1 /* Scalar evolution detector.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009
3 Free Software Foundation, Inc.
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);
1232 case GIMPLE_UNARY_RHS:
1233 if (code == NOP_EXPR)
1235 /* This assignment is under the form "a_1 = (cast) rhs. */
1237 = follow_ssa_edge_expr (loop, stmt, gimple_assign_rhs1 (stmt),
1238 halting_phi, evolution_of_loop, limit);
1239 *evolution_of_loop = chrec_convert (type, *evolution_of_loop, stmt);
1249 /* Checks whether the I-th argument of a PHI comes from a backedge. */
1252 backedge_phi_arg_p (gimple phi, int i)
1254 const_edge e = gimple_phi_arg_edge (phi, i);
1256 /* We would in fact like to test EDGE_DFS_BACK here, but we do not care
1257 about updating it anywhere, and this should work as well most of the
1259 if (e->flags & EDGE_IRREDUCIBLE_LOOP)
1265 /* Helper function for one branch of the condition-phi-node. Return
1266 true if the strongly connected component has been found following
1269 static inline t_bool
1270 follow_ssa_edge_in_condition_phi_branch (int i,
1272 gimple condition_phi,
1274 tree *evolution_of_branch,
1275 tree init_cond, int limit)
1277 tree branch = PHI_ARG_DEF (condition_phi, i);
1278 *evolution_of_branch = chrec_dont_know;
1280 /* Do not follow back edges (they must belong to an irreducible loop, which
1281 we really do not want to worry about). */
1282 if (backedge_phi_arg_p (condition_phi, i))
1285 if (TREE_CODE (branch) == SSA_NAME)
1287 *evolution_of_branch = init_cond;
1288 return follow_ssa_edge (loop, SSA_NAME_DEF_STMT (branch), halting_phi,
1289 evolution_of_branch, limit);
1292 /* This case occurs when one of the condition branches sets
1293 the variable to a constant: i.e. a phi-node like
1294 "a_2 = PHI <a_7(5), 2(6)>;".
1296 FIXME: This case have to be refined correctly:
1297 in some cases it is possible to say something better than
1298 chrec_dont_know, for example using a wrap-around notation. */
1302 /* This function merges the branches of a condition-phi-node in a
1306 follow_ssa_edge_in_condition_phi (struct loop *loop,
1307 gimple condition_phi,
1309 tree *evolution_of_loop, int limit)
1312 tree init = *evolution_of_loop;
1313 tree evolution_of_branch;
1314 t_bool res = follow_ssa_edge_in_condition_phi_branch (0, loop, condition_phi,
1316 &evolution_of_branch,
1318 if (res == t_false || res == t_dont_know)
1321 *evolution_of_loop = evolution_of_branch;
1323 n = gimple_phi_num_args (condition_phi);
1324 for (i = 1; i < n; i++)
1326 /* Quickly give up when the evolution of one of the branches is
1328 if (*evolution_of_loop == chrec_dont_know)
1331 /* Increase the limit by the PHI argument number to avoid exponential
1332 time and memory complexity. */
1333 res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi,
1335 &evolution_of_branch,
1337 if (res == t_false || res == t_dont_know)
1340 *evolution_of_loop = chrec_merge (*evolution_of_loop,
1341 evolution_of_branch);
1347 /* Follow an SSA edge in an inner loop. It computes the overall
1348 effect of the loop, and following the symbolic initial conditions,
1349 it follows the edges in the parent loop. The inner loop is
1350 considered as a single statement. */
1353 follow_ssa_edge_inner_loop_phi (struct loop *outer_loop,
1354 gimple loop_phi_node,
1356 tree *evolution_of_loop, int limit)
1358 struct loop *loop = loop_containing_stmt (loop_phi_node);
1359 tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node));
1361 /* Sometimes, the inner loop is too difficult to analyze, and the
1362 result of the analysis is a symbolic parameter. */
1363 if (ev == PHI_RESULT (loop_phi_node))
1365 t_bool res = t_false;
1366 int i, n = gimple_phi_num_args (loop_phi_node);
1368 for (i = 0; i < n; i++)
1370 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1373 /* Follow the edges that exit the inner loop. */
1374 bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1375 if (!flow_bb_inside_loop_p (loop, bb))
1376 res = follow_ssa_edge_expr (outer_loop, loop_phi_node,
1378 evolution_of_loop, limit);
1383 /* If the path crosses this loop-phi, give up. */
1385 *evolution_of_loop = chrec_dont_know;
1390 /* Otherwise, compute the overall effect of the inner loop. */
1391 ev = compute_overall_effect_of_inner_loop (loop, ev);
1392 return follow_ssa_edge_expr (outer_loop, loop_phi_node, ev, halting_phi,
1393 evolution_of_loop, limit);
1396 /* Follow an SSA edge from a loop-phi-node to itself, constructing a
1397 path that is analyzed on the return walk. */
1400 follow_ssa_edge (struct loop *loop, gimple def, gimple halting_phi,
1401 tree *evolution_of_loop, int limit)
1403 struct loop *def_loop;
1405 if (gimple_nop_p (def))
1408 /* Give up if the path is longer than the MAX that we allow. */
1409 if (limit > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
1412 def_loop = loop_containing_stmt (def);
1414 switch (gimple_code (def))
1417 if (!loop_phi_node_p (def))
1418 /* DEF is a condition-phi-node. Follow the branches, and
1419 record their evolutions. Finally, merge the collected
1420 information and set the approximation to the main
1422 return follow_ssa_edge_in_condition_phi
1423 (loop, def, halting_phi, evolution_of_loop, limit);
1425 /* When the analyzed phi is the halting_phi, the
1426 depth-first search is over: we have found a path from
1427 the halting_phi to itself in the loop. */
1428 if (def == halting_phi)
1431 /* Otherwise, the evolution of the HALTING_PHI depends
1432 on the evolution of another loop-phi-node, i.e. the
1433 evolution function is a higher degree polynomial. */
1434 if (def_loop == loop)
1438 if (flow_loop_nested_p (loop, def_loop))
1439 return follow_ssa_edge_inner_loop_phi
1440 (loop, def, halting_phi, evolution_of_loop, limit + 1);
1446 return follow_ssa_edge_in_rhs (loop, def, halting_phi,
1447 evolution_of_loop, limit);
1450 /* At this level of abstraction, the program is just a set
1451 of GIMPLE_ASSIGNs and PHI_NODEs. In principle there is no
1452 other node to be handled. */
1459 /* Given a LOOP_PHI_NODE, this function determines the evolution
1460 function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop. */
1463 analyze_evolution_in_loop (gimple loop_phi_node,
1466 int i, n = gimple_phi_num_args (loop_phi_node);
1467 tree evolution_function = chrec_not_analyzed_yet;
1468 struct loop *loop = loop_containing_stmt (loop_phi_node);
1471 if (dump_file && (dump_flags & TDF_DETAILS))
1473 fprintf (dump_file, "(analyze_evolution_in_loop \n");
1474 fprintf (dump_file, " (loop_phi_node = ");
1475 print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
1476 fprintf (dump_file, ")\n");
1479 for (i = 0; i < n; i++)
1481 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1486 /* Select the edges that enter the loop body. */
1487 bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1488 if (!flow_bb_inside_loop_p (loop, bb))
1491 if (TREE_CODE (arg) == SSA_NAME)
1493 ssa_chain = SSA_NAME_DEF_STMT (arg);
1495 /* Pass in the initial condition to the follow edge function. */
1497 res = follow_ssa_edge (loop, ssa_chain, loop_phi_node, &ev_fn, 0);
1502 /* When it is impossible to go back on the same
1503 loop_phi_node by following the ssa edges, the
1504 evolution is represented by a peeled chrec, i.e. the
1505 first iteration, EV_FN has the value INIT_COND, then
1506 all the other iterations it has the value of ARG.
1507 For the moment, PEELED_CHREC nodes are not built. */
1509 ev_fn = chrec_dont_know;
1511 /* When there are multiple back edges of the loop (which in fact never
1512 happens currently, but nevertheless), merge their evolutions. */
1513 evolution_function = chrec_merge (evolution_function, ev_fn);
1516 if (dump_file && (dump_flags & TDF_DETAILS))
1518 fprintf (dump_file, " (evolution_function = ");
1519 print_generic_expr (dump_file, evolution_function, 0);
1520 fprintf (dump_file, "))\n");
1523 return evolution_function;
1526 /* Given a loop-phi-node, return the initial conditions of the
1527 variable on entry of the loop. When the CCP has propagated
1528 constants into the loop-phi-node, the initial condition is
1529 instantiated, otherwise the initial condition is kept symbolic.
1530 This analyzer does not analyze the evolution outside the current
1531 loop, and leaves this task to the on-demand tree reconstructor. */
1534 analyze_initial_condition (gimple loop_phi_node)
1537 tree init_cond = chrec_not_analyzed_yet;
1538 struct loop *loop = loop_containing_stmt (loop_phi_node);
1540 if (dump_file && (dump_flags & TDF_DETAILS))
1542 fprintf (dump_file, "(analyze_initial_condition \n");
1543 fprintf (dump_file, " (loop_phi_node = \n");
1544 print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
1545 fprintf (dump_file, ")\n");
1548 n = gimple_phi_num_args (loop_phi_node);
1549 for (i = 0; i < n; i++)
1551 tree branch = PHI_ARG_DEF (loop_phi_node, i);
1552 basic_block bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1554 /* When the branch is oriented to the loop's body, it does
1555 not contribute to the initial condition. */
1556 if (flow_bb_inside_loop_p (loop, bb))
1559 if (init_cond == chrec_not_analyzed_yet)
1565 if (TREE_CODE (branch) == SSA_NAME)
1567 init_cond = chrec_dont_know;
1571 init_cond = chrec_merge (init_cond, branch);
1574 /* Ooops -- a loop without an entry??? */
1575 if (init_cond == chrec_not_analyzed_yet)
1576 init_cond = chrec_dont_know;
1578 if (dump_file && (dump_flags & TDF_DETAILS))
1580 fprintf (dump_file, " (init_cond = ");
1581 print_generic_expr (dump_file, init_cond, 0);
1582 fprintf (dump_file, "))\n");
1588 /* Analyze the scalar evolution for LOOP_PHI_NODE. */
1591 interpret_loop_phi (struct loop *loop, gimple loop_phi_node)
1594 struct loop *phi_loop = loop_containing_stmt (loop_phi_node);
1597 if (phi_loop != loop)
1599 struct loop *subloop;
1600 tree evolution_fn = analyze_scalar_evolution
1601 (phi_loop, PHI_RESULT (loop_phi_node));
1603 /* Dive one level deeper. */
1604 subloop = superloop_at_depth (phi_loop, loop_depth (loop) + 1);
1606 /* Interpret the subloop. */
1607 res = compute_overall_effect_of_inner_loop (subloop, evolution_fn);
1611 /* Otherwise really interpret the loop phi. */
1612 init_cond = analyze_initial_condition (loop_phi_node);
1613 res = analyze_evolution_in_loop (loop_phi_node, init_cond);
1618 /* This function merges the branches of a condition-phi-node,
1619 contained in the outermost loop, and whose arguments are already
1623 interpret_condition_phi (struct loop *loop, gimple condition_phi)
1625 int i, n = gimple_phi_num_args (condition_phi);
1626 tree res = chrec_not_analyzed_yet;
1628 for (i = 0; i < n; i++)
1632 if (backedge_phi_arg_p (condition_phi, i))
1634 res = chrec_dont_know;
1638 branch_chrec = analyze_scalar_evolution
1639 (loop, PHI_ARG_DEF (condition_phi, i));
1641 res = chrec_merge (res, branch_chrec);
1647 /* Interpret the operation RHS1 OP RHS2. If we didn't
1648 analyze this node before, follow the definitions until ending
1649 either on an analyzed GIMPLE_ASSIGN, or on a loop-phi-node. On the
1650 return path, this function propagates evolutions (ala constant copy
1651 propagation). OPND1 is not a GIMPLE expression because we could
1652 analyze the effect of an inner loop: see interpret_loop_phi. */
1655 interpret_rhs_expr (struct loop *loop, gimple at_stmt,
1656 tree type, tree rhs1, enum tree_code code, tree rhs2)
1658 tree res, chrec1, chrec2;
1660 if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS)
1662 if (is_gimple_min_invariant (rhs1))
1663 return chrec_convert (type, rhs1, at_stmt);
1665 if (code == SSA_NAME)
1666 return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
1669 if (code == ASSERT_EXPR)
1671 rhs1 = ASSERT_EXPR_VAR (rhs1);
1672 return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
1676 return chrec_dont_know;
1681 case POINTER_PLUS_EXPR:
1682 chrec1 = analyze_scalar_evolution (loop, rhs1);
1683 chrec2 = analyze_scalar_evolution (loop, rhs2);
1684 chrec1 = chrec_convert (type, chrec1, at_stmt);
1685 chrec2 = chrec_convert (sizetype, chrec2, at_stmt);
1686 res = chrec_fold_plus (type, chrec1, chrec2);
1690 chrec1 = analyze_scalar_evolution (loop, rhs1);
1691 chrec2 = analyze_scalar_evolution (loop, rhs2);
1692 chrec1 = chrec_convert (type, chrec1, at_stmt);
1693 chrec2 = chrec_convert (type, chrec2, at_stmt);
1694 res = chrec_fold_plus (type, chrec1, chrec2);
1698 chrec1 = analyze_scalar_evolution (loop, rhs1);
1699 chrec2 = analyze_scalar_evolution (loop, rhs2);
1700 chrec1 = chrec_convert (type, chrec1, at_stmt);
1701 chrec2 = chrec_convert (type, chrec2, at_stmt);
1702 res = chrec_fold_minus (type, chrec1, chrec2);
1706 chrec1 = analyze_scalar_evolution (loop, rhs1);
1707 chrec1 = chrec_convert (type, chrec1, at_stmt);
1708 /* TYPE may be integer, real or complex, so use fold_convert. */
1709 res = chrec_fold_multiply (type, chrec1,
1710 fold_convert (type, integer_minus_one_node));
1714 /* Handle ~X as -1 - X. */
1715 chrec1 = analyze_scalar_evolution (loop, rhs1);
1716 chrec1 = chrec_convert (type, chrec1, at_stmt);
1717 res = chrec_fold_minus (type,
1718 fold_convert (type, integer_minus_one_node),
1723 chrec1 = analyze_scalar_evolution (loop, rhs1);
1724 chrec2 = analyze_scalar_evolution (loop, rhs2);
1725 chrec1 = chrec_convert (type, chrec1, at_stmt);
1726 chrec2 = chrec_convert (type, chrec2, at_stmt);
1727 res = chrec_fold_multiply (type, chrec1, chrec2);
1731 chrec1 = analyze_scalar_evolution (loop, rhs1);
1732 res = chrec_convert (type, chrec1, at_stmt);
1736 res = chrec_dont_know;
1743 /* Interpret the expression EXPR. */
1746 interpret_expr (struct loop *loop, gimple at_stmt, tree expr)
1748 enum tree_code code;
1749 tree type = TREE_TYPE (expr), op0, op1;
1751 if (automatically_generated_chrec_p (expr))
1754 if (TREE_CODE (expr) == POLYNOMIAL_CHREC)
1755 return chrec_dont_know;
1757 extract_ops_from_tree (expr, &code, &op0, &op1);
1759 return interpret_rhs_expr (loop, at_stmt, type,
1763 /* Interpret the rhs of the assignment STMT. */
1766 interpret_gimple_assign (struct loop *loop, gimple stmt)
1768 tree type = TREE_TYPE (gimple_assign_lhs (stmt));
1769 enum tree_code code = gimple_assign_rhs_code (stmt);
1771 return interpret_rhs_expr (loop, stmt, type,
1772 gimple_assign_rhs1 (stmt), code,
1773 gimple_assign_rhs2 (stmt));
1778 /* This section contains all the entry points:
1779 - number_of_iterations_in_loop,
1780 - analyze_scalar_evolution,
1781 - instantiate_parameters.
1784 /* Compute and return the evolution function in WRTO_LOOP, the nearest
1785 common ancestor of DEF_LOOP and USE_LOOP. */
1788 compute_scalar_evolution_in_loop (struct loop *wrto_loop,
1789 struct loop *def_loop,
1793 if (def_loop == wrto_loop)
1796 def_loop = superloop_at_depth (def_loop, loop_depth (wrto_loop) + 1);
1797 res = compute_overall_effect_of_inner_loop (def_loop, ev);
1799 return analyze_scalar_evolution_1 (wrto_loop, res, chrec_not_analyzed_yet);
1802 /* Helper recursive function. */
1805 analyze_scalar_evolution_1 (struct loop *loop, tree var, tree res)
1807 tree type = TREE_TYPE (var);
1810 struct loop *def_loop;
1812 if (loop == NULL || TREE_CODE (type) == VECTOR_TYPE)
1813 return chrec_dont_know;
1815 if (TREE_CODE (var) != SSA_NAME)
1816 return interpret_expr (loop, NULL, var);
1818 def = SSA_NAME_DEF_STMT (var);
1819 bb = gimple_bb (def);
1820 def_loop = bb ? bb->loop_father : NULL;
1823 || !flow_bb_inside_loop_p (loop, bb))
1825 /* Keep the symbolic form. */
1830 if (res != chrec_not_analyzed_yet)
1832 if (loop != bb->loop_father)
1833 res = compute_scalar_evolution_in_loop
1834 (find_common_loop (loop, bb->loop_father), bb->loop_father, res);
1839 if (loop != def_loop)
1841 res = analyze_scalar_evolution_1 (def_loop, var, chrec_not_analyzed_yet);
1842 res = compute_scalar_evolution_in_loop (loop, def_loop, res);
1847 switch (gimple_code (def))
1850 res = interpret_gimple_assign (loop, def);
1854 if (loop_phi_node_p (def))
1855 res = interpret_loop_phi (loop, def);
1857 res = interpret_condition_phi (loop, def);
1861 res = chrec_dont_know;
1867 /* Keep the symbolic form. */
1868 if (res == chrec_dont_know)
1871 if (loop == def_loop)
1872 set_scalar_evolution (block_before_loop (loop), var, res);
1877 /* Entry point for the scalar evolution analyzer.
1878 Analyzes and returns the scalar evolution of the ssa_name VAR.
1879 LOOP_NB is the identifier number of the loop in which the variable
1882 Example of use: having a pointer VAR to a SSA_NAME node, STMT a
1883 pointer to the statement that uses this variable, in order to
1884 determine the evolution function of the variable, use the following
1887 unsigned loop_nb = loop_containing_stmt (stmt)->num;
1888 tree chrec_with_symbols = analyze_scalar_evolution (loop_nb, var);
1889 tree chrec_instantiated = instantiate_parameters (loop, chrec_with_symbols);
1893 analyze_scalar_evolution (struct loop *loop, tree var)
1897 if (dump_file && (dump_flags & TDF_DETAILS))
1899 fprintf (dump_file, "(analyze_scalar_evolution \n");
1900 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
1901 fprintf (dump_file, " (scalar = ");
1902 print_generic_expr (dump_file, var, 0);
1903 fprintf (dump_file, ")\n");
1906 res = get_scalar_evolution (block_before_loop (loop), var);
1907 res = analyze_scalar_evolution_1 (loop, var, res);
1909 if (dump_file && (dump_flags & TDF_DETAILS))
1910 fprintf (dump_file, ")\n");
1915 /* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to
1916 WRTO_LOOP (which should be a superloop of USE_LOOP)
1918 FOLDED_CASTS is set to true if resolve_mixers used
1919 chrec_convert_aggressive (TODO -- not really, we are way too conservative
1920 at the moment in order to keep things simple).
1922 To illustrate the meaning of USE_LOOP and WRTO_LOOP, consider the following
1925 for (i = 0; i < 100; i++) -- loop 1
1927 for (j = 0; j < 100; j++) -- loop 2
1934 for (t = 0; t < 100; t++) -- loop 3
1941 Both k1 and k2 are invariants in loop3, thus
1942 analyze_scalar_evolution_in_loop (loop3, loop3, k1) = k1
1943 analyze_scalar_evolution_in_loop (loop3, loop3, k2) = k2
1945 As they are invariant, it does not matter whether we consider their
1946 usage in loop 3 or loop 2, hence
1947 analyze_scalar_evolution_in_loop (loop2, loop3, k1) =
1948 analyze_scalar_evolution_in_loop (loop2, loop2, k1) = i
1949 analyze_scalar_evolution_in_loop (loop2, loop3, k2) =
1950 analyze_scalar_evolution_in_loop (loop2, loop2, k2) = [0,+,1]_2
1952 Similarly for their evolutions with respect to loop 1. The values of K2
1953 in the use in loop 2 vary independently on loop 1, thus we cannot express
1954 the evolution with respect to loop 1:
1955 analyze_scalar_evolution_in_loop (loop1, loop3, k1) =
1956 analyze_scalar_evolution_in_loop (loop1, loop2, k1) = [0,+,1]_1
1957 analyze_scalar_evolution_in_loop (loop1, loop3, k2) =
1958 analyze_scalar_evolution_in_loop (loop1, loop2, k2) = dont_know
1960 The value of k2 in the use in loop 1 is known, though:
1961 analyze_scalar_evolution_in_loop (loop1, loop1, k1) = [0,+,1]_1
1962 analyze_scalar_evolution_in_loop (loop1, loop1, k2) = 100
1966 analyze_scalar_evolution_in_loop (struct loop *wrto_loop, struct loop *use_loop,
1967 tree version, bool *folded_casts)
1970 tree ev = version, tmp;
1972 /* We cannot just do
1974 tmp = analyze_scalar_evolution (use_loop, version);
1975 ev = resolve_mixers (wrto_loop, tmp);
1977 as resolve_mixers would query the scalar evolution with respect to
1978 wrto_loop. For example, in the situation described in the function
1979 comment, suppose that wrto_loop = loop1, use_loop = loop3 and
1982 analyze_scalar_evolution (use_loop, version) = k2
1984 and resolve_mixers (loop1, k2) finds that the value of k2 in loop 1
1985 is 100, which is a wrong result, since we are interested in the
1988 Instead, we need to proceed from use_loop to wrto_loop loop by loop,
1989 each time checking that there is no evolution in the inner loop. */
1992 *folded_casts = false;
1995 tmp = analyze_scalar_evolution (use_loop, ev);
1996 ev = resolve_mixers (use_loop, tmp);
1998 if (folded_casts && tmp != ev)
1999 *folded_casts = true;
2001 if (use_loop == wrto_loop)
2004 /* If the value of the use changes in the inner loop, we cannot express
2005 its value in the outer loop (we might try to return interval chrec,
2006 but we do not have a user for it anyway) */
2007 if (!no_evolution_in_loop_p (ev, use_loop->num, &val)
2009 return chrec_dont_know;
2011 use_loop = loop_outer (use_loop);
2015 /* Returns from CACHE the value for VERSION instantiated below
2016 INSTANTIATED_BELOW block. */
2019 get_instantiated_value (htab_t cache, basic_block instantiated_below,
2022 struct scev_info_str *info, pattern;
2024 pattern.var = version;
2025 pattern.instantiated_below = instantiated_below;
2026 info = (struct scev_info_str *) htab_find (cache, &pattern);
2034 /* Sets in CACHE the value of VERSION instantiated below basic block
2035 INSTANTIATED_BELOW to VAL. */
2038 set_instantiated_value (htab_t cache, basic_block instantiated_below,
2039 tree version, tree val)
2041 struct scev_info_str *info, pattern;
2044 pattern.var = version;
2045 pattern.instantiated_below = instantiated_below;
2046 slot = htab_find_slot (cache, &pattern, INSERT);
2049 *slot = new_scev_info_str (instantiated_below, version);
2050 info = (struct scev_info_str *) *slot;
2054 /* Return the closed_loop_phi node for VAR. If there is none, return
2058 loop_closed_phi_def (tree var)
2063 gimple_stmt_iterator psi;
2065 if (var == NULL_TREE
2066 || TREE_CODE (var) != SSA_NAME)
2069 loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var));
2070 exit = single_exit (loop);
2074 for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); gsi_next (&psi))
2076 phi = gsi_stmt (psi);
2077 if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var)
2078 return PHI_RESULT (phi);
2084 /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW
2085 and EVOLUTION_LOOP, that were left under a symbolic form.
2087 CHREC is the scalar evolution to instantiate.
2089 CACHE is the cache of already instantiated values.
2091 FOLD_CONVERSIONS should be set to true when the conversions that
2092 may wrap in signed/pointer type are folded, as long as the value of
2093 the chrec is preserved.
2095 SIZE_EXPR is used for computing the size of the expression to be
2096 instantiated, and to stop if it exceeds some limit. */
2099 instantiate_scev_1 (basic_block instantiate_below,
2100 struct loop *evolution_loop, tree chrec,
2101 bool fold_conversions, htab_t cache, int size_expr)
2103 tree res, op0, op1, op2;
2105 struct loop *def_loop;
2106 tree type = chrec_type (chrec);
2108 /* Give up if the expression is larger than the MAX that we allow. */
2109 if (size_expr++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
2110 return chrec_dont_know;
2112 if (automatically_generated_chrec_p (chrec)
2113 || is_gimple_min_invariant (chrec))
2116 switch (TREE_CODE (chrec))
2119 def_bb = gimple_bb (SSA_NAME_DEF_STMT (chrec));
2121 /* A parameter (or loop invariant and we do not want to include
2122 evolutions in outer loops), nothing to do. */
2124 || loop_depth (def_bb->loop_father) == 0
2125 || dominated_by_p (CDI_DOMINATORS, instantiate_below, def_bb))
2128 /* We cache the value of instantiated variable to avoid exponential
2129 time complexity due to reevaluations. We also store the convenient
2130 value in the cache in order to prevent infinite recursion -- we do
2131 not want to instantiate the SSA_NAME if it is in a mixer
2132 structure. This is used for avoiding the instantiation of
2133 recursively defined functions, such as:
2135 | a_2 -> {0, +, 1, +, a_2}_1 */
2137 res = get_instantiated_value (cache, instantiate_below, chrec);
2141 res = chrec_dont_know;
2142 set_instantiated_value (cache, instantiate_below, chrec, res);
2144 def_loop = find_common_loop (evolution_loop, def_bb->loop_father);
2146 /* If the analysis yields a parametric chrec, instantiate the
2148 res = analyze_scalar_evolution (def_loop, chrec);
2150 /* Don't instantiate loop-closed-ssa phi nodes. */
2151 if (TREE_CODE (res) == SSA_NAME
2152 && (loop_containing_stmt (SSA_NAME_DEF_STMT (res)) == NULL
2153 || (loop_depth (loop_containing_stmt (SSA_NAME_DEF_STMT (res)))
2154 > loop_depth (def_loop))))
2157 res = loop_closed_phi_def (chrec);
2161 if (res == NULL_TREE)
2162 res = chrec_dont_know;
2165 else if (res != chrec_dont_know)
2166 res = instantiate_scev_1 (instantiate_below, evolution_loop, res,
2167 fold_conversions, cache, size_expr);
2169 /* Store the correct value to the cache. */
2170 set_instantiated_value (cache, instantiate_below, chrec, res);
2173 case POLYNOMIAL_CHREC:
2174 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2175 CHREC_LEFT (chrec), fold_conversions, cache,
2177 if (op0 == chrec_dont_know)
2178 return chrec_dont_know;
2180 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2181 CHREC_RIGHT (chrec), fold_conversions, cache,
2183 if (op1 == chrec_dont_know)
2184 return chrec_dont_know;
2186 if (CHREC_LEFT (chrec) != op0
2187 || CHREC_RIGHT (chrec) != op1)
2189 unsigned var = CHREC_VARIABLE (chrec);
2191 /* When the instantiated stride or base has an evolution in an
2192 innermost loop, return chrec_dont_know, as this is not a
2193 valid SCEV representation. In the reduced testcase for
2194 PR40281 we would have {0, +, {1, +, 1}_2}_1 that has no
2196 if ((tree_is_chrec (op0) && CHREC_VARIABLE (op0) > var)
2197 || (tree_is_chrec (op1) && CHREC_VARIABLE (op1) > var))
2198 return chrec_dont_know;
2200 op1 = chrec_convert_rhs (chrec_type (op0), op1, NULL);
2201 chrec = build_polynomial_chrec (var, op0, op1);
2205 case POINTER_PLUS_EXPR:
2207 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2208 TREE_OPERAND (chrec, 0), fold_conversions, cache,
2210 if (op0 == chrec_dont_know)
2211 return chrec_dont_know;
2213 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2214 TREE_OPERAND (chrec, 1), fold_conversions, cache,
2216 if (op1 == chrec_dont_know)
2217 return chrec_dont_know;
2219 if (TREE_OPERAND (chrec, 0) != op0
2220 || TREE_OPERAND (chrec, 1) != op1)
2222 op0 = chrec_convert (type, op0, NULL);
2223 op1 = chrec_convert_rhs (type, op1, NULL);
2224 chrec = chrec_fold_plus (type, op0, op1);
2229 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2230 TREE_OPERAND (chrec, 0), fold_conversions, cache,
2232 if (op0 == chrec_dont_know)
2233 return chrec_dont_know;
2235 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2236 TREE_OPERAND (chrec, 1),
2237 fold_conversions, cache, size_expr);
2238 if (op1 == chrec_dont_know)
2239 return chrec_dont_know;
2241 if (TREE_OPERAND (chrec, 0) != op0
2242 || TREE_OPERAND (chrec, 1) != op1)
2244 op0 = chrec_convert (type, op0, NULL);
2245 op1 = chrec_convert (type, op1, NULL);
2246 chrec = chrec_fold_minus (type, op0, op1);
2251 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2252 TREE_OPERAND (chrec, 0),
2253 fold_conversions, cache, size_expr);
2254 if (op0 == chrec_dont_know)
2255 return chrec_dont_know;
2257 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2258 TREE_OPERAND (chrec, 1),
2259 fold_conversions, cache, size_expr);
2260 if (op1 == chrec_dont_know)
2261 return chrec_dont_know;
2263 if (TREE_OPERAND (chrec, 0) != op0
2264 || TREE_OPERAND (chrec, 1) != op1)
2266 op0 = chrec_convert (type, op0, NULL);
2267 op1 = chrec_convert (type, op1, NULL);
2268 chrec = chrec_fold_multiply (type, op0, op1);
2273 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2274 TREE_OPERAND (chrec, 0),
2275 fold_conversions, cache, size_expr);
2276 if (op0 == chrec_dont_know)
2277 return chrec_dont_know;
2279 if (fold_conversions)
2281 tree tmp = chrec_convert_aggressive (TREE_TYPE (chrec), op0);
2286 if (op0 == TREE_OPERAND (chrec, 0))
2289 /* If we used chrec_convert_aggressive, we can no longer assume that
2290 signed chrecs do not overflow, as chrec_convert does, so avoid
2291 calling it in that case. */
2292 if (fold_conversions)
2293 return fold_convert (TREE_TYPE (chrec), op0);
2295 return chrec_convert (TREE_TYPE (chrec), op0, NULL);
2298 /* Handle ~X as -1 - X. */
2299 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2300 TREE_OPERAND (chrec, 0),
2301 fold_conversions, cache, size_expr);
2302 if (op0 == chrec_dont_know)
2303 return chrec_dont_know;
2305 if (TREE_OPERAND (chrec, 0) != op0)
2307 op0 = chrec_convert (type, op0, NULL);
2308 chrec = chrec_fold_minus (type,
2310 integer_minus_one_node),
2315 case SCEV_NOT_KNOWN:
2316 return chrec_dont_know;
2325 if (VL_EXP_CLASS_P (chrec))
2326 return chrec_dont_know;
2328 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
2331 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2332 TREE_OPERAND (chrec, 0),
2333 fold_conversions, cache, size_expr);
2334 if (op0 == chrec_dont_know)
2335 return chrec_dont_know;
2337 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2338 TREE_OPERAND (chrec, 1),
2339 fold_conversions, cache, size_expr);
2340 if (op1 == chrec_dont_know)
2341 return chrec_dont_know;
2343 op2 = instantiate_scev_1 (instantiate_below, evolution_loop,
2344 TREE_OPERAND (chrec, 2),
2345 fold_conversions, cache, size_expr);
2346 if (op2 == chrec_dont_know)
2347 return chrec_dont_know;
2349 if (op0 == TREE_OPERAND (chrec, 0)
2350 && op1 == TREE_OPERAND (chrec, 1)
2351 && op2 == TREE_OPERAND (chrec, 2))
2354 return fold_build3 (TREE_CODE (chrec),
2355 TREE_TYPE (chrec), op0, op1, op2);
2358 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2359 TREE_OPERAND (chrec, 0),
2360 fold_conversions, cache, size_expr);
2361 if (op0 == chrec_dont_know)
2362 return chrec_dont_know;
2364 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2365 TREE_OPERAND (chrec, 1),
2366 fold_conversions, cache, size_expr);
2367 if (op1 == chrec_dont_know)
2368 return chrec_dont_know;
2370 if (op0 == TREE_OPERAND (chrec, 0)
2371 && op1 == TREE_OPERAND (chrec, 1))
2373 return fold_build2 (TREE_CODE (chrec), TREE_TYPE (chrec), op0, op1);
2376 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2377 TREE_OPERAND (chrec, 0),
2378 fold_conversions, cache, size_expr);
2379 if (op0 == chrec_dont_know)
2380 return chrec_dont_know;
2381 if (op0 == TREE_OPERAND (chrec, 0))
2383 return fold_build1 (TREE_CODE (chrec), TREE_TYPE (chrec), op0);
2392 /* Too complicated to handle. */
2393 return chrec_dont_know;
2396 /* Analyze all the parameters of the chrec that were left under a
2397 symbolic form. INSTANTIATE_BELOW is the basic block that stops the
2398 recursive instantiation of parameters: a parameter is a variable
2399 that is defined in a basic block that dominates INSTANTIATE_BELOW or
2400 a function parameter. */
2403 instantiate_scev (basic_block instantiate_below, struct loop *evolution_loop,
2407 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2409 if (dump_file && (dump_flags & TDF_DETAILS))
2411 fprintf (dump_file, "(instantiate_scev \n");
2412 fprintf (dump_file, " (instantiate_below = %d)\n", instantiate_below->index);
2413 fprintf (dump_file, " (evolution_loop = %d)\n", evolution_loop->num);
2414 fprintf (dump_file, " (chrec = ");
2415 print_generic_expr (dump_file, chrec, 0);
2416 fprintf (dump_file, ")\n");
2419 res = instantiate_scev_1 (instantiate_below, evolution_loop, chrec, false,
2422 if (dump_file && (dump_flags & TDF_DETAILS))
2424 fprintf (dump_file, " (res = ");
2425 print_generic_expr (dump_file, res, 0);
2426 fprintf (dump_file, "))\n");
2429 htab_delete (cache);
2434 /* Similar to instantiate_parameters, but does not introduce the
2435 evolutions in outer loops for LOOP invariants in CHREC, and does not
2436 care about causing overflows, as long as they do not affect value
2437 of an expression. */
2440 resolve_mixers (struct loop *loop, tree chrec)
2442 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2443 tree ret = instantiate_scev_1 (block_before_loop (loop), loop, chrec, true,
2445 htab_delete (cache);
2449 /* Entry point for the analysis of the number of iterations pass.
2450 This function tries to safely approximate the number of iterations
2451 the loop will run. When this property is not decidable at compile
2452 time, the result is chrec_dont_know. Otherwise the result is
2453 a scalar or a symbolic parameter.
2455 Example of analysis: suppose that the loop has an exit condition:
2457 "if (b > 49) goto end_loop;"
2459 and that in a previous analysis we have determined that the
2460 variable 'b' has an evolution function:
2462 "EF = {23, +, 5}_2".
2464 When we evaluate the function at the point 5, i.e. the value of the
2465 variable 'b' after 5 iterations in the loop, we have EF (5) = 48,
2466 and EF (6) = 53. In this case the value of 'b' on exit is '53' and
2467 the loop body has been executed 6 times. */
2470 number_of_latch_executions (struct loop *loop)
2474 struct tree_niter_desc niter_desc;
2476 /* Determine whether the number_of_iterations_in_loop has already
2478 res = loop->nb_iterations;
2481 res = chrec_dont_know;
2483 if (dump_file && (dump_flags & TDF_DETAILS))
2484 fprintf (dump_file, "(number_of_iterations_in_loop\n");
2486 exit = single_exit (loop);
2490 if (!number_of_iterations_exit (loop, exit, &niter_desc, false))
2493 type = TREE_TYPE (niter_desc.niter);
2494 if (integer_nonzerop (niter_desc.may_be_zero))
2495 res = build_int_cst (type, 0);
2496 else if (integer_zerop (niter_desc.may_be_zero))
2497 res = niter_desc.niter;
2499 res = chrec_dont_know;
2502 return set_nb_iterations_in_loop (loop, res);
2505 /* Returns the number of executions of the exit condition of LOOP,
2506 i.e., the number by one higher than number_of_latch_executions.
2507 Note that unlike number_of_latch_executions, this number does
2508 not necessarily fit in the unsigned variant of the type of
2509 the control variable -- if the number of iterations is a constant,
2510 we return chrec_dont_know if adding one to number_of_latch_executions
2511 overflows; however, in case the number of iterations is symbolic
2512 expression, the caller is responsible for dealing with this
2513 the possible overflow. */
2516 number_of_exit_cond_executions (struct loop *loop)
2518 tree ret = number_of_latch_executions (loop);
2519 tree type = chrec_type (ret);
2521 if (chrec_contains_undetermined (ret))
2524 ret = chrec_fold_plus (type, ret, build_int_cst (type, 1));
2525 if (TREE_CODE (ret) == INTEGER_CST
2526 && TREE_OVERFLOW (ret))
2527 return chrec_dont_know;
2532 /* One of the drivers for testing the scalar evolutions analysis.
2533 This function computes the number of iterations for all the loops
2534 from the EXIT_CONDITIONS array. */
2537 number_of_iterations_for_all_loops (VEC(gimple,heap) **exit_conditions)
2540 unsigned nb_chrec_dont_know_loops = 0;
2541 unsigned nb_static_loops = 0;
2544 for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
2546 tree res = number_of_latch_executions (loop_containing_stmt (cond));
2547 if (chrec_contains_undetermined (res))
2548 nb_chrec_dont_know_loops++;
2555 fprintf (dump_file, "\n(\n");
2556 fprintf (dump_file, "-----------------------------------------\n");
2557 fprintf (dump_file, "%d\tnb_chrec_dont_know_loops\n", nb_chrec_dont_know_loops);
2558 fprintf (dump_file, "%d\tnb_static_loops\n", nb_static_loops);
2559 fprintf (dump_file, "%d\tnb_total_loops\n", number_of_loops ());
2560 fprintf (dump_file, "-----------------------------------------\n");
2561 fprintf (dump_file, ")\n\n");
2563 print_loops (dump_file, 3);
2569 /* Counters for the stats. */
2575 unsigned nb_affine_multivar;
2576 unsigned nb_higher_poly;
2577 unsigned nb_chrec_dont_know;
2578 unsigned nb_undetermined;
2581 /* Reset the counters. */
2584 reset_chrecs_counters (struct chrec_stats *stats)
2586 stats->nb_chrecs = 0;
2587 stats->nb_affine = 0;
2588 stats->nb_affine_multivar = 0;
2589 stats->nb_higher_poly = 0;
2590 stats->nb_chrec_dont_know = 0;
2591 stats->nb_undetermined = 0;
2594 /* Dump the contents of a CHREC_STATS structure. */
2597 dump_chrecs_stats (FILE *file, struct chrec_stats *stats)
2599 fprintf (file, "\n(\n");
2600 fprintf (file, "-----------------------------------------\n");
2601 fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine);
2602 fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar);
2603 fprintf (file, "%d\tdegree greater than 2 polynomials\n",
2604 stats->nb_higher_poly);
2605 fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know);
2606 fprintf (file, "-----------------------------------------\n");
2607 fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs);
2608 fprintf (file, "%d\twith undetermined coefficients\n",
2609 stats->nb_undetermined);
2610 fprintf (file, "-----------------------------------------\n");
2611 fprintf (file, "%d\tchrecs in the scev database\n",
2612 (int) htab_elements (scalar_evolution_info));
2613 fprintf (file, "%d\tsets in the scev database\n", nb_set_scev);
2614 fprintf (file, "%d\tgets in the scev database\n", nb_get_scev);
2615 fprintf (file, "-----------------------------------------\n");
2616 fprintf (file, ")\n\n");
2619 /* Gather statistics about CHREC. */
2622 gather_chrec_stats (tree chrec, struct chrec_stats *stats)
2624 if (dump_file && (dump_flags & TDF_STATS))
2626 fprintf (dump_file, "(classify_chrec ");
2627 print_generic_expr (dump_file, chrec, 0);
2628 fprintf (dump_file, "\n");
2633 if (chrec == NULL_TREE)
2635 stats->nb_undetermined++;
2639 switch (TREE_CODE (chrec))
2641 case POLYNOMIAL_CHREC:
2642 if (evolution_function_is_affine_p (chrec))
2644 if (dump_file && (dump_flags & TDF_STATS))
2645 fprintf (dump_file, " affine_univariate\n");
2648 else if (evolution_function_is_affine_multivariate_p (chrec, 0))
2650 if (dump_file && (dump_flags & TDF_STATS))
2651 fprintf (dump_file, " affine_multivariate\n");
2652 stats->nb_affine_multivar++;
2656 if (dump_file && (dump_flags & TDF_STATS))
2657 fprintf (dump_file, " higher_degree_polynomial\n");
2658 stats->nb_higher_poly++;
2667 if (chrec_contains_undetermined (chrec))
2669 if (dump_file && (dump_flags & TDF_STATS))
2670 fprintf (dump_file, " undetermined\n");
2671 stats->nb_undetermined++;
2674 if (dump_file && (dump_flags & TDF_STATS))
2675 fprintf (dump_file, ")\n");
2678 /* One of the drivers for testing the scalar evolutions analysis.
2679 This function analyzes the scalar evolution of all the scalars
2680 defined as loop phi nodes in one of the loops from the
2681 EXIT_CONDITIONS array.
2683 TODO Optimization: A loop is in canonical form if it contains only
2684 a single scalar loop phi node. All the other scalars that have an
2685 evolution in the loop are rewritten in function of this single
2686 index. This allows the parallelization of the loop. */
2689 analyze_scalar_evolution_for_all_loop_phi_nodes (VEC(gimple,heap) **exit_conditions)
2692 struct chrec_stats stats;
2694 gimple_stmt_iterator psi;
2696 reset_chrecs_counters (&stats);
2698 for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
2704 loop = loop_containing_stmt (cond);
2707 for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
2709 phi = gsi_stmt (psi);
2710 if (is_gimple_reg (PHI_RESULT (phi)))
2712 chrec = instantiate_parameters
2714 analyze_scalar_evolution (loop, PHI_RESULT (phi)));
2716 if (dump_file && (dump_flags & TDF_STATS))
2717 gather_chrec_stats (chrec, &stats);
2722 if (dump_file && (dump_flags & TDF_STATS))
2723 dump_chrecs_stats (dump_file, &stats);
2726 /* Callback for htab_traverse, gathers information on chrecs in the
2730 gather_stats_on_scev_database_1 (void **slot, void *stats)
2732 struct scev_info_str *entry = (struct scev_info_str *) *slot;
2734 gather_chrec_stats (entry->chrec, (struct chrec_stats *) stats);
2739 /* Classify the chrecs of the whole database. */
2742 gather_stats_on_scev_database (void)
2744 struct chrec_stats stats;
2749 reset_chrecs_counters (&stats);
2751 htab_traverse (scalar_evolution_info, gather_stats_on_scev_database_1,
2754 dump_chrecs_stats (dump_file, &stats);
2762 initialize_scalar_evolutions_analyzer (void)
2764 /* The elements below are unique. */
2765 if (chrec_dont_know == NULL_TREE)
2767 chrec_not_analyzed_yet = NULL_TREE;
2768 chrec_dont_know = make_node (SCEV_NOT_KNOWN);
2769 chrec_known = make_node (SCEV_KNOWN);
2770 TREE_TYPE (chrec_dont_know) = void_type_node;
2771 TREE_TYPE (chrec_known) = void_type_node;
2775 /* Initialize the analysis of scalar evolutions for LOOPS. */
2778 scev_initialize (void)
2783 scalar_evolution_info = htab_create_alloc (100,
2790 initialize_scalar_evolutions_analyzer ();
2792 FOR_EACH_LOOP (li, loop, 0)
2794 loop->nb_iterations = NULL_TREE;
2798 /* Cleans up the information cached by the scalar evolutions analysis. */
2806 if (!scalar_evolution_info || !current_loops)
2809 htab_empty (scalar_evolution_info);
2810 FOR_EACH_LOOP (li, loop, 0)
2812 loop->nb_iterations = NULL_TREE;
2816 /* Checks whether use of OP in USE_LOOP behaves as a simple affine iv with
2817 respect to WRTO_LOOP and returns its base and step in IV if possible
2818 (see analyze_scalar_evolution_in_loop for more details on USE_LOOP
2819 and WRTO_LOOP). If ALLOW_NONCONSTANT_STEP is true, we want step to be
2820 invariant in LOOP. Otherwise we require it to be an integer constant.
2822 IV->no_overflow is set to true if we are sure the iv cannot overflow (e.g.
2823 because it is computed in signed arithmetics). Consequently, adding an
2826 for (i = IV->base; ; i += IV->step)
2828 is only safe if IV->no_overflow is false, or TYPE_OVERFLOW_UNDEFINED is
2829 false for the type of the induction variable, or you can prove that i does
2830 not wrap by some other argument. Otherwise, this might introduce undefined
2833 for (i = iv->base; ; i = (type) ((unsigned type) i + (unsigned type) iv->step))
2835 must be used instead. */
2838 simple_iv (struct loop *wrto_loop, struct loop *use_loop, tree op,
2839 affine_iv *iv, bool allow_nonconstant_step)
2844 iv->base = NULL_TREE;
2845 iv->step = NULL_TREE;
2846 iv->no_overflow = false;
2848 type = TREE_TYPE (op);
2849 if (TREE_CODE (type) != INTEGER_TYPE
2850 && TREE_CODE (type) != POINTER_TYPE)
2853 ev = analyze_scalar_evolution_in_loop (wrto_loop, use_loop, op,
2855 if (chrec_contains_undetermined (ev)
2856 || chrec_contains_symbols_defined_in_loop (ev, wrto_loop->num))
2859 if (tree_does_not_contain_chrecs (ev))
2862 iv->step = build_int_cst (TREE_TYPE (ev), 0);
2863 iv->no_overflow = true;
2867 if (TREE_CODE (ev) != POLYNOMIAL_CHREC
2868 || CHREC_VARIABLE (ev) != (unsigned) wrto_loop->num)
2871 iv->step = CHREC_RIGHT (ev);
2872 if ((!allow_nonconstant_step && TREE_CODE (iv->step) != INTEGER_CST)
2873 || tree_contains_chrecs (iv->step, NULL))
2876 iv->base = CHREC_LEFT (ev);
2877 if (tree_contains_chrecs (iv->base, NULL))
2880 iv->no_overflow = !folded_casts && TYPE_OVERFLOW_UNDEFINED (type);
2885 /* Runs the analysis of scalar evolutions. */
2888 scev_analysis (void)
2890 VEC(gimple,heap) *exit_conditions;
2892 exit_conditions = VEC_alloc (gimple, heap, 37);
2893 select_loops_exit_conditions (&exit_conditions);
2895 if (dump_file && (dump_flags & TDF_STATS))
2896 analyze_scalar_evolution_for_all_loop_phi_nodes (&exit_conditions);
2898 number_of_iterations_for_all_loops (&exit_conditions);
2899 VEC_free (gimple, heap, exit_conditions);
2902 /* Finalize the scalar evolution analysis. */
2905 scev_finalize (void)
2907 if (!scalar_evolution_info)
2909 htab_delete (scalar_evolution_info);
2910 scalar_evolution_info = NULL;
2913 /* Returns true if the expression EXPR is considered to be too expensive
2914 for scev_const_prop. */
2917 expression_expensive_p (tree expr)
2919 enum tree_code code;
2921 if (is_gimple_val (expr))
2924 code = TREE_CODE (expr);
2925 if (code == TRUNC_DIV_EXPR
2926 || code == CEIL_DIV_EXPR
2927 || code == FLOOR_DIV_EXPR
2928 || code == ROUND_DIV_EXPR
2929 || code == TRUNC_MOD_EXPR
2930 || code == CEIL_MOD_EXPR
2931 || code == FLOOR_MOD_EXPR
2932 || code == ROUND_MOD_EXPR
2933 || code == EXACT_DIV_EXPR)
2935 /* Division by power of two is usually cheap, so we allow it.
2936 Forbid anything else. */
2937 if (!integer_pow2p (TREE_OPERAND (expr, 1)))
2941 switch (TREE_CODE_CLASS (code))
2944 case tcc_comparison:
2945 if (expression_expensive_p (TREE_OPERAND (expr, 1)))
2950 return expression_expensive_p (TREE_OPERAND (expr, 0));
2957 /* Replace ssa names for that scev can prove they are constant by the
2958 appropriate constants. Also perform final value replacement in loops,
2959 in case the replacement expressions are cheap.
2961 We only consider SSA names defined by phi nodes; rest is left to the
2962 ordinary constant propagation pass. */
2965 scev_const_prop (void)
2968 tree name, type, ev;
2970 struct loop *loop, *ex_loop;
2971 bitmap ssa_names_to_remove = NULL;
2974 gimple_stmt_iterator psi;
2976 if (number_of_loops () <= 1)
2981 loop = bb->loop_father;
2983 for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
2985 phi = gsi_stmt (psi);
2986 name = PHI_RESULT (phi);
2988 if (!is_gimple_reg (name))
2991 type = TREE_TYPE (name);
2993 if (!POINTER_TYPE_P (type)
2994 && !INTEGRAL_TYPE_P (type))
2997 ev = resolve_mixers (loop, analyze_scalar_evolution (loop, name));
2998 if (!is_gimple_min_invariant (ev)
2999 || !may_propagate_copy (name, ev))
3002 /* Replace the uses of the name. */
3004 replace_uses_by (name, ev);
3006 if (!ssa_names_to_remove)
3007 ssa_names_to_remove = BITMAP_ALLOC (NULL);
3008 bitmap_set_bit (ssa_names_to_remove, SSA_NAME_VERSION (name));
3012 /* Remove the ssa names that were replaced by constants. We do not
3013 remove them directly in the previous cycle, since this
3014 invalidates scev cache. */
3015 if (ssa_names_to_remove)
3019 EXECUTE_IF_SET_IN_BITMAP (ssa_names_to_remove, 0, i, bi)
3021 gimple_stmt_iterator psi;
3022 name = ssa_name (i);
3023 phi = SSA_NAME_DEF_STMT (name);
3025 gcc_assert (gimple_code (phi) == GIMPLE_PHI);
3026 psi = gsi_for_stmt (phi);
3027 remove_phi_node (&psi, true);
3030 BITMAP_FREE (ssa_names_to_remove);
3034 /* Now the regular final value replacement. */
3035 FOR_EACH_LOOP (li, loop, LI_FROM_INNERMOST)
3038 tree def, rslt, niter;
3039 gimple_stmt_iterator bsi;
3041 /* If we do not know exact number of iterations of the loop, we cannot
3042 replace the final value. */
3043 exit = single_exit (loop);
3047 niter = number_of_latch_executions (loop);
3048 if (niter == chrec_dont_know)
3051 /* Ensure that it is possible to insert new statements somewhere. */
3052 if (!single_pred_p (exit->dest))
3053 split_loop_exit_edge (exit);
3054 bsi = gsi_after_labels (exit->dest);
3056 ex_loop = superloop_at_depth (loop,
3057 loop_depth (exit->dest->loop_father) + 1);
3059 for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); )
3061 phi = gsi_stmt (psi);
3062 rslt = PHI_RESULT (phi);
3063 def = PHI_ARG_DEF_FROM_EDGE (phi, exit);
3064 if (!is_gimple_reg (def))
3070 if (!POINTER_TYPE_P (TREE_TYPE (def))
3071 && !INTEGRAL_TYPE_P (TREE_TYPE (def)))
3077 def = analyze_scalar_evolution_in_loop (ex_loop, loop, def, NULL);
3078 def = compute_overall_effect_of_inner_loop (ex_loop, def);
3079 if (!tree_does_not_contain_chrecs (def)
3080 || chrec_contains_symbols_defined_in_loop (def, ex_loop->num)
3081 /* Moving the computation from the loop may prolong life range
3082 of some ssa names, which may cause problems if they appear
3083 on abnormal edges. */
3084 || contains_abnormal_ssa_name_p (def)
3085 /* Do not emit expensive expressions. The rationale is that
3086 when someone writes a code like
3088 while (n > 45) n -= 45;
3090 he probably knows that n is not large, and does not want it
3091 to be turned into n %= 45. */
3092 || expression_expensive_p (def))
3098 /* Eliminate the PHI node and replace it by a computation outside
3100 def = unshare_expr (def);
3101 remove_phi_node (&psi, false);
3103 def = force_gimple_operand_gsi (&bsi, def, false, NULL_TREE,
3104 true, GSI_SAME_STMT);
3105 ass = gimple_build_assign (rslt, def);
3106 gsi_insert_before (&bsi, ass, GSI_SAME_STMT);
3112 #include "gt-tree-scalar-evolution.h"