1 /* Scalar evolution detector.
2 Copyright (C) 2003, 2004, 2005 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);
257 static tree resolve_mixers (struct loop *, tree);
259 /* The cached information about a ssa name VAR, claiming that inside LOOP,
260 the value of VAR can be expressed as CHREC. */
268 /* Counters for the scev database. */
269 static unsigned nb_set_scev = 0;
270 static unsigned nb_get_scev = 0;
272 /* The following trees are unique elements. Thus the comparison of
273 another element to these elements should be done on the pointer to
274 these trees, and not on their value. */
276 /* The SSA_NAMEs that are not yet analyzed are qualified with NULL_TREE. */
277 tree chrec_not_analyzed_yet;
279 /* Reserved to the cases where the analyzer has detected an
280 undecidable property at compile time. */
281 tree chrec_dont_know;
283 /* When the analyzer has detected that a property will never
284 happen, then it qualifies it with chrec_known. */
287 static bitmap already_instantiated;
289 static htab_t scalar_evolution_info;
292 /* Constructs a new SCEV_INFO_STR structure. */
294 static inline struct scev_info_str *
295 new_scev_info_str (tree var)
297 struct scev_info_str *res;
299 res = XNEW (struct scev_info_str);
301 res->chrec = chrec_not_analyzed_yet;
306 /* Computes a hash function for database element ELT. */
309 hash_scev_info (const void *elt)
311 return SSA_NAME_VERSION (((struct scev_info_str *) elt)->var);
314 /* Compares database elements E1 and E2. */
317 eq_scev_info (const void *e1, const void *e2)
319 const struct scev_info_str *elt1 = (const struct scev_info_str *) e1;
320 const struct scev_info_str *elt2 = (const struct scev_info_str *) e2;
322 return elt1->var == elt2->var;
325 /* Deletes database element E. */
328 del_scev_info (void *e)
333 /* Get the index corresponding to VAR in the current LOOP. If
334 it's the first time we ask for this VAR, then we return
335 chrec_not_analyzed_yet for this VAR and return its index. */
338 find_var_scev_info (tree var)
340 struct scev_info_str *res;
341 struct scev_info_str tmp;
345 slot = htab_find_slot (scalar_evolution_info, &tmp, INSERT);
348 *slot = new_scev_info_str (var);
349 res = (struct scev_info_str *) *slot;
354 /* Return true when CHREC contains symbolic names defined in
358 chrec_contains_symbols_defined_in_loop (tree chrec, unsigned loop_nb)
360 if (chrec == NULL_TREE)
363 if (TREE_INVARIANT (chrec))
366 if (TREE_CODE (chrec) == VAR_DECL
367 || TREE_CODE (chrec) == PARM_DECL
368 || TREE_CODE (chrec) == FUNCTION_DECL
369 || TREE_CODE (chrec) == LABEL_DECL
370 || TREE_CODE (chrec) == RESULT_DECL
371 || TREE_CODE (chrec) == FIELD_DECL)
374 if (TREE_CODE (chrec) == SSA_NAME)
376 tree def = SSA_NAME_DEF_STMT (chrec);
377 struct loop *def_loop = loop_containing_stmt (def);
378 struct loop *loop = current_loops->parray[loop_nb];
380 if (def_loop == NULL)
383 if (loop == def_loop || flow_loop_nested_p (loop, def_loop))
389 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
392 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (chrec, 2),
397 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (chrec, 1),
402 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (chrec, 0),
411 /* Return true when PHI is a loop-phi-node. */
414 loop_phi_node_p (tree phi)
416 /* The implementation of this function is based on the following
417 property: "all the loop-phi-nodes of a loop are contained in the
418 loop's header basic block". */
420 return loop_containing_stmt (phi)->header == bb_for_stmt (phi);
423 /* Compute the scalar evolution for EVOLUTION_FN after crossing LOOP.
424 In general, in the case of multivariate evolutions we want to get
425 the evolution in different loops. LOOP specifies the level for
426 which to get the evolution.
430 | for (j = 0; j < 100; j++)
432 | for (k = 0; k < 100; k++)
434 | i = k + j; - Here the value of i is a function of j, k.
436 | ... = i - Here the value of i is a function of j.
438 | ... = i - Here the value of i is a scalar.
444 | i_1 = phi (i_0, i_2)
448 This loop has the same effect as:
449 LOOP_1 has the same effect as:
453 The overall effect of the loop, "i_0 + 20" in the previous example,
454 is obtained by passing in the parameters: LOOP = 1,
455 EVOLUTION_FN = {i_0, +, 2}_1.
459 compute_overall_effect_of_inner_loop (struct loop *loop, tree evolution_fn)
463 if (evolution_fn == chrec_dont_know)
464 return chrec_dont_know;
466 else if (TREE_CODE (evolution_fn) == POLYNOMIAL_CHREC)
468 if (CHREC_VARIABLE (evolution_fn) >= (unsigned) loop->num)
470 struct loop *inner_loop =
471 current_loops->parray[CHREC_VARIABLE (evolution_fn)];
472 tree nb_iter = number_of_iterations_in_loop (inner_loop);
474 if (nb_iter == chrec_dont_know)
475 return chrec_dont_know;
479 tree type = chrec_type (nb_iter);
481 /* Number of iterations is off by one (the ssa name we
482 analyze must be defined before the exit). */
483 nb_iter = chrec_fold_minus (type, nb_iter,
484 build_int_cst (type, 1));
486 /* evolution_fn is the evolution function in LOOP. Get
487 its value in the nb_iter-th iteration. */
488 res = chrec_apply (inner_loop->num, evolution_fn, nb_iter);
490 /* Continue the computation until ending on a parent of LOOP. */
491 return compute_overall_effect_of_inner_loop (loop, res);
498 /* If the evolution function is an invariant, there is nothing to do. */
499 else if (no_evolution_in_loop_p (evolution_fn, loop->num, &val) && val)
503 return chrec_dont_know;
506 /* Determine whether the CHREC is always positive/negative. If the expression
507 cannot be statically analyzed, return false, otherwise set the answer into
511 chrec_is_positive (tree chrec, bool *value)
513 bool value0, value1, value2;
514 tree type, end_value, nb_iter;
516 switch (TREE_CODE (chrec))
518 case POLYNOMIAL_CHREC:
519 if (!chrec_is_positive (CHREC_LEFT (chrec), &value0)
520 || !chrec_is_positive (CHREC_RIGHT (chrec), &value1))
523 /* FIXME -- overflows. */
524 if (value0 == value1)
530 /* Otherwise the chrec is under the form: "{-197, +, 2}_1",
531 and the proof consists in showing that the sign never
532 changes during the execution of the loop, from 0 to
533 loop->nb_iterations. */
534 if (!evolution_function_is_affine_p (chrec))
537 nb_iter = number_of_iterations_in_loop
538 (current_loops->parray[CHREC_VARIABLE (chrec)]);
540 if (chrec_contains_undetermined (nb_iter))
543 type = chrec_type (nb_iter);
544 nb_iter = chrec_fold_minus (type, nb_iter, build_int_cst (type, 1));
547 /* TODO -- If the test is after the exit, we may decrease the number of
548 iterations by one. */
550 nb_iter = chrec_fold_minus (type, nb_iter, build_int_cst (type, 1));
553 end_value = chrec_apply (CHREC_VARIABLE (chrec), chrec, nb_iter);
555 if (!chrec_is_positive (end_value, &value2))
559 return value0 == value1;
562 *value = (tree_int_cst_sgn (chrec) == 1);
570 /* Associate CHREC to SCALAR. */
573 set_scalar_evolution (tree scalar, tree chrec)
577 if (TREE_CODE (scalar) != SSA_NAME)
580 scalar_info = find_var_scev_info (scalar);
584 if (dump_flags & TDF_DETAILS)
586 fprintf (dump_file, "(set_scalar_evolution \n");
587 fprintf (dump_file, " (scalar = ");
588 print_generic_expr (dump_file, scalar, 0);
589 fprintf (dump_file, ")\n (scalar_evolution = ");
590 print_generic_expr (dump_file, chrec, 0);
591 fprintf (dump_file, "))\n");
593 if (dump_flags & TDF_STATS)
597 *scalar_info = chrec;
600 /* Retrieve the chrec associated to SCALAR in the LOOP. */
603 get_scalar_evolution (tree scalar)
609 if (dump_flags & TDF_DETAILS)
611 fprintf (dump_file, "(get_scalar_evolution \n");
612 fprintf (dump_file, " (scalar = ");
613 print_generic_expr (dump_file, scalar, 0);
614 fprintf (dump_file, ")\n");
616 if (dump_flags & TDF_STATS)
620 switch (TREE_CODE (scalar))
623 res = *find_var_scev_info (scalar);
632 res = chrec_not_analyzed_yet;
636 if (dump_file && (dump_flags & TDF_DETAILS))
638 fprintf (dump_file, " (scalar_evolution = ");
639 print_generic_expr (dump_file, res, 0);
640 fprintf (dump_file, "))\n");
646 /* Helper function for add_to_evolution. Returns the evolution
647 function for an assignment of the form "a = b + c", where "a" and
648 "b" are on the strongly connected component. CHREC_BEFORE is the
649 information that we already have collected up to this point.
650 TO_ADD is the evolution of "c".
652 When CHREC_BEFORE has an evolution part in LOOP_NB, add to this
653 evolution the expression TO_ADD, otherwise construct an evolution
654 part for this loop. */
657 add_to_evolution_1 (unsigned loop_nb, tree chrec_before, tree to_add,
660 tree type, left, right;
662 switch (TREE_CODE (chrec_before))
664 case POLYNOMIAL_CHREC:
665 if (CHREC_VARIABLE (chrec_before) <= loop_nb)
669 type = chrec_type (chrec_before);
671 /* When there is no evolution part in this loop, build it. */
672 if (CHREC_VARIABLE (chrec_before) < loop_nb)
676 right = SCALAR_FLOAT_TYPE_P (type)
677 ? build_real (type, dconst0)
678 : build_int_cst (type, 0);
682 var = CHREC_VARIABLE (chrec_before);
683 left = CHREC_LEFT (chrec_before);
684 right = CHREC_RIGHT (chrec_before);
687 to_add = chrec_convert (type, to_add, at_stmt);
688 right = chrec_convert (type, right, at_stmt);
689 right = chrec_fold_plus (type, right, to_add);
690 return build_polynomial_chrec (var, left, right);
694 /* Search the evolution in LOOP_NB. */
695 left = add_to_evolution_1 (loop_nb, CHREC_LEFT (chrec_before),
697 right = CHREC_RIGHT (chrec_before);
698 right = chrec_convert (chrec_type (left), right, at_stmt);
699 return build_polynomial_chrec (CHREC_VARIABLE (chrec_before),
704 /* These nodes do not depend on a loop. */
705 if (chrec_before == chrec_dont_know)
706 return chrec_dont_know;
709 right = chrec_convert (chrec_type (left), to_add, at_stmt);
710 return build_polynomial_chrec (loop_nb, left, right);
714 /* Add TO_ADD to the evolution part of CHREC_BEFORE in the dimension
717 Description (provided for completeness, for those who read code in
718 a plane, and for my poor 62 bytes brain that would have forgotten
719 all this in the next two or three months):
721 The algorithm of translation of programs from the SSA representation
722 into the chrecs syntax is based on a pattern matching. After having
723 reconstructed the overall tree expression for a loop, there are only
724 two cases that can arise:
726 1. a = loop-phi (init, a + expr)
727 2. a = loop-phi (init, expr)
729 where EXPR is either a scalar constant with respect to the analyzed
730 loop (this is a degree 0 polynomial), or an expression containing
731 other loop-phi definitions (these are higher degree polynomials).
738 | a = phi (init, a + 5)
745 | a = phi (inita, 2 * b + 3)
746 | b = phi (initb, b + 1)
749 For the first case, the semantics of the SSA representation is:
751 | a (x) = init + \sum_{j = 0}^{x - 1} expr (j)
753 that is, there is a loop index "x" that determines the scalar value
754 of the variable during the loop execution. During the first
755 iteration, the value is that of the initial condition INIT, while
756 during the subsequent iterations, it is the sum of the initial
757 condition with the sum of all the values of EXPR from the initial
758 iteration to the before last considered iteration.
760 For the second case, the semantics of the SSA program is:
762 | a (x) = init, if x = 0;
763 | expr (x - 1), otherwise.
765 The second case corresponds to the PEELED_CHREC, whose syntax is
766 close to the syntax of a loop-phi-node:
768 | phi (init, expr) vs. (init, expr)_x
770 The proof of the translation algorithm for the first case is a
771 proof by structural induction based on the degree of EXPR.
774 When EXPR is a constant with respect to the analyzed loop, or in
775 other words when EXPR is a polynomial of degree 0, the evolution of
776 the variable A in the loop is an affine function with an initial
777 condition INIT, and a step EXPR. In order to show this, we start
778 from the semantics of the SSA representation:
780 f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
782 and since "expr (j)" is a constant with respect to "j",
784 f (x) = init + x * expr
786 Finally, based on the semantics of the pure sum chrecs, by
787 identification we get the corresponding chrecs syntax:
789 f (x) = init * \binom{x}{0} + expr * \binom{x}{1}
790 f (x) -> {init, +, expr}_x
793 Suppose that EXPR is a polynomial of degree N with respect to the
794 analyzed loop_x for which we have already determined that it is
795 written under the chrecs syntax:
797 | expr (x) -> {b_0, +, b_1, +, ..., +, b_{n-1}} (x)
799 We start from the semantics of the SSA program:
801 | f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
803 | f (x) = init + \sum_{j = 0}^{x - 1}
804 | (b_0 * \binom{j}{0} + ... + b_{n-1} * \binom{j}{n-1})
806 | f (x) = init + \sum_{j = 0}^{x - 1}
807 | \sum_{k = 0}^{n - 1} (b_k * \binom{j}{k})
809 | f (x) = init + \sum_{k = 0}^{n - 1}
810 | (b_k * \sum_{j = 0}^{x - 1} \binom{j}{k})
812 | f (x) = init + \sum_{k = 0}^{n - 1}
813 | (b_k * \binom{x}{k + 1})
815 | f (x) = init + b_0 * \binom{x}{1} + ...
816 | + b_{n-1} * \binom{x}{n}
818 | f (x) = init * \binom{x}{0} + b_0 * \binom{x}{1} + ...
819 | + b_{n-1} * \binom{x}{n}
822 And finally from the definition of the chrecs syntax, we identify:
823 | f (x) -> {init, +, b_0, +, ..., +, b_{n-1}}_x
825 This shows the mechanism that stands behind the add_to_evolution
826 function. An important point is that the use of symbolic
827 parameters avoids the need of an analysis schedule.
834 | a = phi (inita, a + 2 + b)
835 | b = phi (initb, b + 1)
838 When analyzing "a", the algorithm keeps "b" symbolically:
840 | a -> {inita, +, 2 + b}_1
842 Then, after instantiation, the analyzer ends on the evolution:
844 | a -> {inita, +, 2 + initb, +, 1}_1
849 add_to_evolution (unsigned loop_nb, tree chrec_before, enum tree_code code,
850 tree to_add, tree at_stmt)
852 tree type = chrec_type (to_add);
853 tree res = NULL_TREE;
855 if (to_add == NULL_TREE)
858 /* TO_ADD is either a scalar, or a parameter. TO_ADD is not
859 instantiated at this point. */
860 if (TREE_CODE (to_add) == POLYNOMIAL_CHREC)
861 /* This should not happen. */
862 return chrec_dont_know;
864 if (dump_file && (dump_flags & TDF_DETAILS))
866 fprintf (dump_file, "(add_to_evolution \n");
867 fprintf (dump_file, " (loop_nb = %d)\n", loop_nb);
868 fprintf (dump_file, " (chrec_before = ");
869 print_generic_expr (dump_file, chrec_before, 0);
870 fprintf (dump_file, ")\n (to_add = ");
871 print_generic_expr (dump_file, to_add, 0);
872 fprintf (dump_file, ")\n");
875 if (code == MINUS_EXPR)
876 to_add = chrec_fold_multiply (type, to_add, SCALAR_FLOAT_TYPE_P (type)
877 ? build_real (type, dconstm1)
878 : build_int_cst_type (type, -1));
880 res = add_to_evolution_1 (loop_nb, chrec_before, to_add, at_stmt);
882 if (dump_file && (dump_flags & TDF_DETAILS))
884 fprintf (dump_file, " (res = ");
885 print_generic_expr (dump_file, res, 0);
886 fprintf (dump_file, "))\n");
892 /* Helper function. */
895 set_nb_iterations_in_loop (struct loop *loop,
898 tree type = chrec_type (res);
900 res = chrec_fold_plus (type, res, build_int_cst (type, 1));
902 /* FIXME HWI: However we want to store one iteration less than the
903 count of the loop in order to be compatible with the other
904 nb_iter computations in loop-iv. This also allows the
905 representation of nb_iters that are equal to MAX_INT. */
906 if (TREE_CODE (res) == INTEGER_CST
907 && (TREE_INT_CST_LOW (res) == 0
908 || TREE_OVERFLOW (res)))
909 res = chrec_dont_know;
911 if (dump_file && (dump_flags & TDF_DETAILS))
913 fprintf (dump_file, " (set_nb_iterations_in_loop = ");
914 print_generic_expr (dump_file, res, 0);
915 fprintf (dump_file, "))\n");
918 loop->nb_iterations = res;
924 /* This section selects the loops that will be good candidates for the
925 scalar evolution analysis. For the moment, greedily select all the
926 loop nests we could analyze. */
928 /* Return true when it is possible to analyze the condition expression
932 analyzable_condition (tree expr)
936 if (TREE_CODE (expr) != COND_EXPR)
939 condition = TREE_OPERAND (expr, 0);
941 switch (TREE_CODE (condition))
961 /* For a loop with a single exit edge, return the COND_EXPR that
962 guards the exit edge. If the expression is too difficult to
963 analyze, then give up. */
966 get_loop_exit_condition (struct loop *loop)
968 tree res = NULL_TREE;
969 edge exit_edge = single_exit (loop);
971 if (dump_file && (dump_flags & TDF_DETAILS))
972 fprintf (dump_file, "(get_loop_exit_condition \n ");
978 expr = last_stmt (exit_edge->src);
979 if (analyzable_condition (expr))
983 if (dump_file && (dump_flags & TDF_DETAILS))
985 print_generic_expr (dump_file, res, 0);
986 fprintf (dump_file, ")\n");
992 /* Recursively determine and enqueue the exit conditions for a loop. */
995 get_exit_conditions_rec (struct loop *loop,
996 VEC(tree,heap) **exit_conditions)
1001 /* Recurse on the inner loops, then on the next (sibling) loops. */
1002 get_exit_conditions_rec (loop->inner, exit_conditions);
1003 get_exit_conditions_rec (loop->next, exit_conditions);
1005 if (single_exit (loop))
1007 tree loop_condition = get_loop_exit_condition (loop);
1010 VEC_safe_push (tree, heap, *exit_conditions, loop_condition);
1014 /* Select the candidate loop nests for the analysis. This function
1015 initializes the EXIT_CONDITIONS array. */
1018 select_loops_exit_conditions (VEC(tree,heap) **exit_conditions)
1020 struct loop *function_body = current_loops->tree_root;
1022 get_exit_conditions_rec (function_body->inner, exit_conditions);
1026 /* Depth first search algorithm. */
1028 typedef enum t_bool {
1035 static t_bool follow_ssa_edge (struct loop *loop, tree, tree, tree *, int);
1037 /* Follow the ssa edge into the right hand side RHS of an assignment.
1038 Return true if the strongly connected component has been found. */
1041 follow_ssa_edge_in_rhs (struct loop *loop, tree at_stmt, tree rhs,
1042 tree halting_phi, tree *evolution_of_loop, int limit)
1044 t_bool res = t_false;
1046 tree type_rhs = TREE_TYPE (rhs);
1049 /* The RHS is one of the following cases:
1055 - other cases are not yet handled. */
1056 switch (TREE_CODE (rhs))
1059 /* This assignment is under the form "a_1 = (cast) rhs. */
1060 res = follow_ssa_edge_in_rhs (loop, at_stmt, TREE_OPERAND (rhs, 0),
1061 halting_phi, evolution_of_loop, limit);
1062 *evolution_of_loop = chrec_convert (TREE_TYPE (rhs),
1063 *evolution_of_loop, at_stmt);
1067 /* This assignment is under the form "a_1 = 7". */
1072 /* This assignment is under the form: "a_1 = b_2". */
1073 res = follow_ssa_edge
1074 (loop, SSA_NAME_DEF_STMT (rhs), halting_phi, evolution_of_loop, limit);
1078 /* This case is under the form "rhs0 + rhs1". */
1079 rhs0 = TREE_OPERAND (rhs, 0);
1080 rhs1 = TREE_OPERAND (rhs, 1);
1081 STRIP_TYPE_NOPS (rhs0);
1082 STRIP_TYPE_NOPS (rhs1);
1084 if (TREE_CODE (rhs0) == SSA_NAME)
1086 if (TREE_CODE (rhs1) == SSA_NAME)
1088 /* Match an assignment under the form:
1090 evol = *evolution_of_loop;
1091 res = follow_ssa_edge
1092 (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1096 *evolution_of_loop = add_to_evolution
1098 chrec_convert (type_rhs, evol, at_stmt),
1099 PLUS_EXPR, rhs1, at_stmt);
1101 else if (res == t_false)
1103 res = follow_ssa_edge
1104 (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi,
1105 evolution_of_loop, limit);
1108 *evolution_of_loop = add_to_evolution
1110 chrec_convert (type_rhs, *evolution_of_loop, at_stmt),
1111 PLUS_EXPR, rhs0, at_stmt);
1113 else if (res == t_dont_know)
1114 *evolution_of_loop = chrec_dont_know;
1117 else if (res == t_dont_know)
1118 *evolution_of_loop = chrec_dont_know;
1123 /* Match an assignment under the form:
1125 res = follow_ssa_edge
1126 (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1127 evolution_of_loop, limit);
1129 *evolution_of_loop = add_to_evolution
1130 (loop->num, chrec_convert (type_rhs, *evolution_of_loop,
1132 PLUS_EXPR, rhs1, at_stmt);
1134 else if (res == t_dont_know)
1135 *evolution_of_loop = chrec_dont_know;
1139 else if (TREE_CODE (rhs1) == SSA_NAME)
1141 /* Match an assignment under the form:
1143 res = follow_ssa_edge
1144 (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi,
1145 evolution_of_loop, limit);
1147 *evolution_of_loop = add_to_evolution
1148 (loop->num, chrec_convert (type_rhs, *evolution_of_loop,
1150 PLUS_EXPR, rhs0, at_stmt);
1152 else if (res == t_dont_know)
1153 *evolution_of_loop = chrec_dont_know;
1157 /* Otherwise, match an assignment under the form:
1159 /* And there is nothing to do. */
1165 /* This case is under the form "opnd0 = rhs0 - rhs1". */
1166 rhs0 = TREE_OPERAND (rhs, 0);
1167 rhs1 = TREE_OPERAND (rhs, 1);
1168 STRIP_TYPE_NOPS (rhs0);
1169 STRIP_TYPE_NOPS (rhs1);
1171 if (TREE_CODE (rhs0) == SSA_NAME)
1173 /* Match an assignment under the form:
1175 res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1176 evolution_of_loop, limit);
1178 *evolution_of_loop = add_to_evolution
1179 (loop->num, chrec_convert (type_rhs, *evolution_of_loop, at_stmt),
1180 MINUS_EXPR, rhs1, at_stmt);
1182 else if (res == t_dont_know)
1183 *evolution_of_loop = chrec_dont_know;
1186 /* Otherwise, match an assignment under the form:
1188 /* And there is nothing to do. */
1195 /* This assignment is of the form: "a_1 = ASSERT_EXPR <a_2, ...>"
1196 It must be handled as a copy assignment of the form a_1 = a_2. */
1197 tree op0 = ASSERT_EXPR_VAR (rhs);
1198 if (TREE_CODE (op0) == SSA_NAME)
1199 res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (op0),
1200 halting_phi, evolution_of_loop, limit);
1215 /* Checks whether the I-th argument of a PHI comes from a backedge. */
1218 backedge_phi_arg_p (tree phi, int i)
1220 edge e = PHI_ARG_EDGE (phi, i);
1222 /* We would in fact like to test EDGE_DFS_BACK here, but we do not care
1223 about updating it anywhere, and this should work as well most of the
1225 if (e->flags & EDGE_IRREDUCIBLE_LOOP)
1231 /* Helper function for one branch of the condition-phi-node. Return
1232 true if the strongly connected component has been found following
1235 static inline t_bool
1236 follow_ssa_edge_in_condition_phi_branch (int i,
1240 tree *evolution_of_branch,
1241 tree init_cond, int limit)
1243 tree branch = PHI_ARG_DEF (condition_phi, i);
1244 *evolution_of_branch = chrec_dont_know;
1246 /* Do not follow back edges (they must belong to an irreducible loop, which
1247 we really do not want to worry about). */
1248 if (backedge_phi_arg_p (condition_phi, i))
1251 if (TREE_CODE (branch) == SSA_NAME)
1253 *evolution_of_branch = init_cond;
1254 return follow_ssa_edge (loop, SSA_NAME_DEF_STMT (branch), halting_phi,
1255 evolution_of_branch, limit);
1258 /* This case occurs when one of the condition branches sets
1259 the variable to a constant: i.e. a phi-node like
1260 "a_2 = PHI <a_7(5), 2(6)>;".
1262 FIXME: This case have to be refined correctly:
1263 in some cases it is possible to say something better than
1264 chrec_dont_know, for example using a wrap-around notation. */
1268 /* This function merges the branches of a condition-phi-node in a
1272 follow_ssa_edge_in_condition_phi (struct loop *loop,
1275 tree *evolution_of_loop, int limit)
1278 tree init = *evolution_of_loop;
1279 tree evolution_of_branch;
1280 t_bool res = follow_ssa_edge_in_condition_phi_branch (0, loop, condition_phi,
1282 &evolution_of_branch,
1284 if (res == t_false || res == t_dont_know)
1287 *evolution_of_loop = evolution_of_branch;
1289 for (i = 1; i < PHI_NUM_ARGS (condition_phi); i++)
1291 /* Quickly give up when the evolution of one of the branches is
1293 if (*evolution_of_loop == chrec_dont_know)
1296 res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi,
1298 &evolution_of_branch,
1300 if (res == t_false || res == t_dont_know)
1303 *evolution_of_loop = chrec_merge (*evolution_of_loop,
1304 evolution_of_branch);
1310 /* Follow an SSA edge in an inner loop. It computes the overall
1311 effect of the loop, and following the symbolic initial conditions,
1312 it follows the edges in the parent loop. The inner loop is
1313 considered as a single statement. */
1316 follow_ssa_edge_inner_loop_phi (struct loop *outer_loop,
1319 tree *evolution_of_loop, int limit)
1321 struct loop *loop = loop_containing_stmt (loop_phi_node);
1322 tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node));
1324 /* Sometimes, the inner loop is too difficult to analyze, and the
1325 result of the analysis is a symbolic parameter. */
1326 if (ev == PHI_RESULT (loop_phi_node))
1328 t_bool res = t_false;
1331 for (i = 0; i < PHI_NUM_ARGS (loop_phi_node); i++)
1333 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1336 /* Follow the edges that exit the inner loop. */
1337 bb = PHI_ARG_EDGE (loop_phi_node, i)->src;
1338 if (!flow_bb_inside_loop_p (loop, bb))
1339 res = follow_ssa_edge_in_rhs (outer_loop, loop_phi_node,
1341 evolution_of_loop, limit);
1346 /* If the path crosses this loop-phi, give up. */
1348 *evolution_of_loop = chrec_dont_know;
1353 /* Otherwise, compute the overall effect of the inner loop. */
1354 ev = compute_overall_effect_of_inner_loop (loop, ev);
1355 return follow_ssa_edge_in_rhs (outer_loop, loop_phi_node, ev, halting_phi,
1356 evolution_of_loop, limit);
1359 /* Follow an SSA edge from a loop-phi-node to itself, constructing a
1360 path that is analyzed on the return walk. */
1363 follow_ssa_edge (struct loop *loop, tree def, tree halting_phi,
1364 tree *evolution_of_loop, int limit)
1366 struct loop *def_loop;
1368 if (TREE_CODE (def) == NOP_EXPR)
1371 /* Give up if the path is longer than the MAX that we allow. */
1372 if (limit++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
1375 def_loop = loop_containing_stmt (def);
1377 switch (TREE_CODE (def))
1380 if (!loop_phi_node_p (def))
1381 /* DEF is a condition-phi-node. Follow the branches, and
1382 record their evolutions. Finally, merge the collected
1383 information and set the approximation to the main
1385 return follow_ssa_edge_in_condition_phi
1386 (loop, def, halting_phi, evolution_of_loop, limit);
1388 /* When the analyzed phi is the halting_phi, the
1389 depth-first search is over: we have found a path from
1390 the halting_phi to itself in the loop. */
1391 if (def == halting_phi)
1394 /* Otherwise, the evolution of the HALTING_PHI depends
1395 on the evolution of another loop-phi-node, i.e. the
1396 evolution function is a higher degree polynomial. */
1397 if (def_loop == loop)
1401 if (flow_loop_nested_p (loop, def_loop))
1402 return follow_ssa_edge_inner_loop_phi
1403 (loop, def, halting_phi, evolution_of_loop, limit);
1408 case GIMPLE_MODIFY_STMT:
1409 return follow_ssa_edge_in_rhs (loop, def,
1410 GIMPLE_STMT_OPERAND (def, 1),
1412 evolution_of_loop, limit);
1415 /* At this level of abstraction, the program is just a set
1416 of GIMPLE_MODIFY_STMTs and PHI_NODEs. In principle there is no
1417 other node to be handled. */
1424 /* Given a LOOP_PHI_NODE, this function determines the evolution
1425 function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop. */
1428 analyze_evolution_in_loop (tree loop_phi_node,
1432 tree evolution_function = chrec_not_analyzed_yet;
1433 struct loop *loop = loop_containing_stmt (loop_phi_node);
1436 if (dump_file && (dump_flags & TDF_DETAILS))
1438 fprintf (dump_file, "(analyze_evolution_in_loop \n");
1439 fprintf (dump_file, " (loop_phi_node = ");
1440 print_generic_expr (dump_file, loop_phi_node, 0);
1441 fprintf (dump_file, ")\n");
1444 for (i = 0; i < PHI_NUM_ARGS (loop_phi_node); i++)
1446 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1447 tree ssa_chain, ev_fn;
1450 /* Select the edges that enter the loop body. */
1451 bb = PHI_ARG_EDGE (loop_phi_node, i)->src;
1452 if (!flow_bb_inside_loop_p (loop, bb))
1455 if (TREE_CODE (arg) == SSA_NAME)
1457 ssa_chain = SSA_NAME_DEF_STMT (arg);
1459 /* Pass in the initial condition to the follow edge function. */
1461 res = follow_ssa_edge (loop, ssa_chain, loop_phi_node, &ev_fn, 0);
1466 /* When it is impossible to go back on the same
1467 loop_phi_node by following the ssa edges, the
1468 evolution is represented by a peeled chrec, i.e. the
1469 first iteration, EV_FN has the value INIT_COND, then
1470 all the other iterations it has the value of ARG.
1471 For the moment, PEELED_CHREC nodes are not built. */
1473 ev_fn = chrec_dont_know;
1475 /* When there are multiple back edges of the loop (which in fact never
1476 happens currently, but nevertheless), merge their evolutions. */
1477 evolution_function = chrec_merge (evolution_function, ev_fn);
1480 if (dump_file && (dump_flags & TDF_DETAILS))
1482 fprintf (dump_file, " (evolution_function = ");
1483 print_generic_expr (dump_file, evolution_function, 0);
1484 fprintf (dump_file, "))\n");
1487 return evolution_function;
1490 /* Given a loop-phi-node, return the initial conditions of the
1491 variable on entry of the loop. When the CCP has propagated
1492 constants into the loop-phi-node, the initial condition is
1493 instantiated, otherwise the initial condition is kept symbolic.
1494 This analyzer does not analyze the evolution outside the current
1495 loop, and leaves this task to the on-demand tree reconstructor. */
1498 analyze_initial_condition (tree loop_phi_node)
1501 tree init_cond = chrec_not_analyzed_yet;
1502 struct loop *loop = bb_for_stmt (loop_phi_node)->loop_father;
1504 if (dump_file && (dump_flags & TDF_DETAILS))
1506 fprintf (dump_file, "(analyze_initial_condition \n");
1507 fprintf (dump_file, " (loop_phi_node = \n");
1508 print_generic_expr (dump_file, loop_phi_node, 0);
1509 fprintf (dump_file, ")\n");
1512 for (i = 0; i < PHI_NUM_ARGS (loop_phi_node); i++)
1514 tree branch = PHI_ARG_DEF (loop_phi_node, i);
1515 basic_block bb = PHI_ARG_EDGE (loop_phi_node, i)->src;
1517 /* When the branch is oriented to the loop's body, it does
1518 not contribute to the initial condition. */
1519 if (flow_bb_inside_loop_p (loop, bb))
1522 if (init_cond == chrec_not_analyzed_yet)
1528 if (TREE_CODE (branch) == SSA_NAME)
1530 init_cond = chrec_dont_know;
1534 init_cond = chrec_merge (init_cond, branch);
1537 /* Ooops -- a loop without an entry??? */
1538 if (init_cond == chrec_not_analyzed_yet)
1539 init_cond = chrec_dont_know;
1541 if (dump_file && (dump_flags & TDF_DETAILS))
1543 fprintf (dump_file, " (init_cond = ");
1544 print_generic_expr (dump_file, init_cond, 0);
1545 fprintf (dump_file, "))\n");
1551 /* Analyze the scalar evolution for LOOP_PHI_NODE. */
1554 interpret_loop_phi (struct loop *loop, tree loop_phi_node)
1557 struct loop *phi_loop = loop_containing_stmt (loop_phi_node);
1560 if (phi_loop != loop)
1562 struct loop *subloop;
1563 tree evolution_fn = analyze_scalar_evolution
1564 (phi_loop, PHI_RESULT (loop_phi_node));
1566 /* Dive one level deeper. */
1567 subloop = superloop_at_depth (phi_loop, loop->depth + 1);
1569 /* Interpret the subloop. */
1570 res = compute_overall_effect_of_inner_loop (subloop, evolution_fn);
1574 /* Otherwise really interpret the loop phi. */
1575 init_cond = analyze_initial_condition (loop_phi_node);
1576 res = analyze_evolution_in_loop (loop_phi_node, init_cond);
1581 /* This function merges the branches of a condition-phi-node,
1582 contained in the outermost loop, and whose arguments are already
1586 interpret_condition_phi (struct loop *loop, tree condition_phi)
1589 tree res = chrec_not_analyzed_yet;
1591 for (i = 0; i < PHI_NUM_ARGS (condition_phi); i++)
1595 if (backedge_phi_arg_p (condition_phi, i))
1597 res = chrec_dont_know;
1601 branch_chrec = analyze_scalar_evolution
1602 (loop, PHI_ARG_DEF (condition_phi, i));
1604 res = chrec_merge (res, branch_chrec);
1610 /* Interpret the right hand side of a GIMPLE_MODIFY_STMT OPND1. If we didn't
1611 analyze this node before, follow the definitions until ending
1612 either on an analyzed GIMPLE_MODIFY_STMT, or on a loop-phi-node. On the
1613 return path, this function propagates evolutions (ala constant copy
1614 propagation). OPND1 is not a GIMPLE expression because we could
1615 analyze the effect of an inner loop: see interpret_loop_phi. */
1618 interpret_rhs_modify_stmt (struct loop *loop, tree at_stmt,
1619 tree opnd1, tree type)
1621 tree res, opnd10, opnd11, chrec10, chrec11;
1623 if (is_gimple_min_invariant (opnd1))
1624 return chrec_convert (type, opnd1, at_stmt);
1626 switch (TREE_CODE (opnd1))
1629 opnd10 = TREE_OPERAND (opnd1, 0);
1630 opnd11 = TREE_OPERAND (opnd1, 1);
1631 chrec10 = analyze_scalar_evolution (loop, opnd10);
1632 chrec11 = analyze_scalar_evolution (loop, opnd11);
1633 chrec10 = chrec_convert (type, chrec10, at_stmt);
1634 chrec11 = chrec_convert (type, chrec11, at_stmt);
1635 res = chrec_fold_plus (type, chrec10, chrec11);
1639 opnd10 = TREE_OPERAND (opnd1, 0);
1640 opnd11 = TREE_OPERAND (opnd1, 1);
1641 chrec10 = analyze_scalar_evolution (loop, opnd10);
1642 chrec11 = analyze_scalar_evolution (loop, opnd11);
1643 chrec10 = chrec_convert (type, chrec10, at_stmt);
1644 chrec11 = chrec_convert (type, chrec11, at_stmt);
1645 res = chrec_fold_minus (type, chrec10, chrec11);
1649 opnd10 = TREE_OPERAND (opnd1, 0);
1650 chrec10 = analyze_scalar_evolution (loop, opnd10);
1651 chrec10 = chrec_convert (type, chrec10, at_stmt);
1652 /* TYPE may be integer, real or complex, so use fold_convert. */
1653 res = chrec_fold_multiply (type, chrec10,
1654 fold_convert (type, integer_minus_one_node));
1658 opnd10 = TREE_OPERAND (opnd1, 0);
1659 opnd11 = TREE_OPERAND (opnd1, 1);
1660 chrec10 = analyze_scalar_evolution (loop, opnd10);
1661 chrec11 = analyze_scalar_evolution (loop, opnd11);
1662 chrec10 = chrec_convert (type, chrec10, at_stmt);
1663 chrec11 = chrec_convert (type, chrec11, at_stmt);
1664 res = chrec_fold_multiply (type, chrec10, chrec11);
1668 res = chrec_convert (type, analyze_scalar_evolution (loop, opnd1),
1673 opnd10 = ASSERT_EXPR_VAR (opnd1);
1674 res = chrec_convert (type, analyze_scalar_evolution (loop, opnd10),
1680 opnd10 = TREE_OPERAND (opnd1, 0);
1681 chrec10 = analyze_scalar_evolution (loop, opnd10);
1682 res = chrec_convert (type, chrec10, at_stmt);
1686 res = chrec_dont_know;
1695 /* This section contains all the entry points:
1696 - number_of_iterations_in_loop,
1697 - analyze_scalar_evolution,
1698 - instantiate_parameters.
1701 /* Compute and return the evolution function in WRTO_LOOP, the nearest
1702 common ancestor of DEF_LOOP and USE_LOOP. */
1705 compute_scalar_evolution_in_loop (struct loop *wrto_loop,
1706 struct loop *def_loop,
1710 if (def_loop == wrto_loop)
1713 def_loop = superloop_at_depth (def_loop, wrto_loop->depth + 1);
1714 res = compute_overall_effect_of_inner_loop (def_loop, ev);
1716 return analyze_scalar_evolution_1 (wrto_loop, res, chrec_not_analyzed_yet);
1719 /* Folds EXPR, if it is a cast to pointer, assuming that the created
1720 polynomial_chrec does not wrap. */
1723 fold_used_pointer_cast (tree expr)
1726 tree type, inner_type;
1728 if (TREE_CODE (expr) != NOP_EXPR && TREE_CODE (expr) != CONVERT_EXPR)
1731 op = TREE_OPERAND (expr, 0);
1732 if (TREE_CODE (op) != POLYNOMIAL_CHREC)
1735 type = TREE_TYPE (expr);
1736 inner_type = TREE_TYPE (op);
1738 if (!INTEGRAL_TYPE_P (inner_type)
1739 || TYPE_PRECISION (inner_type) != TYPE_PRECISION (type))
1742 return build_polynomial_chrec (CHREC_VARIABLE (op),
1743 chrec_convert (type, CHREC_LEFT (op), NULL_TREE),
1744 chrec_convert (type, CHREC_RIGHT (op), NULL_TREE));
1747 /* Returns true if EXPR is an expression corresponding to offset of pointer
1751 pointer_offset_p (tree expr)
1753 if (TREE_CODE (expr) == INTEGER_CST)
1756 if ((TREE_CODE (expr) == NOP_EXPR || TREE_CODE (expr) == CONVERT_EXPR)
1757 && INTEGRAL_TYPE_P (TREE_TYPE (TREE_OPERAND (expr, 0))))
1763 /* EXPR is a scalar evolution of a pointer that is dereferenced or used in
1764 comparison. This means that it must point to a part of some object in
1765 memory, which enables us to argue about overflows and possibly simplify
1766 the EXPR. AT_STMT is the statement in which this conversion has to be
1767 performed. Returns the simplified value.
1774 for (i = -n; i < n; i++)
1777 We generate the following code (assuming that size of int and size_t is
1780 for (i = -n; i < n; i++)
1785 tmp1 = (size_t) i; (1)
1786 tmp2 = 4 * tmp1; (2)
1787 tmp3 = (int *) tmp2; (3)
1788 tmp4 = p + tmp3; (4)
1793 We in general assume that pointer arithmetics does not overflow (since its
1794 behavior is undefined in that case). One of the problems is that our
1795 translation does not capture this property very well -- (int *) is
1796 considered unsigned, hence the computation in (4) does overflow if i is
1799 This impreciseness creates complications in scev analysis. The scalar
1800 evolution of i is [-n, +, 1]. Since int and size_t have the same precision
1801 (in this example), and size_t is unsigned (so we do not care about
1802 overflows), we succeed to derive that scev of tmp1 is [(size_t) -n, +, 1]
1803 and scev of tmp2 is [4 * (size_t) -n, +, 4]. With tmp3, we run into
1804 problem -- [(int *) (4 * (size_t) -n), +, 4] wraps, and since we on several
1805 places assume that this is not the case for scevs with pointer type, we
1806 cannot use this scev for tmp3; hence, its scev is
1807 (int *) [(4 * (size_t) -n), +, 4], and scev of tmp4 is
1808 p + (int *) [(4 * (size_t) -n), +, 4]. Most of the optimizers are unable to
1809 work with scevs of this shape.
1811 However, since tmp4 is dereferenced, all its values must belong to a single
1812 object, and taking into account that the precision of int * and size_t is
1813 the same, it is impossible for its scev to wrap. Hence, we can derive that
1814 its evolution is [p + (int *) (4 * (size_t) -n), +, 4], which the optimizers
1817 ??? Maybe we should use different representation for pointer arithmetics,
1818 however that is a long-term project with a lot of potential for creating
1822 fold_used_pointer (tree expr, tree at_stmt)
1824 tree op0, op1, new0, new1;
1825 enum tree_code code = TREE_CODE (expr);
1827 if (code == PLUS_EXPR
1828 || code == MINUS_EXPR)
1830 op0 = TREE_OPERAND (expr, 0);
1831 op1 = TREE_OPERAND (expr, 1);
1833 if (pointer_offset_p (op1))
1835 new0 = fold_used_pointer (op0, at_stmt);
1836 new1 = fold_used_pointer_cast (op1);
1838 else if (code == PLUS_EXPR && pointer_offset_p (op0))
1840 new0 = fold_used_pointer_cast (op0);
1841 new1 = fold_used_pointer (op1, at_stmt);
1846 if (new0 == op0 && new1 == op1)
1849 new0 = chrec_convert (TREE_TYPE (expr), new0, at_stmt);
1850 new1 = chrec_convert (TREE_TYPE (expr), new1, at_stmt);
1852 if (code == PLUS_EXPR)
1853 expr = chrec_fold_plus (TREE_TYPE (expr), new0, new1);
1855 expr = chrec_fold_minus (TREE_TYPE (expr), new0, new1);
1860 return fold_used_pointer_cast (expr);
1863 /* Returns true if PTR is dereferenced, or used in comparison. */
1866 pointer_used_p (tree ptr)
1868 use_operand_p use_p;
1869 imm_use_iterator imm_iter;
1871 struct ptr_info_def *pi = get_ptr_info (ptr);
1872 var_ann_t v_ann = var_ann (SSA_NAME_VAR (ptr));
1874 /* Check whether the pointer has a memory tag; if it does, it is
1875 (or at least used to be) dereferenced. */
1876 if ((pi != NULL && pi->name_mem_tag != NULL)
1877 || v_ann->symbol_mem_tag)
1880 FOR_EACH_IMM_USE_FAST (use_p, imm_iter, ptr)
1882 stmt = USE_STMT (use_p);
1883 if (TREE_CODE (stmt) == COND_EXPR)
1886 if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
1889 rhs = GIMPLE_STMT_OPERAND (stmt, 1);
1890 if (!COMPARISON_CLASS_P (rhs))
1893 if (GIMPLE_STMT_OPERAND (stmt, 0) == ptr
1894 || GIMPLE_STMT_OPERAND (stmt, 1) == ptr)
1901 /* Helper recursive function. */
1904 analyze_scalar_evolution_1 (struct loop *loop, tree var, tree res)
1906 tree def, type = TREE_TYPE (var);
1908 struct loop *def_loop;
1910 if (loop == NULL || TREE_CODE (type) == VECTOR_TYPE)
1911 return chrec_dont_know;
1913 if (TREE_CODE (var) != SSA_NAME)
1914 return interpret_rhs_modify_stmt (loop, NULL_TREE, var, type);
1916 def = SSA_NAME_DEF_STMT (var);
1917 bb = bb_for_stmt (def);
1918 def_loop = bb ? bb->loop_father : NULL;
1921 || !flow_bb_inside_loop_p (loop, bb))
1923 /* Keep the symbolic form. */
1928 if (res != chrec_not_analyzed_yet)
1930 if (loop != bb->loop_father)
1931 res = compute_scalar_evolution_in_loop
1932 (find_common_loop (loop, bb->loop_father), bb->loop_father, res);
1937 if (loop != def_loop)
1939 res = analyze_scalar_evolution_1 (def_loop, var, chrec_not_analyzed_yet);
1940 res = compute_scalar_evolution_in_loop (loop, def_loop, res);
1945 switch (TREE_CODE (def))
1947 case GIMPLE_MODIFY_STMT:
1948 res = interpret_rhs_modify_stmt (loop, def,
1949 GIMPLE_STMT_OPERAND (def, 1), type);
1951 if (POINTER_TYPE_P (type)
1952 && !automatically_generated_chrec_p (res)
1953 && pointer_used_p (var))
1954 res = fold_used_pointer (res, def);
1958 if (loop_phi_node_p (def))
1959 res = interpret_loop_phi (loop, def);
1961 res = interpret_condition_phi (loop, def);
1965 res = chrec_dont_know;
1971 /* Keep the symbolic form. */
1972 if (res == chrec_dont_know)
1975 if (loop == def_loop)
1976 set_scalar_evolution (var, res);
1981 /* Entry point for the scalar evolution analyzer.
1982 Analyzes and returns the scalar evolution of the ssa_name VAR.
1983 LOOP_NB is the identifier number of the loop in which the variable
1986 Example of use: having a pointer VAR to a SSA_NAME node, STMT a
1987 pointer to the statement that uses this variable, in order to
1988 determine the evolution function of the variable, use the following
1991 unsigned loop_nb = loop_containing_stmt (stmt)->num;
1992 tree chrec_with_symbols = analyze_scalar_evolution (loop_nb, var);
1993 tree chrec_instantiated = instantiate_parameters
1994 (loop_nb, chrec_with_symbols);
1998 analyze_scalar_evolution (struct loop *loop, tree var)
2002 if (dump_file && (dump_flags & TDF_DETAILS))
2004 fprintf (dump_file, "(analyze_scalar_evolution \n");
2005 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
2006 fprintf (dump_file, " (scalar = ");
2007 print_generic_expr (dump_file, var, 0);
2008 fprintf (dump_file, ")\n");
2011 res = analyze_scalar_evolution_1 (loop, var, get_scalar_evolution (var));
2013 if (TREE_CODE (var) == SSA_NAME && res == chrec_dont_know)
2016 if (dump_file && (dump_flags & TDF_DETAILS))
2017 fprintf (dump_file, ")\n");
2022 /* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to
2023 WRTO_LOOP (which should be a superloop of both USE_LOOP and definition
2026 FOLDED_CASTS is set to true if resolve_mixers used
2027 chrec_convert_aggressive (TODO -- not really, we are way too conservative
2028 at the moment in order to keep things simple). */
2031 analyze_scalar_evolution_in_loop (struct loop *wrto_loop, struct loop *use_loop,
2032 tree version, bool *folded_casts)
2035 tree ev = version, tmp;
2038 *folded_casts = false;
2041 tmp = analyze_scalar_evolution (use_loop, ev);
2042 ev = resolve_mixers (use_loop, tmp);
2044 if (folded_casts && tmp != ev)
2045 *folded_casts = true;
2047 if (use_loop == wrto_loop)
2050 /* If the value of the use changes in the inner loop, we cannot express
2051 its value in the outer loop (we might try to return interval chrec,
2052 but we do not have a user for it anyway) */
2053 if (!no_evolution_in_loop_p (ev, use_loop->num, &val)
2055 return chrec_dont_know;
2057 use_loop = use_loop->outer;
2061 /* Returns instantiated value for VERSION in CACHE. */
2064 get_instantiated_value (htab_t cache, tree version)
2066 struct scev_info_str *info, pattern;
2068 pattern.var = version;
2069 info = (struct scev_info_str *) htab_find (cache, &pattern);
2077 /* Sets instantiated value for VERSION to VAL in CACHE. */
2080 set_instantiated_value (htab_t cache, tree version, tree val)
2082 struct scev_info_str *info, pattern;
2085 pattern.var = version;
2086 slot = htab_find_slot (cache, &pattern, INSERT);
2089 *slot = new_scev_info_str (version);
2090 info = (struct scev_info_str *) *slot;
2094 /* Return the closed_loop_phi node for VAR. If there is none, return
2098 loop_closed_phi_def (tree var)
2104 if (var == NULL_TREE
2105 || TREE_CODE (var) != SSA_NAME)
2108 loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var));
2109 exit = single_exit (loop);
2113 for (phi = phi_nodes (exit->dest); phi; phi = PHI_CHAIN (phi))
2114 if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var)
2115 return PHI_RESULT (phi);
2120 /* Analyze all the parameters of the chrec that were left under a symbolic form,
2121 with respect to LOOP. CHREC is the chrec to instantiate. CACHE is the cache
2122 of already instantiated values. FLAGS modify the way chrecs are
2123 instantiated. SIZE_EXPR is used for computing the size of the expression to
2124 be instantiated, and to stop if it exceeds some limit. */
2126 /* Values for FLAGS. */
2129 INSERT_SUPERLOOP_CHRECS = 1, /* Loop invariants are replaced with chrecs
2131 FOLD_CONVERSIONS = 2 /* The conversions that may wrap in
2132 signed/pointer type are folded, as long as the
2133 value of the chrec is preserved. */
2137 instantiate_parameters_1 (struct loop *loop, tree chrec, int flags, htab_t cache,
2140 tree res, op0, op1, op2;
2142 struct loop *def_loop;
2143 tree type = chrec_type (chrec);
2145 /* Give up if the expression is larger than the MAX that we allow. */
2146 if (size_expr++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
2147 return chrec_dont_know;
2149 if (automatically_generated_chrec_p (chrec)
2150 || is_gimple_min_invariant (chrec))
2153 switch (TREE_CODE (chrec))
2156 def_bb = bb_for_stmt (SSA_NAME_DEF_STMT (chrec));
2158 /* A parameter (or loop invariant and we do not want to include
2159 evolutions in outer loops), nothing to do. */
2161 || (!(flags & INSERT_SUPERLOOP_CHRECS)
2162 && !flow_bb_inside_loop_p (loop, def_bb)))
2165 /* We cache the value of instantiated variable to avoid exponential
2166 time complexity due to reevaluations. We also store the convenient
2167 value in the cache in order to prevent infinite recursion -- we do
2168 not want to instantiate the SSA_NAME if it is in a mixer
2169 structure. This is used for avoiding the instantiation of
2170 recursively defined functions, such as:
2172 | a_2 -> {0, +, 1, +, a_2}_1 */
2174 res = get_instantiated_value (cache, chrec);
2178 /* Store the convenient value for chrec in the structure. If it
2179 is defined outside of the loop, we may just leave it in symbolic
2180 form, otherwise we need to admit that we do not know its behavior
2182 res = !flow_bb_inside_loop_p (loop, def_bb) ? chrec : chrec_dont_know;
2183 set_instantiated_value (cache, chrec, res);
2185 /* To make things even more complicated, instantiate_parameters_1
2186 calls analyze_scalar_evolution that may call # of iterations
2187 analysis that may in turn call instantiate_parameters_1 again.
2188 To prevent the infinite recursion, keep also the bitmap of
2189 ssa names that are being instantiated globally. */
2190 if (bitmap_bit_p (already_instantiated, SSA_NAME_VERSION (chrec)))
2193 def_loop = find_common_loop (loop, def_bb->loop_father);
2195 /* If the analysis yields a parametric chrec, instantiate the
2197 bitmap_set_bit (already_instantiated, SSA_NAME_VERSION (chrec));
2198 res = analyze_scalar_evolution (def_loop, chrec);
2200 /* Don't instantiate loop-closed-ssa phi nodes. */
2201 if (TREE_CODE (res) == SSA_NAME
2202 && (loop_containing_stmt (SSA_NAME_DEF_STMT (res)) == NULL
2203 || (loop_containing_stmt (SSA_NAME_DEF_STMT (res))->depth
2204 > def_loop->depth)))
2207 res = loop_closed_phi_def (chrec);
2211 if (res == NULL_TREE)
2212 res = chrec_dont_know;
2215 else if (res != chrec_dont_know)
2216 res = instantiate_parameters_1 (loop, res, flags, cache, size_expr);
2218 bitmap_clear_bit (already_instantiated, SSA_NAME_VERSION (chrec));
2220 /* Store the correct value to the cache. */
2221 set_instantiated_value (cache, chrec, res);
2224 case POLYNOMIAL_CHREC:
2225 op0 = instantiate_parameters_1 (loop, CHREC_LEFT (chrec),
2226 flags, cache, size_expr);
2227 if (op0 == chrec_dont_know)
2228 return chrec_dont_know;
2230 op1 = instantiate_parameters_1 (loop, CHREC_RIGHT (chrec),
2231 flags, cache, size_expr);
2232 if (op1 == chrec_dont_know)
2233 return chrec_dont_know;
2235 if (CHREC_LEFT (chrec) != op0
2236 || CHREC_RIGHT (chrec) != op1)
2238 op1 = chrec_convert (chrec_type (op0), op1, NULL_TREE);
2239 chrec = build_polynomial_chrec (CHREC_VARIABLE (chrec), op0, op1);
2244 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2245 flags, cache, size_expr);
2246 if (op0 == chrec_dont_know)
2247 return chrec_dont_know;
2249 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2250 flags, cache, size_expr);
2251 if (op1 == chrec_dont_know)
2252 return chrec_dont_know;
2254 if (TREE_OPERAND (chrec, 0) != op0
2255 || TREE_OPERAND (chrec, 1) != op1)
2257 op0 = chrec_convert (type, op0, NULL_TREE);
2258 op1 = chrec_convert (type, op1, NULL_TREE);
2259 chrec = chrec_fold_plus (type, op0, op1);
2264 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2265 flags, cache, size_expr);
2266 if (op0 == chrec_dont_know)
2267 return chrec_dont_know;
2269 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2270 flags, cache, size_expr);
2271 if (op1 == chrec_dont_know)
2272 return chrec_dont_know;
2274 if (TREE_OPERAND (chrec, 0) != op0
2275 || TREE_OPERAND (chrec, 1) != op1)
2277 op0 = chrec_convert (type, op0, NULL_TREE);
2278 op1 = chrec_convert (type, op1, NULL_TREE);
2279 chrec = chrec_fold_minus (type, op0, op1);
2284 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2285 flags, cache, size_expr);
2286 if (op0 == chrec_dont_know)
2287 return chrec_dont_know;
2289 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2290 flags, cache, size_expr);
2291 if (op1 == chrec_dont_know)
2292 return chrec_dont_know;
2294 if (TREE_OPERAND (chrec, 0) != op0
2295 || TREE_OPERAND (chrec, 1) != op1)
2297 op0 = chrec_convert (type, op0, NULL_TREE);
2298 op1 = chrec_convert (type, op1, NULL_TREE);
2299 chrec = chrec_fold_multiply (type, op0, op1);
2305 case NON_LVALUE_EXPR:
2306 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2307 flags, cache, size_expr);
2308 if (op0 == chrec_dont_know)
2309 return chrec_dont_know;
2311 if (flags & FOLD_CONVERSIONS)
2313 tree tmp = chrec_convert_aggressive (TREE_TYPE (chrec), op0);
2318 if (op0 == TREE_OPERAND (chrec, 0))
2321 /* If we used chrec_convert_aggressive, we can no longer assume that
2322 signed chrecs do not overflow, as chrec_convert does, so avoid
2323 calling it in that case. */
2324 if (flags & FOLD_CONVERSIONS)
2325 return fold_convert (TREE_TYPE (chrec), op0);
2327 return chrec_convert (TREE_TYPE (chrec), op0, NULL_TREE);
2329 case SCEV_NOT_KNOWN:
2330 return chrec_dont_know;
2339 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
2342 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2343 flags, cache, size_expr);
2344 if (op0 == chrec_dont_know)
2345 return chrec_dont_know;
2347 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2348 flags, cache, size_expr);
2349 if (op1 == chrec_dont_know)
2350 return chrec_dont_know;
2352 op2 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 2),
2353 flags, cache, size_expr);
2354 if (op2 == chrec_dont_know)
2355 return chrec_dont_know;
2357 if (op0 == TREE_OPERAND (chrec, 0)
2358 && op1 == TREE_OPERAND (chrec, 1)
2359 && op2 == TREE_OPERAND (chrec, 2))
2362 return fold_build3 (TREE_CODE (chrec),
2363 TREE_TYPE (chrec), op0, op1, op2);
2366 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2367 flags, cache, size_expr);
2368 if (op0 == chrec_dont_know)
2369 return chrec_dont_know;
2371 op1 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 1),
2372 flags, cache, size_expr);
2373 if (op1 == chrec_dont_know)
2374 return chrec_dont_know;
2376 if (op0 == TREE_OPERAND (chrec, 0)
2377 && op1 == TREE_OPERAND (chrec, 1))
2379 return fold_build2 (TREE_CODE (chrec), TREE_TYPE (chrec), op0, op1);
2382 op0 = instantiate_parameters_1 (loop, TREE_OPERAND (chrec, 0),
2383 flags, cache, size_expr);
2384 if (op0 == chrec_dont_know)
2385 return chrec_dont_know;
2386 if (op0 == TREE_OPERAND (chrec, 0))
2388 return fold_build1 (TREE_CODE (chrec), TREE_TYPE (chrec), op0);
2397 /* Too complicated to handle. */
2398 return chrec_dont_know;
2401 /* Analyze all the parameters of the chrec that were left under a
2402 symbolic form. LOOP is the loop in which symbolic names have to
2403 be analyzed and instantiated. */
2406 instantiate_parameters (struct loop *loop,
2410 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2412 if (dump_file && (dump_flags & TDF_DETAILS))
2414 fprintf (dump_file, "(instantiate_parameters \n");
2415 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
2416 fprintf (dump_file, " (chrec = ");
2417 print_generic_expr (dump_file, chrec, 0);
2418 fprintf (dump_file, ")\n");
2421 res = instantiate_parameters_1 (loop, chrec, INSERT_SUPERLOOP_CHRECS, cache,
2424 if (dump_file && (dump_flags & TDF_DETAILS))
2426 fprintf (dump_file, " (res = ");
2427 print_generic_expr (dump_file, res, 0);
2428 fprintf (dump_file, "))\n");
2431 htab_delete (cache);
2436 /* Similar to instantiate_parameters, but does not introduce the
2437 evolutions in outer loops for LOOP invariants in CHREC, and does not
2438 care about causing overflows, as long as they do not affect value
2439 of an expression. */
2442 resolve_mixers (struct loop *loop, tree chrec)
2444 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2445 tree ret = instantiate_parameters_1 (loop, chrec, FOLD_CONVERSIONS, cache, 0);
2446 htab_delete (cache);
2450 /* Entry point for the analysis of the number of iterations pass.
2451 This function tries to safely approximate the number of iterations
2452 the loop will run. When this property is not decidable at compile
2453 time, the result is chrec_dont_know. Otherwise the result is
2454 a scalar or a symbolic parameter.
2456 Example of analysis: suppose that the loop has an exit condition:
2458 "if (b > 49) goto end_loop;"
2460 and that in a previous analysis we have determined that the
2461 variable 'b' has an evolution function:
2463 "EF = {23, +, 5}_2".
2465 When we evaluate the function at the point 5, i.e. the value of the
2466 variable 'b' after 5 iterations in the loop, we have EF (5) = 48,
2467 and EF (6) = 53. In this case the value of 'b' on exit is '53' and
2468 the loop body has been executed 6 times. */
2471 number_of_iterations_in_loop (struct loop *loop)
2475 struct tree_niter_desc niter_desc;
2477 /* Determine whether the number_of_iterations_in_loop has already
2479 res = loop->nb_iterations;
2482 res = chrec_dont_know;
2484 if (dump_file && (dump_flags & TDF_DETAILS))
2485 fprintf (dump_file, "(number_of_iterations_in_loop\n");
2487 exit = single_exit (loop);
2491 if (!number_of_iterations_exit (loop, exit, &niter_desc, false))
2494 type = TREE_TYPE (niter_desc.niter);
2495 if (integer_nonzerop (niter_desc.may_be_zero))
2496 res = build_int_cst (type, 0);
2497 else if (integer_zerop (niter_desc.may_be_zero))
2498 res = niter_desc.niter;
2500 res = chrec_dont_know;
2503 return set_nb_iterations_in_loop (loop, res);
2506 /* One of the drivers for testing the scalar evolutions analysis.
2507 This function computes the number of iterations for all the loops
2508 from the EXIT_CONDITIONS array. */
2511 number_of_iterations_for_all_loops (VEC(tree,heap) **exit_conditions)
2514 unsigned nb_chrec_dont_know_loops = 0;
2515 unsigned nb_static_loops = 0;
2518 for (i = 0; VEC_iterate (tree, *exit_conditions, i, cond); i++)
2520 tree res = number_of_iterations_in_loop (loop_containing_stmt (cond));
2521 if (chrec_contains_undetermined (res))
2522 nb_chrec_dont_know_loops++;
2529 fprintf (dump_file, "\n(\n");
2530 fprintf (dump_file, "-----------------------------------------\n");
2531 fprintf (dump_file, "%d\tnb_chrec_dont_know_loops\n", nb_chrec_dont_know_loops);
2532 fprintf (dump_file, "%d\tnb_static_loops\n", nb_static_loops);
2533 fprintf (dump_file, "%d\tnb_total_loops\n", current_loops->num);
2534 fprintf (dump_file, "-----------------------------------------\n");
2535 fprintf (dump_file, ")\n\n");
2537 print_loop_ir (dump_file);
2543 /* Counters for the stats. */
2549 unsigned nb_affine_multivar;
2550 unsigned nb_higher_poly;
2551 unsigned nb_chrec_dont_know;
2552 unsigned nb_undetermined;
2555 /* Reset the counters. */
2558 reset_chrecs_counters (struct chrec_stats *stats)
2560 stats->nb_chrecs = 0;
2561 stats->nb_affine = 0;
2562 stats->nb_affine_multivar = 0;
2563 stats->nb_higher_poly = 0;
2564 stats->nb_chrec_dont_know = 0;
2565 stats->nb_undetermined = 0;
2568 /* Dump the contents of a CHREC_STATS structure. */
2571 dump_chrecs_stats (FILE *file, struct chrec_stats *stats)
2573 fprintf (file, "\n(\n");
2574 fprintf (file, "-----------------------------------------\n");
2575 fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine);
2576 fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar);
2577 fprintf (file, "%d\tdegree greater than 2 polynomials\n",
2578 stats->nb_higher_poly);
2579 fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know);
2580 fprintf (file, "-----------------------------------------\n");
2581 fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs);
2582 fprintf (file, "%d\twith undetermined coefficients\n",
2583 stats->nb_undetermined);
2584 fprintf (file, "-----------------------------------------\n");
2585 fprintf (file, "%d\tchrecs in the scev database\n",
2586 (int) htab_elements (scalar_evolution_info));
2587 fprintf (file, "%d\tsets in the scev database\n", nb_set_scev);
2588 fprintf (file, "%d\tgets in the scev database\n", nb_get_scev);
2589 fprintf (file, "-----------------------------------------\n");
2590 fprintf (file, ")\n\n");
2593 /* Gather statistics about CHREC. */
2596 gather_chrec_stats (tree chrec, struct chrec_stats *stats)
2598 if (dump_file && (dump_flags & TDF_STATS))
2600 fprintf (dump_file, "(classify_chrec ");
2601 print_generic_expr (dump_file, chrec, 0);
2602 fprintf (dump_file, "\n");
2607 if (chrec == NULL_TREE)
2609 stats->nb_undetermined++;
2613 switch (TREE_CODE (chrec))
2615 case POLYNOMIAL_CHREC:
2616 if (evolution_function_is_affine_p (chrec))
2618 if (dump_file && (dump_flags & TDF_STATS))
2619 fprintf (dump_file, " affine_univariate\n");
2622 else if (evolution_function_is_affine_multivariate_p (chrec))
2624 if (dump_file && (dump_flags & TDF_STATS))
2625 fprintf (dump_file, " affine_multivariate\n");
2626 stats->nb_affine_multivar++;
2630 if (dump_file && (dump_flags & TDF_STATS))
2631 fprintf (dump_file, " higher_degree_polynomial\n");
2632 stats->nb_higher_poly++;
2641 if (chrec_contains_undetermined (chrec))
2643 if (dump_file && (dump_flags & TDF_STATS))
2644 fprintf (dump_file, " undetermined\n");
2645 stats->nb_undetermined++;
2648 if (dump_file && (dump_flags & TDF_STATS))
2649 fprintf (dump_file, ")\n");
2652 /* One of the drivers for testing the scalar evolutions analysis.
2653 This function analyzes the scalar evolution of all the scalars
2654 defined as loop phi nodes in one of the loops from the
2655 EXIT_CONDITIONS array.
2657 TODO Optimization: A loop is in canonical form if it contains only
2658 a single scalar loop phi node. All the other scalars that have an
2659 evolution in the loop are rewritten in function of this single
2660 index. This allows the parallelization of the loop. */
2663 analyze_scalar_evolution_for_all_loop_phi_nodes (VEC(tree,heap) **exit_conditions)
2666 struct chrec_stats stats;
2669 reset_chrecs_counters (&stats);
2671 for (i = 0; VEC_iterate (tree, *exit_conditions, i, cond); i++)
2677 loop = loop_containing_stmt (cond);
2680 for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
2681 if (is_gimple_reg (PHI_RESULT (phi)))
2683 chrec = instantiate_parameters
2685 analyze_scalar_evolution (loop, PHI_RESULT (phi)));
2687 if (dump_file && (dump_flags & TDF_STATS))
2688 gather_chrec_stats (chrec, &stats);
2692 if (dump_file && (dump_flags & TDF_STATS))
2693 dump_chrecs_stats (dump_file, &stats);
2696 /* Callback for htab_traverse, gathers information on chrecs in the
2700 gather_stats_on_scev_database_1 (void **slot, void *stats)
2702 struct scev_info_str *entry = (struct scev_info_str *) *slot;
2704 gather_chrec_stats (entry->chrec, (struct chrec_stats *) stats);
2709 /* Classify the chrecs of the whole database. */
2712 gather_stats_on_scev_database (void)
2714 struct chrec_stats stats;
2719 reset_chrecs_counters (&stats);
2721 htab_traverse (scalar_evolution_info, gather_stats_on_scev_database_1,
2724 dump_chrecs_stats (dump_file, &stats);
2732 initialize_scalar_evolutions_analyzer (void)
2734 /* The elements below are unique. */
2735 if (chrec_dont_know == NULL_TREE)
2737 chrec_not_analyzed_yet = NULL_TREE;
2738 chrec_dont_know = make_node (SCEV_NOT_KNOWN);
2739 chrec_known = make_node (SCEV_KNOWN);
2740 TREE_TYPE (chrec_dont_know) = void_type_node;
2741 TREE_TYPE (chrec_known) = void_type_node;
2745 /* Initialize the analysis of scalar evolutions for LOOPS. */
2748 scev_initialize (void)
2752 scalar_evolution_info = htab_create (100, hash_scev_info,
2753 eq_scev_info, del_scev_info);
2754 already_instantiated = BITMAP_ALLOC (NULL);
2756 initialize_scalar_evolutions_analyzer ();
2758 for (i = 1; i < current_loops->num; i++)
2759 if (current_loops->parray[i])
2760 current_loops->parray[i]->nb_iterations = NULL_TREE;
2763 /* Cleans up the information cached by the scalar evolutions analysis. */
2771 if (!scalar_evolution_info || !current_loops)
2774 htab_empty (scalar_evolution_info);
2775 for (i = 1; i < current_loops->num; i++)
2777 loop = current_loops->parray[i];
2779 loop->nb_iterations = NULL_TREE;
2783 /* Checks whether OP behaves as a simple affine iv of LOOP in STMT and returns
2784 its base and step in IV if possible. If ALLOW_NONCONSTANT_STEP is true, we
2785 want step to be invariant in LOOP. Otherwise we require it to be an
2786 integer constant. IV->no_overflow is set to true if we are sure the iv cannot
2787 overflow (e.g. because it is computed in signed arithmetics). */
2790 simple_iv (struct loop *loop, tree stmt, tree op, affine_iv *iv,
2791 bool allow_nonconstant_step)
2793 basic_block bb = bb_for_stmt (stmt);
2797 iv->base = NULL_TREE;
2798 iv->step = NULL_TREE;
2799 iv->no_overflow = false;
2801 type = TREE_TYPE (op);
2802 if (TREE_CODE (type) != INTEGER_TYPE
2803 && TREE_CODE (type) != POINTER_TYPE)
2806 ev = analyze_scalar_evolution_in_loop (loop, bb->loop_father, op,
2808 if (chrec_contains_undetermined (ev))
2811 if (tree_does_not_contain_chrecs (ev)
2812 && !chrec_contains_symbols_defined_in_loop (ev, loop->num))
2815 iv->no_overflow = true;
2819 if (TREE_CODE (ev) != POLYNOMIAL_CHREC
2820 || CHREC_VARIABLE (ev) != (unsigned) loop->num)
2823 iv->step = CHREC_RIGHT (ev);
2824 if (allow_nonconstant_step)
2826 if (tree_contains_chrecs (iv->step, NULL)
2827 || chrec_contains_symbols_defined_in_loop (iv->step, loop->num))
2830 else if (TREE_CODE (iv->step) != INTEGER_CST)
2833 iv->base = CHREC_LEFT (ev);
2834 if (tree_contains_chrecs (iv->base, NULL)
2835 || chrec_contains_symbols_defined_in_loop (iv->base, loop->num))
2838 iv->no_overflow = (!folded_casts
2840 && !TYPE_UNSIGNED (type));
2844 /* Runs the analysis of scalar evolutions. */
2847 scev_analysis (void)
2849 VEC(tree,heap) *exit_conditions;
2851 exit_conditions = VEC_alloc (tree, heap, 37);
2852 select_loops_exit_conditions (&exit_conditions);
2854 if (dump_file && (dump_flags & TDF_STATS))
2855 analyze_scalar_evolution_for_all_loop_phi_nodes (&exit_conditions);
2857 number_of_iterations_for_all_loops (&exit_conditions);
2858 VEC_free (tree, heap, exit_conditions);
2861 /* Finalize the scalar evolution analysis. */
2864 scev_finalize (void)
2866 htab_delete (scalar_evolution_info);
2867 BITMAP_FREE (already_instantiated);
2870 /* Returns true if EXPR looks expensive. */
2873 expression_expensive_p (tree expr)
2875 return force_expr_to_var_cost (expr) >= target_spill_cost;
2878 /* Replace ssa names for that scev can prove they are constant by the
2879 appropriate constants. Also perform final value replacement in loops,
2880 in case the replacement expressions are cheap.
2882 We only consider SSA names defined by phi nodes; rest is left to the
2883 ordinary constant propagation pass. */
2886 scev_const_prop (void)
2889 tree name, phi, next_phi, type, ev;
2890 struct loop *loop, *ex_loop;
2891 bitmap ssa_names_to_remove = NULL;
2899 loop = bb->loop_father;
2901 for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
2903 name = PHI_RESULT (phi);
2905 if (!is_gimple_reg (name))
2908 type = TREE_TYPE (name);
2910 if (!POINTER_TYPE_P (type)
2911 && !INTEGRAL_TYPE_P (type))
2914 ev = resolve_mixers (loop, analyze_scalar_evolution (loop, name));
2915 if (!is_gimple_min_invariant (ev)
2916 || !may_propagate_copy (name, ev))
2919 /* Replace the uses of the name. */
2921 replace_uses_by (name, ev);
2923 if (!ssa_names_to_remove)
2924 ssa_names_to_remove = BITMAP_ALLOC (NULL);
2925 bitmap_set_bit (ssa_names_to_remove, SSA_NAME_VERSION (name));
2929 /* Remove the ssa names that were replaced by constants. We do not remove them
2930 directly in the previous cycle, since this invalidates scev cache. */
2931 if (ssa_names_to_remove)
2936 EXECUTE_IF_SET_IN_BITMAP (ssa_names_to_remove, 0, i, bi)
2938 name = ssa_name (i);
2939 phi = SSA_NAME_DEF_STMT (name);
2941 gcc_assert (TREE_CODE (phi) == PHI_NODE);
2942 remove_phi_node (phi, NULL);
2945 BITMAP_FREE (ssa_names_to_remove);
2949 /* Now the regular final value replacement. */
2950 for (i = current_loops->num - 1; i > 0; i--)
2953 tree def, rslt, ass, niter;
2954 block_stmt_iterator bsi;
2956 loop = current_loops->parray[i];
2960 /* If we do not know exact number of iterations of the loop, we cannot
2961 replace the final value. */
2962 exit = single_exit (loop);
2966 niter = number_of_iterations_in_loop (loop);
2967 if (niter == chrec_dont_know
2968 /* If computing the number of iterations is expensive, it may be
2969 better not to introduce computations involving it. */
2970 || expression_expensive_p (niter))
2973 /* Ensure that it is possible to insert new statements somewhere. */
2974 if (!single_pred_p (exit->dest))
2975 split_loop_exit_edge (exit);
2976 tree_block_label (exit->dest);
2977 bsi = bsi_after_labels (exit->dest);
2979 ex_loop = superloop_at_depth (loop, exit->dest->loop_father->depth + 1);
2981 for (phi = phi_nodes (exit->dest); phi; phi = next_phi)
2983 next_phi = PHI_CHAIN (phi);
2984 rslt = PHI_RESULT (phi);
2985 def = PHI_ARG_DEF_FROM_EDGE (phi, exit);
2986 if (!is_gimple_reg (def))
2989 if (!POINTER_TYPE_P (TREE_TYPE (def))
2990 && !INTEGRAL_TYPE_P (TREE_TYPE (def)))
2993 def = analyze_scalar_evolution_in_loop (ex_loop, loop, def, NULL);
2994 def = compute_overall_effect_of_inner_loop (ex_loop, def);
2995 if (!tree_does_not_contain_chrecs (def)
2996 || chrec_contains_symbols_defined_in_loop (def, ex_loop->num)
2997 /* Moving the computation from the loop may prolong life range
2998 of some ssa names, which may cause problems if they appear
2999 on abnormal edges. */
3000 || contains_abnormal_ssa_name_p (def))
3003 /* Eliminate the phi node and replace it by a computation outside
3005 def = unshare_expr (def);
3006 SET_PHI_RESULT (phi, NULL_TREE);
3007 remove_phi_node (phi, NULL_TREE);
3009 ass = build2 (GIMPLE_MODIFY_STMT, void_type_node, rslt, NULL_TREE);
3010 SSA_NAME_DEF_STMT (rslt) = ass;
3012 block_stmt_iterator dest = bsi;
3013 bsi_insert_before (&dest, ass, BSI_NEW_STMT);
3014 def = force_gimple_operand_bsi (&dest, def, false, NULL_TREE);
3016 GIMPLE_STMT_OPERAND (ass, 1) = def;