1 /* Scalar evolution detector.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
3 Contributed by Sebastian Pop <s.pop@laposte.net>
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 2, or (at your option) any later
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 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 COPYING. If not, write to the Free
19 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
25 This pass analyzes the evolution of scalar variables in loop
26 structures. The algorithm is based on the SSA representation,
27 and on the loop hierarchy tree. This algorithm is not based on
28 the notion of versions of a variable, as it was the case for the
29 previous implementations of the scalar evolution algorithm, but
30 it assumes that each defined name is unique.
32 The notation used in this file is called "chains of recurrences",
33 and has been proposed by Eugene Zima, Robert Van Engelen, and
34 others for describing induction variables in programs. For example
35 "b -> {0, +, 2}_1" means that the scalar variable "b" is equal to 0
36 when entering in the loop_1 and has a step 2 in this loop, in other
37 words "for (b = 0; b < N; b+=2);". Note that the coefficients of
38 this chain of recurrence (or chrec [shrek]) can contain the name of
39 other variables, in which case they are called parametric chrecs.
40 For example, "b -> {a, +, 2}_1" means that the initial value of "b"
41 is the value of "a". In most of the cases these parametric chrecs
42 are fully instantiated before their use because symbolic names can
43 hide some difficult cases such as self-references described later
44 (see the Fibonacci example).
46 A short sketch of the algorithm is:
48 Given a scalar variable to be analyzed, follow the SSA edge to
51 - When the definition is a GIMPLE_MODIFY_STMT: if the right hand side
52 (RHS) of the definition cannot be statically analyzed, the answer
53 of the analyzer is: "don't know".
54 Otherwise, for all the variables that are not yet analyzed in the
55 RHS, try to determine their evolution, and finally try to
56 evaluate the operation of the RHS that gives the evolution
57 function of the analyzed variable.
59 - When the definition is a condition-phi-node: determine the
60 evolution function for all the branches of the phi node, and
61 finally merge these evolutions (see chrec_merge).
63 - When the definition is a loop-phi-node: determine its initial
64 condition, that is the SSA edge defined in an outer loop, and
65 keep it symbolic. Then determine the SSA edges that are defined
66 in the body of the loop. Follow the inner edges until ending on
67 another loop-phi-node of the same analyzed loop. If the reached
68 loop-phi-node is not the starting loop-phi-node, then we keep
69 this definition under a symbolic form. If the reached
70 loop-phi-node is the same as the starting one, then we compute a
71 symbolic stride on the return path. The result is then the
72 symbolic chrec {initial_condition, +, symbolic_stride}_loop.
76 Example 1: Illustration of the basic algorithm.
82 | if (c > 10) exit_loop
85 Suppose that we want to know the number of iterations of the
86 loop_1. The exit_loop is controlled by a COND_EXPR (c > 10). We
87 ask the scalar evolution analyzer two questions: what's the
88 scalar evolution (scev) of "c", and what's the scev of "10". For
89 "10" the answer is "10" since it is a scalar constant. For the
90 scalar variable "c", it follows the SSA edge to its definition,
91 "c = b + 1", and then asks again what's the scev of "b".
92 Following the SSA edge, we end on a loop-phi-node "b = phi (a,
93 c)", where the initial condition is "a", and the inner loop edge
94 is "c". The initial condition is kept under a symbolic form (it
95 may be the case that the copy constant propagation has done its
96 work and we end with the constant "3" as one of the edges of the
97 loop-phi-node). The update edge is followed to the end of the
98 loop, and until reaching again the starting loop-phi-node: b -> c
99 -> b. At this point we have drawn a path from "b" to "b" from
100 which we compute the stride in the loop: in this example it is
101 "+1". The resulting scev for "b" is "b -> {a, +, 1}_1". Now
102 that the scev for "b" is known, it is possible to compute the
103 scev for "c", that is "c -> {a + 1, +, 1}_1". In order to
104 determine the number of iterations in the loop_1, we have to
105 instantiate_parameters ({a + 1, +, 1}_1), that gives after some
106 more analysis the scev {4, +, 1}_1, or in other words, this is
107 the function "f (x) = x + 4", where x is the iteration count of
108 the loop_1. Now we have to solve the inequality "x + 4 > 10",
109 and take the smallest iteration number for which the loop is
110 exited: x = 7. This loop runs from x = 0 to x = 7, and in total
111 there are 8 iterations. In terms of loop normalization, we have
112 created a variable that is implicitly defined, "x" or just "_1",
113 and all the other analyzed scalars of the loop are defined in
114 function of this variable:
120 or in terms of a C program:
123 | for (x = 0; x <= 7; x++)
129 Example 2: Illustration of the algorithm on nested loops.
140 For analyzing the scalar evolution of "a", the algorithm follows
141 the SSA edge into the loop's body: "a -> b". "b" is an inner
142 loop-phi-node, and its analysis as in Example 1, gives:
147 Following the SSA edge for the initial condition, we end on "c = a
148 + 2", and then on the starting loop-phi-node "a". From this point,
149 the loop stride is computed: back on "c = a + 2" we get a "+2" in
150 the loop_1, then on the loop-phi-node "b" we compute the overall
151 effect of the inner loop that is "b = c + 30", and we get a "+30"
152 in the loop_1. That means that the overall stride in loop_1 is
153 equal to "+32", and the result is:
158 Example 3: Higher degree polynomials.
172 instantiate_parameters ({5, +, a}_1) -> {5, +, 2, +, 1}_1
173 instantiate_parameters ({5 + a, +, a}_1) -> {7, +, 3, +, 1}_1
175 Example 4: Lucas, Fibonacci, or mixers in general.
187 The syntax "(1, c)_1" stands for a PEELED_CHREC that has the
188 following semantics: during the first iteration of the loop_1, the
189 variable contains the value 1, and then it contains the value "c".
190 Note that this syntax is close to the syntax of the loop-phi-node:
191 "a -> (1, c)_1" vs. "a = phi (1, c)".
193 The symbolic chrec representation contains all the semantics of the
194 original code. What is more difficult is to use this information.
196 Example 5: Flip-flops, or exchangers.
208 Based on these symbolic chrecs, it is possible to refine this
209 information into the more precise PERIODIC_CHRECs:
214 This transformation is not yet implemented.
218 You can find a more detailed description of the algorithm in:
219 http://icps.u-strasbg.fr/~pop/DEA_03_Pop.pdf
220 http://icps.u-strasbg.fr/~pop/DEA_03_Pop.ps.gz. But note that
221 this is a preliminary report and some of the details of the
222 algorithm have changed. I'm working on a research report that
223 updates the description of the algorithms to reflect the design
224 choices used in this implementation.
226 A set of slides show a high level overview of the algorithm and run
227 an example through the scalar evolution analyzer:
228 http://cri.ensmp.fr/~pop/gcc/mar04/slides.pdf
230 The slides that I have presented at the GCC Summit'04 are available
231 at: http://cri.ensmp.fr/~pop/gcc/20040604/gccsummit-lno-spop.pdf
236 #include "coretypes.h"
242 /* These RTL headers are needed for basic-block.h. */
244 #include "basic-block.h"
245 #include "diagnostic.h"
246 #include "tree-flow.h"
247 #include "tree-dump.h"
250 #include "tree-chrec.h"
251 #include "tree-scalar-evolution.h"
252 #include "tree-pass.h"
256 static tree analyze_scalar_evolution_1 (struct loop *, tree, tree);
258 /* The cached information about a ssa name VAR, claiming that inside LOOP,
259 the value of VAR can be expressed as CHREC. */
261 struct scev_info_str GTY(())
267 /* Counters for the scev database. */
268 static unsigned nb_set_scev = 0;
269 static unsigned nb_get_scev = 0;
271 /* The following trees are unique elements. Thus the comparison of
272 another element to these elements should be done on the pointer to
273 these trees, and not on their value. */
275 /* The SSA_NAMEs that are not yet analyzed are qualified with NULL_TREE. */
276 tree chrec_not_analyzed_yet;
278 /* Reserved to the cases where the analyzer has detected an
279 undecidable property at compile time. */
280 tree chrec_dont_know;
282 /* When the analyzer has detected that a property will never
283 happen, then it qualifies it with chrec_known. */
286 static bitmap already_instantiated;
288 static GTY ((param_is (struct scev_info_str))) htab_t scalar_evolution_info;
291 /* Constructs a new SCEV_INFO_STR structure. */
293 static inline struct scev_info_str *
294 new_scev_info_str (tree var)
296 struct scev_info_str *res;
298 res = GGC_NEW (struct scev_info_str);
300 res->chrec = chrec_not_analyzed_yet;
305 /* Computes a hash function for database element ELT. */
308 hash_scev_info (const void *elt)
310 return SSA_NAME_VERSION (((struct scev_info_str *) elt)->var);
313 /* Compares database elements E1 and E2. */
316 eq_scev_info (const void *e1, const void *e2)
318 const struct scev_info_str *elt1 = (const struct scev_info_str *) e1;
319 const struct scev_info_str *elt2 = (const struct scev_info_str *) e2;
321 return elt1->var == elt2->var;
324 /* Deletes database element E. */
327 del_scev_info (void *e)
332 /* Get the index corresponding to VAR in the current LOOP. If
333 it's the first time we ask for this VAR, then we return
334 chrec_not_analyzed_yet for this VAR and return its index. */
337 find_var_scev_info (tree var)
339 struct scev_info_str *res;
340 struct scev_info_str tmp;
344 slot = htab_find_slot (scalar_evolution_info, &tmp, INSERT);
347 *slot = new_scev_info_str (var);
348 res = (struct scev_info_str *) *slot;
353 /* Return true when CHREC contains symbolic names defined in
357 chrec_contains_symbols_defined_in_loop (tree chrec, unsigned loop_nb)
361 if (chrec == NULL_TREE)
364 if (TREE_INVARIANT (chrec))
367 if (TREE_CODE (chrec) == VAR_DECL
368 || TREE_CODE (chrec) == PARM_DECL
369 || TREE_CODE (chrec) == FUNCTION_DECL
370 || TREE_CODE (chrec) == LABEL_DECL
371 || TREE_CODE (chrec) == RESULT_DECL
372 || TREE_CODE (chrec) == FIELD_DECL)
375 if (TREE_CODE (chrec) == SSA_NAME)
377 tree def = SSA_NAME_DEF_STMT (chrec);
378 struct loop *def_loop = loop_containing_stmt (def);
379 struct loop *loop = get_loop (loop_nb);
381 if (def_loop == NULL)
384 if (loop == def_loop || flow_loop_nested_p (loop, def_loop))
390 n = TREE_OPERAND_LENGTH (chrec);
391 for (i = 0; i < n; i++)
392 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (chrec, i),
398 /* Return true when PHI is a loop-phi-node. */
401 loop_phi_node_p (tree phi)
403 /* The implementation of this function is based on the following
404 property: "all the loop-phi-nodes of a loop are contained in the
405 loop's header basic block". */
407 return loop_containing_stmt (phi)->header == bb_for_stmt (phi);
410 /* Compute the scalar evolution for EVOLUTION_FN after crossing LOOP.
411 In general, in the case of multivariate evolutions we want to get
412 the evolution in different loops. LOOP specifies the level for
413 which to get the evolution.
417 | for (j = 0; j < 100; j++)
419 | for (k = 0; k < 100; k++)
421 | i = k + j; - Here the value of i is a function of j, k.
423 | ... = i - Here the value of i is a function of j.
425 | ... = i - Here the value of i is a scalar.
431 | i_1 = phi (i_0, i_2)
435 This loop has the same effect as:
436 LOOP_1 has the same effect as:
440 The overall effect of the loop, "i_0 + 20" in the previous example,
441 is obtained by passing in the parameters: LOOP = 1,
442 EVOLUTION_FN = {i_0, +, 2}_1.
446 compute_overall_effect_of_inner_loop (struct loop *loop, tree evolution_fn)
450 if (evolution_fn == chrec_dont_know)
451 return chrec_dont_know;
453 else if (TREE_CODE (evolution_fn) == POLYNOMIAL_CHREC)
455 struct loop *inner_loop = get_chrec_loop (evolution_fn);
457 if (inner_loop == loop
458 || flow_loop_nested_p (loop, inner_loop))
460 tree nb_iter = number_of_latch_executions (inner_loop);
462 if (nb_iter == chrec_dont_know)
463 return chrec_dont_know;
468 /* evolution_fn is the evolution function in LOOP. Get
469 its value in the nb_iter-th iteration. */
470 res = chrec_apply (inner_loop->num, evolution_fn, nb_iter);
472 /* Continue the computation until ending on a parent of LOOP. */
473 return compute_overall_effect_of_inner_loop (loop, res);
480 /* If the evolution function is an invariant, there is nothing to do. */
481 else if (no_evolution_in_loop_p (evolution_fn, loop->num, &val) && val)
485 return chrec_dont_know;
488 /* Determine whether the CHREC is always positive/negative. If the expression
489 cannot be statically analyzed, return false, otherwise set the answer into
493 chrec_is_positive (tree chrec, bool *value)
495 bool value0, value1, value2;
496 tree end_value, nb_iter;
498 switch (TREE_CODE (chrec))
500 case POLYNOMIAL_CHREC:
501 if (!chrec_is_positive (CHREC_LEFT (chrec), &value0)
502 || !chrec_is_positive (CHREC_RIGHT (chrec), &value1))
505 /* FIXME -- overflows. */
506 if (value0 == value1)
512 /* Otherwise the chrec is under the form: "{-197, +, 2}_1",
513 and the proof consists in showing that the sign never
514 changes during the execution of the loop, from 0 to
515 loop->nb_iterations. */
516 if (!evolution_function_is_affine_p (chrec))
519 nb_iter = number_of_latch_executions (get_chrec_loop (chrec));
520 if (chrec_contains_undetermined (nb_iter))
524 /* TODO -- If the test is after the exit, we may decrease the number of
525 iterations by one. */
527 nb_iter = chrec_fold_minus (type, nb_iter, build_int_cst (type, 1));
530 end_value = chrec_apply (CHREC_VARIABLE (chrec), chrec, nb_iter);
532 if (!chrec_is_positive (end_value, &value2))
536 return value0 == value1;
539 *value = (tree_int_cst_sgn (chrec) == 1);
547 /* Associate CHREC to SCALAR. */
550 set_scalar_evolution (tree scalar, tree chrec)
554 if (TREE_CODE (scalar) != SSA_NAME)
557 scalar_info = find_var_scev_info (scalar);
561 if (dump_flags & TDF_DETAILS)
563 fprintf (dump_file, "(set_scalar_evolution \n");
564 fprintf (dump_file, " (scalar = ");
565 print_generic_expr (dump_file, scalar, 0);
566 fprintf (dump_file, ")\n (scalar_evolution = ");
567 print_generic_expr (dump_file, chrec, 0);
568 fprintf (dump_file, "))\n");
570 if (dump_flags & TDF_STATS)
574 *scalar_info = chrec;
577 /* Retrieve the chrec associated to SCALAR in the LOOP. */
580 get_scalar_evolution (tree scalar)
586 if (dump_flags & TDF_DETAILS)
588 fprintf (dump_file, "(get_scalar_evolution \n");
589 fprintf (dump_file, " (scalar = ");
590 print_generic_expr (dump_file, scalar, 0);
591 fprintf (dump_file, ")\n");
593 if (dump_flags & TDF_STATS)
597 switch (TREE_CODE (scalar))
600 res = *find_var_scev_info (scalar);
609 res = chrec_not_analyzed_yet;
613 if (dump_file && (dump_flags & TDF_DETAILS))
615 fprintf (dump_file, " (scalar_evolution = ");
616 print_generic_expr (dump_file, res, 0);
617 fprintf (dump_file, "))\n");
623 /* Helper function for add_to_evolution. Returns the evolution
624 function for an assignment of the form "a = b + c", where "a" and
625 "b" are on the strongly connected component. CHREC_BEFORE is the
626 information that we already have collected up to this point.
627 TO_ADD is the evolution of "c".
629 When CHREC_BEFORE has an evolution part in LOOP_NB, add to this
630 evolution the expression TO_ADD, otherwise construct an evolution
631 part for this loop. */
634 add_to_evolution_1 (unsigned loop_nb, tree chrec_before, tree to_add,
637 tree type, left, right;
638 struct loop *loop = get_loop (loop_nb), *chloop;
640 switch (TREE_CODE (chrec_before))
642 case POLYNOMIAL_CHREC:
643 chloop = get_chrec_loop (chrec_before);
645 || flow_loop_nested_p (chloop, loop))
649 type = chrec_type (chrec_before);
651 /* When there is no evolution part in this loop, build it. */
656 right = SCALAR_FLOAT_TYPE_P (type)
657 ? build_real (type, dconst0)
658 : build_int_cst (type, 0);
662 var = CHREC_VARIABLE (chrec_before);
663 left = CHREC_LEFT (chrec_before);
664 right = CHREC_RIGHT (chrec_before);
667 to_add = chrec_convert (type, to_add, at_stmt);
668 right = chrec_convert (type, right, at_stmt);
669 right = chrec_fold_plus (type, right, to_add);
670 return build_polynomial_chrec (var, left, right);
674 gcc_assert (flow_loop_nested_p (loop, chloop));
676 /* Search the evolution in LOOP_NB. */
677 left = add_to_evolution_1 (loop_nb, CHREC_LEFT (chrec_before),
679 right = CHREC_RIGHT (chrec_before);
680 right = chrec_convert (chrec_type (left), right, at_stmt);
681 return build_polynomial_chrec (CHREC_VARIABLE (chrec_before),
686 /* These nodes do not depend on a loop. */
687 if (chrec_before == chrec_dont_know)
688 return chrec_dont_know;
691 right = chrec_convert (chrec_type (left), to_add, at_stmt);
692 return build_polynomial_chrec (loop_nb, left, right);
696 /* Add TO_ADD to the evolution part of CHREC_BEFORE in the dimension
699 Description (provided for completeness, for those who read code in
700 a plane, and for my poor 62 bytes brain that would have forgotten
701 all this in the next two or three months):
703 The algorithm of translation of programs from the SSA representation
704 into the chrecs syntax is based on a pattern matching. After having
705 reconstructed the overall tree expression for a loop, there are only
706 two cases that can arise:
708 1. a = loop-phi (init, a + expr)
709 2. a = loop-phi (init, expr)
711 where EXPR is either a scalar constant with respect to the analyzed
712 loop (this is a degree 0 polynomial), or an expression containing
713 other loop-phi definitions (these are higher degree polynomials).
720 | a = phi (init, a + 5)
727 | a = phi (inita, 2 * b + 3)
728 | b = phi (initb, b + 1)
731 For the first case, the semantics of the SSA representation is:
733 | a (x) = init + \sum_{j = 0}^{x - 1} expr (j)
735 that is, there is a loop index "x" that determines the scalar value
736 of the variable during the loop execution. During the first
737 iteration, the value is that of the initial condition INIT, while
738 during the subsequent iterations, it is the sum of the initial
739 condition with the sum of all the values of EXPR from the initial
740 iteration to the before last considered iteration.
742 For the second case, the semantics of the SSA program is:
744 | a (x) = init, if x = 0;
745 | expr (x - 1), otherwise.
747 The second case corresponds to the PEELED_CHREC, whose syntax is
748 close to the syntax of a loop-phi-node:
750 | phi (init, expr) vs. (init, expr)_x
752 The proof of the translation algorithm for the first case is a
753 proof by structural induction based on the degree of EXPR.
756 When EXPR is a constant with respect to the analyzed loop, or in
757 other words when EXPR is a polynomial of degree 0, the evolution of
758 the variable A in the loop is an affine function with an initial
759 condition INIT, and a step EXPR. In order to show this, we start
760 from the semantics of the SSA representation:
762 f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
764 and since "expr (j)" is a constant with respect to "j",
766 f (x) = init + x * expr
768 Finally, based on the semantics of the pure sum chrecs, by
769 identification we get the corresponding chrecs syntax:
771 f (x) = init * \binom{x}{0} + expr * \binom{x}{1}
772 f (x) -> {init, +, expr}_x
775 Suppose that EXPR is a polynomial of degree N with respect to the
776 analyzed loop_x for which we have already determined that it is
777 written under the chrecs syntax:
779 | expr (x) -> {b_0, +, b_1, +, ..., +, b_{n-1}} (x)
781 We start from the semantics of the SSA program:
783 | f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
785 | f (x) = init + \sum_{j = 0}^{x - 1}
786 | (b_0 * \binom{j}{0} + ... + b_{n-1} * \binom{j}{n-1})
788 | f (x) = init + \sum_{j = 0}^{x - 1}
789 | \sum_{k = 0}^{n - 1} (b_k * \binom{j}{k})
791 | f (x) = init + \sum_{k = 0}^{n - 1}
792 | (b_k * \sum_{j = 0}^{x - 1} \binom{j}{k})
794 | f (x) = init + \sum_{k = 0}^{n - 1}
795 | (b_k * \binom{x}{k + 1})
797 | f (x) = init + b_0 * \binom{x}{1} + ...
798 | + b_{n-1} * \binom{x}{n}
800 | f (x) = init * \binom{x}{0} + b_0 * \binom{x}{1} + ...
801 | + b_{n-1} * \binom{x}{n}
804 And finally from the definition of the chrecs syntax, we identify:
805 | f (x) -> {init, +, b_0, +, ..., +, b_{n-1}}_x
807 This shows the mechanism that stands behind the add_to_evolution
808 function. An important point is that the use of symbolic
809 parameters avoids the need of an analysis schedule.
816 | a = phi (inita, a + 2 + b)
817 | b = phi (initb, b + 1)
820 When analyzing "a", the algorithm keeps "b" symbolically:
822 | a -> {inita, +, 2 + b}_1
824 Then, after instantiation, the analyzer ends on the evolution:
826 | a -> {inita, +, 2 + initb, +, 1}_1
831 add_to_evolution (unsigned loop_nb, tree chrec_before, enum tree_code code,
832 tree to_add, tree at_stmt)
834 tree type = chrec_type (to_add);
835 tree res = NULL_TREE;
837 if (to_add == NULL_TREE)
840 /* TO_ADD is either a scalar, or a parameter. TO_ADD is not
841 instantiated at this point. */
842 if (TREE_CODE (to_add) == POLYNOMIAL_CHREC)
843 /* This should not happen. */
844 return chrec_dont_know;
846 if (dump_file && (dump_flags & TDF_DETAILS))
848 fprintf (dump_file, "(add_to_evolution \n");
849 fprintf (dump_file, " (loop_nb = %d)\n", loop_nb);
850 fprintf (dump_file, " (chrec_before = ");
851 print_generic_expr (dump_file, chrec_before, 0);
852 fprintf (dump_file, ")\n (to_add = ");
853 print_generic_expr (dump_file, to_add, 0);
854 fprintf (dump_file, ")\n");
857 if (code == MINUS_EXPR)
858 to_add = chrec_fold_multiply (type, to_add, SCALAR_FLOAT_TYPE_P (type)
859 ? build_real (type, dconstm1)
860 : build_int_cst_type (type, -1));
862 res = add_to_evolution_1 (loop_nb, chrec_before, to_add, at_stmt);
864 if (dump_file && (dump_flags & TDF_DETAILS))
866 fprintf (dump_file, " (res = ");
867 print_generic_expr (dump_file, res, 0);
868 fprintf (dump_file, "))\n");
874 /* Helper function. */
877 set_nb_iterations_in_loop (struct loop *loop,
880 if (dump_file && (dump_flags & TDF_DETAILS))
882 fprintf (dump_file, " (set_nb_iterations_in_loop = ");
883 print_generic_expr (dump_file, res, 0);
884 fprintf (dump_file, "))\n");
887 loop->nb_iterations = res;
893 /* This section selects the loops that will be good candidates for the
894 scalar evolution analysis. For the moment, greedily select all the
895 loop nests we could analyze. */
897 /* Return true when it is possible to analyze the condition expression
901 analyzable_condition (tree expr)
905 if (TREE_CODE (expr) != COND_EXPR)
908 condition = TREE_OPERAND (expr, 0);
910 switch (TREE_CODE (condition))
930 /* For a loop with a single exit edge, return the COND_EXPR that
931 guards the exit edge. If the expression is too difficult to
932 analyze, then give up. */
935 get_loop_exit_condition (struct loop *loop)
937 tree res = NULL_TREE;
938 edge exit_edge = single_exit (loop);
940 if (dump_file && (dump_flags & TDF_DETAILS))
941 fprintf (dump_file, "(get_loop_exit_condition \n ");
947 expr = last_stmt (exit_edge->src);
948 if (analyzable_condition (expr))
952 if (dump_file && (dump_flags & TDF_DETAILS))
954 print_generic_expr (dump_file, res, 0);
955 fprintf (dump_file, ")\n");
961 /* Recursively determine and enqueue the exit conditions for a loop. */
964 get_exit_conditions_rec (struct loop *loop,
965 VEC(tree,heap) **exit_conditions)
970 /* Recurse on the inner loops, then on the next (sibling) loops. */
971 get_exit_conditions_rec (loop->inner, exit_conditions);
972 get_exit_conditions_rec (loop->next, exit_conditions);
974 if (single_exit (loop))
976 tree loop_condition = get_loop_exit_condition (loop);
979 VEC_safe_push (tree, heap, *exit_conditions, loop_condition);
983 /* Select the candidate loop nests for the analysis. This function
984 initializes the EXIT_CONDITIONS array. */
987 select_loops_exit_conditions (VEC(tree,heap) **exit_conditions)
989 struct loop *function_body = current_loops->tree_root;
991 get_exit_conditions_rec (function_body->inner, exit_conditions);
995 /* Depth first search algorithm. */
997 typedef enum t_bool {
1004 static t_bool follow_ssa_edge (struct loop *loop, tree, tree, tree *, int);
1006 /* Follow the ssa edge into the right hand side RHS of an assignment.
1007 Return true if the strongly connected component has been found. */
1010 follow_ssa_edge_in_rhs (struct loop *loop, tree at_stmt, tree rhs,
1011 tree halting_phi, tree *evolution_of_loop, int limit)
1013 t_bool res = t_false;
1015 tree type_rhs = TREE_TYPE (rhs);
1018 /* The RHS is one of the following cases:
1024 - other cases are not yet handled. */
1025 switch (TREE_CODE (rhs))
1028 /* This assignment is under the form "a_1 = (cast) rhs. */
1029 res = follow_ssa_edge_in_rhs (loop, at_stmt, TREE_OPERAND (rhs, 0),
1030 halting_phi, evolution_of_loop, limit);
1031 *evolution_of_loop = chrec_convert (TREE_TYPE (rhs),
1032 *evolution_of_loop, at_stmt);
1036 /* This assignment is under the form "a_1 = 7". */
1041 /* This assignment is under the form: "a_1 = b_2". */
1042 res = follow_ssa_edge
1043 (loop, SSA_NAME_DEF_STMT (rhs), halting_phi, evolution_of_loop, limit);
1047 /* This case is under the form "rhs0 + rhs1". */
1048 rhs0 = TREE_OPERAND (rhs, 0);
1049 rhs1 = TREE_OPERAND (rhs, 1);
1050 STRIP_TYPE_NOPS (rhs0);
1051 STRIP_TYPE_NOPS (rhs1);
1053 if (TREE_CODE (rhs0) == SSA_NAME)
1055 if (TREE_CODE (rhs1) == SSA_NAME)
1057 /* Match an assignment under the form:
1060 /* We want only assignments of form "name + name" contribute to
1061 LIMIT, as the other cases do not necessarily contribute to
1062 the complexity of the expression. */
1065 evol = *evolution_of_loop;
1066 res = follow_ssa_edge
1067 (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1071 *evolution_of_loop = add_to_evolution
1073 chrec_convert (type_rhs, evol, at_stmt),
1074 PLUS_EXPR, rhs1, at_stmt);
1076 else if (res == t_false)
1078 res = follow_ssa_edge
1079 (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi,
1080 evolution_of_loop, limit);
1083 *evolution_of_loop = add_to_evolution
1085 chrec_convert (type_rhs, *evolution_of_loop, at_stmt),
1086 PLUS_EXPR, rhs0, at_stmt);
1088 else if (res == t_dont_know)
1089 *evolution_of_loop = chrec_dont_know;
1092 else if (res == t_dont_know)
1093 *evolution_of_loop = chrec_dont_know;
1098 /* Match an assignment under the form:
1100 res = follow_ssa_edge
1101 (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1102 evolution_of_loop, limit);
1104 *evolution_of_loop = add_to_evolution
1105 (loop->num, chrec_convert (type_rhs, *evolution_of_loop,
1107 PLUS_EXPR, rhs1, at_stmt);
1109 else if (res == t_dont_know)
1110 *evolution_of_loop = chrec_dont_know;
1114 else if (TREE_CODE (rhs1) == SSA_NAME)
1116 /* Match an assignment under the form:
1118 res = follow_ssa_edge
1119 (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi,
1120 evolution_of_loop, limit);
1122 *evolution_of_loop = add_to_evolution
1123 (loop->num, chrec_convert (type_rhs, *evolution_of_loop,
1125 PLUS_EXPR, rhs0, at_stmt);
1127 else if (res == t_dont_know)
1128 *evolution_of_loop = chrec_dont_know;
1132 /* Otherwise, match an assignment under the form:
1134 /* And there is nothing to do. */
1140 /* This case is under the form "opnd0 = rhs0 - rhs1". */
1141 rhs0 = TREE_OPERAND (rhs, 0);
1142 rhs1 = TREE_OPERAND (rhs, 1);
1143 STRIP_TYPE_NOPS (rhs0);
1144 STRIP_TYPE_NOPS (rhs1);
1146 if (TREE_CODE (rhs0) == SSA_NAME)
1148 /* Match an assignment under the form:
1151 /* We want only assignments of form "name - name" contribute to
1152 LIMIT, as the other cases do not necessarily contribute to
1153 the complexity of the expression. */
1154 if (TREE_CODE (rhs1) == SSA_NAME)
1157 res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1158 evolution_of_loop, limit);
1160 *evolution_of_loop = add_to_evolution
1161 (loop->num, chrec_convert (type_rhs, *evolution_of_loop, at_stmt),
1162 MINUS_EXPR, rhs1, at_stmt);
1164 else if (res == t_dont_know)
1165 *evolution_of_loop = chrec_dont_know;
1168 /* Otherwise, match an assignment under the form:
1170 /* And there is nothing to do. */
1177 /* This assignment is of the form: "a_1 = ASSERT_EXPR <a_2, ...>"
1178 It must be handled as a copy assignment of the form a_1 = a_2. */
1179 tree op0 = ASSERT_EXPR_VAR (rhs);
1180 if (TREE_CODE (op0) == SSA_NAME)
1181 res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (op0),
1182 halting_phi, evolution_of_loop, limit);
1197 /* Checks whether the I-th argument of a PHI comes from a backedge. */
1200 backedge_phi_arg_p (tree phi, int i)
1202 edge e = PHI_ARG_EDGE (phi, i);
1204 /* We would in fact like to test EDGE_DFS_BACK here, but we do not care
1205 about updating it anywhere, and this should work as well most of the
1207 if (e->flags & EDGE_IRREDUCIBLE_LOOP)
1213 /* Helper function for one branch of the condition-phi-node. Return
1214 true if the strongly connected component has been found following
1217 static inline t_bool
1218 follow_ssa_edge_in_condition_phi_branch (int i,
1222 tree *evolution_of_branch,
1223 tree init_cond, int limit)
1225 tree branch = PHI_ARG_DEF (condition_phi, i);
1226 *evolution_of_branch = chrec_dont_know;
1228 /* Do not follow back edges (they must belong to an irreducible loop, which
1229 we really do not want to worry about). */
1230 if (backedge_phi_arg_p (condition_phi, i))
1233 if (TREE_CODE (branch) == SSA_NAME)
1235 *evolution_of_branch = init_cond;
1236 return follow_ssa_edge (loop, SSA_NAME_DEF_STMT (branch), halting_phi,
1237 evolution_of_branch, limit);
1240 /* This case occurs when one of the condition branches sets
1241 the variable to a constant: i.e. a phi-node like
1242 "a_2 = PHI <a_7(5), 2(6)>;".
1244 FIXME: This case have to be refined correctly:
1245 in some cases it is possible to say something better than
1246 chrec_dont_know, for example using a wrap-around notation. */
1250 /* This function merges the branches of a condition-phi-node in a
1254 follow_ssa_edge_in_condition_phi (struct loop *loop,
1257 tree *evolution_of_loop, int limit)
1260 tree init = *evolution_of_loop;
1261 tree evolution_of_branch;
1262 t_bool res = follow_ssa_edge_in_condition_phi_branch (0, loop, condition_phi,
1264 &evolution_of_branch,
1266 if (res == t_false || res == t_dont_know)
1269 *evolution_of_loop = evolution_of_branch;
1271 /* If the phi node is just a copy, do not increase the limit. */
1272 if (PHI_NUM_ARGS (condition_phi) > 1)
1275 for (i = 1; i < PHI_NUM_ARGS (condition_phi); i++)
1277 /* Quickly give up when the evolution of one of the branches is
1279 if (*evolution_of_loop == chrec_dont_know)
1282 res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi,
1284 &evolution_of_branch,
1286 if (res == t_false || res == t_dont_know)
1289 *evolution_of_loop = chrec_merge (*evolution_of_loop,
1290 evolution_of_branch);
1296 /* Follow an SSA edge in an inner loop. It computes the overall
1297 effect of the loop, and following the symbolic initial conditions,
1298 it follows the edges in the parent loop. The inner loop is
1299 considered as a single statement. */
1302 follow_ssa_edge_inner_loop_phi (struct loop *outer_loop,
1305 tree *evolution_of_loop, int limit)
1307 struct loop *loop = loop_containing_stmt (loop_phi_node);
1308 tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node));
1310 /* Sometimes, the inner loop is too difficult to analyze, and the
1311 result of the analysis is a symbolic parameter. */
1312 if (ev == PHI_RESULT (loop_phi_node))
1314 t_bool res = t_false;
1317 for (i = 0; i < PHI_NUM_ARGS (loop_phi_node); i++)
1319 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1322 /* Follow the edges that exit the inner loop. */
1323 bb = PHI_ARG_EDGE (loop_phi_node, i)->src;
1324 if (!flow_bb_inside_loop_p (loop, bb))
1325 res = follow_ssa_edge_in_rhs (outer_loop, loop_phi_node,
1327 evolution_of_loop, limit);
1332 /* If the path crosses this loop-phi, give up. */
1334 *evolution_of_loop = chrec_dont_know;
1339 /* Otherwise, compute the overall effect of the inner loop. */
1340 ev = compute_overall_effect_of_inner_loop (loop, ev);
1341 return follow_ssa_edge_in_rhs (outer_loop, loop_phi_node, ev, halting_phi,
1342 evolution_of_loop, limit);
1345 /* Follow an SSA edge from a loop-phi-node to itself, constructing a
1346 path that is analyzed on the return walk. */
1349 follow_ssa_edge (struct loop *loop, tree def, tree halting_phi,
1350 tree *evolution_of_loop, int limit)
1352 struct loop *def_loop;
1354 if (TREE_CODE (def) == NOP_EXPR)
1357 /* Give up if the path is longer than the MAX that we allow. */
1358 if (limit > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
1361 def_loop = loop_containing_stmt (def);
1363 switch (TREE_CODE (def))
1366 if (!loop_phi_node_p (def))
1367 /* DEF is a condition-phi-node. Follow the branches, and
1368 record their evolutions. Finally, merge the collected
1369 information and set the approximation to the main
1371 return follow_ssa_edge_in_condition_phi
1372 (loop, def, halting_phi, evolution_of_loop, limit);
1374 /* When the analyzed phi is the halting_phi, the
1375 depth-first search is over: we have found a path from
1376 the halting_phi to itself in the loop. */
1377 if (def == halting_phi)
1380 /* Otherwise, the evolution of the HALTING_PHI depends
1381 on the evolution of another loop-phi-node, i.e. the
1382 evolution function is a higher degree polynomial. */
1383 if (def_loop == loop)
1387 if (flow_loop_nested_p (loop, def_loop))
1388 return follow_ssa_edge_inner_loop_phi
1389 (loop, def, halting_phi, evolution_of_loop, limit + 1);
1394 case GIMPLE_MODIFY_STMT:
1395 return follow_ssa_edge_in_rhs (loop, def,
1396 GIMPLE_STMT_OPERAND (def, 1),
1398 evolution_of_loop, limit);
1401 /* At this level of abstraction, the program is just a set
1402 of GIMPLE_MODIFY_STMTs and PHI_NODEs. In principle there is no
1403 other node to be handled. */
1410 /* Given a LOOP_PHI_NODE, this function determines the evolution
1411 function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop. */
1414 analyze_evolution_in_loop (tree loop_phi_node,
1418 tree evolution_function = chrec_not_analyzed_yet;
1419 struct loop *loop = loop_containing_stmt (loop_phi_node);
1422 if (dump_file && (dump_flags & TDF_DETAILS))
1424 fprintf (dump_file, "(analyze_evolution_in_loop \n");
1425 fprintf (dump_file, " (loop_phi_node = ");
1426 print_generic_expr (dump_file, loop_phi_node, 0);
1427 fprintf (dump_file, ")\n");
1430 for (i = 0; i < PHI_NUM_ARGS (loop_phi_node); i++)
1432 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1433 tree ssa_chain, ev_fn;
1436 /* Select the edges that enter the loop body. */
1437 bb = PHI_ARG_EDGE (loop_phi_node, i)->src;
1438 if (!flow_bb_inside_loop_p (loop, bb))
1441 if (TREE_CODE (arg) == SSA_NAME)
1443 ssa_chain = SSA_NAME_DEF_STMT (arg);
1445 /* Pass in the initial condition to the follow edge function. */
1447 res = follow_ssa_edge (loop, ssa_chain, loop_phi_node, &ev_fn, 0);
1452 /* When it is impossible to go back on the same
1453 loop_phi_node by following the ssa edges, the
1454 evolution is represented by a peeled chrec, i.e. the
1455 first iteration, EV_FN has the value INIT_COND, then
1456 all the other iterations it has the value of ARG.
1457 For the moment, PEELED_CHREC nodes are not built. */
1459 ev_fn = chrec_dont_know;
1461 /* When there are multiple back edges of the loop (which in fact never
1462 happens currently, but nevertheless), merge their evolutions. */
1463 evolution_function = chrec_merge (evolution_function, ev_fn);
1466 if (dump_file && (dump_flags & TDF_DETAILS))
1468 fprintf (dump_file, " (evolution_function = ");
1469 print_generic_expr (dump_file, evolution_function, 0);
1470 fprintf (dump_file, "))\n");
1473 return evolution_function;
1476 /* Given a loop-phi-node, return the initial conditions of the
1477 variable on entry of the loop. When the CCP has propagated
1478 constants into the loop-phi-node, the initial condition is
1479 instantiated, otherwise the initial condition is kept symbolic.
1480 This analyzer does not analyze the evolution outside the current
1481 loop, and leaves this task to the on-demand tree reconstructor. */
1484 analyze_initial_condition (tree loop_phi_node)
1487 tree init_cond = chrec_not_analyzed_yet;
1488 struct loop *loop = bb_for_stmt (loop_phi_node)->loop_father;
1490 if (dump_file && (dump_flags & TDF_DETAILS))
1492 fprintf (dump_file, "(analyze_initial_condition \n");
1493 fprintf (dump_file, " (loop_phi_node = \n");
1494 print_generic_expr (dump_file, loop_phi_node, 0);
1495 fprintf (dump_file, ")\n");
1498 for (i = 0; i < PHI_NUM_ARGS (loop_phi_node); i++)
1500 tree branch = PHI_ARG_DEF (loop_phi_node, i);
1501 basic_block bb = PHI_ARG_EDGE (loop_phi_node, i)->src;
1503 /* When the branch is oriented to the loop's body, it does
1504 not contribute to the initial condition. */
1505 if (flow_bb_inside_loop_p (loop, bb))
1508 if (init_cond == chrec_not_analyzed_yet)
1514 if (TREE_CODE (branch) == SSA_NAME)
1516 init_cond = chrec_dont_know;
1520 init_cond = chrec_merge (init_cond, branch);
1523 /* Ooops -- a loop without an entry??? */
1524 if (init_cond == chrec_not_analyzed_yet)
1525 init_cond = chrec_dont_know;
1527 if (dump_file && (dump_flags & TDF_DETAILS))
1529 fprintf (dump_file, " (init_cond = ");
1530 print_generic_expr (dump_file, init_cond, 0);
1531 fprintf (dump_file, "))\n");
1537 /* Analyze the scalar evolution for LOOP_PHI_NODE. */
1540 interpret_loop_phi (struct loop *loop, tree loop_phi_node)
1543 struct loop *phi_loop = loop_containing_stmt (loop_phi_node);
1546 if (phi_loop != loop)
1548 struct loop *subloop;
1549 tree evolution_fn = analyze_scalar_evolution
1550 (phi_loop, PHI_RESULT (loop_phi_node));
1552 /* Dive one level deeper. */
1553 subloop = superloop_at_depth (phi_loop, loop_depth (loop) + 1);
1555 /* Interpret the subloop. */
1556 res = compute_overall_effect_of_inner_loop (subloop, evolution_fn);
1560 /* Otherwise really interpret the loop phi. */
1561 init_cond = analyze_initial_condition (loop_phi_node);
1562 res = analyze_evolution_in_loop (loop_phi_node, init_cond);
1567 /* This function merges the branches of a condition-phi-node,
1568 contained in the outermost loop, and whose arguments are already
1572 interpret_condition_phi (struct loop *loop, tree condition_phi)
1575 tree res = chrec_not_analyzed_yet;
1577 for (i = 0; i < PHI_NUM_ARGS (condition_phi); i++)
1581 if (backedge_phi_arg_p (condition_phi, i))
1583 res = chrec_dont_know;
1587 branch_chrec = analyze_scalar_evolution
1588 (loop, PHI_ARG_DEF (condition_phi, i));
1590 res = chrec_merge (res, branch_chrec);
1596 /* Interpret the right hand side of a GIMPLE_MODIFY_STMT OPND1. If we didn't
1597 analyze this node before, follow the definitions until ending
1598 either on an analyzed GIMPLE_MODIFY_STMT, or on a loop-phi-node. On the
1599 return path, this function propagates evolutions (ala constant copy
1600 propagation). OPND1 is not a GIMPLE expression because we could
1601 analyze the effect of an inner loop: see interpret_loop_phi. */
1604 interpret_rhs_modify_stmt (struct loop *loop, tree at_stmt,
1605 tree opnd1, tree type)
1607 tree res, opnd10, opnd11, chrec10, chrec11;
1609 if (is_gimple_min_invariant (opnd1))
1610 return chrec_convert (type, opnd1, at_stmt);
1612 switch (TREE_CODE (opnd1))
1615 opnd10 = TREE_OPERAND (opnd1, 0);
1616 opnd11 = TREE_OPERAND (opnd1, 1);
1617 chrec10 = analyze_scalar_evolution (loop, opnd10);
1618 chrec11 = analyze_scalar_evolution (loop, opnd11);
1619 chrec10 = chrec_convert (type, chrec10, at_stmt);
1620 chrec11 = chrec_convert (type, chrec11, at_stmt);
1621 res = chrec_fold_plus (type, chrec10, chrec11);
1625 opnd10 = TREE_OPERAND (opnd1, 0);
1626 opnd11 = TREE_OPERAND (opnd1, 1);
1627 chrec10 = analyze_scalar_evolution (loop, opnd10);
1628 chrec11 = analyze_scalar_evolution (loop, opnd11);
1629 chrec10 = chrec_convert (type, chrec10, at_stmt);
1630 chrec11 = chrec_convert (type, chrec11, at_stmt);
1631 res = chrec_fold_minus (type, chrec10, chrec11);
1635 opnd10 = TREE_OPERAND (opnd1, 0);
1636 chrec10 = analyze_scalar_evolution (loop, opnd10);
1637 chrec10 = chrec_convert (type, chrec10, at_stmt);
1638 /* TYPE may be integer, real or complex, so use fold_convert. */
1639 res = chrec_fold_multiply (type, chrec10,
1640 fold_convert (type, integer_minus_one_node));
1644 opnd10 = TREE_OPERAND (opnd1, 0);
1645 opnd11 = TREE_OPERAND (opnd1, 1);
1646 chrec10 = analyze_scalar_evolution (loop, opnd10);
1647 chrec11 = analyze_scalar_evolution (loop, opnd11);
1648 chrec10 = chrec_convert (type, chrec10, at_stmt);
1649 chrec11 = chrec_convert (type, chrec11, at_stmt);
1650 res = chrec_fold_multiply (type, chrec10, chrec11);
1654 res = chrec_convert (type, analyze_scalar_evolution (loop, opnd1),
1659 opnd10 = ASSERT_EXPR_VAR (opnd1);
1660 res = chrec_convert (type, analyze_scalar_evolution (loop, opnd10),
1666 opnd10 = TREE_OPERAND (opnd1, 0);
1667 chrec10 = analyze_scalar_evolution (loop, opnd10);
1668 res = chrec_convert (type, chrec10, at_stmt);
1672 res = chrec_dont_know;
1681 /* This section contains all the entry points:
1682 - number_of_iterations_in_loop,
1683 - analyze_scalar_evolution,
1684 - instantiate_parameters.
1687 /* Compute and return the evolution function in WRTO_LOOP, the nearest
1688 common ancestor of DEF_LOOP and USE_LOOP. */
1691 compute_scalar_evolution_in_loop (struct loop *wrto_loop,
1692 struct loop *def_loop,
1696 if (def_loop == wrto_loop)
1699 def_loop = superloop_at_depth (def_loop, loop_depth (wrto_loop) + 1);
1700 res = compute_overall_effect_of_inner_loop (def_loop, ev);
1702 return analyze_scalar_evolution_1 (wrto_loop, res, chrec_not_analyzed_yet);
1705 /* Folds EXPR, if it is a cast to pointer, assuming that the created
1706 polynomial_chrec does not wrap. */
1709 fold_used_pointer_cast (tree expr)
1712 tree type, inner_type;
1714 if (TREE_CODE (expr) != NOP_EXPR && TREE_CODE (expr) != CONVERT_EXPR)
1717 op = TREE_OPERAND (expr, 0);
1718 if (TREE_CODE (op) != POLYNOMIAL_CHREC)
1721 type = TREE_TYPE (expr);
1722 inner_type = TREE_TYPE (op);
1724 if (!INTEGRAL_TYPE_P (inner_type)
1725 || TYPE_PRECISION (inner_type) != TYPE_PRECISION (type))
1728 return build_polynomial_chrec (CHREC_VARIABLE (op),
1729 chrec_convert (type, CHREC_LEFT (op), NULL_TREE),
1730 chrec_convert (type, CHREC_RIGHT (op), NULL_TREE));
1733 /* Returns true if EXPR is an expression corresponding to offset of pointer
1737 pointer_offset_p (tree expr)
1739 if (TREE_CODE (expr) == INTEGER_CST)
1742 if ((TREE_CODE (expr) == NOP_EXPR || TREE_CODE (expr) == CONVERT_EXPR)
1743 && INTEGRAL_TYPE_P (TREE_TYPE (TREE_OPERAND (expr, 0))))
1749 /* EXPR is a scalar evolution of a pointer that is dereferenced or used in
1750 comparison. This means that it must point to a part of some object in
1751 memory, which enables us to argue about overflows and possibly simplify
1752 the EXPR. AT_STMT is the statement in which this conversion has to be
1753 performed. Returns the simplified value.
1760 for (i = -n; i < n; i++)
1763 We generate the following code (assuming that size of int and size_t is
1766 for (i = -n; i < n; i++)
1771 tmp1 = (size_t) i; (1)
1772 tmp2 = 4 * tmp1; (2)
1773 tmp3 = (int *) tmp2; (3)
1774 tmp4 = p + tmp3; (4)
1779 We in general assume that pointer arithmetics does not overflow (since its
1780 behavior is undefined in that case). One of the problems is that our
1781 translation does not capture this property very well -- (int *) is
1782 considered unsigned, hence the computation in (4) does overflow if i is
1785 This impreciseness creates complications in scev analysis. The scalar
1786 evolution of i is [-n, +, 1]. Since int and size_t have the same precision
1787 (in this example), and size_t is unsigned (so we do not care about
1788 overflows), we succeed to derive that scev of tmp1 is [(size_t) -n, +, 1]
1789 and scev of tmp2 is [4 * (size_t) -n, +, 4]. With tmp3, we run into
1790 problem -- [(int *) (4 * (size_t) -n), +, 4] wraps, and since we on several
1791 places assume that this is not the case for scevs with pointer type, we
1792 cannot use this scev for tmp3; hence, its scev is
1793 (int *) [(4 * (size_t) -n), +, 4], and scev of tmp4 is
1794 p + (int *) [(4 * (size_t) -n), +, 4]. Most of the optimizers are unable to
1795 work with scevs of this shape.
1797 However, since tmp4 is dereferenced, all its values must belong to a single
1798 object, and taking into account that the precision of int * and size_t is
1799 the same, it is impossible for its scev to wrap. Hence, we can derive that
1800 its evolution is [p + (int *) (4 * (size_t) -n), +, 4], which the optimizers
1803 ??? Maybe we should use different representation for pointer arithmetics,
1804 however that is a long-term project with a lot of potential for creating
1808 fold_used_pointer (tree expr, tree at_stmt)
1810 tree op0, op1, new0, new1;
1811 enum tree_code code = TREE_CODE (expr);
1813 if (code == PLUS_EXPR
1814 || code == MINUS_EXPR)
1816 op0 = TREE_OPERAND (expr, 0);
1817 op1 = TREE_OPERAND (expr, 1);
1819 if (pointer_offset_p (op1))
1821 new0 = fold_used_pointer (op0, at_stmt);
1822 new1 = fold_used_pointer_cast (op1);
1824 else if (code == PLUS_EXPR && pointer_offset_p (op0))
1826 new0 = fold_used_pointer_cast (op0);
1827 new1 = fold_used_pointer (op1, at_stmt);
1832 if (new0 == op0 && new1 == op1)
1835 new0 = chrec_convert (TREE_TYPE (expr), new0, at_stmt);
1836 new1 = chrec_convert (TREE_TYPE (expr), new1, at_stmt);
1838 if (code == PLUS_EXPR)
1839 expr = chrec_fold_plus (TREE_TYPE (expr), new0, new1);
1841 expr = chrec_fold_minus (TREE_TYPE (expr), new0, new1);
1846 return fold_used_pointer_cast (expr);
1849 /* Returns true if PTR is dereferenced, or used in comparison. */
1852 pointer_used_p (tree ptr)
1854 use_operand_p use_p;
1855 imm_use_iterator imm_iter;
1857 struct ptr_info_def *pi = get_ptr_info (ptr);
1859 /* Check whether the pointer has a memory tag; if it does, it is
1860 (or at least used to be) dereferenced. */
1861 if ((pi != NULL && pi->name_mem_tag != NULL)
1862 || symbol_mem_tag (SSA_NAME_VAR (ptr)))
1865 FOR_EACH_IMM_USE_FAST (use_p, imm_iter, ptr)
1867 stmt = USE_STMT (use_p);
1868 if (TREE_CODE (stmt) == COND_EXPR)
1871 if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
1874 rhs = GIMPLE_STMT_OPERAND (stmt, 1);
1875 if (!COMPARISON_CLASS_P (rhs))
1878 if (GIMPLE_STMT_OPERAND (stmt, 0) == ptr
1879 || GIMPLE_STMT_OPERAND (stmt, 1) == ptr)
1886 /* Helper recursive function. */
1889 analyze_scalar_evolution_1 (struct loop *loop, tree var, tree res)
1891 tree def, type = TREE_TYPE (var);
1893 struct loop *def_loop;
1895 if (loop == NULL || TREE_CODE (type) == VECTOR_TYPE)
1896 return chrec_dont_know;
1898 if (TREE_CODE (var) != SSA_NAME)
1899 return interpret_rhs_modify_stmt (loop, NULL_TREE, var, type);
1901 def = SSA_NAME_DEF_STMT (var);
1902 bb = bb_for_stmt (def);
1903 def_loop = bb ? bb->loop_father : NULL;
1906 || !flow_bb_inside_loop_p (loop, bb))
1908 /* Keep the symbolic form. */
1913 if (res != chrec_not_analyzed_yet)
1915 if (loop != bb->loop_father)
1916 res = compute_scalar_evolution_in_loop
1917 (find_common_loop (loop, bb->loop_father), bb->loop_father, res);
1922 if (loop != def_loop)
1924 res = analyze_scalar_evolution_1 (def_loop, var, chrec_not_analyzed_yet);
1925 res = compute_scalar_evolution_in_loop (loop, def_loop, res);
1930 switch (TREE_CODE (def))
1932 case GIMPLE_MODIFY_STMT:
1933 res = interpret_rhs_modify_stmt (loop, def,
1934 GIMPLE_STMT_OPERAND (def, 1), type);
1936 if (POINTER_TYPE_P (type)
1937 && !automatically_generated_chrec_p (res)
1938 && pointer_used_p (var))
1939 res = fold_used_pointer (res, def);
1943 if (loop_phi_node_p (def))
1944 res = interpret_loop_phi (loop, def);
1946 res = interpret_condition_phi (loop, def);
1950 res = chrec_dont_know;
1956 /* Keep the symbolic form. */
1957 if (res == chrec_dont_know)
1960 if (loop == def_loop)
1961 set_scalar_evolution (var, res);
1966 /* Entry point for the scalar evolution analyzer.
1967 Analyzes and returns the scalar evolution of the ssa_name VAR.
1968 LOOP_NB is the identifier number of the loop in which the variable
1971 Example of use: having a pointer VAR to a SSA_NAME node, STMT a
1972 pointer to the statement that uses this variable, in order to
1973 determine the evolution function of the variable, use the following
1976 unsigned loop_nb = loop_containing_stmt (stmt)->num;
1977 tree chrec_with_symbols = analyze_scalar_evolution (loop_nb, var);
1978 tree chrec_instantiated = instantiate_parameters
1979 (loop_nb, chrec_with_symbols);
1983 analyze_scalar_evolution (struct loop *loop, tree var)
1987 if (dump_file && (dump_flags & TDF_DETAILS))
1989 fprintf (dump_file, "(analyze_scalar_evolution \n");
1990 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
1991 fprintf (dump_file, " (scalar = ");
1992 print_generic_expr (dump_file, var, 0);
1993 fprintf (dump_file, ")\n");
1996 res = analyze_scalar_evolution_1 (loop, var, get_scalar_evolution (var));
1998 if (TREE_CODE (var) == SSA_NAME && res == chrec_dont_know)
2001 if (dump_file && (dump_flags & TDF_DETAILS))
2002 fprintf (dump_file, ")\n");
2007 /* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to
2008 WRTO_LOOP (which should be a superloop of both USE_LOOP and definition
2011 FOLDED_CASTS is set to true if resolve_mixers used
2012 chrec_convert_aggressive (TODO -- not really, we are way too conservative
2013 at the moment in order to keep things simple). */
2016 analyze_scalar_evolution_in_loop (struct loop *wrto_loop, struct loop *use_loop,
2017 tree version, bool *folded_casts)
2020 tree ev = version, tmp;
2023 *folded_casts = false;
2026 tmp = analyze_scalar_evolution (use_loop, ev);
2027 ev = resolve_mixers (use_loop, tmp);
2029 if (folded_casts && tmp != ev)
2030 *folded_casts = true;
2032 if (use_loop == wrto_loop)
2035 /* If the value of the use changes in the inner loop, we cannot express
2036 its value in the outer loop (we might try to return interval chrec,
2037 but we do not have a user for it anyway) */
2038 if (!no_evolution_in_loop_p (ev, use_loop->num, &val)
2040 return chrec_dont_know;
2042 use_loop = loop_outer (use_loop);
2046 /* Returns instantiated value for VERSION in CACHE. */
2049 get_instantiated_value (htab_t cache, tree version)
2051 struct scev_info_str *info, pattern;
2053 pattern.var = version;
2054 info = (struct scev_info_str *) htab_find (cache, &pattern);
2062 /* Sets instantiated value for VERSION to VAL in CACHE. */
2065 set_instantiated_value (htab_t cache, tree version, tree val)
2067 struct scev_info_str *info, pattern;
2070 pattern.var = version;
2071 slot = htab_find_slot (cache, &pattern, INSERT);
2074 *slot = new_scev_info_str (version);
2075 info = (struct scev_info_str *) *slot;
2079 /* Return the closed_loop_phi node for VAR. If there is none, return
2083 loop_closed_phi_def (tree var)
2089 if (var == NULL_TREE
2090 || TREE_CODE (var) != SSA_NAME)
2093 loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var));
2094 exit = single_exit (loop);
2098 for (phi = phi_nodes (exit->dest); phi; phi = PHI_CHAIN (phi))
2099 if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var)
2100 return PHI_RESULT (phi);
2105 /* Analyze all the parameters of the chrec that were left under a symbolic form,
2106 with respect to LOOP. CHREC is the chrec to instantiate. CACHE is the cache
2107 of already instantiated values. FLAGS modify the way chrecs are
2108 instantiated. SIZE_EXPR is used for computing the size of the expression to
2109 be instantiated, and to stop if it exceeds some limit. */
2111 /* Values for FLAGS. */
2114 INSERT_SUPERLOOP_CHRECS = 1, /* Loop invariants are replaced with chrecs
2116 FOLD_CONVERSIONS = 2 /* The conversions that may wrap in
2117 signed/pointer type are folded, as long as the
2118 value of the chrec is preserved. */
2122 instantiate_parameters_1 (struct loop *loop, tree chrec, int flags, htab_t cache,
2125 tree res, op0, op1, op2;
2127 struct loop *def_loop;
2128 tree type = chrec_type (chrec);
2130 /* Give up if the expression is larger than the MAX that we allow. */
2131 if (size_expr++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
2132 return chrec_dont_know;
2134 if (automatically_generated_chrec_p (chrec)
2135 || is_gimple_min_invariant (chrec))
2138 switch (TREE_CODE (chrec))
2141 def_bb = bb_for_stmt (SSA_NAME_DEF_STMT (chrec));
2143 /* A parameter (or loop invariant and we do not want to include
2144 evolutions in outer loops), nothing to do. */
2146 || (!(flags & INSERT_SUPERLOOP_CHRECS)
2147 && !flow_bb_inside_loop_p (loop, def_bb)))
2150 /* We cache the value of instantiated variable to avoid exponential
2151 time complexity due to reevaluations. We also store the convenient
2152 value in the cache in order to prevent infinite recursion -- we do
2153 not want to instantiate the SSA_NAME if it is in a mixer
2154 structure. This is used for avoiding the instantiation of
2155 recursively defined functions, such as:
2157 | a_2 -> {0, +, 1, +, a_2}_1 */
2159 res = get_instantiated_value (cache, chrec);
2163 /* Store the convenient value for chrec in the structure. If it
2164 is defined outside of the loop, we may just leave it in symbolic
2165 form, otherwise we need to admit that we do not know its behavior
2167 res = !flow_bb_inside_loop_p (loop, def_bb) ? chrec : chrec_dont_know;
2168 set_instantiated_value (cache, chrec, res);
2170 /* To make things even more complicated, instantiate_parameters_1
2171 calls analyze_scalar_evolution that may call # of iterations
2172 analysis that may in turn call instantiate_parameters_1 again.
2173 To prevent the infinite recursion, keep also the bitmap of
2174 ssa names that are being instantiated globally. */
2175 if (bitmap_bit_p (already_instantiated, SSA_NAME_VERSION (chrec)))
2178 def_loop = find_common_loop (loop, def_bb->loop_father);
2180 /* If the analysis yields a parametric chrec, instantiate the
2182 bitmap_set_bit (already_instantiated, SSA_NAME_VERSION (chrec));
2183 res = analyze_scalar_evolution (def_loop, chrec);
2185 /* Don't instantiate loop-closed-ssa phi nodes. */
2186 if (TREE_CODE (res) == SSA_NAME
2187 && (loop_containing_stmt (SSA_NAME_DEF_STMT (res)) == NULL
2188 || (loop_depth (loop_containing_stmt (SSA_NAME_DEF_STMT (res)))
2189 > loop_depth (def_loop))))
2192 res = loop_closed_phi_def (chrec);
2196 if (res == NULL_TREE)
2197 res = chrec_dont_know;
2200 else if (res != chrec_dont_know)
2201 res = instantiate_parameters_1 (loop, res, flags, cache, size_expr);
2203 bitmap_clear_bit (already_instantiated, SSA_NAME_VERSION (chrec));
2205 /* Store the correct value to the cache. */
2206 set_instantiated_value (cache, chrec, res);
2209 case POLYNOMIAL_CHREC:
2210 op0 = instantiate_parameters_1 (loop, CHREC_LEFT (chrec),
2211 flags, cache, size_expr);
2212 if (op0 == chrec_dont_know)
2213 return chrec_dont_know;
2215 op1 = instantiate_parameters_1 (loop, CHREC_RIGHT (chrec),
2216 flags, cache, size_expr);
2217 if (op1 == chrec_dont_know)
2218 return chrec_dont_know;
2220 if (CHREC_LEFT (chrec) != op0
2221 || CHREC_RIGHT (chrec) != op1)
2223 op1 = chrec_convert (chrec_type (op0), op1, NULL_TREE);
2224 chrec = build_polynomial_chrec (CHREC_VARIABLE (chrec), op0, op1);
2229 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2230 flags, cache, size_expr);
2231 if (op0 == chrec_dont_know)
2232 return chrec_dont_know;
2234 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2235 flags, cache, size_expr);
2236 if (op1 == chrec_dont_know)
2237 return chrec_dont_know;
2239 if (TREE_OPERAND (chrec, 0) != op0
2240 || TREE_OPERAND (chrec, 1) != op1)
2242 op0 = chrec_convert (type, op0, NULL_TREE);
2243 op1 = chrec_convert (type, op1, NULL_TREE);
2244 chrec = chrec_fold_plus (type, op0, op1);
2249 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2250 flags, cache, size_expr);
2251 if (op0 == chrec_dont_know)
2252 return chrec_dont_know;
2254 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2255 flags, cache, size_expr);
2256 if (op1 == chrec_dont_know)
2257 return chrec_dont_know;
2259 if (TREE_OPERAND (chrec, 0) != op0
2260 || TREE_OPERAND (chrec, 1) != op1)
2262 op0 = chrec_convert (type, op0, NULL_TREE);
2263 op1 = chrec_convert (type, op1, NULL_TREE);
2264 chrec = chrec_fold_minus (type, op0, op1);
2269 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2270 flags, cache, size_expr);
2271 if (op0 == chrec_dont_know)
2272 return chrec_dont_know;
2274 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2275 flags, cache, size_expr);
2276 if (op1 == chrec_dont_know)
2277 return chrec_dont_know;
2279 if (TREE_OPERAND (chrec, 0) != op0
2280 || TREE_OPERAND (chrec, 1) != op1)
2282 op0 = chrec_convert (type, op0, NULL_TREE);
2283 op1 = chrec_convert (type, op1, NULL_TREE);
2284 chrec = chrec_fold_multiply (type, op0, op1);
2290 case NON_LVALUE_EXPR:
2291 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2292 flags, cache, size_expr);
2293 if (op0 == chrec_dont_know)
2294 return chrec_dont_know;
2296 if (flags & FOLD_CONVERSIONS)
2298 tree tmp = chrec_convert_aggressive (TREE_TYPE (chrec), op0);
2303 if (op0 == TREE_OPERAND (chrec, 0))
2306 /* If we used chrec_convert_aggressive, we can no longer assume that
2307 signed chrecs do not overflow, as chrec_convert does, so avoid
2308 calling it in that case. */
2309 if (flags & FOLD_CONVERSIONS)
2310 return fold_convert (TREE_TYPE (chrec), op0);
2312 return chrec_convert (TREE_TYPE (chrec), op0, NULL_TREE);
2314 case SCEV_NOT_KNOWN:
2315 return chrec_dont_know;
2324 gcc_assert (!VL_EXP_CLASS_P (chrec));
2325 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
2328 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2329 flags, cache, size_expr);
2330 if (op0 == chrec_dont_know)
2331 return chrec_dont_know;
2333 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2334 flags, cache, size_expr);
2335 if (op1 == chrec_dont_know)
2336 return chrec_dont_know;
2338 op2 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 2),
2339 flags, cache, size_expr);
2340 if (op2 == chrec_dont_know)
2341 return chrec_dont_know;
2343 if (op0 == TREE_OPERAND (chrec, 0)
2344 && op1 == TREE_OPERAND (chrec, 1)
2345 && op2 == TREE_OPERAND (chrec, 2))
2348 return fold_build3 (TREE_CODE (chrec),
2349 TREE_TYPE (chrec), op0, op1, op2);
2352 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2353 flags, cache, size_expr);
2354 if (op0 == chrec_dont_know)
2355 return chrec_dont_know;
2357 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2358 flags, cache, size_expr);
2359 if (op1 == chrec_dont_know)
2360 return chrec_dont_know;
2362 if (op0 == TREE_OPERAND (chrec, 0)
2363 && op1 == TREE_OPERAND (chrec, 1))
2365 return fold_build2 (TREE_CODE (chrec), TREE_TYPE (chrec), op0, op1);
2368 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2369 flags, cache, size_expr);
2370 if (op0 == chrec_dont_know)
2371 return chrec_dont_know;
2372 if (op0 == TREE_OPERAND (chrec, 0))
2374 return fold_build1 (TREE_CODE (chrec), TREE_TYPE (chrec), op0);
2383 /* Too complicated to handle. */
2384 return chrec_dont_know;
2387 /* Analyze all the parameters of the chrec that were left under a
2388 symbolic form. LOOP is the loop in which symbolic names have to
2389 be analyzed and instantiated. */
2392 instantiate_parameters (struct loop *loop,
2396 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2398 if (dump_file && (dump_flags & TDF_DETAILS))
2400 fprintf (dump_file, "(instantiate_parameters \n");
2401 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
2402 fprintf (dump_file, " (chrec = ");
2403 print_generic_expr (dump_file, chrec, 0);
2404 fprintf (dump_file, ")\n");
2407 res = instantiate_parameters_1 (loop, chrec, INSERT_SUPERLOOP_CHRECS, cache,
2410 if (dump_file && (dump_flags & TDF_DETAILS))
2412 fprintf (dump_file, " (res = ");
2413 print_generic_expr (dump_file, res, 0);
2414 fprintf (dump_file, "))\n");
2417 htab_delete (cache);
2422 /* Similar to instantiate_parameters, but does not introduce the
2423 evolutions in outer loops for LOOP invariants in CHREC, and does not
2424 care about causing overflows, as long as they do not affect value
2425 of an expression. */
2428 resolve_mixers (struct loop *loop, tree chrec)
2430 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2431 tree ret = instantiate_parameters_1 (loop, chrec, FOLD_CONVERSIONS, cache, 0);
2432 htab_delete (cache);
2436 /* Entry point for the analysis of the number of iterations pass.
2437 This function tries to safely approximate the number of iterations
2438 the loop will run. When this property is not decidable at compile
2439 time, the result is chrec_dont_know. Otherwise the result is
2440 a scalar or a symbolic parameter.
2442 Example of analysis: suppose that the loop has an exit condition:
2444 "if (b > 49) goto end_loop;"
2446 and that in a previous analysis we have determined that the
2447 variable 'b' has an evolution function:
2449 "EF = {23, +, 5}_2".
2451 When we evaluate the function at the point 5, i.e. the value of the
2452 variable 'b' after 5 iterations in the loop, we have EF (5) = 48,
2453 and EF (6) = 53. In this case the value of 'b' on exit is '53' and
2454 the loop body has been executed 6 times. */
2457 number_of_latch_executions (struct loop *loop)
2461 struct tree_niter_desc niter_desc;
2463 /* Determine whether the number_of_iterations_in_loop has already
2465 res = loop->nb_iterations;
2468 res = chrec_dont_know;
2470 if (dump_file && (dump_flags & TDF_DETAILS))
2471 fprintf (dump_file, "(number_of_iterations_in_loop\n");
2473 exit = single_exit (loop);
2477 if (!number_of_iterations_exit (loop, exit, &niter_desc, false))
2480 type = TREE_TYPE (niter_desc.niter);
2481 if (integer_nonzerop (niter_desc.may_be_zero))
2482 res = build_int_cst (type, 0);
2483 else if (integer_zerop (niter_desc.may_be_zero))
2484 res = niter_desc.niter;
2486 res = chrec_dont_know;
2489 return set_nb_iterations_in_loop (loop, res);
2492 /* Returns the number of executions of the exit condition of LOOP,
2493 i.e., the number by one higher than number_of_latch_executions.
2494 Note that unline number_of_latch_executions, this number does
2495 not necessarily fit in the unsigned variant of the type of
2496 the control variable -- if the number of iterations is a constant,
2497 we return chrec_dont_know if adding one to number_of_latch_executions
2498 overflows; however, in case the number of iterations is symbolic
2499 expression, the caller is responsible for dealing with this
2500 the possible overflow. */
2503 number_of_exit_cond_executions (struct loop *loop)
2505 tree ret = number_of_latch_executions (loop);
2506 tree type = chrec_type (ret);
2508 if (chrec_contains_undetermined (ret))
2511 ret = chrec_fold_plus (type, ret, build_int_cst (type, 1));
2512 if (TREE_CODE (ret) == INTEGER_CST
2513 && TREE_OVERFLOW (ret))
2514 return chrec_dont_know;
2519 /* One of the drivers for testing the scalar evolutions analysis.
2520 This function computes the number of iterations for all the loops
2521 from the EXIT_CONDITIONS array. */
2524 number_of_iterations_for_all_loops (VEC(tree,heap) **exit_conditions)
2527 unsigned nb_chrec_dont_know_loops = 0;
2528 unsigned nb_static_loops = 0;
2531 for (i = 0; VEC_iterate (tree, *exit_conditions, i, cond); i++)
2533 tree res = number_of_latch_executions (loop_containing_stmt (cond));
2534 if (chrec_contains_undetermined (res))
2535 nb_chrec_dont_know_loops++;
2542 fprintf (dump_file, "\n(\n");
2543 fprintf (dump_file, "-----------------------------------------\n");
2544 fprintf (dump_file, "%d\tnb_chrec_dont_know_loops\n", nb_chrec_dont_know_loops);
2545 fprintf (dump_file, "%d\tnb_static_loops\n", nb_static_loops);
2546 fprintf (dump_file, "%d\tnb_total_loops\n", number_of_loops ());
2547 fprintf (dump_file, "-----------------------------------------\n");
2548 fprintf (dump_file, ")\n\n");
2550 print_loop_ir (dump_file);
2556 /* Counters for the stats. */
2562 unsigned nb_affine_multivar;
2563 unsigned nb_higher_poly;
2564 unsigned nb_chrec_dont_know;
2565 unsigned nb_undetermined;
2568 /* Reset the counters. */
2571 reset_chrecs_counters (struct chrec_stats *stats)
2573 stats->nb_chrecs = 0;
2574 stats->nb_affine = 0;
2575 stats->nb_affine_multivar = 0;
2576 stats->nb_higher_poly = 0;
2577 stats->nb_chrec_dont_know = 0;
2578 stats->nb_undetermined = 0;
2581 /* Dump the contents of a CHREC_STATS structure. */
2584 dump_chrecs_stats (FILE *file, struct chrec_stats *stats)
2586 fprintf (file, "\n(\n");
2587 fprintf (file, "-----------------------------------------\n");
2588 fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine);
2589 fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar);
2590 fprintf (file, "%d\tdegree greater than 2 polynomials\n",
2591 stats->nb_higher_poly);
2592 fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know);
2593 fprintf (file, "-----------------------------------------\n");
2594 fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs);
2595 fprintf (file, "%d\twith undetermined coefficients\n",
2596 stats->nb_undetermined);
2597 fprintf (file, "-----------------------------------------\n");
2598 fprintf (file, "%d\tchrecs in the scev database\n",
2599 (int) htab_elements (scalar_evolution_info));
2600 fprintf (file, "%d\tsets in the scev database\n", nb_set_scev);
2601 fprintf (file, "%d\tgets in the scev database\n", nb_get_scev);
2602 fprintf (file, "-----------------------------------------\n");
2603 fprintf (file, ")\n\n");
2606 /* Gather statistics about CHREC. */
2609 gather_chrec_stats (tree chrec, struct chrec_stats *stats)
2611 if (dump_file && (dump_flags & TDF_STATS))
2613 fprintf (dump_file, "(classify_chrec ");
2614 print_generic_expr (dump_file, chrec, 0);
2615 fprintf (dump_file, "\n");
2620 if (chrec == NULL_TREE)
2622 stats->nb_undetermined++;
2626 switch (TREE_CODE (chrec))
2628 case POLYNOMIAL_CHREC:
2629 if (evolution_function_is_affine_p (chrec))
2631 if (dump_file && (dump_flags & TDF_STATS))
2632 fprintf (dump_file, " affine_univariate\n");
2635 else if (evolution_function_is_affine_multivariate_p (chrec, 0))
2637 if (dump_file && (dump_flags & TDF_STATS))
2638 fprintf (dump_file, " affine_multivariate\n");
2639 stats->nb_affine_multivar++;
2643 if (dump_file && (dump_flags & TDF_STATS))
2644 fprintf (dump_file, " higher_degree_polynomial\n");
2645 stats->nb_higher_poly++;
2654 if (chrec_contains_undetermined (chrec))
2656 if (dump_file && (dump_flags & TDF_STATS))
2657 fprintf (dump_file, " undetermined\n");
2658 stats->nb_undetermined++;
2661 if (dump_file && (dump_flags & TDF_STATS))
2662 fprintf (dump_file, ")\n");
2665 /* One of the drivers for testing the scalar evolutions analysis.
2666 This function analyzes the scalar evolution of all the scalars
2667 defined as loop phi nodes in one of the loops from the
2668 EXIT_CONDITIONS array.
2670 TODO Optimization: A loop is in canonical form if it contains only
2671 a single scalar loop phi node. All the other scalars that have an
2672 evolution in the loop are rewritten in function of this single
2673 index. This allows the parallelization of the loop. */
2676 analyze_scalar_evolution_for_all_loop_phi_nodes (VEC(tree,heap) **exit_conditions)
2679 struct chrec_stats stats;
2682 reset_chrecs_counters (&stats);
2684 for (i = 0; VEC_iterate (tree, *exit_conditions, i, cond); i++)
2690 loop = loop_containing_stmt (cond);
2693 for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
2694 if (is_gimple_reg (PHI_RESULT (phi)))
2696 chrec = instantiate_parameters
2698 analyze_scalar_evolution (loop, PHI_RESULT (phi)));
2700 if (dump_file && (dump_flags & TDF_STATS))
2701 gather_chrec_stats (chrec, &stats);
2705 if (dump_file && (dump_flags & TDF_STATS))
2706 dump_chrecs_stats (dump_file, &stats);
2709 /* Callback for htab_traverse, gathers information on chrecs in the
2713 gather_stats_on_scev_database_1 (void **slot, void *stats)
2715 struct scev_info_str *entry = (struct scev_info_str *) *slot;
2717 gather_chrec_stats (entry->chrec, (struct chrec_stats *) stats);
2722 /* Classify the chrecs of the whole database. */
2725 gather_stats_on_scev_database (void)
2727 struct chrec_stats stats;
2732 reset_chrecs_counters (&stats);
2734 htab_traverse (scalar_evolution_info, gather_stats_on_scev_database_1,
2737 dump_chrecs_stats (dump_file, &stats);
2745 initialize_scalar_evolutions_analyzer (void)
2747 /* The elements below are unique. */
2748 if (chrec_dont_know == NULL_TREE)
2750 chrec_not_analyzed_yet = NULL_TREE;
2751 chrec_dont_know = make_node (SCEV_NOT_KNOWN);
2752 chrec_known = make_node (SCEV_KNOWN);
2753 TREE_TYPE (chrec_dont_know) = void_type_node;
2754 TREE_TYPE (chrec_known) = void_type_node;
2758 /* Initialize the analysis of scalar evolutions for LOOPS. */
2761 scev_initialize (void)
2766 scalar_evolution_info = htab_create_alloc (100,
2772 already_instantiated = BITMAP_ALLOC (NULL);
2774 initialize_scalar_evolutions_analyzer ();
2776 FOR_EACH_LOOP (li, loop, 0)
2778 loop->nb_iterations = NULL_TREE;
2782 /* Cleans up the information cached by the scalar evolutions analysis. */
2790 if (!scalar_evolution_info || !current_loops)
2793 htab_empty (scalar_evolution_info);
2794 FOR_EACH_LOOP (li, loop, 0)
2796 loop->nb_iterations = NULL_TREE;
2800 /* Checks whether OP behaves as a simple affine iv of LOOP in STMT and returns
2801 its base and step in IV if possible. If ALLOW_NONCONSTANT_STEP is true, we
2802 want step to be invariant in LOOP. Otherwise we require it to be an
2803 integer constant. IV->no_overflow is set to true if we are sure the iv cannot
2804 overflow (e.g. because it is computed in signed arithmetics). */
2807 simple_iv (struct loop *loop, tree stmt, tree op, affine_iv *iv,
2808 bool allow_nonconstant_step)
2810 basic_block bb = bb_for_stmt (stmt);
2814 iv->base = NULL_TREE;
2815 iv->step = NULL_TREE;
2816 iv->no_overflow = false;
2818 type = TREE_TYPE (op);
2819 if (TREE_CODE (type) != INTEGER_TYPE
2820 && TREE_CODE (type) != POINTER_TYPE)
2823 ev = analyze_scalar_evolution_in_loop (loop, bb->loop_father, op,
2825 if (chrec_contains_undetermined (ev))
2828 if (tree_does_not_contain_chrecs (ev)
2829 && !chrec_contains_symbols_defined_in_loop (ev, loop->num))
2832 iv->step = build_int_cst (TREE_TYPE (ev), 0);
2833 iv->no_overflow = true;
2837 if (TREE_CODE (ev) != POLYNOMIAL_CHREC
2838 || CHREC_VARIABLE (ev) != (unsigned) loop->num)
2841 iv->step = CHREC_RIGHT (ev);
2842 if (allow_nonconstant_step)
2844 if (tree_contains_chrecs (iv->step, NULL)
2845 || chrec_contains_symbols_defined_in_loop (iv->step, loop->num))
2848 else if (TREE_CODE (iv->step) != INTEGER_CST)
2851 iv->base = CHREC_LEFT (ev);
2852 if (tree_contains_chrecs (iv->base, NULL)
2853 || chrec_contains_symbols_defined_in_loop (iv->base, loop->num))
2856 iv->no_overflow = !folded_casts && TYPE_OVERFLOW_UNDEFINED (type);
2861 /* Runs the analysis of scalar evolutions. */
2864 scev_analysis (void)
2866 VEC(tree,heap) *exit_conditions;
2868 exit_conditions = VEC_alloc (tree, heap, 37);
2869 select_loops_exit_conditions (&exit_conditions);
2871 if (dump_file && (dump_flags & TDF_STATS))
2872 analyze_scalar_evolution_for_all_loop_phi_nodes (&exit_conditions);
2874 number_of_iterations_for_all_loops (&exit_conditions);
2875 VEC_free (tree, heap, exit_conditions);
2878 /* Finalize the scalar evolution analysis. */
2881 scev_finalize (void)
2883 if (!scalar_evolution_info)
2885 htab_delete (scalar_evolution_info);
2886 BITMAP_FREE (already_instantiated);
2887 scalar_evolution_info = NULL;
2890 /* Replace ssa names for that scev can prove they are constant by the
2891 appropriate constants. Also perform final value replacement in loops,
2892 in case the replacement expressions are cheap.
2894 We only consider SSA names defined by phi nodes; rest is left to the
2895 ordinary constant propagation pass. */
2898 scev_const_prop (void)
2901 tree name, phi, next_phi, type, ev;
2902 struct loop *loop, *ex_loop;
2903 bitmap ssa_names_to_remove = NULL;
2907 if (number_of_loops () <= 1)
2912 loop = bb->loop_father;
2914 for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
2916 name = PHI_RESULT (phi);
2918 if (!is_gimple_reg (name))
2921 type = TREE_TYPE (name);
2923 if (!POINTER_TYPE_P (type)
2924 && !INTEGRAL_TYPE_P (type))
2927 ev = resolve_mixers (loop, analyze_scalar_evolution (loop, name));
2928 if (!is_gimple_min_invariant (ev)
2929 || !may_propagate_copy (name, ev))
2932 /* Replace the uses of the name. */
2934 replace_uses_by (name, ev);
2936 if (!ssa_names_to_remove)
2937 ssa_names_to_remove = BITMAP_ALLOC (NULL);
2938 bitmap_set_bit (ssa_names_to_remove, SSA_NAME_VERSION (name));
2942 /* Remove the ssa names that were replaced by constants. We do not
2943 remove them directly in the previous cycle, since this
2944 invalidates scev cache. */
2945 if (ssa_names_to_remove)
2949 EXECUTE_IF_SET_IN_BITMAP (ssa_names_to_remove, 0, i, bi)
2951 name = ssa_name (i);
2952 phi = SSA_NAME_DEF_STMT (name);
2954 gcc_assert (TREE_CODE (phi) == PHI_NODE);
2955 remove_phi_node (phi, NULL, true);
2958 BITMAP_FREE (ssa_names_to_remove);
2962 /* Now the regular final value replacement. */
2963 FOR_EACH_LOOP (li, loop, LI_FROM_INNERMOST)
2966 tree def, rslt, ass, niter;
2967 block_stmt_iterator bsi;
2969 /* If we do not know exact number of iterations of the loop, we cannot
2970 replace the final value. */
2971 exit = single_exit (loop);
2975 niter = number_of_latch_executions (loop);
2976 /* We used to check here whether the computation of NITER is expensive,
2977 and avoided final value elimination if that is the case. The problem
2978 is that it is hard to evaluate whether the expression is too
2979 expensive, as we do not know what optimization opportunities the
2980 the elimination of the final value may reveal. Therefore, we now
2981 eliminate the final values of induction variables unconditionally. */
2982 if (niter == chrec_dont_know)
2985 /* Ensure that it is possible to insert new statements somewhere. */
2986 if (!single_pred_p (exit->dest))
2987 split_loop_exit_edge (exit);
2988 bsi = bsi_after_labels (exit->dest);
2990 ex_loop = superloop_at_depth (loop,
2991 loop_depth (exit->dest->loop_father) + 1);
2993 for (phi = phi_nodes (exit->dest); phi; phi = next_phi)
2995 next_phi = PHI_CHAIN (phi);
2996 rslt = PHI_RESULT (phi);
2997 def = PHI_ARG_DEF_FROM_EDGE (phi, exit);
2998 if (!is_gimple_reg (def))
3001 if (!POINTER_TYPE_P (TREE_TYPE (def))
3002 && !INTEGRAL_TYPE_P (TREE_TYPE (def)))
3005 def = analyze_scalar_evolution_in_loop (ex_loop, loop, def, NULL);
3006 def = compute_overall_effect_of_inner_loop (ex_loop, def);
3007 if (!tree_does_not_contain_chrecs (def)
3008 || chrec_contains_symbols_defined_in_loop (def, ex_loop->num)
3009 /* Moving the computation from the loop may prolong life range
3010 of some ssa names, which may cause problems if they appear
3011 on abnormal edges. */
3012 || contains_abnormal_ssa_name_p (def))
3015 /* Eliminate the PHI node and replace it by a computation outside
3017 def = unshare_expr (def);
3018 remove_phi_node (phi, NULL_TREE, false);
3020 ass = build_gimple_modify_stmt (rslt, NULL_TREE);
3021 SSA_NAME_DEF_STMT (rslt) = ass;
3023 block_stmt_iterator dest = bsi;
3024 bsi_insert_before (&dest, ass, BSI_NEW_STMT);
3025 def = force_gimple_operand_bsi (&dest, def, false, NULL_TREE);
3027 GIMPLE_STMT_OPERAND (ass, 1) = def;
3034 #include "gt-tree-scalar-evolution.h"