1 /* Functions to determine/estimate number of iterations of a loop.
2 Copyright (C) 2004, 2005, 2006, 2007, 2008 Free Software Foundation,
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"
28 #include "hard-reg-set.h"
29 #include "basic-block.h"
31 #include "diagnostic.h"
33 #include "tree-flow.h"
34 #include "tree-dump.h"
36 #include "tree-pass.h"
38 #include "tree-chrec.h"
39 #include "tree-scalar-evolution.h"
40 #include "tree-data-ref.h"
44 #include "tree-inline.h"
47 #define SWAP(X, Y) do { affine_iv *tmp = (X); (X) = (Y); (Y) = tmp; } while (0)
49 /* The maximum number of dominator BBs we search for conditions
50 of loop header copies we use for simplifying a conditional
52 #define MAX_DOMINATORS_TO_WALK 8
56 Analysis of number of iterations of an affine exit test.
60 /* Bounds on some value, BELOW <= X <= UP. */
68 /* Splits expression EXPR to a variable part VAR and constant OFFSET. */
71 split_to_var_and_offset (tree expr, tree *var, mpz_t offset)
73 tree type = TREE_TYPE (expr);
79 mpz_set_ui (offset, 0);
81 switch (TREE_CODE (expr))
88 case POINTER_PLUS_EXPR:
89 op0 = TREE_OPERAND (expr, 0);
90 op1 = TREE_OPERAND (expr, 1);
92 if (TREE_CODE (op1) != INTEGER_CST)
96 /* Always sign extend the offset. */
97 off = double_int_sext (tree_to_double_int (op1),
98 TYPE_PRECISION (type));
99 mpz_set_double_int (offset, off, false);
103 *var = build_int_cst_type (type, 0);
104 off = tree_to_double_int (expr);
105 mpz_set_double_int (offset, off, TYPE_UNSIGNED (type));
113 /* Stores estimate on the minimum/maximum value of the expression VAR + OFF
114 in TYPE to MIN and MAX. */
117 determine_value_range (tree type, tree var, mpz_t off,
118 mpz_t min, mpz_t max)
120 /* If the expression is a constant, we know its value exactly. */
121 if (integer_zerop (var))
128 /* If the computation may wrap, we know nothing about the value, except for
129 the range of the type. */
130 get_type_static_bounds (type, min, max);
131 if (!nowrap_type_p (type))
134 /* Since the addition of OFF does not wrap, if OFF is positive, then we may
135 add it to MIN, otherwise to MAX. */
136 if (mpz_sgn (off) < 0)
137 mpz_add (max, max, off);
139 mpz_add (min, min, off);
142 /* Stores the bounds on the difference of the values of the expressions
143 (var + X) and (var + Y), computed in TYPE, to BNDS. */
146 bound_difference_of_offsetted_base (tree type, mpz_t x, mpz_t y,
149 int rel = mpz_cmp (x, y);
150 bool may_wrap = !nowrap_type_p (type);
153 /* If X == Y, then the expressions are always equal.
154 If X > Y, there are the following possibilities:
155 a) neither of var + X and var + Y overflow or underflow, or both of
156 them do. Then their difference is X - Y.
157 b) var + X overflows, and var + Y does not. Then the values of the
158 expressions are var + X - M and var + Y, where M is the range of
159 the type, and their difference is X - Y - M.
160 c) var + Y underflows and var + X does not. Their difference again
162 Therefore, if the arithmetics in type does not overflow, then the
163 bounds are (X - Y, X - Y), otherwise they are (X - Y - M, X - Y)
164 Similarly, if X < Y, the bounds are either (X - Y, X - Y) or
165 (X - Y, X - Y + M). */
169 mpz_set_ui (bnds->below, 0);
170 mpz_set_ui (bnds->up, 0);
175 mpz_set_double_int (m, double_int_mask (TYPE_PRECISION (type)), true);
176 mpz_add_ui (m, m, 1);
177 mpz_sub (bnds->up, x, y);
178 mpz_set (bnds->below, bnds->up);
183 mpz_sub (bnds->below, bnds->below, m);
185 mpz_add (bnds->up, bnds->up, m);
191 /* From condition C0 CMP C1 derives information regarding the
192 difference of values of VARX + OFFX and VARY + OFFY, computed in TYPE,
193 and stores it to BNDS. */
196 refine_bounds_using_guard (tree type, tree varx, mpz_t offx,
197 tree vary, mpz_t offy,
198 tree c0, enum tree_code cmp, tree c1,
201 tree varc0, varc1, tmp, ctype;
202 mpz_t offc0, offc1, loffx, loffy, bnd;
204 bool no_wrap = nowrap_type_p (type);
213 STRIP_SIGN_NOPS (c0);
214 STRIP_SIGN_NOPS (c1);
215 ctype = TREE_TYPE (c0);
216 if (!useless_type_conversion_p (ctype, type))
222 /* We could derive quite precise information from EQ_EXPR, however, such
223 a guard is unlikely to appear, so we do not bother with handling
228 /* NE_EXPR comparisons do not contain much of useful information, except for
229 special case of comparing with the bounds of the type. */
230 if (TREE_CODE (c1) != INTEGER_CST
231 || !INTEGRAL_TYPE_P (type))
234 /* Ensure that the condition speaks about an expression in the same type
236 ctype = TREE_TYPE (c0);
237 if (TYPE_PRECISION (ctype) != TYPE_PRECISION (type))
239 c0 = fold_convert (type, c0);
240 c1 = fold_convert (type, c1);
242 if (TYPE_MIN_VALUE (type)
243 && operand_equal_p (c1, TYPE_MIN_VALUE (type), 0))
248 if (TYPE_MAX_VALUE (type)
249 && operand_equal_p (c1, TYPE_MAX_VALUE (type), 0))
262 split_to_var_and_offset (expand_simple_operations (c0), &varc0, offc0);
263 split_to_var_and_offset (expand_simple_operations (c1), &varc1, offc1);
265 /* We are only interested in comparisons of expressions based on VARX and
266 VARY. TODO -- we might also be able to derive some bounds from
267 expressions containing just one of the variables. */
269 if (operand_equal_p (varx, varc1, 0))
271 tmp = varc0; varc0 = varc1; varc1 = tmp;
272 mpz_swap (offc0, offc1);
273 cmp = swap_tree_comparison (cmp);
276 if (!operand_equal_p (varx, varc0, 0)
277 || !operand_equal_p (vary, varc1, 0))
280 mpz_init_set (loffx, offx);
281 mpz_init_set (loffy, offy);
283 if (cmp == GT_EXPR || cmp == GE_EXPR)
285 tmp = varx; varx = vary; vary = tmp;
286 mpz_swap (offc0, offc1);
287 mpz_swap (loffx, loffy);
288 cmp = swap_tree_comparison (cmp);
292 /* If there is no overflow, the condition implies that
294 (VARX + OFFX) cmp (VARY + OFFY) + (OFFX - OFFY + OFFC1 - OFFC0).
296 The overflows and underflows may complicate things a bit; each
297 overflow decreases the appropriate offset by M, and underflow
298 increases it by M. The above inequality would not necessarily be
301 -- VARX + OFFX underflows and VARX + OFFC0 does not, or
302 VARX + OFFC0 overflows, but VARX + OFFX does not.
303 This may only happen if OFFX < OFFC0.
304 -- VARY + OFFY overflows and VARY + OFFC1 does not, or
305 VARY + OFFC1 underflows and VARY + OFFY does not.
306 This may only happen if OFFY > OFFC1. */
315 x_ok = (integer_zerop (varx)
316 || mpz_cmp (loffx, offc0) >= 0);
317 y_ok = (integer_zerop (vary)
318 || mpz_cmp (loffy, offc1) <= 0);
324 mpz_sub (bnd, loffx, loffy);
325 mpz_add (bnd, bnd, offc1);
326 mpz_sub (bnd, bnd, offc0);
329 mpz_sub_ui (bnd, bnd, 1);
334 if (mpz_cmp (bnds->below, bnd) < 0)
335 mpz_set (bnds->below, bnd);
339 if (mpz_cmp (bnd, bnds->up) < 0)
340 mpz_set (bnds->up, bnd);
352 /* Stores the bounds on the value of the expression X - Y in LOOP to BNDS.
353 The subtraction is considered to be performed in arbitrary precision,
356 We do not attempt to be too clever regarding the value ranges of X and
357 Y; most of the time, they are just integers or ssa names offsetted by
358 integer. However, we try to use the information contained in the
359 comparisons before the loop (usually created by loop header copying). */
362 bound_difference (struct loop *loop, tree x, tree y, bounds *bnds)
364 tree type = TREE_TYPE (x);
367 mpz_t minx, maxx, miny, maxy;
375 /* Get rid of unnecessary casts, but preserve the value of
380 mpz_init (bnds->below);
384 split_to_var_and_offset (x, &varx, offx);
385 split_to_var_and_offset (y, &vary, offy);
387 if (!integer_zerop (varx)
388 && operand_equal_p (varx, vary, 0))
390 /* Special case VARX == VARY -- we just need to compare the
391 offsets. The matters are a bit more complicated in the
392 case addition of offsets may wrap. */
393 bound_difference_of_offsetted_base (type, offx, offy, bnds);
397 /* Otherwise, use the value ranges to determine the initial
398 estimates on below and up. */
403 determine_value_range (type, varx, offx, minx, maxx);
404 determine_value_range (type, vary, offy, miny, maxy);
406 mpz_sub (bnds->below, minx, maxy);
407 mpz_sub (bnds->up, maxx, miny);
414 /* If both X and Y are constants, we cannot get any more precise. */
415 if (integer_zerop (varx) && integer_zerop (vary))
418 /* Now walk the dominators of the loop header and use the entry
419 guards to refine the estimates. */
420 for (bb = loop->header;
421 bb != ENTRY_BLOCK_PTR && cnt < MAX_DOMINATORS_TO_WALK;
422 bb = get_immediate_dominator (CDI_DOMINATORS, bb))
424 if (!single_pred_p (bb))
426 e = single_pred_edge (bb);
428 if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
431 cond = last_stmt (e->src);
432 c0 = gimple_cond_lhs (cond);
433 cmp = gimple_cond_code (cond);
434 c1 = gimple_cond_rhs (cond);
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 (!iv0->no_overflow && !integer_zerop (mod))
702 bound = fold_build2 (MINUS_EXPR, type1,
703 TYPE_MAX_VALUE (type1), tmod);
704 if (POINTER_TYPE_P (type))
705 bound = fold_convert (type, bound);
706 assumption = fold_build2 (LE_EXPR, boolean_type_node,
708 if (integer_zerop (assumption))
711 if (mpz_cmp (mmod, bnds->below) < 0)
712 noloop = boolean_false_node;
713 else if (POINTER_TYPE_P (type))
714 noloop = fold_build2 (GT_EXPR, boolean_type_node,
716 fold_build2 (POINTER_PLUS_EXPR, type,
719 noloop = fold_build2 (GT_EXPR, boolean_type_node,
721 fold_build2 (PLUS_EXPR, type1,
726 /* The final value of the iv is iv0->base - MOD, assuming that this
727 computation does not overflow, and that
728 iv0->base - MOD <= iv1->base. */
729 if (!iv1->no_overflow && !integer_zerop (mod))
731 bound = fold_build2 (PLUS_EXPR, type1,
732 TYPE_MIN_VALUE (type1), tmod);
733 if (POINTER_TYPE_P (type))
734 bound = fold_convert (type, bound);
735 assumption = fold_build2 (GE_EXPR, boolean_type_node,
737 if (integer_zerop (assumption))
740 if (mpz_cmp (mmod, bnds->below) < 0)
741 noloop = boolean_false_node;
742 else if (POINTER_TYPE_P (type))
743 noloop = fold_build2 (GT_EXPR, boolean_type_node,
744 fold_build2 (POINTER_PLUS_EXPR, type,
746 fold_build1 (NEGATE_EXPR,
750 noloop = fold_build2 (GT_EXPR, boolean_type_node,
751 fold_build2 (MINUS_EXPR, type1,
756 if (!integer_nonzerop (assumption))
757 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
760 if (!integer_zerop (noloop))
761 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
764 bounds_add (bnds, tree_to_double_int (mod), type);
765 *delta = fold_build2 (PLUS_EXPR, niter_type, *delta, mod);
773 /* Add assertions to NITER that ensure that the control variable of the loop
774 with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
775 are TYPE. Returns false if we can prove that there is an overflow, true
776 otherwise. STEP is the absolute value of the step. */
779 assert_no_overflow_lt (tree type, affine_iv *iv0, affine_iv *iv1,
780 struct tree_niter_desc *niter, tree step)
782 tree bound, d, assumption, diff;
783 tree niter_type = TREE_TYPE (step);
785 if (integer_nonzerop (iv0->step))
787 /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
788 if (iv0->no_overflow)
791 /* If iv0->base is a constant, we can determine the last value before
792 overflow precisely; otherwise we conservatively assume
795 if (TREE_CODE (iv0->base) == INTEGER_CST)
797 d = fold_build2 (MINUS_EXPR, niter_type,
798 fold_convert (niter_type, TYPE_MAX_VALUE (type)),
799 fold_convert (niter_type, iv0->base));
800 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
803 diff = fold_build2 (MINUS_EXPR, niter_type, step,
804 build_int_cst (niter_type, 1));
805 bound = fold_build2 (MINUS_EXPR, type,
806 TYPE_MAX_VALUE (type), fold_convert (type, diff));
807 assumption = fold_build2 (LE_EXPR, boolean_type_node,
812 /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
813 if (iv1->no_overflow)
816 if (TREE_CODE (iv1->base) == INTEGER_CST)
818 d = fold_build2 (MINUS_EXPR, niter_type,
819 fold_convert (niter_type, iv1->base),
820 fold_convert (niter_type, TYPE_MIN_VALUE (type)));
821 diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
824 diff = fold_build2 (MINUS_EXPR, niter_type, step,
825 build_int_cst (niter_type, 1));
826 bound = fold_build2 (PLUS_EXPR, type,
827 TYPE_MIN_VALUE (type), fold_convert (type, diff));
828 assumption = fold_build2 (GE_EXPR, boolean_type_node,
832 if (integer_zerop (assumption))
834 if (!integer_nonzerop (assumption))
835 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
836 niter->assumptions, assumption);
838 iv0->no_overflow = true;
839 iv1->no_overflow = true;
843 /* Add an assumption to NITER that a loop whose ending condition
844 is IV0 < IV1 rolls. TYPE is the type of the control iv. BNDS
845 bounds the value of IV1->base - IV0->base. */
848 assert_loop_rolls_lt (tree type, affine_iv *iv0, affine_iv *iv1,
849 struct tree_niter_desc *niter, bounds *bnds)
851 tree assumption = boolean_true_node, bound, diff;
852 tree mbz, mbzl, mbzr, type1;
853 bool rolls_p, no_overflow_p;
857 /* We are going to compute the number of iterations as
858 (iv1->base - iv0->base + step - 1) / step, computed in the unsigned
859 variant of TYPE. This formula only works if
861 -step + 1 <= (iv1->base - iv0->base) <= MAX - step + 1
863 (where MAX is the maximum value of the unsigned variant of TYPE, and
864 the computations in this formula are performed in full precision
867 Usually, for loops with exit condition iv0->base + step * i < iv1->base,
868 we have a condition of form iv0->base - step < iv1->base before the loop,
869 and for loops iv0->base < iv1->base - step * i the condition
870 iv0->base < iv1->base + step, due to loop header copying, which enable us
871 to prove the lower bound.
873 The upper bound is more complicated. Unless the expressions for initial
874 and final value themselves contain enough information, we usually cannot
875 derive it from the context. */
877 /* First check whether the answer does not follow from the bounds we gathered
879 if (integer_nonzerop (iv0->step))
880 dstep = tree_to_double_int (iv0->step);
883 dstep = double_int_sext (tree_to_double_int (iv1->step),
884 TYPE_PRECISION (type));
885 dstep = double_int_neg (dstep);
889 mpz_set_double_int (mstep, dstep, true);
890 mpz_neg (mstep, mstep);
891 mpz_add_ui (mstep, mstep, 1);
893 rolls_p = mpz_cmp (mstep, bnds->below) <= 0;
896 mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
897 mpz_add (max, max, mstep);
898 no_overflow_p = (mpz_cmp (bnds->up, max) <= 0
899 /* For pointers, only values lying inside a single object
900 can be compared or manipulated by pointer arithmetics.
901 Gcc in general does not allow or handle objects larger
902 than half of the address space, hence the upper bound
903 is satisfied for pointers. */
904 || POINTER_TYPE_P (type));
908 if (rolls_p && no_overflow_p)
912 if (POINTER_TYPE_P (type))
915 /* Now the hard part; we must formulate the assumption(s) as expressions, and
916 we must be careful not to introduce overflow. */
918 if (integer_nonzerop (iv0->step))
920 diff = fold_build2 (MINUS_EXPR, type1,
921 iv0->step, build_int_cst (type1, 1));
923 /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
924 0 address never belongs to any object, we can assume this for
926 if (!POINTER_TYPE_P (type))
928 bound = fold_build2 (PLUS_EXPR, type1,
929 TYPE_MIN_VALUE (type), diff);
930 assumption = fold_build2 (GE_EXPR, boolean_type_node,
934 /* And then we can compute iv0->base - diff, and compare it with
936 mbzl = fold_build2 (MINUS_EXPR, type1,
937 fold_convert (type1, iv0->base), diff);
938 mbzr = fold_convert (type1, iv1->base);
942 diff = fold_build2 (PLUS_EXPR, type1,
943 iv1->step, build_int_cst (type1, 1));
945 if (!POINTER_TYPE_P (type))
947 bound = fold_build2 (PLUS_EXPR, type1,
948 TYPE_MAX_VALUE (type), diff);
949 assumption = fold_build2 (LE_EXPR, boolean_type_node,
953 mbzl = fold_convert (type1, iv0->base);
954 mbzr = fold_build2 (MINUS_EXPR, type1,
955 fold_convert (type1, iv1->base), diff);
958 if (!integer_nonzerop (assumption))
959 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
960 niter->assumptions, assumption);
963 mbz = fold_build2 (GT_EXPR, boolean_type_node, mbzl, mbzr);
964 niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
965 niter->may_be_zero, mbz);
969 /* Determines number of iterations of loop whose ending condition
970 is IV0 < IV1. TYPE is the type of the iv. The number of
971 iterations is stored to NITER. BNDS bounds the difference
972 IV1->base - IV0->base. */
975 number_of_iterations_lt (tree type, affine_iv *iv0, affine_iv *iv1,
976 struct tree_niter_desc *niter,
977 bool never_infinite ATTRIBUTE_UNUSED,
980 tree niter_type = unsigned_type_for (type);
984 if (integer_nonzerop (iv0->step))
986 niter->control = *iv0;
987 niter->cmp = LT_EXPR;
988 niter->bound = iv1->base;
992 niter->control = *iv1;
993 niter->cmp = GT_EXPR;
994 niter->bound = iv0->base;
997 delta = fold_build2 (MINUS_EXPR, niter_type,
998 fold_convert (niter_type, iv1->base),
999 fold_convert (niter_type, iv0->base));
1001 /* First handle the special case that the step is +-1. */
1002 if ((integer_onep (iv0->step) && integer_zerop (iv1->step))
1003 || (integer_all_onesp (iv1->step) && integer_zerop (iv0->step)))
1005 /* for (i = iv0->base; i < iv1->base; i++)
1009 for (i = iv1->base; i > iv0->base; i--).
1011 In both cases # of iterations is iv1->base - iv0->base, assuming that
1012 iv1->base >= iv0->base.
1014 First try to derive a lower bound on the value of
1015 iv1->base - iv0->base, computed in full precision. If the difference
1016 is nonnegative, we are done, otherwise we must record the
1019 if (mpz_sgn (bnds->below) < 0)
1020 niter->may_be_zero = fold_build2 (LT_EXPR, boolean_type_node,
1021 iv1->base, iv0->base);
1022 niter->niter = delta;
1023 niter->max = mpz_get_double_int (niter_type, bnds->up, false);
1027 if (integer_nonzerop (iv0->step))
1028 step = fold_convert (niter_type, iv0->step);
1030 step = fold_convert (niter_type,
1031 fold_build1 (NEGATE_EXPR, type, iv1->step));
1033 /* If we can determine the final value of the control iv exactly, we can
1034 transform the condition to != comparison. In particular, this will be
1035 the case if DELTA is constant. */
1036 if (number_of_iterations_lt_to_ne (type, iv0, iv1, niter, &delta, step,
1041 zps.base = build_int_cst (niter_type, 0);
1043 /* number_of_iterations_lt_to_ne will add assumptions that ensure that
1044 zps does not overflow. */
1045 zps.no_overflow = true;
1047 return number_of_iterations_ne (type, &zps, delta, niter, true, bnds);
1050 /* Make sure that the control iv does not overflow. */
1051 if (!assert_no_overflow_lt (type, iv0, iv1, niter, step))
1054 /* We determine the number of iterations as (delta + step - 1) / step. For
1055 this to work, we must know that iv1->base >= iv0->base - step + 1,
1056 otherwise the loop does not roll. */
1057 assert_loop_rolls_lt (type, iv0, iv1, niter, bnds);
1059 s = fold_build2 (MINUS_EXPR, niter_type,
1060 step, build_int_cst (niter_type, 1));
1061 delta = fold_build2 (PLUS_EXPR, niter_type, delta, s);
1062 niter->niter = fold_build2 (FLOOR_DIV_EXPR, niter_type, delta, step);
1066 mpz_set_double_int (mstep, tree_to_double_int (step), true);
1067 mpz_add (tmp, bnds->up, mstep);
1068 mpz_sub_ui (tmp, tmp, 1);
1069 mpz_fdiv_q (tmp, tmp, mstep);
1070 niter->max = mpz_get_double_int (niter_type, tmp, false);
1077 /* Determines number of iterations of loop whose ending condition
1078 is IV0 <= IV1. TYPE is the type of the iv. The number of
1079 iterations is stored to NITER. NEVER_INFINITE is true if
1080 we know that this condition must eventually become false (we derived this
1081 earlier, and possibly set NITER->assumptions to make sure this
1082 is the case). BNDS bounds the difference IV1->base - IV0->base. */
1085 number_of_iterations_le (tree type, affine_iv *iv0, affine_iv *iv1,
1086 struct tree_niter_desc *niter, bool never_infinite,
1091 if (POINTER_TYPE_P (type))
1094 /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
1095 IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
1096 value of the type. This we must know anyway, since if it is
1097 equal to this value, the loop rolls forever. */
1099 if (!never_infinite)
1101 if (integer_nonzerop (iv0->step))
1102 assumption = fold_build2 (NE_EXPR, boolean_type_node,
1103 iv1->base, TYPE_MAX_VALUE (type));
1105 assumption = fold_build2 (NE_EXPR, boolean_type_node,
1106 iv0->base, TYPE_MIN_VALUE (type));
1108 if (integer_zerop (assumption))
1110 if (!integer_nonzerop (assumption))
1111 niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
1112 niter->assumptions, assumption);
1115 if (integer_nonzerop (iv0->step))
1117 if (POINTER_TYPE_P (type))
1118 iv1->base = fold_build2 (POINTER_PLUS_EXPR, type, iv1->base,
1119 build_int_cst (type1, 1));
1121 iv1->base = fold_build2 (PLUS_EXPR, type1, iv1->base,
1122 build_int_cst (type1, 1));
1124 else if (POINTER_TYPE_P (type))
1125 iv0->base = fold_build2 (POINTER_PLUS_EXPR, type, iv0->base,
1126 fold_build1 (NEGATE_EXPR, type1,
1127 build_int_cst (type1, 1)));
1129 iv0->base = fold_build2 (MINUS_EXPR, type1,
1130 iv0->base, build_int_cst (type1, 1));
1132 bounds_add (bnds, double_int_one, type1);
1134 return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite, bnds);
1137 /* Dumps description of affine induction variable IV to FILE. */
1140 dump_affine_iv (FILE *file, affine_iv *iv)
1142 if (!integer_zerop (iv->step))
1143 fprintf (file, "[");
1145 print_generic_expr (dump_file, iv->base, TDF_SLIM);
1147 if (!integer_zerop (iv->step))
1149 fprintf (file, ", + , ");
1150 print_generic_expr (dump_file, iv->step, TDF_SLIM);
1151 fprintf (file, "]%s", iv->no_overflow ? "(no_overflow)" : "");
1155 /* Determine the number of iterations according to condition (for staying
1156 inside loop) which compares two induction variables using comparison
1157 operator CODE. The induction variable on left side of the comparison
1158 is IV0, the right-hand side is IV1. Both induction variables must have
1159 type TYPE, which must be an integer or pointer type. The steps of the
1160 ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
1162 LOOP is the loop whose number of iterations we are determining.
1164 ONLY_EXIT is true if we are sure this is the only way the loop could be
1165 exited (including possibly non-returning function calls, exceptions, etc.)
1166 -- in this case we can use the information whether the control induction
1167 variables can overflow or not in a more efficient way.
1169 The results (number of iterations and assumptions as described in
1170 comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
1171 Returns false if it fails to determine number of iterations, true if it
1172 was determined (possibly with some assumptions). */
1175 number_of_iterations_cond (struct loop *loop,
1176 tree type, affine_iv *iv0, enum tree_code code,
1177 affine_iv *iv1, struct tree_niter_desc *niter,
1180 bool never_infinite, ret;
1183 /* The meaning of these assumptions is this:
1185 then the rest of information does not have to be valid
1186 if may_be_zero then the loop does not roll, even if
1188 niter->assumptions = boolean_true_node;
1189 niter->may_be_zero = boolean_false_node;
1190 niter->niter = NULL_TREE;
1191 niter->max = double_int_zero;
1193 niter->bound = NULL_TREE;
1194 niter->cmp = ERROR_MARK;
1196 /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
1197 the control variable is on lhs. */
1198 if (code == GE_EXPR || code == GT_EXPR
1199 || (code == NE_EXPR && integer_zerop (iv0->step)))
1202 code = swap_tree_comparison (code);
1207 /* If this is not the only possible exit from the loop, the information
1208 that the induction variables cannot overflow as derived from
1209 signedness analysis cannot be relied upon. We use them e.g. in the
1210 following way: given loop for (i = 0; i <= n; i++), if i is
1211 signed, it cannot overflow, thus this loop is equivalent to
1212 for (i = 0; i < n + 1; i++); however, if n == MAX, but the loop
1213 is exited in some other way before i overflows, this transformation
1214 is incorrect (the new loop exits immediately). */
1215 iv0->no_overflow = false;
1216 iv1->no_overflow = false;
1219 if (POINTER_TYPE_P (type))
1221 /* Comparison of pointers is undefined unless both iv0 and iv1 point
1222 to the same object. If they do, the control variable cannot wrap
1223 (as wrap around the bounds of memory will never return a pointer
1224 that would be guaranteed to point to the same object, even if we
1225 avoid undefined behavior by casting to size_t and back). The
1226 restrictions on pointer arithmetics and comparisons of pointers
1227 ensure that using the no-overflow assumptions is correct in this
1228 case even if ONLY_EXIT is false. */
1229 iv0->no_overflow = true;
1230 iv1->no_overflow = true;
1233 /* If the control induction variable does not overflow, the loop obviously
1234 cannot be infinite. */
1235 if (!integer_zerop (iv0->step) && iv0->no_overflow)
1236 never_infinite = true;
1237 else if (!integer_zerop (iv1->step) && iv1->no_overflow)
1238 never_infinite = true;
1240 never_infinite = false;
1242 /* We can handle the case when neither of the sides of the comparison is
1243 invariant, provided that the test is NE_EXPR. This rarely occurs in
1244 practice, but it is simple enough to manage. */
1245 if (!integer_zerop (iv0->step) && !integer_zerop (iv1->step))
1247 if (code != NE_EXPR)
1250 iv0->step = fold_binary_to_constant (MINUS_EXPR, type,
1251 iv0->step, iv1->step);
1252 iv0->no_overflow = false;
1253 iv1->step = build_int_cst (type, 0);
1254 iv1->no_overflow = true;
1257 /* If the result of the comparison is a constant, the loop is weird. More
1258 precise handling would be possible, but the situation is not common enough
1259 to waste time on it. */
1260 if (integer_zerop (iv0->step) && integer_zerop (iv1->step))
1263 /* Ignore loops of while (i-- < 10) type. */
1264 if (code != NE_EXPR)
1266 if (iv0->step && tree_int_cst_sign_bit (iv0->step))
1269 if (!integer_zerop (iv1->step) && !tree_int_cst_sign_bit (iv1->step))
1273 /* If the loop exits immediately, there is nothing to do. */
1274 if (integer_zerop (fold_build2 (code, boolean_type_node, iv0->base, iv1->base)))
1276 niter->niter = build_int_cst (unsigned_type_for (type), 0);
1277 niter->max = double_int_zero;
1281 /* OK, now we know we have a senseful loop. Handle several cases, depending
1282 on what comparison operator is used. */
1283 bound_difference (loop, iv1->base, iv0->base, &bnds);
1285 if (dump_file && (dump_flags & TDF_DETAILS))
1288 "Analyzing # of iterations of loop %d\n", loop->num);
1290 fprintf (dump_file, " exit condition ");
1291 dump_affine_iv (dump_file, iv0);
1292 fprintf (dump_file, " %s ",
1293 code == NE_EXPR ? "!="
1294 : code == LT_EXPR ? "<"
1296 dump_affine_iv (dump_file, iv1);
1297 fprintf (dump_file, "\n");
1299 fprintf (dump_file, " bounds on difference of bases: ");
1300 mpz_out_str (dump_file, 10, bnds.below);
1301 fprintf (dump_file, " ... ");
1302 mpz_out_str (dump_file, 10, bnds.up);
1303 fprintf (dump_file, "\n");
1309 gcc_assert (integer_zerop (iv1->step));
1310 ret = number_of_iterations_ne (type, iv0, iv1->base, niter,
1311 never_infinite, &bnds);
1315 ret = number_of_iterations_lt (type, iv0, iv1, niter, never_infinite,
1320 ret = number_of_iterations_le (type, iv0, iv1, niter, never_infinite,
1328 mpz_clear (bnds.up);
1329 mpz_clear (bnds.below);
1331 if (dump_file && (dump_flags & TDF_DETAILS))
1335 fprintf (dump_file, " result:\n");
1336 if (!integer_nonzerop (niter->assumptions))
1338 fprintf (dump_file, " under assumptions ");
1339 print_generic_expr (dump_file, niter->assumptions, TDF_SLIM);
1340 fprintf (dump_file, "\n");
1343 if (!integer_zerop (niter->may_be_zero))
1345 fprintf (dump_file, " zero if ");
1346 print_generic_expr (dump_file, niter->may_be_zero, TDF_SLIM);
1347 fprintf (dump_file, "\n");
1350 fprintf (dump_file, " # of iterations ");
1351 print_generic_expr (dump_file, niter->niter, TDF_SLIM);
1352 fprintf (dump_file, ", bounded by ");
1353 dump_double_int (dump_file, niter->max, true);
1354 fprintf (dump_file, "\n");
1357 fprintf (dump_file, " failed\n\n");
1362 /* Substitute NEW for OLD in EXPR and fold the result. */
1365 simplify_replace_tree (tree expr, tree old, tree new_tree)
1368 tree ret = NULL_TREE, e, se;
1374 || operand_equal_p (expr, old, 0))
1375 return unshare_expr (new_tree);
1380 n = TREE_OPERAND_LENGTH (expr);
1381 for (i = 0; i < n; i++)
1383 e = TREE_OPERAND (expr, i);
1384 se = simplify_replace_tree (e, old, new_tree);
1389 ret = copy_node (expr);
1391 TREE_OPERAND (ret, i) = se;
1394 return (ret ? fold (ret) : expr);
1397 /* Expand definitions of ssa names in EXPR as long as they are simple
1398 enough, and return the new expression. */
1401 expand_simple_operations (tree expr)
1404 tree ret = NULL_TREE, e, ee, e1;
1405 enum tree_code code;
1408 if (expr == NULL_TREE)
1411 if (is_gimple_min_invariant (expr))
1414 code = TREE_CODE (expr);
1415 if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code)))
1417 n = TREE_OPERAND_LENGTH (expr);
1418 for (i = 0; i < n; i++)
1420 e = TREE_OPERAND (expr, i);
1421 ee = expand_simple_operations (e);
1426 ret = copy_node (expr);
1428 TREE_OPERAND (ret, i) = ee;
1434 fold_defer_overflow_warnings ();
1436 fold_undefer_and_ignore_overflow_warnings ();
1440 if (TREE_CODE (expr) != SSA_NAME)
1443 stmt = SSA_NAME_DEF_STMT (expr);
1444 if (gimple_code (stmt) == GIMPLE_PHI)
1446 basic_block src, dest;
1448 if (gimple_phi_num_args (stmt) != 1)
1450 e = PHI_ARG_DEF (stmt, 0);
1452 /* Avoid propagating through loop exit phi nodes, which
1453 could break loop-closed SSA form restrictions. */
1454 dest = gimple_bb (stmt);
1455 src = single_pred (dest);
1456 if (TREE_CODE (e) == SSA_NAME
1457 && src->loop_father != dest->loop_father)
1460 return expand_simple_operations (e);
1462 if (gimple_code (stmt) != GIMPLE_ASSIGN)
1465 e = gimple_assign_rhs1 (stmt);
1466 code = gimple_assign_rhs_code (stmt);
1467 if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS)
1469 if (is_gimple_min_invariant (e))
1472 if (code == SSA_NAME)
1473 return expand_simple_operations (e);
1481 /* Casts are simple. */
1482 ee = expand_simple_operations (e);
1483 return fold_build1 (code, TREE_TYPE (expr), ee);
1487 case POINTER_PLUS_EXPR:
1488 /* And increments and decrements by a constant are simple. */
1489 e1 = gimple_assign_rhs2 (stmt);
1490 if (!is_gimple_min_invariant (e1))
1493 ee = expand_simple_operations (e);
1494 return fold_build2 (code, TREE_TYPE (expr), ee, e1);
1501 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1502 expression (or EXPR unchanged, if no simplification was possible). */
1505 tree_simplify_using_condition_1 (tree cond, tree expr)
1508 tree e, te, e0, e1, e2, notcond;
1509 enum tree_code code = TREE_CODE (expr);
1511 if (code == INTEGER_CST)
1514 if (code == TRUTH_OR_EXPR
1515 || code == TRUTH_AND_EXPR
1516 || code == COND_EXPR)
1520 e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
1521 if (TREE_OPERAND (expr, 0) != e0)
1524 e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
1525 if (TREE_OPERAND (expr, 1) != e1)
1528 if (code == COND_EXPR)
1530 e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
1531 if (TREE_OPERAND (expr, 2) != e2)
1539 if (code == COND_EXPR)
1540 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
1542 expr = fold_build2 (code, boolean_type_node, e0, e1);
1548 /* In case COND is equality, we may be able to simplify EXPR by copy/constant
1549 propagation, and vice versa. Fold does not handle this, since it is
1550 considered too expensive. */
1551 if (TREE_CODE (cond) == EQ_EXPR)
1553 e0 = TREE_OPERAND (cond, 0);
1554 e1 = TREE_OPERAND (cond, 1);
1556 /* We know that e0 == e1. Check whether we cannot simplify expr
1558 e = simplify_replace_tree (expr, e0, e1);
1559 if (integer_zerop (e) || integer_nonzerop (e))
1562 e = simplify_replace_tree (expr, e1, e0);
1563 if (integer_zerop (e) || integer_nonzerop (e))
1566 if (TREE_CODE (expr) == EQ_EXPR)
1568 e0 = TREE_OPERAND (expr, 0);
1569 e1 = TREE_OPERAND (expr, 1);
1571 /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
1572 e = simplify_replace_tree (cond, e0, e1);
1573 if (integer_zerop (e))
1575 e = simplify_replace_tree (cond, e1, e0);
1576 if (integer_zerop (e))
1579 if (TREE_CODE (expr) == NE_EXPR)
1581 e0 = TREE_OPERAND (expr, 0);
1582 e1 = TREE_OPERAND (expr, 1);
1584 /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
1585 e = simplify_replace_tree (cond, e0, e1);
1586 if (integer_zerop (e))
1587 return boolean_true_node;
1588 e = simplify_replace_tree (cond, e1, e0);
1589 if (integer_zerop (e))
1590 return boolean_true_node;
1593 te = expand_simple_operations (expr);
1595 /* Check whether COND ==> EXPR. */
1596 notcond = invert_truthvalue (cond);
1597 e = fold_binary (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
1598 if (e && integer_nonzerop (e))
1601 /* Check whether COND ==> not EXPR. */
1602 e = fold_binary (TRUTH_AND_EXPR, boolean_type_node, cond, te);
1603 if (e && integer_zerop (e))
1609 /* Tries to simplify EXPR using the condition COND. Returns the simplified
1610 expression (or EXPR unchanged, if no simplification was possible).
1611 Wrapper around tree_simplify_using_condition_1 that ensures that chains
1612 of simple operations in definitions of ssa names in COND are expanded,
1613 so that things like casts or incrementing the value of the bound before
1614 the loop do not cause us to fail. */
1617 tree_simplify_using_condition (tree cond, tree expr)
1619 cond = expand_simple_operations (cond);
1621 return tree_simplify_using_condition_1 (cond, expr);
1624 /* Tries to simplify EXPR using the conditions on entry to LOOP.
1625 Returns the simplified expression (or EXPR unchanged, if no
1626 simplification was possible).*/
1629 simplify_using_initial_conditions (struct loop *loop, tree expr)
1637 if (TREE_CODE (expr) == INTEGER_CST)
1640 /* Limit walking the dominators to avoid quadraticness in
1641 the number of BBs times the number of loops in degenerate
1643 for (bb = loop->header;
1644 bb != ENTRY_BLOCK_PTR && cnt < MAX_DOMINATORS_TO_WALK;
1645 bb = get_immediate_dominator (CDI_DOMINATORS, bb))
1647 if (!single_pred_p (bb))
1649 e = single_pred_edge (bb);
1651 if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
1654 stmt = last_stmt (e->src);
1655 cond = fold_build2 (gimple_cond_code (stmt),
1657 gimple_cond_lhs (stmt),
1658 gimple_cond_rhs (stmt));
1659 if (e->flags & EDGE_FALSE_VALUE)
1660 cond = invert_truthvalue (cond);
1661 expr = tree_simplify_using_condition (cond, expr);
1668 /* Tries to simplify EXPR using the evolutions of the loop invariants
1669 in the superloops of LOOP. Returns the simplified expression
1670 (or EXPR unchanged, if no simplification was possible). */
1673 simplify_using_outer_evolutions (struct loop *loop, tree expr)
1675 enum tree_code code = TREE_CODE (expr);
1679 if (is_gimple_min_invariant (expr))
1682 if (code == TRUTH_OR_EXPR
1683 || code == TRUTH_AND_EXPR
1684 || code == COND_EXPR)
1688 e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
1689 if (TREE_OPERAND (expr, 0) != e0)
1692 e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
1693 if (TREE_OPERAND (expr, 1) != e1)
1696 if (code == COND_EXPR)
1698 e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
1699 if (TREE_OPERAND (expr, 2) != e2)
1707 if (code == COND_EXPR)
1708 expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
1710 expr = fold_build2 (code, boolean_type_node, e0, e1);
1716 e = instantiate_parameters (loop, expr);
1717 if (is_gimple_min_invariant (e))
1723 /* Returns true if EXIT is the only possible exit from LOOP. */
1726 loop_only_exit_p (const struct loop *loop, const_edge exit)
1729 gimple_stmt_iterator bsi;
1733 if (exit != single_exit (loop))
1736 body = get_loop_body (loop);
1737 for (i = 0; i < loop->num_nodes; i++)
1739 for (bsi = gsi_start_bb (body[i]); !gsi_end_p (bsi); gsi_next (&bsi))
1741 call = gsi_stmt (bsi);
1742 if (gimple_code (call) != GIMPLE_CALL)
1745 if (gimple_has_side_effects (call))
1757 /* Stores description of number of iterations of LOOP derived from
1758 EXIT (an exit edge of the LOOP) in NITER. Returns true if some
1759 useful information could be derived (and fields of NITER has
1760 meaning described in comments at struct tree_niter_desc
1761 declaration), false otherwise. If WARN is true and
1762 -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
1763 potentially unsafe assumptions. */
1766 number_of_iterations_exit (struct loop *loop, edge exit,
1767 struct tree_niter_desc *niter,
1773 enum tree_code code;
1776 if (!dominated_by_p (CDI_DOMINATORS, loop->latch, exit->src))
1779 niter->assumptions = boolean_false_node;
1780 stmt = last_stmt (exit->src);
1781 if (!stmt || gimple_code (stmt) != GIMPLE_COND)
1784 /* We want the condition for staying inside loop. */
1785 code = gimple_cond_code (stmt);
1786 if (exit->flags & EDGE_TRUE_VALUE)
1787 code = invert_tree_comparison (code, false);
1802 op0 = gimple_cond_lhs (stmt);
1803 op1 = gimple_cond_rhs (stmt);
1804 type = TREE_TYPE (op0);
1806 if (TREE_CODE (type) != INTEGER_TYPE
1807 && !POINTER_TYPE_P (type))
1810 if (!simple_iv (loop, loop_containing_stmt (stmt), op0, &iv0, false))
1812 if (!simple_iv (loop, loop_containing_stmt (stmt), op1, &iv1, false))
1815 /* We don't want to see undefined signed overflow warnings while
1816 computing the number of iterations. */
1817 fold_defer_overflow_warnings ();
1819 iv0.base = expand_simple_operations (iv0.base);
1820 iv1.base = expand_simple_operations (iv1.base);
1821 if (!number_of_iterations_cond (loop, type, &iv0, code, &iv1, niter,
1822 loop_only_exit_p (loop, exit)))
1824 fold_undefer_and_ignore_overflow_warnings ();
1830 niter->assumptions = simplify_using_outer_evolutions (loop,
1831 niter->assumptions);
1832 niter->may_be_zero = simplify_using_outer_evolutions (loop,
1833 niter->may_be_zero);
1834 niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
1838 = simplify_using_initial_conditions (loop,
1839 niter->assumptions);
1841 = simplify_using_initial_conditions (loop,
1842 niter->may_be_zero);
1844 fold_undefer_and_ignore_overflow_warnings ();
1846 if (integer_onep (niter->assumptions))
1849 /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
1850 But if we can prove that there is overflow or some other source of weird
1851 behavior, ignore the loop even with -funsafe-loop-optimizations. */
1852 if (integer_zerop (niter->assumptions))
1855 if (flag_unsafe_loop_optimizations)
1856 niter->assumptions = boolean_true_node;
1860 const char *wording;
1861 location_t loc = gimple_location (stmt);
1863 /* We can provide a more specific warning if one of the operator is
1864 constant and the other advances by +1 or -1. */
1865 if (!integer_zerop (iv1.step)
1866 ? (integer_zerop (iv0.step)
1867 && (integer_onep (iv1.step) || integer_all_onesp (iv1.step)))
1868 : (integer_onep (iv0.step) || integer_all_onesp (iv0.step)))
1870 flag_unsafe_loop_optimizations
1871 ? N_("assuming that the loop is not infinite")
1872 : N_("cannot optimize possibly infinite loops");
1875 flag_unsafe_loop_optimizations
1876 ? N_("assuming that the loop counter does not overflow")
1877 : N_("cannot optimize loop, the loop counter may overflow");
1879 if (LOCATION_LINE (loc) > 0)
1880 warning (OPT_Wunsafe_loop_optimizations, "%H%s", &loc, gettext (wording));
1882 warning (OPT_Wunsafe_loop_optimizations, "%s", gettext (wording));
1885 return flag_unsafe_loop_optimizations;
1888 /* Try to determine the number of iterations of LOOP. If we succeed,
1889 expression giving number of iterations is returned and *EXIT is
1890 set to the edge from that the information is obtained. Otherwise
1891 chrec_dont_know is returned. */
1894 find_loop_niter (struct loop *loop, edge *exit)
1897 VEC (edge, heap) *exits = get_loop_exit_edges (loop);
1899 tree niter = NULL_TREE, aniter;
1900 struct tree_niter_desc desc;
1903 for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
1905 if (!just_once_each_iteration_p (loop, ex->src))
1908 if (!number_of_iterations_exit (loop, ex, &desc, false))
1911 if (integer_nonzerop (desc.may_be_zero))
1913 /* We exit in the first iteration through this exit.
1914 We won't find anything better. */
1915 niter = build_int_cst (unsigned_type_node, 0);
1920 if (!integer_zerop (desc.may_be_zero))
1923 aniter = desc.niter;
1927 /* Nothing recorded yet. */
1933 /* Prefer constants, the lower the better. */
1934 if (TREE_CODE (aniter) != INTEGER_CST)
1937 if (TREE_CODE (niter) != INTEGER_CST)
1944 if (tree_int_cst_lt (aniter, niter))
1951 VEC_free (edge, heap, exits);
1953 return niter ? niter : chrec_dont_know;
1958 Analysis of a number of iterations of a loop by a brute-force evaluation.
1962 /* Bound on the number of iterations we try to evaluate. */
1964 #define MAX_ITERATIONS_TO_TRACK \
1965 ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
1967 /* Returns the loop phi node of LOOP such that ssa name X is derived from its
1968 result by a chain of operations such that all but exactly one of their
1969 operands are constants. */
1972 chain_of_csts_start (struct loop *loop, tree x)
1974 gimple stmt = SSA_NAME_DEF_STMT (x);
1976 basic_block bb = gimple_bb (stmt);
1977 enum tree_code code;
1980 || !flow_bb_inside_loop_p (loop, bb))
1983 if (gimple_code (stmt) == GIMPLE_PHI)
1985 if (bb == loop->header)
1991 if (gimple_code (stmt) != GIMPLE_ASSIGN)
1994 code = gimple_assign_rhs_code (stmt);
1995 if (gimple_references_memory_p (stmt)
1996 /* Before alias information is computed, operand scanning marks
1997 statements that write memory volatile. However, the statements
1998 that only read memory are not marked, thus gimple_references_memory_p
1999 returns false for them. */
2000 || TREE_CODE_CLASS (code) == tcc_reference
2001 || TREE_CODE_CLASS (code) == tcc_declaration
2002 || SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_DEF) == NULL_DEF_OPERAND_P)
2005 use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
2006 if (use == NULL_USE_OPERAND_P)
2009 return chain_of_csts_start (loop, use);
2012 /* Determines whether the expression X is derived from a result of a phi node
2013 in header of LOOP such that
2015 * the derivation of X consists only from operations with constants
2016 * the initial value of the phi node is constant
2017 * the value of the phi node in the next iteration can be derived from the
2018 value in the current iteration by a chain of operations with constants.
2020 If such phi node exists, it is returned, otherwise NULL is returned. */
2023 get_base_for (struct loop *loop, tree x)
2028 if (is_gimple_min_invariant (x))
2031 phi = chain_of_csts_start (loop, x);
2035 init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
2036 next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
2038 if (TREE_CODE (next) != SSA_NAME)
2041 if (!is_gimple_min_invariant (init))
2044 if (chain_of_csts_start (loop, next) != phi)
2050 /* Given an expression X, then
2052 * if X is NULL_TREE, we return the constant BASE.
2053 * otherwise X is a SSA name, whose value in the considered loop is derived
2054 by a chain of operations with constant from a result of a phi node in
2055 the header of the loop. Then we return value of X when the value of the
2056 result of this phi node is given by the constant BASE. */
2059 get_val_for (tree x, tree base)
2063 gcc_assert (is_gimple_min_invariant (base));
2068 stmt = SSA_NAME_DEF_STMT (x);
2069 if (gimple_code (stmt) == GIMPLE_PHI)
2072 gcc_assert (is_gimple_assign (stmt));
2074 /* STMT must be either an assignment of a single SSA name or an
2075 expression involving an SSA name and a constant. Try to fold that
2076 expression using the value for the SSA name. */
2077 if (gimple_assign_ssa_name_copy_p (stmt))
2078 return get_val_for (gimple_assign_rhs1 (stmt), base);
2079 else if (gimple_assign_rhs_class (stmt) == GIMPLE_UNARY_RHS
2080 && TREE_CODE (gimple_assign_rhs1 (stmt)) == SSA_NAME)
2082 return fold_build1 (gimple_assign_rhs_code (stmt),
2083 gimple_expr_type (stmt),
2084 get_val_for (gimple_assign_rhs1 (stmt), base));
2086 else if (gimple_assign_rhs_class (stmt) == GIMPLE_BINARY_RHS)
2088 tree rhs1 = gimple_assign_rhs1 (stmt);
2089 tree rhs2 = gimple_assign_rhs2 (stmt);
2090 if (TREE_CODE (rhs1) == SSA_NAME)
2091 rhs1 = get_val_for (rhs1, base);
2092 else if (TREE_CODE (rhs2) == SSA_NAME)
2093 rhs2 = get_val_for (rhs2, base);
2096 return fold_build2 (gimple_assign_rhs_code (stmt),
2097 gimple_expr_type (stmt), rhs1, rhs2);
2104 /* Tries to count the number of iterations of LOOP till it exits by EXIT
2105 by brute force -- i.e. by determining the value of the operands of the
2106 condition at EXIT in first few iterations of the loop (assuming that
2107 these values are constant) and determining the first one in that the
2108 condition is not satisfied. Returns the constant giving the number
2109 of the iterations of LOOP if successful, chrec_dont_know otherwise. */
2112 loop_niter_by_eval (struct loop *loop, edge exit)
2115 tree op[2], val[2], next[2], aval[2];
2120 cond = last_stmt (exit->src);
2121 if (!cond || gimple_code (cond) != GIMPLE_COND)
2122 return chrec_dont_know;
2124 cmp = gimple_cond_code (cond);
2125 if (exit->flags & EDGE_TRUE_VALUE)
2126 cmp = invert_tree_comparison (cmp, false);
2136 op[0] = gimple_cond_lhs (cond);
2137 op[1] = gimple_cond_rhs (cond);
2141 return chrec_dont_know;
2144 for (j = 0; j < 2; j++)
2146 if (is_gimple_min_invariant (op[j]))
2149 next[j] = NULL_TREE;
2154 phi = get_base_for (loop, op[j]);
2156 return chrec_dont_know;
2157 val[j] = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
2158 next[j] = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
2162 /* Don't issue signed overflow warnings. */
2163 fold_defer_overflow_warnings ();
2165 for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
2167 for (j = 0; j < 2; j++)
2168 aval[j] = get_val_for (op[j], val[j]);
2170 acnd = fold_binary (cmp, boolean_type_node, aval[0], aval[1]);
2171 if (acnd && integer_zerop (acnd))
2173 fold_undefer_and_ignore_overflow_warnings ();
2174 if (dump_file && (dump_flags & TDF_DETAILS))
2176 "Proved that loop %d iterates %d times using brute force.\n",
2178 return build_int_cst (unsigned_type_node, i);
2181 for (j = 0; j < 2; j++)
2183 val[j] = get_val_for (next[j], val[j]);
2184 if (!is_gimple_min_invariant (val[j]))
2186 fold_undefer_and_ignore_overflow_warnings ();
2187 return chrec_dont_know;
2192 fold_undefer_and_ignore_overflow_warnings ();
2194 return chrec_dont_know;
2197 /* Finds the exit of the LOOP by that the loop exits after a constant
2198 number of iterations and stores the exit edge to *EXIT. The constant
2199 giving the number of iterations of LOOP is returned. The number of
2200 iterations is determined using loop_niter_by_eval (i.e. by brute force
2201 evaluation). If we are unable to find the exit for that loop_niter_by_eval
2202 determines the number of iterations, chrec_dont_know is returned. */
2205 find_loop_niter_by_eval (struct loop *loop, edge *exit)
2208 VEC (edge, heap) *exits = get_loop_exit_edges (loop);
2210 tree niter = NULL_TREE, aniter;
2213 for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
2215 if (!just_once_each_iteration_p (loop, ex->src))
2218 aniter = loop_niter_by_eval (loop, ex);
2219 if (chrec_contains_undetermined (aniter))
2223 && !tree_int_cst_lt (aniter, niter))
2229 VEC_free (edge, heap, exits);
2231 return niter ? niter : chrec_dont_know;
2236 Analysis of upper bounds on number of iterations of a loop.
2240 static double_int derive_constant_upper_bound_ops (tree, tree,
2241 enum tree_code, tree);
2243 /* Returns a constant upper bound on the value of the right-hand side of
2244 an assignment statement STMT. */
2247 derive_constant_upper_bound_assign (gimple stmt)
2249 enum tree_code code = gimple_assign_rhs_code (stmt);
2250 tree op0 = gimple_assign_rhs1 (stmt);
2251 tree op1 = gimple_assign_rhs2 (stmt);
2253 return derive_constant_upper_bound_ops (TREE_TYPE (gimple_assign_lhs (stmt)),
2257 /* Returns a constant upper bound on the value of expression VAL. VAL
2258 is considered to be unsigned. If its type is signed, its value must
2262 derive_constant_upper_bound (tree val)
2264 enum tree_code code;
2267 extract_ops_from_tree (val, &code, &op0, &op1);
2268 return derive_constant_upper_bound_ops (TREE_TYPE (val), op0, code, op1);
2271 /* Returns a constant upper bound on the value of expression OP0 CODE OP1,
2272 whose type is TYPE. The expression is considered to be unsigned. If
2273 its type is signed, its value must be nonnegative. */
2276 derive_constant_upper_bound_ops (tree type, tree op0,
2277 enum tree_code code, tree op1)
2280 double_int bnd, max, mmax, cst;
2283 if (INTEGRAL_TYPE_P (type))
2284 maxt = TYPE_MAX_VALUE (type);
2286 maxt = upper_bound_in_type (type, type);
2288 max = tree_to_double_int (maxt);
2293 return tree_to_double_int (op0);
2296 subtype = TREE_TYPE (op0);
2297 if (!TYPE_UNSIGNED (subtype)
2298 /* If TYPE is also signed, the fact that VAL is nonnegative implies
2299 that OP0 is nonnegative. */
2300 && TYPE_UNSIGNED (type)
2301 && !tree_expr_nonnegative_p (op0))
2303 /* If we cannot prove that the casted expression is nonnegative,
2304 we cannot establish more useful upper bound than the precision
2305 of the type gives us. */
2309 /* We now know that op0 is an nonnegative value. Try deriving an upper
2311 bnd = derive_constant_upper_bound (op0);
2313 /* If the bound does not fit in TYPE, max. value of TYPE could be
2315 if (double_int_ucmp (max, bnd) < 0)
2321 case POINTER_PLUS_EXPR:
2323 if (TREE_CODE (op1) != INTEGER_CST
2324 || !tree_expr_nonnegative_p (op0))
2327 /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
2328 choose the most logical way how to treat this constant regardless
2329 of the signedness of the type. */
2330 cst = tree_to_double_int (op1);
2331 cst = double_int_sext (cst, TYPE_PRECISION (type));
2332 if (code != MINUS_EXPR)
2333 cst = double_int_neg (cst);
2335 bnd = derive_constant_upper_bound (op0);
2337 if (double_int_negative_p (cst))
2339 cst = double_int_neg (cst);
2340 /* Avoid CST == 0x80000... */
2341 if (double_int_negative_p (cst))
2344 /* OP0 + CST. We need to check that
2345 BND <= MAX (type) - CST. */
2347 mmax = double_int_add (max, double_int_neg (cst));
2348 if (double_int_ucmp (bnd, mmax) > 0)
2351 return double_int_add (bnd, cst);
2355 /* OP0 - CST, where CST >= 0.
2357 If TYPE is signed, we have already verified that OP0 >= 0, and we
2358 know that the result is nonnegative. This implies that
2361 If TYPE is unsigned, we must additionally know that OP0 >= CST,
2362 otherwise the operation underflows.
2365 /* This should only happen if the type is unsigned; however, for
2366 buggy programs that use overflowing signed arithmetics even with
2367 -fno-wrapv, this condition may also be true for signed values. */
2368 if (double_int_ucmp (bnd, cst) < 0)
2371 if (TYPE_UNSIGNED (type))
2373 tree tem = fold_binary (GE_EXPR, boolean_type_node, op0,
2374 double_int_to_tree (type, cst));
2375 if (!tem || integer_nonzerop (tem))
2379 bnd = double_int_add (bnd, double_int_neg (cst));
2384 case FLOOR_DIV_EXPR:
2385 case EXACT_DIV_EXPR:
2386 if (TREE_CODE (op1) != INTEGER_CST
2387 || tree_int_cst_sign_bit (op1))
2390 bnd = derive_constant_upper_bound (op0);
2391 return double_int_udiv (bnd, tree_to_double_int (op1), FLOOR_DIV_EXPR);
2394 if (TREE_CODE (op1) != INTEGER_CST
2395 || tree_int_cst_sign_bit (op1))
2397 return tree_to_double_int (op1);
2400 stmt = SSA_NAME_DEF_STMT (op0);
2401 if (gimple_code (stmt) != GIMPLE_ASSIGN
2402 || gimple_assign_lhs (stmt) != op0)
2404 return derive_constant_upper_bound_assign (stmt);
2411 /* Records that every statement in LOOP is executed I_BOUND times.
2412 REALISTIC is true if I_BOUND is expected to be close to the real number
2413 of iterations. UPPER is true if we are sure the loop iterates at most
2417 record_niter_bound (struct loop *loop, double_int i_bound, bool realistic,
2420 /* Update the bounds only when there is no previous estimation, or when the current
2421 estimation is smaller. */
2423 && (!loop->any_upper_bound
2424 || double_int_ucmp (i_bound, loop->nb_iterations_upper_bound) < 0))
2426 loop->any_upper_bound = true;
2427 loop->nb_iterations_upper_bound = i_bound;
2430 && (!loop->any_estimate
2431 || double_int_ucmp (i_bound, loop->nb_iterations_estimate) < 0))
2433 loop->any_estimate = true;
2434 loop->nb_iterations_estimate = i_bound;
2438 /* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. IS_EXIT
2439 is true if the loop is exited immediately after STMT, and this exit
2440 is taken at last when the STMT is executed BOUND + 1 times.
2441 REALISTIC is true if BOUND is expected to be close to the real number
2442 of iterations. UPPER is true if we are sure the loop iterates at most
2443 BOUND times. I_BOUND is an unsigned double_int upper estimate on BOUND. */
2446 record_estimate (struct loop *loop, tree bound, double_int i_bound,
2447 gimple at_stmt, bool is_exit, bool realistic, bool upper)
2452 if (dump_file && (dump_flags & TDF_DETAILS))
2454 fprintf (dump_file, "Statement %s", is_exit ? "(exit)" : "");
2455 print_gimple_stmt (dump_file, at_stmt, 0, TDF_SLIM);
2456 fprintf (dump_file, " is %sexecuted at most ",
2457 upper ? "" : "probably ");
2458 print_generic_expr (dump_file, bound, TDF_SLIM);
2459 fprintf (dump_file, " (bounded by ");
2460 dump_double_int (dump_file, i_bound, true);
2461 fprintf (dump_file, ") + 1 times in loop %d.\n", loop->num);
2464 /* If the I_BOUND is just an estimate of BOUND, it rarely is close to the
2465 real number of iterations. */
2466 if (TREE_CODE (bound) != INTEGER_CST)
2468 if (!upper && !realistic)
2471 /* If we have a guaranteed upper bound, record it in the appropriate
2475 struct nb_iter_bound *elt = GGC_NEW (struct nb_iter_bound);
2477 elt->bound = i_bound;
2478 elt->stmt = at_stmt;
2479 elt->is_exit = is_exit;
2480 elt->next = loop->bounds;
2484 /* Update the number of iteration estimates according to the bound.
2485 If at_stmt is an exit, then every statement in the loop is
2486 executed at most BOUND + 1 times. If it is not an exit, then
2487 some of the statements before it could be executed BOUND + 2
2488 times, if an exit of LOOP is before stmt. */
2489 exit = single_exit (loop);
2492 && dominated_by_p (CDI_DOMINATORS,
2493 exit->src, gimple_bb (at_stmt))))
2494 delta = double_int_one;
2496 delta = double_int_two;
2497 i_bound = double_int_add (i_bound, delta);
2499 /* If an overflow occurred, ignore the result. */
2500 if (double_int_ucmp (i_bound, delta) < 0)
2503 record_niter_bound (loop, i_bound, realistic, upper);
2506 /* Record the estimate on number of iterations of LOOP based on the fact that
2507 the induction variable BASE + STEP * i evaluated in STMT does not wrap and
2508 its values belong to the range <LOW, HIGH>. REALISTIC is true if the
2509 estimated number of iterations is expected to be close to the real one.
2510 UPPER is true if we are sure the induction variable does not wrap. */
2513 record_nonwrapping_iv (struct loop *loop, tree base, tree step, gimple stmt,
2514 tree low, tree high, bool realistic, bool upper)
2516 tree niter_bound, extreme, delta;
2517 tree type = TREE_TYPE (base), unsigned_type;
2520 if (TREE_CODE (step) != INTEGER_CST || integer_zerop (step))
2523 if (dump_file && (dump_flags & TDF_DETAILS))
2525 fprintf (dump_file, "Induction variable (");
2526 print_generic_expr (dump_file, TREE_TYPE (base), TDF_SLIM);
2527 fprintf (dump_file, ") ");
2528 print_generic_expr (dump_file, base, TDF_SLIM);
2529 fprintf (dump_file, " + ");
2530 print_generic_expr (dump_file, step, TDF_SLIM);
2531 fprintf (dump_file, " * iteration does not wrap in statement ");
2532 print_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
2533 fprintf (dump_file, " in loop %d.\n", loop->num);
2536 unsigned_type = unsigned_type_for (type);
2537 base = fold_convert (unsigned_type, base);
2538 step = fold_convert (unsigned_type, step);
2540 if (tree_int_cst_sign_bit (step))
2542 extreme = fold_convert (unsigned_type, low);
2543 if (TREE_CODE (base) != INTEGER_CST)
2544 base = fold_convert (unsigned_type, high);
2545 delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
2546 step = fold_build1 (NEGATE_EXPR, unsigned_type, step);
2550 extreme = fold_convert (unsigned_type, high);
2551 if (TREE_CODE (base) != INTEGER_CST)
2552 base = fold_convert (unsigned_type, low);
2553 delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
2556 /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
2557 would get out of the range. */
2558 niter_bound = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step);
2559 max = derive_constant_upper_bound (niter_bound);
2560 record_estimate (loop, niter_bound, max, stmt, false, realistic, upper);
2563 /* Returns true if REF is a reference to an array at the end of a dynamically
2564 allocated structure. If this is the case, the array may be allocated larger
2565 than its upper bound implies. */
2568 array_at_struct_end_p (tree ref)
2570 tree base = get_base_address (ref);
2573 /* Unless the reference is through a pointer, the size of the array matches
2575 if (!base || !INDIRECT_REF_P (base))
2578 for (;handled_component_p (ref); ref = parent)
2580 parent = TREE_OPERAND (ref, 0);
2582 if (TREE_CODE (ref) == COMPONENT_REF)
2584 /* All fields of a union are at its end. */
2585 if (TREE_CODE (TREE_TYPE (parent)) == UNION_TYPE)
2588 /* Unless the field is at the end of the struct, we are done. */
2589 field = TREE_OPERAND (ref, 1);
2590 if (TREE_CHAIN (field))
2594 /* The other options are ARRAY_REF, ARRAY_RANGE_REF, VIEW_CONVERT_EXPR.
2595 In all these cases, we might be accessing the last element, and
2596 although in practice this will probably never happen, it is legal for
2597 the indices of this last element to exceed the bounds of the array.
2598 Therefore, continue checking. */
2601 gcc_assert (INDIRECT_REF_P (ref));
2605 /* Determine information about number of iterations a LOOP from the index
2606 IDX of a data reference accessed in STMT. RELIABLE is true if STMT is
2607 guaranteed to be executed in every iteration of LOOP. Callback for
2618 idx_infer_loop_bounds (tree base, tree *idx, void *dta)
2620 struct ilb_data *data = (struct ilb_data *) dta;
2621 tree ev, init, step;
2622 tree low, high, type, next;
2623 bool sign, upper = data->reliable, at_end = false;
2624 struct loop *loop = data->loop;
2626 if (TREE_CODE (base) != ARRAY_REF)
2629 /* For arrays at the end of the structure, we are not guaranteed that they
2630 do not really extend over their declared size. However, for arrays of
2631 size greater than one, this is unlikely to be intended. */
2632 if (array_at_struct_end_p (base))
2638 ev = instantiate_parameters (loop, analyze_scalar_evolution (loop, *idx));
2639 init = initial_condition (ev);
2640 step = evolution_part_in_loop_num (ev, loop->num);
2644 || TREE_CODE (step) != INTEGER_CST
2645 || integer_zerop (step)
2646 || tree_contains_chrecs (init, NULL)
2647 || chrec_contains_symbols_defined_in_loop (init, loop->num))
2650 low = array_ref_low_bound (base);
2651 high = array_ref_up_bound (base);
2653 /* The case of nonconstant bounds could be handled, but it would be
2655 if (TREE_CODE (low) != INTEGER_CST
2657 || TREE_CODE (high) != INTEGER_CST)
2659 sign = tree_int_cst_sign_bit (step);
2660 type = TREE_TYPE (step);
2662 /* The array of length 1 at the end of a structure most likely extends
2663 beyond its bounds. */
2665 && operand_equal_p (low, high, 0))
2668 /* In case the relevant bound of the array does not fit in type, or
2669 it does, but bound + step (in type) still belongs into the range of the
2670 array, the index may wrap and still stay within the range of the array
2671 (consider e.g. if the array is indexed by the full range of
2674 To make things simpler, we require both bounds to fit into type, although
2675 there are cases where this would not be strictly necessary. */
2676 if (!int_fits_type_p (high, type)
2677 || !int_fits_type_p (low, type))
2679 low = fold_convert (type, low);
2680 high = fold_convert (type, high);
2683 next = fold_binary (PLUS_EXPR, type, low, step);
2685 next = fold_binary (PLUS_EXPR, type, high, step);
2687 if (tree_int_cst_compare (low, next) <= 0
2688 && tree_int_cst_compare (next, high) <= 0)
2691 record_nonwrapping_iv (loop, init, step, data->stmt, low, high, true, upper);
2695 /* Determine information about number of iterations a LOOP from the bounds
2696 of arrays in the data reference REF accessed in STMT. RELIABLE is true if
2697 STMT is guaranteed to be executed in every iteration of LOOP.*/
2700 infer_loop_bounds_from_ref (struct loop *loop, gimple stmt, tree ref,
2703 struct ilb_data data;
2707 data.reliable = reliable;
2708 for_each_index (&ref, idx_infer_loop_bounds, &data);
2711 /* Determine information about number of iterations of a LOOP from the way
2712 arrays are used in STMT. RELIABLE is true if STMT is guaranteed to be
2713 executed in every iteration of LOOP. */
2716 infer_loop_bounds_from_array (struct loop *loop, gimple stmt, bool reliable)
2718 if (is_gimple_assign (stmt))
2720 tree op0 = gimple_assign_lhs (stmt);
2721 tree op1 = gimple_assign_rhs1 (stmt);
2723 /* For each memory access, analyze its access function
2724 and record a bound on the loop iteration domain. */
2725 if (REFERENCE_CLASS_P (op0))
2726 infer_loop_bounds_from_ref (loop, stmt, op0, reliable);
2728 if (REFERENCE_CLASS_P (op1))
2729 infer_loop_bounds_from_ref (loop, stmt, op1, reliable);
2731 else if (is_gimple_call (stmt))
2734 unsigned i, n = gimple_call_num_args (stmt);
2736 lhs = gimple_call_lhs (stmt);
2737 if (lhs && REFERENCE_CLASS_P (lhs))
2738 infer_loop_bounds_from_ref (loop, stmt, lhs, reliable);
2740 for (i = 0; i < n; i++)
2742 arg = gimple_call_arg (stmt, i);
2743 if (REFERENCE_CLASS_P (arg))
2744 infer_loop_bounds_from_ref (loop, stmt, arg, reliable);
2749 /* Determine information about number of iterations of a LOOP from the fact
2750 that signed arithmetics in STMT does not overflow. */
2753 infer_loop_bounds_from_signedness (struct loop *loop, gimple stmt)
2755 tree def, base, step, scev, type, low, high;
2757 if (gimple_code (stmt) != GIMPLE_ASSIGN)
2760 def = gimple_assign_lhs (stmt);
2762 if (TREE_CODE (def) != SSA_NAME)
2765 type = TREE_TYPE (def);
2766 if (!INTEGRAL_TYPE_P (type)
2767 || !TYPE_OVERFLOW_UNDEFINED (type))
2770 scev = instantiate_parameters (loop, analyze_scalar_evolution (loop, def));
2771 if (chrec_contains_undetermined (scev))
2774 base = initial_condition_in_loop_num (scev, loop->num);
2775 step = evolution_part_in_loop_num (scev, loop->num);
2778 || TREE_CODE (step) != INTEGER_CST
2779 || tree_contains_chrecs (base, NULL)
2780 || chrec_contains_symbols_defined_in_loop (base, loop->num))
2783 low = lower_bound_in_type (type, type);
2784 high = upper_bound_in_type (type, type);
2786 record_nonwrapping_iv (loop, base, step, stmt, low, high, false, true);
2789 /* The following analyzers are extracting informations on the bounds
2790 of LOOP from the following undefined behaviors:
2792 - data references should not access elements over the statically
2795 - signed variables should not overflow when flag_wrapv is not set.
2799 infer_loop_bounds_from_undefined (struct loop *loop)
2803 gimple_stmt_iterator bsi;
2807 bbs = get_loop_body (loop);
2809 for (i = 0; i < loop->num_nodes; i++)
2813 /* If BB is not executed in each iteration of the loop, we cannot
2814 use the operations in it to infer reliable upper bound on the
2815 # of iterations of the loop. However, we can use it as a guess. */
2816 reliable = dominated_by_p (CDI_DOMINATORS, loop->latch, bb);
2818 for (bsi = gsi_start_bb (bb); !gsi_end_p (bsi); gsi_next (&bsi))
2820 gimple stmt = gsi_stmt (bsi);
2822 infer_loop_bounds_from_array (loop, stmt, reliable);
2825 infer_loop_bounds_from_signedness (loop, stmt);
2833 /* Converts VAL to double_int. */
2836 gcov_type_to_double_int (gcov_type val)
2840 ret.low = (unsigned HOST_WIDE_INT) val;
2841 /* If HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_WIDEST_INT, avoid shifting by
2842 the size of type. */
2843 val >>= HOST_BITS_PER_WIDE_INT - 1;
2845 ret.high = (unsigned HOST_WIDE_INT) val;
2850 /* Records estimates on numbers of iterations of LOOP. */
2853 estimate_numbers_of_iterations_loop (struct loop *loop)
2855 VEC (edge, heap) *exits;
2858 struct tree_niter_desc niter_desc;
2862 /* Give up if we already have tried to compute an estimation. */
2863 if (loop->estimate_state != EST_NOT_COMPUTED)
2865 loop->estimate_state = EST_AVAILABLE;
2866 loop->any_upper_bound = false;
2867 loop->any_estimate = false;
2869 exits = get_loop_exit_edges (loop);
2870 for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
2872 if (!number_of_iterations_exit (loop, ex, &niter_desc, false))
2875 niter = niter_desc.niter;
2876 type = TREE_TYPE (niter);
2877 if (TREE_CODE (niter_desc.may_be_zero) != INTEGER_CST)
2878 niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
2879 build_int_cst (type, 0),
2881 record_estimate (loop, niter, niter_desc.max,
2882 last_stmt (ex->src),
2885 VEC_free (edge, heap, exits);
2887 infer_loop_bounds_from_undefined (loop);
2889 /* If we have a measured profile, use it to estimate the number of
2891 if (loop->header->count != 0)
2893 gcov_type nit = expected_loop_iterations_unbounded (loop) + 1;
2894 bound = gcov_type_to_double_int (nit);
2895 record_niter_bound (loop, bound, true, false);
2898 /* If an upper bound is smaller than the realistic estimate of the
2899 number of iterations, use the upper bound instead. */
2900 if (loop->any_upper_bound
2901 && loop->any_estimate
2902 && double_int_ucmp (loop->nb_iterations_upper_bound,
2903 loop->nb_iterations_estimate) < 0)
2904 loop->nb_iterations_estimate = loop->nb_iterations_upper_bound;
2907 /* Records estimates on numbers of iterations of loops. */
2910 estimate_numbers_of_iterations (void)
2915 /* We don't want to issue signed overflow warnings while getting
2916 loop iteration estimates. */
2917 fold_defer_overflow_warnings ();
2919 FOR_EACH_LOOP (li, loop, 0)
2921 estimate_numbers_of_iterations_loop (loop);
2924 fold_undefer_and_ignore_overflow_warnings ();
2927 /* Returns true if statement S1 dominates statement S2. */
2930 stmt_dominates_stmt_p (gimple s1, gimple s2)
2932 basic_block bb1 = gimple_bb (s1), bb2 = gimple_bb (s2);
2940 gimple_stmt_iterator bsi;
2942 if (gimple_code (s2) == GIMPLE_PHI)
2945 if (gimple_code (s1) == GIMPLE_PHI)
2948 for (bsi = gsi_start_bb (bb1); gsi_stmt (bsi) != s2; gsi_next (&bsi))
2949 if (gsi_stmt (bsi) == s1)
2955 return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
2958 /* Returns true when we can prove that the number of executions of
2959 STMT in the loop is at most NITER, according to the bound on
2960 the number of executions of the statement NITER_BOUND->stmt recorded in
2961 NITER_BOUND. If STMT is NULL, we must prove this bound for all
2962 statements in the loop. */
2965 n_of_executions_at_most (gimple stmt,
2966 struct nb_iter_bound *niter_bound,
2969 double_int bound = niter_bound->bound;
2970 tree nit_type = TREE_TYPE (niter), e;
2973 gcc_assert (TYPE_UNSIGNED (nit_type));
2975 /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
2976 the number of iterations is small. */
2977 if (!double_int_fits_to_tree_p (nit_type, bound))
2980 /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
2981 times. This means that:
2983 -- if NITER_BOUND->is_exit is true, then everything before
2984 NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
2985 times, and everything after it at most NITER_BOUND->bound times.
2987 -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
2988 is executed, then NITER_BOUND->stmt is executed as well in the same
2989 iteration (we conclude that if both statements belong to the same
2990 basic block, or if STMT is after NITER_BOUND->stmt), then STMT
2991 is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
2992 executed at most NITER_BOUND->bound + 2 times. */
2994 if (niter_bound->is_exit)
2997 && stmt != niter_bound->stmt
2998 && stmt_dominates_stmt_p (niter_bound->stmt, stmt))
3006 || (gimple_bb (stmt) != gimple_bb (niter_bound->stmt)
3007 && !stmt_dominates_stmt_p (niter_bound->stmt, stmt)))
3009 bound = double_int_add (bound, double_int_one);
3010 if (double_int_zero_p (bound)
3011 || !double_int_fits_to_tree_p (nit_type, bound))
3017 e = fold_binary (cmp, boolean_type_node,
3018 niter, double_int_to_tree (nit_type, bound));
3019 return e && integer_nonzerop (e);
3022 /* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
3025 nowrap_type_p (tree type)
3027 if (INTEGRAL_TYPE_P (type)
3028 && TYPE_OVERFLOW_UNDEFINED (type))
3031 if (POINTER_TYPE_P (type))
3037 /* Return false only when the induction variable BASE + STEP * I is
3038 known to not overflow: i.e. when the number of iterations is small
3039 enough with respect to the step and initial condition in order to
3040 keep the evolution confined in TYPEs bounds. Return true when the
3041 iv is known to overflow or when the property is not computable.
3043 USE_OVERFLOW_SEMANTICS is true if this function should assume that
3044 the rules for overflow of the given language apply (e.g., that signed
3045 arithmetics in C does not overflow). */
3048 scev_probably_wraps_p (tree base, tree step,
3049 gimple at_stmt, struct loop *loop,
3050 bool use_overflow_semantics)
3052 struct nb_iter_bound *bound;
3053 tree delta, step_abs;
3054 tree unsigned_type, valid_niter;
3055 tree type = TREE_TYPE (step);
3057 /* FIXME: We really need something like
3058 http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
3060 We used to test for the following situation that frequently appears
3061 during address arithmetics:
3063 D.1621_13 = (long unsigned intD.4) D.1620_12;
3064 D.1622_14 = D.1621_13 * 8;
3065 D.1623_15 = (doubleD.29 *) D.1622_14;
3067 And derived that the sequence corresponding to D_14
3068 can be proved to not wrap because it is used for computing a
3069 memory access; however, this is not really the case -- for example,
3070 if D_12 = (unsigned char) [254,+,1], then D_14 has values
3071 2032, 2040, 0, 8, ..., but the code is still legal. */
3073 if (chrec_contains_undetermined (base)
3074 || chrec_contains_undetermined (step))
3077 if (integer_zerop (step))
3080 /* If we can use the fact that signed and pointer arithmetics does not
3081 wrap, we are done. */
3082 if (use_overflow_semantics && nowrap_type_p (TREE_TYPE (base)))
3085 /* To be able to use estimates on number of iterations of the loop,
3086 we must have an upper bound on the absolute value of the step. */
3087 if (TREE_CODE (step) != INTEGER_CST)
3090 /* Don't issue signed overflow warnings. */
3091 fold_defer_overflow_warnings ();
3093 /* Otherwise, compute the number of iterations before we reach the
3094 bound of the type, and verify that the loop is exited before this
3096 unsigned_type = unsigned_type_for (type);
3097 base = fold_convert (unsigned_type, base);
3099 if (tree_int_cst_sign_bit (step))
3101 tree extreme = fold_convert (unsigned_type,
3102 lower_bound_in_type (type, type));
3103 delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
3104 step_abs = fold_build1 (NEGATE_EXPR, unsigned_type,
3105 fold_convert (unsigned_type, step));
3109 tree extreme = fold_convert (unsigned_type,
3110 upper_bound_in_type (type, type));
3111 delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
3112 step_abs = fold_convert (unsigned_type, step);
3115 valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step_abs);
3117 estimate_numbers_of_iterations_loop (loop);
3118 for (bound = loop->bounds; bound; bound = bound->next)
3120 if (n_of_executions_at_most (at_stmt, bound, valid_niter))
3122 fold_undefer_and_ignore_overflow_warnings ();
3127 fold_undefer_and_ignore_overflow_warnings ();
3129 /* At this point we still don't have a proof that the iv does not
3130 overflow: give up. */
3134 /* Frees the information on upper bounds on numbers of iterations of LOOP. */
3137 free_numbers_of_iterations_estimates_loop (struct loop *loop)
3139 struct nb_iter_bound *bound, *next;
3141 loop->nb_iterations = NULL;
3142 loop->estimate_state = EST_NOT_COMPUTED;
3143 for (bound = loop->bounds; bound; bound = next)
3149 loop->bounds = NULL;
3152 /* Frees the information on upper bounds on numbers of iterations of loops. */
3155 free_numbers_of_iterations_estimates (void)
3160 FOR_EACH_LOOP (li, loop, 0)
3162 free_numbers_of_iterations_estimates_loop (loop);
3166 /* Substitute value VAL for ssa name NAME inside expressions held
3170 substitute_in_loop_info (struct loop *loop, tree name, tree val)
3172 loop->nb_iterations = simplify_replace_tree (loop->nb_iterations, name, val);