1 /* Scalar evolution detector.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008 Free Software
4 Contributed by Sebastian Pop <s.pop@laposte.net>
6 This file is part of GCC.
8 GCC is free software; you can redistribute it and/or modify it under
9 the terms of the GNU General Public License as published by the Free
10 Software Foundation; either version 3, or (at your option) any later
13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
18 You should have received a copy of the GNU General Public License
19 along with GCC; see the file COPYING3. If not see
20 <http://www.gnu.org/licenses/>. */
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_ASSIGN: 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 (loop_1, {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 2a: 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 2b: Multivariate chains of recurrences.
171 Analyzing the access function of array A with
172 instantiate_parameters (loop_1, "j + k"), we obtain the
173 instantiation and the analysis of the scalar variables "j" and "k"
174 in loop_1. This leads to the scalar evolution {4, +, 1}_1: the end
175 value of loop_2 for "j" is 4, and the evolution of "k" in loop_1 is
176 {0, +, 1}_1. To obtain the evolution function in loop_3 and
177 instantiate the scalar variables up to loop_1, one has to use:
178 instantiate_scev (block_before_loop (loop_1), loop_3, "j + k").
179 The result of this call is {{0, +, 1}_1, +, 1}_2.
181 Example 3: Higher degree polynomials.
195 instantiate_parameters (loop_1, {5, +, a}_1) -> {5, +, 2, +, 1}_1
196 instantiate_parameters (loop_1, {5 + a, +, a}_1) -> {7, +, 3, +, 1}_1
198 Example 4: Lucas, Fibonacci, or mixers in general.
210 The syntax "(1, c)_1" stands for a PEELED_CHREC that has the
211 following semantics: during the first iteration of the loop_1, the
212 variable contains the value 1, and then it contains the value "c".
213 Note that this syntax is close to the syntax of the loop-phi-node:
214 "a -> (1, c)_1" vs. "a = phi (1, c)".
216 The symbolic chrec representation contains all the semantics of the
217 original code. What is more difficult is to use this information.
219 Example 5: Flip-flops, or exchangers.
231 Based on these symbolic chrecs, it is possible to refine this
232 information into the more precise PERIODIC_CHRECs:
237 This transformation is not yet implemented.
241 You can find a more detailed description of the algorithm in:
242 http://icps.u-strasbg.fr/~pop/DEA_03_Pop.pdf
243 http://icps.u-strasbg.fr/~pop/DEA_03_Pop.ps.gz. But note that
244 this is a preliminary report and some of the details of the
245 algorithm have changed. I'm working on a research report that
246 updates the description of the algorithms to reflect the design
247 choices used in this implementation.
249 A set of slides show a high level overview of the algorithm and run
250 an example through the scalar evolution analyzer:
251 http://cri.ensmp.fr/~pop/gcc/mar04/slides.pdf
253 The slides that I have presented at the GCC Summit'04 are available
254 at: http://cri.ensmp.fr/~pop/gcc/20040604/gccsummit-lno-spop.pdf
259 #include "coretypes.h"
265 /* These RTL headers are needed for basic-block.h. */
267 #include "basic-block.h"
268 #include "diagnostic.h"
269 #include "tree-flow.h"
270 #include "tree-dump.h"
273 #include "tree-chrec.h"
274 #include "tree-scalar-evolution.h"
275 #include "tree-pass.h"
279 static tree analyze_scalar_evolution_1 (struct loop *, tree, tree);
281 /* The cached information about an SSA name VAR, claiming that below
282 basic block INSTANTIATED_BELOW, the value of VAR can be expressed
285 struct scev_info_str GTY(())
287 basic_block instantiated_below;
292 /* Counters for the scev database. */
293 static unsigned nb_set_scev = 0;
294 static unsigned nb_get_scev = 0;
296 /* The following trees are unique elements. Thus the comparison of
297 another element to these elements should be done on the pointer to
298 these trees, and not on their value. */
300 /* The SSA_NAMEs that are not yet analyzed are qualified with NULL_TREE. */
301 tree chrec_not_analyzed_yet;
303 /* Reserved to the cases where the analyzer has detected an
304 undecidable property at compile time. */
305 tree chrec_dont_know;
307 /* When the analyzer has detected that a property will never
308 happen, then it qualifies it with chrec_known. */
311 static GTY ((param_is (struct scev_info_str))) htab_t scalar_evolution_info;
314 /* Constructs a new SCEV_INFO_STR structure for VAR and INSTANTIATED_BELOW. */
316 static inline struct scev_info_str *
317 new_scev_info_str (basic_block instantiated_below, tree var)
319 struct scev_info_str *res;
321 res = GGC_NEW (struct scev_info_str);
323 res->chrec = chrec_not_analyzed_yet;
324 res->instantiated_below = instantiated_below;
329 /* Computes a hash function for database element ELT. */
332 hash_scev_info (const void *elt)
334 return SSA_NAME_VERSION (((const struct scev_info_str *) elt)->var);
337 /* Compares database elements E1 and E2. */
340 eq_scev_info (const void *e1, const void *e2)
342 const struct scev_info_str *elt1 = (const struct scev_info_str *) e1;
343 const struct scev_info_str *elt2 = (const struct scev_info_str *) e2;
345 return (elt1->var == elt2->var
346 && elt1->instantiated_below == elt2->instantiated_below);
349 /* Deletes database element E. */
352 del_scev_info (void *e)
357 /* Get the scalar evolution of VAR for INSTANTIATED_BELOW basic block.
358 A first query on VAR returns chrec_not_analyzed_yet. */
361 find_var_scev_info (basic_block instantiated_below, tree var)
363 struct scev_info_str *res;
364 struct scev_info_str tmp;
368 tmp.instantiated_below = instantiated_below;
369 slot = htab_find_slot (scalar_evolution_info, &tmp, INSERT);
372 *slot = new_scev_info_str (instantiated_below, var);
373 res = (struct scev_info_str *) *slot;
378 /* Return true when CHREC contains symbolic names defined in
382 chrec_contains_symbols_defined_in_loop (const_tree chrec, unsigned loop_nb)
386 if (chrec == NULL_TREE)
389 if (is_gimple_min_invariant (chrec))
392 if (TREE_CODE (chrec) == VAR_DECL
393 || TREE_CODE (chrec) == PARM_DECL
394 || TREE_CODE (chrec) == FUNCTION_DECL
395 || TREE_CODE (chrec) == LABEL_DECL
396 || TREE_CODE (chrec) == RESULT_DECL
397 || TREE_CODE (chrec) == FIELD_DECL)
400 if (TREE_CODE (chrec) == SSA_NAME)
402 gimple def = SSA_NAME_DEF_STMT (chrec);
403 struct loop *def_loop = loop_containing_stmt (def);
404 struct loop *loop = get_loop (loop_nb);
406 if (def_loop == NULL)
409 if (loop == def_loop || flow_loop_nested_p (loop, def_loop))
415 n = TREE_OPERAND_LENGTH (chrec);
416 for (i = 0; i < n; i++)
417 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (chrec, i),
423 /* Return true when PHI is a loop-phi-node. */
426 loop_phi_node_p (gimple phi)
428 /* The implementation of this function is based on the following
429 property: "all the loop-phi-nodes of a loop are contained in the
430 loop's header basic block". */
432 return loop_containing_stmt (phi)->header == gimple_bb (phi);
435 /* Compute the scalar evolution for EVOLUTION_FN after crossing LOOP.
436 In general, in the case of multivariate evolutions we want to get
437 the evolution in different loops. LOOP specifies the level for
438 which to get the evolution.
442 | for (j = 0; j < 100; j++)
444 | for (k = 0; k < 100; k++)
446 | i = k + j; - Here the value of i is a function of j, k.
448 | ... = i - Here the value of i is a function of j.
450 | ... = i - Here the value of i is a scalar.
456 | i_1 = phi (i_0, i_2)
460 This loop has the same effect as:
461 LOOP_1 has the same effect as:
465 The overall effect of the loop, "i_0 + 20" in the previous example,
466 is obtained by passing in the parameters: LOOP = 1,
467 EVOLUTION_FN = {i_0, +, 2}_1.
471 compute_overall_effect_of_inner_loop (struct loop *loop, tree evolution_fn)
475 if (evolution_fn == chrec_dont_know)
476 return chrec_dont_know;
478 else if (TREE_CODE (evolution_fn) == POLYNOMIAL_CHREC)
480 struct loop *inner_loop = get_chrec_loop (evolution_fn);
482 if (inner_loop == loop
483 || flow_loop_nested_p (loop, inner_loop))
485 tree nb_iter = number_of_latch_executions (inner_loop);
487 if (nb_iter == chrec_dont_know)
488 return chrec_dont_know;
493 /* evolution_fn is the evolution function in LOOP. Get
494 its value in the nb_iter-th iteration. */
495 res = chrec_apply (inner_loop->num, evolution_fn, nb_iter);
497 /* Continue the computation until ending on a parent of LOOP. */
498 return compute_overall_effect_of_inner_loop (loop, res);
505 /* If the evolution function is an invariant, there is nothing to do. */
506 else if (no_evolution_in_loop_p (evolution_fn, loop->num, &val) && val)
510 return chrec_dont_know;
513 /* Determine whether the CHREC is always positive/negative. If the expression
514 cannot be statically analyzed, return false, otherwise set the answer into
518 chrec_is_positive (tree chrec, bool *value)
520 bool value0, value1, value2;
521 tree end_value, nb_iter;
523 switch (TREE_CODE (chrec))
525 case POLYNOMIAL_CHREC:
526 if (!chrec_is_positive (CHREC_LEFT (chrec), &value0)
527 || !chrec_is_positive (CHREC_RIGHT (chrec), &value1))
530 /* FIXME -- overflows. */
531 if (value0 == value1)
537 /* Otherwise the chrec is under the form: "{-197, +, 2}_1",
538 and the proof consists in showing that the sign never
539 changes during the execution of the loop, from 0 to
540 loop->nb_iterations. */
541 if (!evolution_function_is_affine_p (chrec))
544 nb_iter = number_of_latch_executions (get_chrec_loop (chrec));
545 if (chrec_contains_undetermined (nb_iter))
549 /* TODO -- If the test is after the exit, we may decrease the number of
550 iterations by one. */
552 nb_iter = chrec_fold_minus (type, nb_iter, build_int_cst (type, 1));
555 end_value = chrec_apply (CHREC_VARIABLE (chrec), chrec, nb_iter);
557 if (!chrec_is_positive (end_value, &value2))
561 return value0 == value1;
564 *value = (tree_int_cst_sgn (chrec) == 1);
572 /* Associate CHREC to SCALAR. */
575 set_scalar_evolution (basic_block instantiated_below, tree scalar, tree chrec)
579 if (TREE_CODE (scalar) != SSA_NAME)
582 scalar_info = find_var_scev_info (instantiated_below, scalar);
586 if (dump_flags & TDF_DETAILS)
588 fprintf (dump_file, "(set_scalar_evolution \n");
589 fprintf (dump_file, " instantiated_below = %d \n",
590 instantiated_below->index);
591 fprintf (dump_file, " (scalar = ");
592 print_generic_expr (dump_file, scalar, 0);
593 fprintf (dump_file, ")\n (scalar_evolution = ");
594 print_generic_expr (dump_file, chrec, 0);
595 fprintf (dump_file, "))\n");
597 if (dump_flags & TDF_STATS)
601 *scalar_info = chrec;
604 /* Retrieve the chrec associated to SCALAR instantiated below
605 INSTANTIATED_BELOW block. */
608 get_scalar_evolution (basic_block instantiated_below, tree scalar)
614 if (dump_flags & TDF_DETAILS)
616 fprintf (dump_file, "(get_scalar_evolution \n");
617 fprintf (dump_file, " (scalar = ");
618 print_generic_expr (dump_file, scalar, 0);
619 fprintf (dump_file, ")\n");
621 if (dump_flags & TDF_STATS)
625 switch (TREE_CODE (scalar))
628 res = *find_var_scev_info (instantiated_below, scalar);
638 res = chrec_not_analyzed_yet;
642 if (dump_file && (dump_flags & TDF_DETAILS))
644 fprintf (dump_file, " (scalar_evolution = ");
645 print_generic_expr (dump_file, res, 0);
646 fprintf (dump_file, "))\n");
652 /* Helper function for add_to_evolution. Returns the evolution
653 function for an assignment of the form "a = b + c", where "a" and
654 "b" are on the strongly connected component. CHREC_BEFORE is the
655 information that we already have collected up to this point.
656 TO_ADD is the evolution of "c".
658 When CHREC_BEFORE has an evolution part in LOOP_NB, add to this
659 evolution the expression TO_ADD, otherwise construct an evolution
660 part for this loop. */
663 add_to_evolution_1 (unsigned loop_nb, tree chrec_before, tree to_add,
666 tree type, left, right;
667 struct loop *loop = get_loop (loop_nb), *chloop;
669 switch (TREE_CODE (chrec_before))
671 case POLYNOMIAL_CHREC:
672 chloop = get_chrec_loop (chrec_before);
674 || flow_loop_nested_p (chloop, loop))
678 type = chrec_type (chrec_before);
680 /* When there is no evolution part in this loop, build it. */
685 right = SCALAR_FLOAT_TYPE_P (type)
686 ? build_real (type, dconst0)
687 : build_int_cst (type, 0);
691 var = CHREC_VARIABLE (chrec_before);
692 left = CHREC_LEFT (chrec_before);
693 right = CHREC_RIGHT (chrec_before);
696 to_add = chrec_convert (type, to_add, at_stmt);
697 right = chrec_convert_rhs (type, right, at_stmt);
698 right = chrec_fold_plus (chrec_type (right), right, to_add);
699 return build_polynomial_chrec (var, left, right);
703 gcc_assert (flow_loop_nested_p (loop, chloop));
705 /* Search the evolution in LOOP_NB. */
706 left = add_to_evolution_1 (loop_nb, CHREC_LEFT (chrec_before),
708 right = CHREC_RIGHT (chrec_before);
709 right = chrec_convert_rhs (chrec_type (left), right, at_stmt);
710 return build_polynomial_chrec (CHREC_VARIABLE (chrec_before),
715 /* These nodes do not depend on a loop. */
716 if (chrec_before == chrec_dont_know)
717 return chrec_dont_know;
720 right = chrec_convert_rhs (chrec_type (left), to_add, at_stmt);
721 return build_polynomial_chrec (loop_nb, left, right);
725 /* Add TO_ADD to the evolution part of CHREC_BEFORE in the dimension
728 Description (provided for completeness, for those who read code in
729 a plane, and for my poor 62 bytes brain that would have forgotten
730 all this in the next two or three months):
732 The algorithm of translation of programs from the SSA representation
733 into the chrecs syntax is based on a pattern matching. After having
734 reconstructed the overall tree expression for a loop, there are only
735 two cases that can arise:
737 1. a = loop-phi (init, a + expr)
738 2. a = loop-phi (init, expr)
740 where EXPR is either a scalar constant with respect to the analyzed
741 loop (this is a degree 0 polynomial), or an expression containing
742 other loop-phi definitions (these are higher degree polynomials).
749 | a = phi (init, a + 5)
756 | a = phi (inita, 2 * b + 3)
757 | b = phi (initb, b + 1)
760 For the first case, the semantics of the SSA representation is:
762 | a (x) = init + \sum_{j = 0}^{x - 1} expr (j)
764 that is, there is a loop index "x" that determines the scalar value
765 of the variable during the loop execution. During the first
766 iteration, the value is that of the initial condition INIT, while
767 during the subsequent iterations, it is the sum of the initial
768 condition with the sum of all the values of EXPR from the initial
769 iteration to the before last considered iteration.
771 For the second case, the semantics of the SSA program is:
773 | a (x) = init, if x = 0;
774 | expr (x - 1), otherwise.
776 The second case corresponds to the PEELED_CHREC, whose syntax is
777 close to the syntax of a loop-phi-node:
779 | phi (init, expr) vs. (init, expr)_x
781 The proof of the translation algorithm for the first case is a
782 proof by structural induction based on the degree of EXPR.
785 When EXPR is a constant with respect to the analyzed loop, or in
786 other words when EXPR is a polynomial of degree 0, the evolution of
787 the variable A in the loop is an affine function with an initial
788 condition INIT, and a step EXPR. In order to show this, we start
789 from the semantics of the SSA representation:
791 f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
793 and since "expr (j)" is a constant with respect to "j",
795 f (x) = init + x * expr
797 Finally, based on the semantics of the pure sum chrecs, by
798 identification we get the corresponding chrecs syntax:
800 f (x) = init * \binom{x}{0} + expr * \binom{x}{1}
801 f (x) -> {init, +, expr}_x
804 Suppose that EXPR is a polynomial of degree N with respect to the
805 analyzed loop_x for which we have already determined that it is
806 written under the chrecs syntax:
808 | expr (x) -> {b_0, +, b_1, +, ..., +, b_{n-1}} (x)
810 We start from the semantics of the SSA program:
812 | f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
814 | f (x) = init + \sum_{j = 0}^{x - 1}
815 | (b_0 * \binom{j}{0} + ... + b_{n-1} * \binom{j}{n-1})
817 | f (x) = init + \sum_{j = 0}^{x - 1}
818 | \sum_{k = 0}^{n - 1} (b_k * \binom{j}{k})
820 | f (x) = init + \sum_{k = 0}^{n - 1}
821 | (b_k * \sum_{j = 0}^{x - 1} \binom{j}{k})
823 | f (x) = init + \sum_{k = 0}^{n - 1}
824 | (b_k * \binom{x}{k + 1})
826 | f (x) = init + b_0 * \binom{x}{1} + ...
827 | + b_{n-1} * \binom{x}{n}
829 | f (x) = init * \binom{x}{0} + b_0 * \binom{x}{1} + ...
830 | + b_{n-1} * \binom{x}{n}
833 And finally from the definition of the chrecs syntax, we identify:
834 | f (x) -> {init, +, b_0, +, ..., +, b_{n-1}}_x
836 This shows the mechanism that stands behind the add_to_evolution
837 function. An important point is that the use of symbolic
838 parameters avoids the need of an analysis schedule.
845 | a = phi (inita, a + 2 + b)
846 | b = phi (initb, b + 1)
849 When analyzing "a", the algorithm keeps "b" symbolically:
851 | a -> {inita, +, 2 + b}_1
853 Then, after instantiation, the analyzer ends on the evolution:
855 | a -> {inita, +, 2 + initb, +, 1}_1
860 add_to_evolution (unsigned loop_nb, tree chrec_before, enum tree_code code,
861 tree to_add, gimple at_stmt)
863 tree type = chrec_type (to_add);
864 tree res = NULL_TREE;
866 if (to_add == NULL_TREE)
869 /* TO_ADD is either a scalar, or a parameter. TO_ADD is not
870 instantiated at this point. */
871 if (TREE_CODE (to_add) == POLYNOMIAL_CHREC)
872 /* This should not happen. */
873 return chrec_dont_know;
875 if (dump_file && (dump_flags & TDF_DETAILS))
877 fprintf (dump_file, "(add_to_evolution \n");
878 fprintf (dump_file, " (loop_nb = %d)\n", loop_nb);
879 fprintf (dump_file, " (chrec_before = ");
880 print_generic_expr (dump_file, chrec_before, 0);
881 fprintf (dump_file, ")\n (to_add = ");
882 print_generic_expr (dump_file, to_add, 0);
883 fprintf (dump_file, ")\n");
886 if (code == MINUS_EXPR)
887 to_add = chrec_fold_multiply (type, to_add, SCALAR_FLOAT_TYPE_P (type)
888 ? build_real (type, dconstm1)
889 : build_int_cst_type (type, -1));
891 res = add_to_evolution_1 (loop_nb, chrec_before, to_add, at_stmt);
893 if (dump_file && (dump_flags & TDF_DETAILS))
895 fprintf (dump_file, " (res = ");
896 print_generic_expr (dump_file, res, 0);
897 fprintf (dump_file, "))\n");
903 /* Helper function. */
906 set_nb_iterations_in_loop (struct loop *loop,
909 if (dump_file && (dump_flags & TDF_DETAILS))
911 fprintf (dump_file, " (set_nb_iterations_in_loop = ");
912 print_generic_expr (dump_file, res, 0);
913 fprintf (dump_file, "))\n");
916 loop->nb_iterations = res;
922 /* This section selects the loops that will be good candidates for the
923 scalar evolution analysis. For the moment, greedily select all the
924 loop nests we could analyze. */
926 /* For a loop with a single exit edge, return the COND_EXPR that
927 guards the exit edge. If the expression is too difficult to
928 analyze, then give up. */
931 get_loop_exit_condition (const struct loop *loop)
934 edge exit_edge = single_exit (loop);
936 if (dump_file && (dump_flags & TDF_DETAILS))
937 fprintf (dump_file, "(get_loop_exit_condition \n ");
943 stmt = last_stmt (exit_edge->src);
944 if (gimple_code (stmt) == GIMPLE_COND)
948 if (dump_file && (dump_flags & TDF_DETAILS))
950 print_gimple_stmt (dump_file, res, 0, 0);
951 fprintf (dump_file, ")\n");
957 /* Recursively determine and enqueue the exit conditions for a loop. */
960 get_exit_conditions_rec (struct loop *loop,
961 VEC(gimple,heap) **exit_conditions)
966 /* Recurse on the inner loops, then on the next (sibling) loops. */
967 get_exit_conditions_rec (loop->inner, exit_conditions);
968 get_exit_conditions_rec (loop->next, exit_conditions);
970 if (single_exit (loop))
972 gimple loop_condition = get_loop_exit_condition (loop);
975 VEC_safe_push (gimple, heap, *exit_conditions, loop_condition);
979 /* Select the candidate loop nests for the analysis. This function
980 initializes the EXIT_CONDITIONS array. */
983 select_loops_exit_conditions (VEC(gimple,heap) **exit_conditions)
985 struct loop *function_body = current_loops->tree_root;
987 get_exit_conditions_rec (function_body->inner, exit_conditions);
991 /* Depth first search algorithm. */
993 typedef enum t_bool {
1000 static t_bool follow_ssa_edge (struct loop *loop, gimple, gimple, tree *, int);
1002 /* Follow the ssa edge into the binary expression RHS0 CODE RHS1.
1003 Return true if the strongly connected component has been found. */
1006 follow_ssa_edge_binary (struct loop *loop, gimple at_stmt,
1007 tree type, tree rhs0, enum tree_code code, tree rhs1,
1008 gimple halting_phi, tree *evolution_of_loop, int limit)
1010 t_bool res = t_false;
1015 case POINTER_PLUS_EXPR:
1017 if (TREE_CODE (rhs0) == SSA_NAME)
1019 if (TREE_CODE (rhs1) == SSA_NAME)
1021 /* Match an assignment under the form:
1024 /* We want only assignments of form "name + name" contribute to
1025 LIMIT, as the other cases do not necessarily contribute to
1026 the complexity of the expression. */
1029 evol = *evolution_of_loop;
1030 res = follow_ssa_edge
1031 (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi, &evol, limit);
1034 *evolution_of_loop = add_to_evolution
1036 chrec_convert (type, evol, at_stmt),
1037 code, rhs1, at_stmt);
1039 else if (res == t_false)
1041 res = follow_ssa_edge
1042 (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi,
1043 evolution_of_loop, limit);
1046 *evolution_of_loop = add_to_evolution
1048 chrec_convert (type, *evolution_of_loop, at_stmt),
1049 code, rhs0, at_stmt);
1051 else if (res == t_dont_know)
1052 *evolution_of_loop = chrec_dont_know;
1055 else if (res == t_dont_know)
1056 *evolution_of_loop = chrec_dont_know;
1061 /* Match an assignment under the form:
1063 res = follow_ssa_edge
1064 (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1065 evolution_of_loop, limit);
1067 *evolution_of_loop = add_to_evolution
1068 (loop->num, chrec_convert (type, *evolution_of_loop,
1070 code, rhs1, at_stmt);
1072 else if (res == t_dont_know)
1073 *evolution_of_loop = chrec_dont_know;
1077 else if (TREE_CODE (rhs1) == SSA_NAME)
1079 /* Match an assignment under the form:
1081 res = follow_ssa_edge
1082 (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi,
1083 evolution_of_loop, limit);
1085 *evolution_of_loop = add_to_evolution
1086 (loop->num, chrec_convert (type, *evolution_of_loop,
1088 code, rhs0, at_stmt);
1090 else if (res == t_dont_know)
1091 *evolution_of_loop = chrec_dont_know;
1095 /* Otherwise, match an assignment under the form:
1097 /* And there is nothing to do. */
1102 /* This case is under the form "opnd0 = rhs0 - rhs1". */
1103 if (TREE_CODE (rhs0) == SSA_NAME)
1105 /* Match an assignment under the form:
1108 /* We want only assignments of form "name - name" contribute to
1109 LIMIT, as the other cases do not necessarily contribute to
1110 the complexity of the expression. */
1111 if (TREE_CODE (rhs1) == SSA_NAME)
1114 res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi,
1115 evolution_of_loop, limit);
1117 *evolution_of_loop = add_to_evolution
1118 (loop->num, chrec_convert (type, *evolution_of_loop, at_stmt),
1119 MINUS_EXPR, rhs1, at_stmt);
1121 else if (res == t_dont_know)
1122 *evolution_of_loop = chrec_dont_know;
1125 /* Otherwise, match an assignment under the form:
1127 /* And there is nothing to do. */
1138 /* Follow the ssa edge into the expression EXPR.
1139 Return true if the strongly connected component has been found. */
1142 follow_ssa_edge_expr (struct loop *loop, gimple at_stmt, tree expr,
1143 gimple halting_phi, tree *evolution_of_loop, int limit)
1145 t_bool res = t_false;
1147 tree type = TREE_TYPE (expr);
1148 enum tree_code code;
1150 /* The EXPR is one of the following cases:
1154 - a POINTER_PLUS_EXPR,
1157 - other cases are not yet handled. */
1158 code = TREE_CODE (expr);
1162 /* This assignment is under the form "a_1 = (cast) rhs. */
1163 res = follow_ssa_edge_expr (loop, at_stmt, TREE_OPERAND (expr, 0),
1164 halting_phi, evolution_of_loop, limit);
1165 *evolution_of_loop = chrec_convert (type, *evolution_of_loop, at_stmt);
1169 /* This assignment is under the form "a_1 = 7". */
1174 /* This assignment is under the form: "a_1 = b_2". */
1175 res = follow_ssa_edge
1176 (loop, SSA_NAME_DEF_STMT (expr), halting_phi, evolution_of_loop, limit);
1179 case POINTER_PLUS_EXPR:
1182 /* This case is under the form "rhs0 +- rhs1". */
1183 rhs0 = TREE_OPERAND (expr, 0);
1184 rhs1 = TREE_OPERAND (expr, 1);
1185 STRIP_TYPE_NOPS (rhs0);
1186 STRIP_TYPE_NOPS (rhs1);
1187 return follow_ssa_edge_binary (loop, at_stmt, type, rhs0, code, rhs1,
1188 halting_phi, evolution_of_loop, limit);
1192 /* This assignment is of the form: "a_1 = ASSERT_EXPR <a_2, ...>"
1193 It must be handled as a copy assignment of the form a_1 = a_2. */
1194 tree op0 = ASSERT_EXPR_VAR (expr);
1195 if (TREE_CODE (op0) == SSA_NAME)
1196 res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (op0),
1197 halting_phi, evolution_of_loop, limit);
1212 /* Follow the ssa edge into the right hand side of an assignment STMT.
1213 Return true if the strongly connected component has been found. */
1216 follow_ssa_edge_in_rhs (struct loop *loop, gimple stmt,
1217 gimple halting_phi, tree *evolution_of_loop, int limit)
1219 tree type = TREE_TYPE (gimple_assign_lhs (stmt));
1220 enum tree_code code = gimple_assign_rhs_code (stmt);
1222 switch (get_gimple_rhs_class (code))
1224 case GIMPLE_BINARY_RHS:
1225 return follow_ssa_edge_binary (loop, stmt, type,
1226 gimple_assign_rhs1 (stmt), code,
1227 gimple_assign_rhs2 (stmt),
1228 halting_phi, evolution_of_loop, limit);
1229 case GIMPLE_SINGLE_RHS:
1230 return follow_ssa_edge_expr (loop, stmt, gimple_assign_rhs1 (stmt),
1231 halting_phi, evolution_of_loop, limit);
1237 /* Checks whether the I-th argument of a PHI comes from a backedge. */
1240 backedge_phi_arg_p (gimple phi, int i)
1242 const_edge e = gimple_phi_arg_edge (phi, i);
1244 /* We would in fact like to test EDGE_DFS_BACK here, but we do not care
1245 about updating it anywhere, and this should work as well most of the
1247 if (e->flags & EDGE_IRREDUCIBLE_LOOP)
1253 /* Helper function for one branch of the condition-phi-node. Return
1254 true if the strongly connected component has been found following
1257 static inline t_bool
1258 follow_ssa_edge_in_condition_phi_branch (int i,
1260 gimple condition_phi,
1262 tree *evolution_of_branch,
1263 tree init_cond, int limit)
1265 tree branch = PHI_ARG_DEF (condition_phi, i);
1266 *evolution_of_branch = chrec_dont_know;
1268 /* Do not follow back edges (they must belong to an irreducible loop, which
1269 we really do not want to worry about). */
1270 if (backedge_phi_arg_p (condition_phi, i))
1273 if (TREE_CODE (branch) == SSA_NAME)
1275 *evolution_of_branch = init_cond;
1276 return follow_ssa_edge (loop, SSA_NAME_DEF_STMT (branch), halting_phi,
1277 evolution_of_branch, limit);
1280 /* This case occurs when one of the condition branches sets
1281 the variable to a constant: i.e. a phi-node like
1282 "a_2 = PHI <a_7(5), 2(6)>;".
1284 FIXME: This case have to be refined correctly:
1285 in some cases it is possible to say something better than
1286 chrec_dont_know, for example using a wrap-around notation. */
1290 /* This function merges the branches of a condition-phi-node in a
1294 follow_ssa_edge_in_condition_phi (struct loop *loop,
1295 gimple condition_phi,
1297 tree *evolution_of_loop, int limit)
1300 tree init = *evolution_of_loop;
1301 tree evolution_of_branch;
1302 t_bool res = follow_ssa_edge_in_condition_phi_branch (0, loop, condition_phi,
1304 &evolution_of_branch,
1306 if (res == t_false || res == t_dont_know)
1309 *evolution_of_loop = evolution_of_branch;
1311 /* If the phi node is just a copy, do not increase the limit. */
1312 n = gimple_phi_num_args (condition_phi);
1316 for (i = 1; i < n; i++)
1318 /* Quickly give up when the evolution of one of the branches is
1320 if (*evolution_of_loop == chrec_dont_know)
1323 res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi,
1325 &evolution_of_branch,
1327 if (res == t_false || res == t_dont_know)
1330 *evolution_of_loop = chrec_merge (*evolution_of_loop,
1331 evolution_of_branch);
1337 /* Follow an SSA edge in an inner loop. It computes the overall
1338 effect of the loop, and following the symbolic initial conditions,
1339 it follows the edges in the parent loop. The inner loop is
1340 considered as a single statement. */
1343 follow_ssa_edge_inner_loop_phi (struct loop *outer_loop,
1344 gimple loop_phi_node,
1346 tree *evolution_of_loop, int limit)
1348 struct loop *loop = loop_containing_stmt (loop_phi_node);
1349 tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node));
1351 /* Sometimes, the inner loop is too difficult to analyze, and the
1352 result of the analysis is a symbolic parameter. */
1353 if (ev == PHI_RESULT (loop_phi_node))
1355 t_bool res = t_false;
1356 int i, n = gimple_phi_num_args (loop_phi_node);
1358 for (i = 0; i < n; i++)
1360 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1363 /* Follow the edges that exit the inner loop. */
1364 bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1365 if (!flow_bb_inside_loop_p (loop, bb))
1366 res = follow_ssa_edge_expr (outer_loop, loop_phi_node,
1368 evolution_of_loop, limit);
1373 /* If the path crosses this loop-phi, give up. */
1375 *evolution_of_loop = chrec_dont_know;
1380 /* Otherwise, compute the overall effect of the inner loop. */
1381 ev = compute_overall_effect_of_inner_loop (loop, ev);
1382 return follow_ssa_edge_expr (outer_loop, loop_phi_node, ev, halting_phi,
1383 evolution_of_loop, limit);
1386 /* Follow an SSA edge from a loop-phi-node to itself, constructing a
1387 path that is analyzed on the return walk. */
1390 follow_ssa_edge (struct loop *loop, gimple def, gimple halting_phi,
1391 tree *evolution_of_loop, int limit)
1393 struct loop *def_loop;
1395 if (gimple_nop_p (def))
1398 /* Give up if the path is longer than the MAX that we allow. */
1399 if (limit > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
1402 def_loop = loop_containing_stmt (def);
1404 switch (gimple_code (def))
1407 if (!loop_phi_node_p (def))
1408 /* DEF is a condition-phi-node. Follow the branches, and
1409 record their evolutions. Finally, merge the collected
1410 information and set the approximation to the main
1412 return follow_ssa_edge_in_condition_phi
1413 (loop, def, halting_phi, evolution_of_loop, limit);
1415 /* When the analyzed phi is the halting_phi, the
1416 depth-first search is over: we have found a path from
1417 the halting_phi to itself in the loop. */
1418 if (def == halting_phi)
1421 /* Otherwise, the evolution of the HALTING_PHI depends
1422 on the evolution of another loop-phi-node, i.e. the
1423 evolution function is a higher degree polynomial. */
1424 if (def_loop == loop)
1428 if (flow_loop_nested_p (loop, def_loop))
1429 return follow_ssa_edge_inner_loop_phi
1430 (loop, def, halting_phi, evolution_of_loop, limit + 1);
1436 return follow_ssa_edge_in_rhs (loop, def, halting_phi,
1437 evolution_of_loop, limit);
1440 /* At this level of abstraction, the program is just a set
1441 of GIMPLE_ASSIGNs and PHI_NODEs. In principle there is no
1442 other node to be handled. */
1449 /* Given a LOOP_PHI_NODE, this function determines the evolution
1450 function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop. */
1453 analyze_evolution_in_loop (gimple loop_phi_node,
1456 int i, n = gimple_phi_num_args (loop_phi_node);
1457 tree evolution_function = chrec_not_analyzed_yet;
1458 struct loop *loop = loop_containing_stmt (loop_phi_node);
1461 if (dump_file && (dump_flags & TDF_DETAILS))
1463 fprintf (dump_file, "(analyze_evolution_in_loop \n");
1464 fprintf (dump_file, " (loop_phi_node = ");
1465 print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
1466 fprintf (dump_file, ")\n");
1469 for (i = 0; i < n; i++)
1471 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1476 /* Select the edges that enter the loop body. */
1477 bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1478 if (!flow_bb_inside_loop_p (loop, bb))
1481 if (TREE_CODE (arg) == SSA_NAME)
1483 ssa_chain = SSA_NAME_DEF_STMT (arg);
1485 /* Pass in the initial condition to the follow edge function. */
1487 res = follow_ssa_edge (loop, ssa_chain, loop_phi_node, &ev_fn, 0);
1492 /* When it is impossible to go back on the same
1493 loop_phi_node by following the ssa edges, the
1494 evolution is represented by a peeled chrec, i.e. the
1495 first iteration, EV_FN has the value INIT_COND, then
1496 all the other iterations it has the value of ARG.
1497 For the moment, PEELED_CHREC nodes are not built. */
1499 ev_fn = chrec_dont_know;
1501 /* When there are multiple back edges of the loop (which in fact never
1502 happens currently, but nevertheless), merge their evolutions. */
1503 evolution_function = chrec_merge (evolution_function, ev_fn);
1506 if (dump_file && (dump_flags & TDF_DETAILS))
1508 fprintf (dump_file, " (evolution_function = ");
1509 print_generic_expr (dump_file, evolution_function, 0);
1510 fprintf (dump_file, "))\n");
1513 return evolution_function;
1516 /* Given a loop-phi-node, return the initial conditions of the
1517 variable on entry of the loop. When the CCP has propagated
1518 constants into the loop-phi-node, the initial condition is
1519 instantiated, otherwise the initial condition is kept symbolic.
1520 This analyzer does not analyze the evolution outside the current
1521 loop, and leaves this task to the on-demand tree reconstructor. */
1524 analyze_initial_condition (gimple loop_phi_node)
1527 tree init_cond = chrec_not_analyzed_yet;
1528 struct loop *loop = loop_containing_stmt (loop_phi_node);
1530 if (dump_file && (dump_flags & TDF_DETAILS))
1532 fprintf (dump_file, "(analyze_initial_condition \n");
1533 fprintf (dump_file, " (loop_phi_node = \n");
1534 print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
1535 fprintf (dump_file, ")\n");
1538 n = gimple_phi_num_args (loop_phi_node);
1539 for (i = 0; i < n; i++)
1541 tree branch = PHI_ARG_DEF (loop_phi_node, i);
1542 basic_block bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1544 /* When the branch is oriented to the loop's body, it does
1545 not contribute to the initial condition. */
1546 if (flow_bb_inside_loop_p (loop, bb))
1549 if (init_cond == chrec_not_analyzed_yet)
1555 if (TREE_CODE (branch) == SSA_NAME)
1557 init_cond = chrec_dont_know;
1561 init_cond = chrec_merge (init_cond, branch);
1564 /* Ooops -- a loop without an entry??? */
1565 if (init_cond == chrec_not_analyzed_yet)
1566 init_cond = chrec_dont_know;
1568 if (dump_file && (dump_flags & TDF_DETAILS))
1570 fprintf (dump_file, " (init_cond = ");
1571 print_generic_expr (dump_file, init_cond, 0);
1572 fprintf (dump_file, "))\n");
1578 /* Analyze the scalar evolution for LOOP_PHI_NODE. */
1581 interpret_loop_phi (struct loop *loop, gimple loop_phi_node)
1584 struct loop *phi_loop = loop_containing_stmt (loop_phi_node);
1587 if (phi_loop != loop)
1589 struct loop *subloop;
1590 tree evolution_fn = analyze_scalar_evolution
1591 (phi_loop, PHI_RESULT (loop_phi_node));
1593 /* Dive one level deeper. */
1594 subloop = superloop_at_depth (phi_loop, loop_depth (loop) + 1);
1596 /* Interpret the subloop. */
1597 res = compute_overall_effect_of_inner_loop (subloop, evolution_fn);
1601 /* Otherwise really interpret the loop phi. */
1602 init_cond = analyze_initial_condition (loop_phi_node);
1603 res = analyze_evolution_in_loop (loop_phi_node, init_cond);
1608 /* This function merges the branches of a condition-phi-node,
1609 contained in the outermost loop, and whose arguments are already
1613 interpret_condition_phi (struct loop *loop, gimple condition_phi)
1615 int i, n = gimple_phi_num_args (condition_phi);
1616 tree res = chrec_not_analyzed_yet;
1618 for (i = 0; i < n; i++)
1622 if (backedge_phi_arg_p (condition_phi, i))
1624 res = chrec_dont_know;
1628 branch_chrec = analyze_scalar_evolution
1629 (loop, PHI_ARG_DEF (condition_phi, i));
1631 res = chrec_merge (res, branch_chrec);
1637 /* Interpret the operation RHS1 OP RHS2. If we didn't
1638 analyze this node before, follow the definitions until ending
1639 either on an analyzed GIMPLE_ASSIGN, or on a loop-phi-node. On the
1640 return path, this function propagates evolutions (ala constant copy
1641 propagation). OPND1 is not a GIMPLE expression because we could
1642 analyze the effect of an inner loop: see interpret_loop_phi. */
1645 interpret_rhs_expr (struct loop *loop, gimple at_stmt,
1646 tree type, tree rhs1, enum tree_code code, tree rhs2)
1648 tree res, chrec1, chrec2;
1650 if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS)
1652 if (is_gimple_min_invariant (rhs1))
1653 return chrec_convert (type, rhs1, at_stmt);
1655 if (code == SSA_NAME)
1656 return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
1659 if (code == ASSERT_EXPR)
1661 rhs1 = ASSERT_EXPR_VAR (rhs1);
1662 return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
1666 return chrec_dont_know;
1671 case POINTER_PLUS_EXPR:
1672 chrec1 = analyze_scalar_evolution (loop, rhs1);
1673 chrec2 = analyze_scalar_evolution (loop, rhs2);
1674 chrec1 = chrec_convert (type, chrec1, at_stmt);
1675 chrec2 = chrec_convert (sizetype, chrec2, at_stmt);
1676 res = chrec_fold_plus (type, chrec1, chrec2);
1680 chrec1 = analyze_scalar_evolution (loop, rhs1);
1681 chrec2 = analyze_scalar_evolution (loop, rhs2);
1682 chrec1 = chrec_convert (type, chrec1, at_stmt);
1683 chrec2 = chrec_convert (type, chrec2, at_stmt);
1684 res = chrec_fold_plus (type, chrec1, chrec2);
1688 chrec1 = analyze_scalar_evolution (loop, rhs1);
1689 chrec2 = analyze_scalar_evolution (loop, rhs2);
1690 chrec1 = chrec_convert (type, chrec1, at_stmt);
1691 chrec2 = chrec_convert (type, chrec2, at_stmt);
1692 res = chrec_fold_minus (type, chrec1, chrec2);
1696 chrec1 = analyze_scalar_evolution (loop, rhs1);
1697 chrec1 = chrec_convert (type, chrec1, at_stmt);
1698 /* TYPE may be integer, real or complex, so use fold_convert. */
1699 res = chrec_fold_multiply (type, chrec1,
1700 fold_convert (type, integer_minus_one_node));
1704 chrec1 = analyze_scalar_evolution (loop, rhs1);
1705 chrec2 = analyze_scalar_evolution (loop, rhs2);
1706 chrec1 = chrec_convert (type, chrec1, at_stmt);
1707 chrec2 = chrec_convert (type, chrec2, at_stmt);
1708 res = chrec_fold_multiply (type, chrec1, chrec2);
1712 chrec1 = analyze_scalar_evolution (loop, rhs1);
1713 res = chrec_convert (type, chrec1, at_stmt);
1717 res = chrec_dont_know;
1724 /* Interpret the expression EXPR. */
1727 interpret_expr (struct loop *loop, gimple at_stmt, tree expr)
1729 enum tree_code code;
1730 tree type = TREE_TYPE (expr), op0, op1;
1732 if (automatically_generated_chrec_p (expr))
1735 if (TREE_CODE (expr) == POLYNOMIAL_CHREC)
1736 return chrec_dont_know;
1738 extract_ops_from_tree (expr, &code, &op0, &op1);
1740 return interpret_rhs_expr (loop, at_stmt, type,
1744 /* Interpret the rhs of the assignment STMT. */
1747 interpret_gimple_assign (struct loop *loop, gimple stmt)
1749 tree type = TREE_TYPE (gimple_assign_lhs (stmt));
1750 enum tree_code code = gimple_assign_rhs_code (stmt);
1752 return interpret_rhs_expr (loop, stmt, type,
1753 gimple_assign_rhs1 (stmt), code,
1754 gimple_assign_rhs2 (stmt));
1759 /* This section contains all the entry points:
1760 - number_of_iterations_in_loop,
1761 - analyze_scalar_evolution,
1762 - instantiate_parameters.
1765 /* Compute and return the evolution function in WRTO_LOOP, the nearest
1766 common ancestor of DEF_LOOP and USE_LOOP. */
1769 compute_scalar_evolution_in_loop (struct loop *wrto_loop,
1770 struct loop *def_loop,
1774 if (def_loop == wrto_loop)
1777 def_loop = superloop_at_depth (def_loop, loop_depth (wrto_loop) + 1);
1778 res = compute_overall_effect_of_inner_loop (def_loop, ev);
1780 return analyze_scalar_evolution_1 (wrto_loop, res, chrec_not_analyzed_yet);
1783 /* Helper recursive function. */
1786 analyze_scalar_evolution_1 (struct loop *loop, tree var, tree res)
1788 tree type = TREE_TYPE (var);
1791 struct loop *def_loop;
1793 if (loop == NULL || TREE_CODE (type) == VECTOR_TYPE)
1794 return chrec_dont_know;
1796 if (TREE_CODE (var) != SSA_NAME)
1797 return interpret_expr (loop, NULL, var);
1799 def = SSA_NAME_DEF_STMT (var);
1800 bb = gimple_bb (def);
1801 def_loop = bb ? bb->loop_father : NULL;
1804 || !flow_bb_inside_loop_p (loop, bb))
1806 /* Keep the symbolic form. */
1811 if (res != chrec_not_analyzed_yet)
1813 if (loop != bb->loop_father)
1814 res = compute_scalar_evolution_in_loop
1815 (find_common_loop (loop, bb->loop_father), bb->loop_father, res);
1820 if (loop != def_loop)
1822 res = analyze_scalar_evolution_1 (def_loop, var, chrec_not_analyzed_yet);
1823 res = compute_scalar_evolution_in_loop (loop, def_loop, res);
1828 switch (gimple_code (def))
1831 res = interpret_gimple_assign (loop, def);
1835 if (loop_phi_node_p (def))
1836 res = interpret_loop_phi (loop, def);
1838 res = interpret_condition_phi (loop, def);
1842 res = chrec_dont_know;
1848 /* Keep the symbolic form. */
1849 if (res == chrec_dont_know)
1852 if (loop == def_loop)
1853 set_scalar_evolution (block_before_loop (loop), var, res);
1858 /* Entry point for the scalar evolution analyzer.
1859 Analyzes and returns the scalar evolution of the ssa_name VAR.
1860 LOOP_NB is the identifier number of the loop in which the variable
1863 Example of use: having a pointer VAR to a SSA_NAME node, STMT a
1864 pointer to the statement that uses this variable, in order to
1865 determine the evolution function of the variable, use the following
1868 unsigned loop_nb = loop_containing_stmt (stmt)->num;
1869 tree chrec_with_symbols = analyze_scalar_evolution (loop_nb, var);
1870 tree chrec_instantiated = instantiate_parameters (loop, chrec_with_symbols);
1874 analyze_scalar_evolution (struct loop *loop, tree var)
1878 if (dump_file && (dump_flags & TDF_DETAILS))
1880 fprintf (dump_file, "(analyze_scalar_evolution \n");
1881 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
1882 fprintf (dump_file, " (scalar = ");
1883 print_generic_expr (dump_file, var, 0);
1884 fprintf (dump_file, ")\n");
1887 res = get_scalar_evolution (block_before_loop (loop), var);
1888 res = analyze_scalar_evolution_1 (loop, var, res);
1890 if (dump_file && (dump_flags & TDF_DETAILS))
1891 fprintf (dump_file, ")\n");
1896 /* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to
1897 WRTO_LOOP (which should be a superloop of both USE_LOOP and definition
1900 FOLDED_CASTS is set to true if resolve_mixers used
1901 chrec_convert_aggressive (TODO -- not really, we are way too conservative
1902 at the moment in order to keep things simple). */
1905 analyze_scalar_evolution_in_loop (struct loop *wrto_loop, struct loop *use_loop,
1906 tree version, bool *folded_casts)
1909 tree ev = version, tmp;
1912 *folded_casts = false;
1915 tmp = analyze_scalar_evolution (use_loop, ev);
1916 ev = resolve_mixers (use_loop, tmp);
1918 if (folded_casts && tmp != ev)
1919 *folded_casts = true;
1921 if (use_loop == wrto_loop)
1924 /* If the value of the use changes in the inner loop, we cannot express
1925 its value in the outer loop (we might try to return interval chrec,
1926 but we do not have a user for it anyway) */
1927 if (!no_evolution_in_loop_p (ev, use_loop->num, &val)
1929 return chrec_dont_know;
1931 use_loop = loop_outer (use_loop);
1935 /* Returns from CACHE the value for VERSION instantiated below
1936 INSTANTIATED_BELOW block. */
1939 get_instantiated_value (htab_t cache, basic_block instantiated_below,
1942 struct scev_info_str *info, pattern;
1944 pattern.var = version;
1945 pattern.instantiated_below = instantiated_below;
1946 info = (struct scev_info_str *) htab_find (cache, &pattern);
1954 /* Sets in CACHE the value of VERSION instantiated below basic block
1955 INSTANTIATED_BELOW to VAL. */
1958 set_instantiated_value (htab_t cache, basic_block instantiated_below,
1959 tree version, tree val)
1961 struct scev_info_str *info, pattern;
1964 pattern.var = version;
1965 slot = htab_find_slot (cache, &pattern, INSERT);
1968 *slot = new_scev_info_str (instantiated_below, version);
1969 info = (struct scev_info_str *) *slot;
1973 /* Return the closed_loop_phi node for VAR. If there is none, return
1977 loop_closed_phi_def (tree var)
1982 gimple_stmt_iterator psi;
1984 if (var == NULL_TREE
1985 || TREE_CODE (var) != SSA_NAME)
1988 loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var));
1989 exit = single_exit (loop);
1993 for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); gsi_next (&psi))
1995 phi = gsi_stmt (psi);
1996 if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var)
1997 return PHI_RESULT (phi);
2003 /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW
2004 and EVOLUTION_LOOP, that were left under a symbolic form.
2006 CHREC is the scalar evolution to instantiate.
2008 CACHE is the cache of already instantiated values.
2010 FOLD_CONVERSIONS should be set to true when the conversions that
2011 may wrap in signed/pointer type are folded, as long as the value of
2012 the chrec is preserved.
2014 SIZE_EXPR is used for computing the size of the expression to be
2015 instantiated, and to stop if it exceeds some limit. */
2018 instantiate_scev_1 (basic_block instantiate_below,
2019 struct loop *evolution_loop, tree chrec,
2020 bool fold_conversions, htab_t cache, int size_expr)
2022 tree res, op0, op1, op2;
2024 struct loop *def_loop;
2025 tree type = chrec_type (chrec);
2027 /* Give up if the expression is larger than the MAX that we allow. */
2028 if (size_expr++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
2029 return chrec_dont_know;
2031 if (automatically_generated_chrec_p (chrec)
2032 || is_gimple_min_invariant (chrec))
2035 switch (TREE_CODE (chrec))
2038 def_bb = gimple_bb (SSA_NAME_DEF_STMT (chrec));
2040 /* A parameter (or loop invariant and we do not want to include
2041 evolutions in outer loops), nothing to do. */
2043 || loop_depth (def_bb->loop_father) == 0
2044 || dominated_by_p (CDI_DOMINATORS, instantiate_below, def_bb))
2047 /* We cache the value of instantiated variable to avoid exponential
2048 time complexity due to reevaluations. We also store the convenient
2049 value in the cache in order to prevent infinite recursion -- we do
2050 not want to instantiate the SSA_NAME if it is in a mixer
2051 structure. This is used for avoiding the instantiation of
2052 recursively defined functions, such as:
2054 | a_2 -> {0, +, 1, +, a_2}_1 */
2056 res = get_instantiated_value (cache, instantiate_below, chrec);
2060 res = chrec_dont_know;
2061 set_instantiated_value (cache, instantiate_below, chrec, res);
2063 def_loop = find_common_loop (evolution_loop, def_bb->loop_father);
2065 /* If the analysis yields a parametric chrec, instantiate the
2067 res = analyze_scalar_evolution (def_loop, chrec);
2069 /* Don't instantiate loop-closed-ssa phi nodes. */
2070 if (TREE_CODE (res) == SSA_NAME
2071 && (loop_containing_stmt (SSA_NAME_DEF_STMT (res)) == NULL
2072 || (loop_depth (loop_containing_stmt (SSA_NAME_DEF_STMT (res)))
2073 > loop_depth (def_loop))))
2076 res = loop_closed_phi_def (chrec);
2080 if (res == NULL_TREE)
2081 res = chrec_dont_know;
2084 else if (res != chrec_dont_know)
2085 res = instantiate_scev_1 (instantiate_below, evolution_loop, res,
2086 fold_conversions, cache, size_expr);
2088 /* Store the correct value to the cache. */
2089 set_instantiated_value (cache, instantiate_below, chrec, res);
2092 case POLYNOMIAL_CHREC:
2093 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2094 CHREC_LEFT (chrec), fold_conversions, cache,
2096 if (op0 == chrec_dont_know)
2097 return chrec_dont_know;
2099 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2100 CHREC_RIGHT (chrec), fold_conversions, cache,
2102 if (op1 == chrec_dont_know)
2103 return chrec_dont_know;
2105 if (CHREC_LEFT (chrec) != op0
2106 || CHREC_RIGHT (chrec) != op1)
2108 op1 = chrec_convert_rhs (chrec_type (op0), op1, NULL);
2109 chrec = build_polynomial_chrec (CHREC_VARIABLE (chrec), op0, op1);
2113 case POINTER_PLUS_EXPR:
2115 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2116 TREE_OPERAND (chrec, 0), fold_conversions, cache,
2118 if (op0 == chrec_dont_know)
2119 return chrec_dont_know;
2121 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2122 TREE_OPERAND (chrec, 1), fold_conversions, cache,
2124 if (op1 == chrec_dont_know)
2125 return chrec_dont_know;
2127 if (TREE_OPERAND (chrec, 0) != op0
2128 || TREE_OPERAND (chrec, 1) != op1)
2130 op0 = chrec_convert (type, op0, NULL);
2131 op1 = chrec_convert_rhs (type, op1, NULL);
2132 chrec = chrec_fold_plus (type, op0, op1);
2137 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2138 TREE_OPERAND (chrec, 0), fold_conversions, cache,
2140 if (op0 == chrec_dont_know)
2141 return chrec_dont_know;
2143 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2144 TREE_OPERAND (chrec, 1),
2145 fold_conversions, cache, size_expr);
2146 if (op1 == chrec_dont_know)
2147 return chrec_dont_know;
2149 if (TREE_OPERAND (chrec, 0) != op0
2150 || TREE_OPERAND (chrec, 1) != op1)
2152 op0 = chrec_convert (type, op0, NULL);
2153 op1 = chrec_convert (type, op1, NULL);
2154 chrec = chrec_fold_minus (type, op0, op1);
2159 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2160 TREE_OPERAND (chrec, 0),
2161 fold_conversions, cache, size_expr);
2162 if (op0 == chrec_dont_know)
2163 return chrec_dont_know;
2165 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2166 TREE_OPERAND (chrec, 1),
2167 fold_conversions, cache, size_expr);
2168 if (op1 == chrec_dont_know)
2169 return chrec_dont_know;
2171 if (TREE_OPERAND (chrec, 0) != op0
2172 || TREE_OPERAND (chrec, 1) != op1)
2174 op0 = chrec_convert (type, op0, NULL);
2175 op1 = chrec_convert (type, op1, NULL);
2176 chrec = chrec_fold_multiply (type, op0, op1);
2181 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2182 TREE_OPERAND (chrec, 0),
2183 fold_conversions, cache, size_expr);
2184 if (op0 == chrec_dont_know)
2185 return chrec_dont_know;
2187 if (fold_conversions)
2189 tree tmp = chrec_convert_aggressive (TREE_TYPE (chrec), op0);
2194 if (op0 == TREE_OPERAND (chrec, 0))
2197 /* If we used chrec_convert_aggressive, we can no longer assume that
2198 signed chrecs do not overflow, as chrec_convert does, so avoid
2199 calling it in that case. */
2200 if (fold_conversions)
2201 return fold_convert (TREE_TYPE (chrec), op0);
2203 return chrec_convert (TREE_TYPE (chrec), op0, NULL);
2205 case SCEV_NOT_KNOWN:
2206 return chrec_dont_know;
2215 gcc_assert (!VL_EXP_CLASS_P (chrec));
2216 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
2219 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2220 TREE_OPERAND (chrec, 0),
2221 fold_conversions, cache, size_expr);
2222 if (op0 == chrec_dont_know)
2223 return chrec_dont_know;
2225 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2226 TREE_OPERAND (chrec, 1),
2227 fold_conversions, cache, size_expr);
2228 if (op1 == chrec_dont_know)
2229 return chrec_dont_know;
2231 op2 = instantiate_scev_1 (instantiate_below, evolution_loop,
2232 TREE_OPERAND (chrec, 2),
2233 fold_conversions, cache, size_expr);
2234 if (op2 == chrec_dont_know)
2235 return chrec_dont_know;
2237 if (op0 == TREE_OPERAND (chrec, 0)
2238 && op1 == TREE_OPERAND (chrec, 1)
2239 && op2 == TREE_OPERAND (chrec, 2))
2242 return fold_build3 (TREE_CODE (chrec),
2243 TREE_TYPE (chrec), op0, op1, op2);
2246 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2247 TREE_OPERAND (chrec, 0),
2248 fold_conversions, cache, size_expr);
2249 if (op0 == chrec_dont_know)
2250 return chrec_dont_know;
2252 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2253 TREE_OPERAND (chrec, 1),
2254 fold_conversions, cache, size_expr);
2255 if (op1 == chrec_dont_know)
2256 return chrec_dont_know;
2258 if (op0 == TREE_OPERAND (chrec, 0)
2259 && op1 == TREE_OPERAND (chrec, 1))
2261 return fold_build2 (TREE_CODE (chrec), TREE_TYPE (chrec), op0, op1);
2264 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2265 TREE_OPERAND (chrec, 0),
2266 fold_conversions, cache, size_expr);
2267 if (op0 == chrec_dont_know)
2268 return chrec_dont_know;
2269 if (op0 == TREE_OPERAND (chrec, 0))
2271 return fold_build1 (TREE_CODE (chrec), TREE_TYPE (chrec), op0);
2280 /* Too complicated to handle. */
2281 return chrec_dont_know;
2284 /* Analyze all the parameters of the chrec that were left under a
2285 symbolic form. INSTANTIATE_BELOW is the basic block that stops the
2286 recursive instantiation of parameters: a parameter is a variable
2287 that is defined in a basic block that dominates INSTANTIATE_BELOW or
2288 a function parameter. */
2291 instantiate_scev (basic_block instantiate_below, struct loop *evolution_loop,
2295 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2297 if (dump_file && (dump_flags & TDF_DETAILS))
2299 fprintf (dump_file, "(instantiate_scev \n");
2300 fprintf (dump_file, " (instantiate_below = %d)\n", instantiate_below->index);
2301 fprintf (dump_file, " (evolution_loop = %d)\n", evolution_loop->num);
2302 fprintf (dump_file, " (chrec = ");
2303 print_generic_expr (dump_file, chrec, 0);
2304 fprintf (dump_file, ")\n");
2307 res = instantiate_scev_1 (instantiate_below, evolution_loop, chrec, false,
2310 if (dump_file && (dump_flags & TDF_DETAILS))
2312 fprintf (dump_file, " (res = ");
2313 print_generic_expr (dump_file, res, 0);
2314 fprintf (dump_file, "))\n");
2317 htab_delete (cache);
2322 /* Similar to instantiate_parameters, but does not introduce the
2323 evolutions in outer loops for LOOP invariants in CHREC, and does not
2324 care about causing overflows, as long as they do not affect value
2325 of an expression. */
2328 resolve_mixers (struct loop *loop, tree chrec)
2330 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2331 tree ret = instantiate_scev_1 (block_before_loop (loop), loop, chrec, true,
2333 htab_delete (cache);
2337 /* Entry point for the analysis of the number of iterations pass.
2338 This function tries to safely approximate the number of iterations
2339 the loop will run. When this property is not decidable at compile
2340 time, the result is chrec_dont_know. Otherwise the result is
2341 a scalar or a symbolic parameter.
2343 Example of analysis: suppose that the loop has an exit condition:
2345 "if (b > 49) goto end_loop;"
2347 and that in a previous analysis we have determined that the
2348 variable 'b' has an evolution function:
2350 "EF = {23, +, 5}_2".
2352 When we evaluate the function at the point 5, i.e. the value of the
2353 variable 'b' after 5 iterations in the loop, we have EF (5) = 48,
2354 and EF (6) = 53. In this case the value of 'b' on exit is '53' and
2355 the loop body has been executed 6 times. */
2358 number_of_latch_executions (struct loop *loop)
2362 struct tree_niter_desc niter_desc;
2364 /* Determine whether the number_of_iterations_in_loop has already
2366 res = loop->nb_iterations;
2369 res = chrec_dont_know;
2371 if (dump_file && (dump_flags & TDF_DETAILS))
2372 fprintf (dump_file, "(number_of_iterations_in_loop\n");
2374 exit = single_exit (loop);
2378 if (!number_of_iterations_exit (loop, exit, &niter_desc, false))
2381 type = TREE_TYPE (niter_desc.niter);
2382 if (integer_nonzerop (niter_desc.may_be_zero))
2383 res = build_int_cst (type, 0);
2384 else if (integer_zerop (niter_desc.may_be_zero))
2385 res = niter_desc.niter;
2387 res = chrec_dont_know;
2390 return set_nb_iterations_in_loop (loop, res);
2393 /* Returns the number of executions of the exit condition of LOOP,
2394 i.e., the number by one higher than number_of_latch_executions.
2395 Note that unlike number_of_latch_executions, this number does
2396 not necessarily fit in the unsigned variant of the type of
2397 the control variable -- if the number of iterations is a constant,
2398 we return chrec_dont_know if adding one to number_of_latch_executions
2399 overflows; however, in case the number of iterations is symbolic
2400 expression, the caller is responsible for dealing with this
2401 the possible overflow. */
2404 number_of_exit_cond_executions (struct loop *loop)
2406 tree ret = number_of_latch_executions (loop);
2407 tree type = chrec_type (ret);
2409 if (chrec_contains_undetermined (ret))
2412 ret = chrec_fold_plus (type, ret, build_int_cst (type, 1));
2413 if (TREE_CODE (ret) == INTEGER_CST
2414 && TREE_OVERFLOW (ret))
2415 return chrec_dont_know;
2420 /* One of the drivers for testing the scalar evolutions analysis.
2421 This function computes the number of iterations for all the loops
2422 from the EXIT_CONDITIONS array. */
2425 number_of_iterations_for_all_loops (VEC(gimple,heap) **exit_conditions)
2428 unsigned nb_chrec_dont_know_loops = 0;
2429 unsigned nb_static_loops = 0;
2432 for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
2434 tree res = number_of_latch_executions (loop_containing_stmt (cond));
2435 if (chrec_contains_undetermined (res))
2436 nb_chrec_dont_know_loops++;
2443 fprintf (dump_file, "\n(\n");
2444 fprintf (dump_file, "-----------------------------------------\n");
2445 fprintf (dump_file, "%d\tnb_chrec_dont_know_loops\n", nb_chrec_dont_know_loops);
2446 fprintf (dump_file, "%d\tnb_static_loops\n", nb_static_loops);
2447 fprintf (dump_file, "%d\tnb_total_loops\n", number_of_loops ());
2448 fprintf (dump_file, "-----------------------------------------\n");
2449 fprintf (dump_file, ")\n\n");
2451 print_loops (dump_file, 3);
2457 /* Counters for the stats. */
2463 unsigned nb_affine_multivar;
2464 unsigned nb_higher_poly;
2465 unsigned nb_chrec_dont_know;
2466 unsigned nb_undetermined;
2469 /* Reset the counters. */
2472 reset_chrecs_counters (struct chrec_stats *stats)
2474 stats->nb_chrecs = 0;
2475 stats->nb_affine = 0;
2476 stats->nb_affine_multivar = 0;
2477 stats->nb_higher_poly = 0;
2478 stats->nb_chrec_dont_know = 0;
2479 stats->nb_undetermined = 0;
2482 /* Dump the contents of a CHREC_STATS structure. */
2485 dump_chrecs_stats (FILE *file, struct chrec_stats *stats)
2487 fprintf (file, "\n(\n");
2488 fprintf (file, "-----------------------------------------\n");
2489 fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine);
2490 fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar);
2491 fprintf (file, "%d\tdegree greater than 2 polynomials\n",
2492 stats->nb_higher_poly);
2493 fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know);
2494 fprintf (file, "-----------------------------------------\n");
2495 fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs);
2496 fprintf (file, "%d\twith undetermined coefficients\n",
2497 stats->nb_undetermined);
2498 fprintf (file, "-----------------------------------------\n");
2499 fprintf (file, "%d\tchrecs in the scev database\n",
2500 (int) htab_elements (scalar_evolution_info));
2501 fprintf (file, "%d\tsets in the scev database\n", nb_set_scev);
2502 fprintf (file, "%d\tgets in the scev database\n", nb_get_scev);
2503 fprintf (file, "-----------------------------------------\n");
2504 fprintf (file, ")\n\n");
2507 /* Gather statistics about CHREC. */
2510 gather_chrec_stats (tree chrec, struct chrec_stats *stats)
2512 if (dump_file && (dump_flags & TDF_STATS))
2514 fprintf (dump_file, "(classify_chrec ");
2515 print_generic_expr (dump_file, chrec, 0);
2516 fprintf (dump_file, "\n");
2521 if (chrec == NULL_TREE)
2523 stats->nb_undetermined++;
2527 switch (TREE_CODE (chrec))
2529 case POLYNOMIAL_CHREC:
2530 if (evolution_function_is_affine_p (chrec))
2532 if (dump_file && (dump_flags & TDF_STATS))
2533 fprintf (dump_file, " affine_univariate\n");
2536 else if (evolution_function_is_affine_multivariate_p (chrec, 0))
2538 if (dump_file && (dump_flags & TDF_STATS))
2539 fprintf (dump_file, " affine_multivariate\n");
2540 stats->nb_affine_multivar++;
2544 if (dump_file && (dump_flags & TDF_STATS))
2545 fprintf (dump_file, " higher_degree_polynomial\n");
2546 stats->nb_higher_poly++;
2555 if (chrec_contains_undetermined (chrec))
2557 if (dump_file && (dump_flags & TDF_STATS))
2558 fprintf (dump_file, " undetermined\n");
2559 stats->nb_undetermined++;
2562 if (dump_file && (dump_flags & TDF_STATS))
2563 fprintf (dump_file, ")\n");
2566 /* One of the drivers for testing the scalar evolutions analysis.
2567 This function analyzes the scalar evolution of all the scalars
2568 defined as loop phi nodes in one of the loops from the
2569 EXIT_CONDITIONS array.
2571 TODO Optimization: A loop is in canonical form if it contains only
2572 a single scalar loop phi node. All the other scalars that have an
2573 evolution in the loop are rewritten in function of this single
2574 index. This allows the parallelization of the loop. */
2577 analyze_scalar_evolution_for_all_loop_phi_nodes (VEC(gimple,heap) **exit_conditions)
2580 struct chrec_stats stats;
2582 gimple_stmt_iterator psi;
2584 reset_chrecs_counters (&stats);
2586 for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
2592 loop = loop_containing_stmt (cond);
2595 for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
2597 phi = gsi_stmt (psi);
2598 if (is_gimple_reg (PHI_RESULT (phi)))
2600 chrec = instantiate_parameters
2602 analyze_scalar_evolution (loop, PHI_RESULT (phi)));
2604 if (dump_file && (dump_flags & TDF_STATS))
2605 gather_chrec_stats (chrec, &stats);
2610 if (dump_file && (dump_flags & TDF_STATS))
2611 dump_chrecs_stats (dump_file, &stats);
2614 /* Callback for htab_traverse, gathers information on chrecs in the
2618 gather_stats_on_scev_database_1 (void **slot, void *stats)
2620 struct scev_info_str *entry = (struct scev_info_str *) *slot;
2622 gather_chrec_stats (entry->chrec, (struct chrec_stats *) stats);
2627 /* Classify the chrecs of the whole database. */
2630 gather_stats_on_scev_database (void)
2632 struct chrec_stats stats;
2637 reset_chrecs_counters (&stats);
2639 htab_traverse (scalar_evolution_info, gather_stats_on_scev_database_1,
2642 dump_chrecs_stats (dump_file, &stats);
2650 initialize_scalar_evolutions_analyzer (void)
2652 /* The elements below are unique. */
2653 if (chrec_dont_know == NULL_TREE)
2655 chrec_not_analyzed_yet = NULL_TREE;
2656 chrec_dont_know = make_node (SCEV_NOT_KNOWN);
2657 chrec_known = make_node (SCEV_KNOWN);
2658 TREE_TYPE (chrec_dont_know) = void_type_node;
2659 TREE_TYPE (chrec_known) = void_type_node;
2663 /* Initialize the analysis of scalar evolutions for LOOPS. */
2666 scev_initialize (void)
2671 scalar_evolution_info = htab_create_alloc (100,
2678 initialize_scalar_evolutions_analyzer ();
2680 FOR_EACH_LOOP (li, loop, 0)
2682 loop->nb_iterations = NULL_TREE;
2686 /* Cleans up the information cached by the scalar evolutions analysis. */
2694 if (!scalar_evolution_info || !current_loops)
2697 htab_empty (scalar_evolution_info);
2698 FOR_EACH_LOOP (li, loop, 0)
2700 loop->nb_iterations = NULL_TREE;
2704 /* Checks whether OP behaves as a simple affine iv of LOOP in STMT and returns
2705 its base and step in IV if possible. If ALLOW_NONCONSTANT_STEP is true, we
2706 want step to be invariant in LOOP. Otherwise we require it to be an
2707 integer constant. IV->no_overflow is set to true if we are sure the iv cannot
2708 overflow (e.g. because it is computed in signed arithmetics). */
2711 simple_iv (struct loop *loop, gimple stmt, tree op, affine_iv *iv,
2712 bool allow_nonconstant_step)
2714 basic_block bb = gimple_bb (stmt);
2718 iv->base = NULL_TREE;
2719 iv->step = NULL_TREE;
2720 iv->no_overflow = false;
2722 type = TREE_TYPE (op);
2723 if (TREE_CODE (type) != INTEGER_TYPE
2724 && TREE_CODE (type) != POINTER_TYPE)
2727 ev = analyze_scalar_evolution_in_loop (loop, bb->loop_father, op,
2729 if (chrec_contains_undetermined (ev))
2732 if (tree_does_not_contain_chrecs (ev)
2733 && !chrec_contains_symbols_defined_in_loop (ev, loop->num))
2736 iv->step = build_int_cst (TREE_TYPE (ev), 0);
2737 iv->no_overflow = true;
2741 if (TREE_CODE (ev) != POLYNOMIAL_CHREC
2742 || CHREC_VARIABLE (ev) != (unsigned) loop->num)
2745 iv->step = CHREC_RIGHT (ev);
2746 if (allow_nonconstant_step)
2748 if (tree_contains_chrecs (iv->step, NULL)
2749 || chrec_contains_symbols_defined_in_loop (iv->step, loop->num))
2752 else if (TREE_CODE (iv->step) != INTEGER_CST)
2755 iv->base = CHREC_LEFT (ev);
2756 if (tree_contains_chrecs (iv->base, NULL)
2757 || chrec_contains_symbols_defined_in_loop (iv->base, loop->num))
2760 iv->no_overflow = !folded_casts && TYPE_OVERFLOW_UNDEFINED (type);
2765 /* Runs the analysis of scalar evolutions. */
2768 scev_analysis (void)
2770 VEC(gimple,heap) *exit_conditions;
2772 exit_conditions = VEC_alloc (gimple, heap, 37);
2773 select_loops_exit_conditions (&exit_conditions);
2775 if (dump_file && (dump_flags & TDF_STATS))
2776 analyze_scalar_evolution_for_all_loop_phi_nodes (&exit_conditions);
2778 number_of_iterations_for_all_loops (&exit_conditions);
2779 VEC_free (gimple, heap, exit_conditions);
2782 /* Finalize the scalar evolution analysis. */
2785 scev_finalize (void)
2787 if (!scalar_evolution_info)
2789 htab_delete (scalar_evolution_info);
2790 scalar_evolution_info = NULL;
2793 /* Replace ssa names for that scev can prove they are constant by the
2794 appropriate constants. Also perform final value replacement in loops,
2795 in case the replacement expressions are cheap.
2797 We only consider SSA names defined by phi nodes; rest is left to the
2798 ordinary constant propagation pass. */
2801 scev_const_prop (void)
2804 tree name, type, ev;
2806 struct loop *loop, *ex_loop;
2807 bitmap ssa_names_to_remove = NULL;
2810 gimple_stmt_iterator psi;
2812 if (number_of_loops () <= 1)
2817 loop = bb->loop_father;
2819 for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
2821 phi = gsi_stmt (psi);
2822 name = PHI_RESULT (phi);
2824 if (!is_gimple_reg (name))
2827 type = TREE_TYPE (name);
2829 if (!POINTER_TYPE_P (type)
2830 && !INTEGRAL_TYPE_P (type))
2833 ev = resolve_mixers (loop, analyze_scalar_evolution (loop, name));
2834 if (!is_gimple_min_invariant (ev)
2835 || !may_propagate_copy (name, ev))
2838 /* Replace the uses of the name. */
2840 replace_uses_by (name, ev);
2842 if (!ssa_names_to_remove)
2843 ssa_names_to_remove = BITMAP_ALLOC (NULL);
2844 bitmap_set_bit (ssa_names_to_remove, SSA_NAME_VERSION (name));
2848 /* Remove the ssa names that were replaced by constants. We do not
2849 remove them directly in the previous cycle, since this
2850 invalidates scev cache. */
2851 if (ssa_names_to_remove)
2855 EXECUTE_IF_SET_IN_BITMAP (ssa_names_to_remove, 0, i, bi)
2857 gimple_stmt_iterator psi;
2858 name = ssa_name (i);
2859 phi = SSA_NAME_DEF_STMT (name);
2861 gcc_assert (gimple_code (phi) == GIMPLE_PHI);
2862 psi = gsi_for_stmt (phi);
2863 remove_phi_node (&psi, true);
2866 BITMAP_FREE (ssa_names_to_remove);
2870 /* Now the regular final value replacement. */
2871 FOR_EACH_LOOP (li, loop, LI_FROM_INNERMOST)
2874 tree def, rslt, niter;
2875 gimple_stmt_iterator bsi;
2877 /* If we do not know exact number of iterations of the loop, we cannot
2878 replace the final value. */
2879 exit = single_exit (loop);
2883 niter = number_of_latch_executions (loop);
2884 /* We used to check here whether the computation of NITER is expensive,
2885 and avoided final value elimination if that is the case. The problem
2886 is that it is hard to evaluate whether the expression is too
2887 expensive, as we do not know what optimization opportunities the
2888 elimination of the final value may reveal. Therefore, we now
2889 eliminate the final values of induction variables unconditionally. */
2890 if (niter == chrec_dont_know)
2893 /* Ensure that it is possible to insert new statements somewhere. */
2894 if (!single_pred_p (exit->dest))
2895 split_loop_exit_edge (exit);
2896 bsi = gsi_after_labels (exit->dest);
2898 ex_loop = superloop_at_depth (loop,
2899 loop_depth (exit->dest->loop_father) + 1);
2901 for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); )
2903 phi = gsi_stmt (psi);
2904 rslt = PHI_RESULT (phi);
2905 def = PHI_ARG_DEF_FROM_EDGE (phi, exit);
2906 if (!is_gimple_reg (def))
2912 if (!POINTER_TYPE_P (TREE_TYPE (def))
2913 && !INTEGRAL_TYPE_P (TREE_TYPE (def)))
2919 def = analyze_scalar_evolution_in_loop (ex_loop, loop, def, NULL);
2920 def = compute_overall_effect_of_inner_loop (ex_loop, def);
2921 if (!tree_does_not_contain_chrecs (def)
2922 || chrec_contains_symbols_defined_in_loop (def, ex_loop->num)
2923 /* Moving the computation from the loop may prolong life range
2924 of some ssa names, which may cause problems if they appear
2925 on abnormal edges. */
2926 || contains_abnormal_ssa_name_p (def))
2932 /* Eliminate the PHI node and replace it by a computation outside
2934 def = unshare_expr (def);
2935 remove_phi_node (&psi, false);
2937 def = force_gimple_operand_gsi (&bsi, def, false, NULL_TREE,
2938 true, GSI_SAME_STMT);
2939 ass = gimple_build_assign (rslt, def);
2940 gsi_insert_before (&bsi, ass, GSI_SAME_STMT);
2946 #include "gt-tree-scalar-evolution.h"