (GE_EXPR, boolean_type_node, op0,
2275 double_int_to_tree (type, cst));
2276 if (!tem || integer_nonzerop (tem))
2280 bnd = double_int_add (bnd, double_int_neg (cst));
2285 case FLOOR_DIV_EXPR:
2286 case EXACT_DIV_EXPR:
2287 op0 = TREE_OPERAND (val, 0);
2288 op1 = TREE_OPERAND (val, 1);
2289 if (TREE_CODE (op1) != INTEGER_CST
2290 || tree_int_cst_sign_bit (op1))
2293 bnd = derive_constant_upper_bound (op0);
2294 return double_int_udiv (bnd, tree_to_double_int (op1), FLOOR_DIV_EXPR);
2297 op1 = TREE_OPERAND (val, 1);
2298 if (TREE_CODE (op1) != INTEGER_CST
2299 || tree_int_cst_sign_bit (op1))
2301 return tree_to_double_int (op1);
2304 stmt = SSA_NAME_DEF_STMT (val);
2305 if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT
2306 || GIMPLE_STMT_OPERAND (stmt, 0) != val)
2308 return derive_constant_upper_bound (GIMPLE_STMT_OPERAND (stmt, 1));
2315 /* Records that every statement in LOOP is executed I_BOUND times.
2316 REALISTIC is true if I_BOUND is expected to be close the the real number
2317 of iterations. UPPER is true if we are sure the loop iterates at most
2321 record_niter_bound (struct loop *loop, double_int i_bound, bool realistic,
2324 /* Update the bounds only when there is no previous estimation, or when the current
2325 estimation is smaller. */
2327 && (!loop->any_upper_bound
2328 || double_int_ucmp (i_bound, loop->nb_iterations_upper_bound) < 0))
2330 loop->any_upper_bound = true;
2331 loop->nb_iterations_upper_bound = i_bound;
2334 && (!loop->any_estimate
2335 || double_int_ucmp (i_bound, loop->nb_iterations_estimate) < 0))
2337 loop->any_estimate = true;
2338 loop->nb_iterations_estimate = i_bound;
2342 /* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. IS_EXIT
2343 is true if the loop is exited immediately after STMT, and this exit
2344 is taken at last when the STMT is executed BOUND + 1 times.
2345 REALISTIC is true if BOUND is expected to be close the the real number
2346 of iterations. UPPER is true if we are sure the loop iterates at most
2347 BOUND times. I_BOUND is an unsigned double_int upper estimate on BOUND. */
2350 record_estimate (struct loop *loop, tree bound, double_int i_bound,
2351 tree at_stmt, bool is_exit, bool realistic, bool upper)
2356 if (dump_file && (dump_flags & TDF_DETAILS))
2358 fprintf (dump_file, "Statement %s", is_exit ? "(exit)" : "");
2359 print_generic_expr (dump_file, at_stmt, TDF_SLIM);
2360 fprintf (dump_file, " is %sexecuted at most ",
2361 upper ? "" : "probably ");
2362 print_generic_expr (dump_file, bound, TDF_SLIM);
2363 fprintf (dump_file, " (bounded by ");
2364 dump_double_int (dump_file, i_bound, true);
2365 fprintf (dump_file, ") + 1 times in loop %d.\n", loop->num);
2368 /* If the I_BOUND is just an estimate of BOUND, it rarely is close to the
2369 real number of iterations. */
2370 if (TREE_CODE (bound) != INTEGER_CST)
2372 if (!upper && !realistic)
2375 /* If we have a guaranteed upper bound, record it in the appropriate
2379 struct nb_iter_bound *elt = GGC_NEW (struct nb_iter_bound);
2381 elt->bound = i_bound;
2382 elt->stmt = at_stmt;
2383 elt->is_exit = is_exit;
2384 elt->next = loop->bounds;
2388 /* Update the number of iteration estimates according to the bound.
2389 If at_stmt is an exit, then every statement in the loop is
2390 executed at most BOUND + 1 times. If it is not an exit, then
2391 some of the statements before it could be executed BOUND + 2
2392 times, if an exit of LOOP is before stmt. */
2393 exit = single_exit (loop);
2396 && dominated_by_p (CDI_DOMINATORS,
2397 exit->src, bb_for_stmt (at_stmt))))
2398 delta = double_int_one;
2400 delta = double_int_two;
2401 i_bound = double_int_add (i_bound, delta);
2403 /* If an overflow occurred, ignore the result. */
2404 if (double_int_ucmp (i_bound, delta) < 0)
2407 record_niter_bound (loop, i_bound, realistic, upper);
2410 /* Record the estimate on number of iterations of LOOP based on the fact that
2411 the induction variable BASE + STEP * i evaluated in STMT does not wrap and
2412 its values belong to the range <LOW, HIGH>. REALISTIC is true if the
2413 estimated number of iterations is expected to be close to the real one.
2414 UPPER is true if we are sure the induction variable does not wrap. */
2417 record_nonwrapping_iv (struct loop *loop, tree base, tree step, tree stmt,
2418 tree low, tree high, bool realistic, bool upper)
2420 tree niter_bound, extreme, delta;
2421 tree type = TREE_TYPE (base), unsigned_type;
2424 if (TREE_CODE (step) != INTEGER_CST || integer_zerop (step))
2427 if (dump_file && (dump_flags & TDF_DETAILS))
2429 fprintf (dump_file, "Induction variable (");
2430 print_generic_expr (dump_file, TREE_TYPE (base), TDF_SLIM);
2431 fprintf (dump_file, ") ");
2432 print_generic_expr (dump_file, base, TDF_SLIM);
2433 fprintf (dump_file, " + ");
2434 print_generic_expr (dump_file, step, TDF_SLIM);
2435 fprintf (dump_file, " * iteration does not wrap in statement ");
2436 print_generic_expr (dump_file, stmt, TDF_SLIM);
2437 fprintf (dump_file, " in loop %d.\n", loop->num);
2440 unsigned_type = unsigned_type_for (type);
2441 base = fold_convert (unsigned_type, base);
2442 step = fold_convert (unsigned_type, step);
2444 if (tree_int_cst_sign_bit (step))
2446 extreme = fold_convert (unsigned_type, low);
2447 if (TREE_CODE (base) != INTEGER_CST)
2448 base = fold_convert (unsigned_type, high);
2449 delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
2450 step = fold_build1 (NEGATE_EXPR, unsigned_type, step);
2454 extreme = fold_convert (unsigned_type, high);
2455 if (TREE_CODE (base) != INTEGER_CST)
2456 base = fold_convert (unsigned_type, low);
2457 delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
2460 /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
2461 would get out of the range. */
2462 niter_bound = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step);
2463 max = derive_constant_upper_bound (niter_bound);
2464 record_estimate (loop, niter_bound, max, stmt, false, realistic, upper);
2467 /* Returns true if REF is a reference to an array at the end of a dynamically
2468 allocated structure. If this is the case, the array may be allocated larger
2469 than its upper bound implies. */
2472 array_at_struct_end_p (tree ref)
2474 tree base = get_base_address (ref);
2477 /* Unless the reference is through a pointer, the size of the array matches
2479 if (!base || !INDIRECT_REF_P (base))
2482 for (;handled_component_p (ref); ref = parent)
2484 parent = TREE_OPERAND (ref, 0);
2486 if (TREE_CODE (ref) == COMPONENT_REF)
2488 /* All fields of a union are at its end. */
2489 if (TREE_CODE (TREE_TYPE (parent)) == UNION_TYPE)
2492 /* Unless the field is at the end of the struct, we are done. */
2493 field = TREE_OPERAND (ref, 1);
2494 if (TREE_CHAIN (field))
2498 /* The other options are ARRAY_REF, ARRAY_RANGE_REF, VIEW_CONVERT_EXPR.
2499 In all these cases, we might be accessing the last element, and
2500 although in practice this will probably never happen, it is legal for
2501 the indices of this last element to exceed the bounds of the array.
2502 Therefore, continue checking. */
2505 gcc_assert (INDIRECT_REF_P (ref));
2509 /* Determine information about number of iterations a LOOP from the index
2510 IDX of a data reference accessed in STMT. RELIABLE is true if STMT is
2511 guaranteed to be executed in every iteration of LOOP. Callback for
2522 idx_infer_loop_bounds (tree base, tree *idx, void *dta)
2524 struct ilb_data *data = (struct ilb_data *) dta;
2525 tree ev, init, step;
2526 tree low, high, type, next;
2527 bool sign, upper = data->reliable, at_end = false;
2528 struct loop *loop = data->loop;
2530 if (TREE_CODE (base) != ARRAY_REF)
2533 /* For arrays at the end of the structure, we are not guaranteed that they
2534 do not really extend over their declared size. However, for arrays of
2535 size greater than one, this is unlikely to be intended. */
2536 if (array_at_struct_end_p (base))
2542 ev = instantiate_parameters (loop, analyze_scalar_evolution (loop, *idx));
2543 init = initial_condition (ev);
2544 step = evolution_part_in_loop_num (ev, loop->num);
2548 || TREE_CODE (step) != INTEGER_CST
2549 || integer_zerop (step)
2550 || tree_contains_chrecs (init, NULL)
2551 || chrec_contains_symbols_defined_in_loop (init, loop->num))
2554 low = array_ref_low_bound (base);
2555 high = array_ref_up_bound (base);
2557 /* The case of nonconstant bounds could be handled, but it would be
2559 if (TREE_CODE (low) != INTEGER_CST
2561 || TREE_CODE (high) != INTEGER_CST)
2563 sign = tree_int_cst_sign_bit (step);
2564 type = TREE_TYPE (step);
2566 /* The array of length 1 at the end of a structure most likely extends
2567 beyond its bounds. */
2569 && operand_equal_p (low, high, 0))
2572 /* In case the relevant bound of the array does not fit in type, or
2573 it does, but bound + step (in type) still belongs into the range of the
2574 array, the index may wrap and still stay within the range of the array
2575 (consider e.g. if the array is indexed by the full range of
2578 To make things simpler, we require both bounds to fit into type, although
2579 there are cases where this would not be strictly necessary. */
2580 if (!int_fits_type_p (high, type)
2581 || !int_fits_type_p (low, type))
2583 low = fold_convert (type, low);
2584 high = fold_convert (type, high);
2587 next = fold_binary (PLUS_EXPR, type, low, step);
2589 next = fold_binary (PLUS_EXPR, type, high, step);
2591 if (tree_int_cst_compare (low, next) <= 0
2592 && tree_int_cst_compare (next, high) <= 0)
2595 record_nonwrapping_iv (loop, init, step, data->stmt, low, high, true, upper);
2599 /* Determine information about number of iterations a LOOP from the bounds
2600 of arrays in the data reference REF accessed in STMT. RELIABLE is true if
2601 STMT is guaranteed to be executed in every iteration of LOOP.*/
2604 infer_loop_bounds_from_ref (struct loop *loop, tree stmt, tree ref,
2607 struct ilb_data data;
2611 data.reliable = reliable;
2612 for_each_index (&ref, idx_infer_loop_bounds, &data);
2615 /* Determine information about number of iterations of a LOOP from the way
2616 arrays are used in STMT. RELIABLE is true if STMT is guaranteed to be
2617 executed in every iteration of LOOP. */
2620 infer_loop_bounds_from_array (struct loop *loop, tree stmt, bool reliable)
2624 if (TREE_CODE (stmt) == GIMPLE_MODIFY_STMT)
2626 tree op0 = GIMPLE_STMT_OPERAND (stmt, 0);
2627 tree op1 = GIMPLE_STMT_OPERAND (stmt, 1);
2629 /* For each memory access, analyze its access function
2630 and record a bound on the loop iteration domain. */
2631 if (REFERENCE_CLASS_P (op0))
2632 infer_loop_bounds_from_ref (loop, stmt, op0, reliable);
2634 if (REFERENCE_CLASS_P (op1))
2635 infer_loop_bounds_from_ref (loop, stmt, op1, reliable);
2639 call = get_call_expr_in (stmt);
2643 call_expr_arg_iterator iter;
2645 FOR_EACH_CALL_EXPR_ARG (arg, iter, call)
2646 if (REFERENCE_CLASS_P (arg))
2647 infer_loop_bounds_from_ref (loop, stmt, arg, reliable);
2651 /* Determine information about number of iterations of a LOOP from the fact
2652 that signed arithmetics in STMT does not overflow. */
2655 infer_loop_bounds_from_signedness (struct loop *loop, tree stmt)
2657 tree def, base, step, scev, type, low, high;
2659 if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
2662 def = GIMPLE_STMT_OPERAND (stmt, 0);
2664 if (TREE_CODE (def) != SSA_NAME)
2667 type = TREE_TYPE (def);
2668 if (!INTEGRAL_TYPE_P (type)
2669 || !TYPE_OVERFLOW_UNDEFINED (type))
2672 scev = instantiate_parameters (loop, analyze_scalar_evolution (loop, def));
2673 if (chrec_contains_undetermined (scev))
2676 base = initial_condition_in_loop_num (scev, loop->num);
2677 step = evolution_part_in_loop_num (scev, loop->num);
2680 || TREE_CODE (step) != INTEGER_CST
2681 || tree_contains_chrecs (base, NULL)
2682 || chrec_contains_symbols_defined_in_loop (base, loop->num))
2685 low = lower_bound_in_type (type, type);
2686 high = upper_bound_in_type (type, type);
2688 record_nonwrapping_iv (loop, base, step, stmt, low, high, false, true);
2691 /* The following analyzers are extracting informations on the bounds
2692 of LOOP from the following undefined behaviors:
2694 - data references should not access elements over the statically
2697 - signed variables should not overflow when flag_wrapv is not set.
2701 infer_loop_bounds_from_undefined (struct loop *loop)
2705 block_stmt_iterator bsi;
2709 bbs = get_loop_body (loop);
2711 for (i = 0; i < loop->num_nodes; i++)
2715 /* If BB is not executed in each iteration of the loop, we cannot
2716 use the operations in it to infer reliable upper bound on the
2717 # of iterations of the loop. However, we can use it as a guess. */
2718 reliable = dominated_by_p (CDI_DOMINATORS, loop->latch, bb);
2720 for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
2722 tree stmt = bsi_stmt (bsi);
2724 infer_loop_bounds_from_array (loop, stmt, reliable);
2727 infer_loop_bounds_from_signedness (loop, stmt);
2735 /* Converts VAL to double_int. */
2738 gcov_type_to_double_int (gcov_type val)
2742 ret.low = (unsigned HOST_WIDE_INT) val;
2743 /* If HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_WIDEST_INT, avoid shifting by
2744 the size of type. */
2745 val >>= HOST_BITS_PER_WIDE_INT - 1;
2747 ret.high = (unsigned HOST_WIDE_INT) val;
2752 /* Records estimates on numbers of iterations of LOOP. */
2755 estimate_numbers_of_iterations_loop (struct loop *loop)
2757 VEC (edge, heap) *exits;
2760 struct tree_niter_desc niter_desc;
2764 /* Give up if we already have tried to compute an estimation. */
2765 if (loop->estimate_state != EST_NOT_COMPUTED)
2767 loop->estimate_state = EST_AVAILABLE;
2768 loop->any_upper_bound = false;
2769 loop->any_estimate = false;
2771 exits = get_loop_exit_edges (loop);
2772 for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
2774 if (!number_of_iterations_exit (loop, ex, &niter_desc, false))
2777 niter = niter_desc.niter;
2778 type = TREE_TYPE (niter);
2779 if (TREE_CODE (niter_desc.may_be_zero) != INTEGER_CST)
2780 niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
2781 build_int_cst (type, 0),
2783 record_estimate (loop, niter, niter_desc.max,
2784 last_stmt (ex->src),
2787 VEC_free (edge, heap, exits);
2789 infer_loop_bounds_from_undefined (loop);
2791 /* If we have a measured profile, use it to estimate the number of
2793 if (loop->header->count != 0)
2795 gcov_type nit = expected_loop_iterations_unbounded (loop) + 1;
2796 bound = gcov_type_to_double_int (nit);
2797 record_niter_bound (loop, bound, true, false);
2800 /* If an upper bound is smaller than the realistic estimate of the
2801 number of iterations, use the upper bound instead. */
2802 if (loop->any_upper_bound
2803 && loop->any_estimate
2804 && double_int_ucmp (loop->nb_iterations_upper_bound,
2805 loop->nb_iterations_estimate) < 0)
2806 loop->nb_iterations_estimate = loop->nb_iterations_upper_bound;
2809 /* Records estimates on numbers of iterations of loops. */
2812 estimate_numbers_of_iterations (void)
2817 /* We don't want to issue signed overflow warnings while getting
2818 loop iteration estimates. */
2819 fold_defer_overflow_warnings ();
2821 FOR_EACH_LOOP (li, loop, 0)
2823 estimate_numbers_of_iterations_loop (loop);
2826 fold_undefer_and_ignore_overflow_warnings ();
2829 /* Returns true if statement S1 dominates statement S2. */
2832 stmt_dominates_stmt_p (tree s1, tree s2)
2834 basic_block bb1 = bb_for_stmt (s1), bb2 = bb_for_stmt (s2);
2842 block_stmt_iterator bsi;
2844 for (bsi = bsi_start (bb1); bsi_stmt (bsi) != s2; bsi_next (&bsi))
2845 if (bsi_stmt (bsi) == s1)
2851 return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
2854 /* Returns true when we can prove that the number of executions of
2855 STMT in the loop is at most NITER, according to the bound on
2856 the number of executions of the statement NITER_BOUND->stmt recorded in
2857 NITER_BOUND. If STMT is NULL, we must prove this bound for all
2858 statements in the loop. */
2861 n_of_executions_at_most (tree stmt,
2862 struct nb_iter_bound *niter_bound,
2865 double_int bound = niter_bound->bound;
2866 tree nit_type = TREE_TYPE (niter), e;
2869 gcc_assert (TYPE_UNSIGNED (nit_type));
2871 /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
2872 the number of iterations is small. */
2873 if (!double_int_fits_to_tree_p (nit_type, bound))
2876 /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
2877 times. This means that:
2879 -- if NITER_BOUND->is_exit is true, then everything before
2880 NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
2881 times, and everything after it at most NITER_BOUND->bound times.
2883 -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
2884 is executed, then NITER_BOUND->stmt is executed as well in the same
2885 iteration (we conclude that if both statements belong to the same
2886 basic block, or if STMT is after NITER_BOUND->stmt), then STMT
2887 is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
2888 executed at most NITER_BOUND->bound + 2 times. */
2890 if (niter_bound->is_exit)
2893 && stmt != niter_bound->stmt
2894 && stmt_dominates_stmt_p (niter_bound->stmt, stmt))
2902 || (bb_for_stmt (stmt) != bb_for_stmt (niter_bound->stmt)
2903 && !stmt_dominates_stmt_p (niter_bound->stmt, stmt)))
2905 bound = double_int_add (bound, double_int_one);
2906 if (double_int_zero_p (bound)
2907 || !double_int_fits_to_tree_p (nit_type, bound))
2913 e = fold_binary (cmp, boolean_type_node,
2914 niter, double_int_to_tree (nit_type, bound));
2915 return e && integer_nonzerop (e);
2918 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
2921 nowrap_type_p (tree type)
2923 if (INTEGRAL_TYPE_P (type)
2924 && TYPE_OVERFLOW_UNDEFINED (type))
2927 if (POINTER_TYPE_P (type))
2933 /* Return false only when the induction variable BASE + STEP * I is
2934 known to not overflow: i.e. when the number of iterations is small
2935 enough with respect to the step and initial condition in order to
2936 keep the evolution confined in TYPEs bounds. Return true when the
2937 iv is known to overflow or when the property is not computable.
2939 USE_OVERFLOW_SEMANTICS is true if this function should assume that
2940 the rules for overflow of the given language apply (e.g., that signed
2941 arithmetics in C does not overflow). */
2944 scev_probably_wraps_p (tree base, tree step,
2945 tree at_stmt, struct loop *loop,
2946 bool use_overflow_semantics)
2948 struct nb_iter_bound *bound;
2949 tree delta, step_abs;
2950 tree unsigned_type, valid_niter;
2951 tree type = TREE_TYPE (step);
2953 /* FIXME: We really need something like
2954 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
2956 We used to test for the following situation that frequently appears
2957 during address arithmetics:
2959 D.1621_13 = (long unsigned intD.4) D.1620_12;
2960 D.1622_14 = D.1621_13 * 8;
2961 D.1623_15 = (doubleD.29 *) D.1622_14;
2963 And derived that the sequence corresponding to D_14
2964 can be proved to not wrap because it is used for computing a
2965 memory access; however, this is not really the case -- for example,
2966 if D_12 = (unsigned char) [254,+,1], then D_14 has values
2967 2032, 2040, 0, 8, ..., but the code is still legal. */
2969 if (chrec_contains_undetermined (base)
2970 || chrec_contains_undetermined (step))
2973 if (integer_zerop (step))
2976 /* If we can use the fact that signed and pointer arithmetics does not
2977 wrap, we are done. */
2978 if (use_overflow_semantics && nowrap_type_p (type))
2981 /* To be able to use estimates on number of iterations of the loop,
2982 we must have an upper bound on the absolute value of the step. */
2983 if (TREE_CODE (step) != INTEGER_CST)
2986 /* Don't issue signed overflow warnings. */
2987 fold_defer_overflow_warnings ();
2989 /* Otherwise, compute the number of iterations before we reach the
2990 bound of the type, and verify that the loop is exited before this
2992 unsigned_type = unsigned_type_for (type);
2993 base = fold_convert (unsigned_type, base);
2995 if (tree_int_cst_sign_bit (step))
2997 tree extreme = fold_convert (unsigned_type,
2998 lower_bound_in_type (type, type));
2999 delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
3000 step_abs = fold_build1 (NEGATE_EXPR, unsigned_type,
3001 fold_convert (unsigned_type, step));
3005 tree extreme = fold_convert (unsigned_type,
3006 upper_bound_in_type (type, type));
3007 delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
3008 step_abs = fold_convert (unsigned_type, step);
3011 valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step_abs);
3013 estimate_numbers_of_iterations_loop (loop);
3014 for (bound = loop->bounds; bound; bound = bound->next)
3016 if (n_of_executions_at_most (at_stmt, bound, valid_niter))
3018 fold_undefer_and_ignore_overflow_warnings ();
3023 fold_undefer_and_ignore_overflow_warnings ();
3025 /* At this point we still don't have a proof that the iv does not
3026 overflow: give up. */
3030 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
3033 free_numbers_of_iterations_estimates_loop (struct loop *loop)
3035 struct nb_iter_bound *bound, *next;
3037 loop->nb_iterations = NULL;
3038 loop->estimate_state = EST_NOT_COMPUTED;
3039 for (bound = loop->bounds; bound; bound = next)
3045 loop->bounds = NULL;
3048 /* Frees the information on upper bounds on numbers of iterations of loops. */
3051 free_numbers_of_iterations_estimates (void)
3056 FOR_EACH_LOOP (li, loop, 0)
3058 free_numbers_of_iterations_estimates_loop (loop);
3062 /* Substitute value VAL for ssa name NAME inside expressions held
3066 substitute_in_loop_info (struct loop *loop, tree name, tree val)
3068 loop->nb_iterations = simplify_replace_tree (loop->nb_iterations, name, val);