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 /* If the phi node is just a copy, do not increase the limit. */
1324 n = gimple_phi_num_args (condition_phi);
1328 for (i = 1; i < n; i++)
1330 /* Quickly give up when the evolution of one of the branches is
1332 if (*evolution_of_loop == chrec_dont_know)
1335 res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi,
1337 &evolution_of_branch,
1339 if (res == t_false || res == t_dont_know)
1342 *evolution_of_loop = chrec_merge (*evolution_of_loop,
1343 evolution_of_branch);
1349 /* Follow an SSA edge in an inner loop. It computes the overall
1350 effect of the loop, and following the symbolic initial conditions,
1351 it follows the edges in the parent loop. The inner loop is
1352 considered as a single statement. */
1355 follow_ssa_edge_inner_loop_phi (struct loop *outer_loop,
1356 gimple loop_phi_node,
1358 tree *evolution_of_loop, int limit)
1360 struct loop *loop = loop_containing_stmt (loop_phi_node);
1361 tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node));
1363 /* Sometimes, the inner loop is too difficult to analyze, and the
1364 result of the analysis is a symbolic parameter. */
1365 if (ev == PHI_RESULT (loop_phi_node))
1367 t_bool res = t_false;
1368 int i, n = gimple_phi_num_args (loop_phi_node);
1370 for (i = 0; i < n; i++)
1372 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1375 /* Follow the edges that exit the inner loop. */
1376 bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1377 if (!flow_bb_inside_loop_p (loop, bb))
1378 res = follow_ssa_edge_expr (outer_loop, loop_phi_node,
1380 evolution_of_loop, limit);
1385 /* If the path crosses this loop-phi, give up. */
1387 *evolution_of_loop = chrec_dont_know;
1392 /* Otherwise, compute the overall effect of the inner loop. */
1393 ev = compute_overall_effect_of_inner_loop (loop, ev);
1394 return follow_ssa_edge_expr (outer_loop, loop_phi_node, ev, halting_phi,
1395 evolution_of_loop, limit);
1398 /* Follow an SSA edge from a loop-phi-node to itself, constructing a
1399 path that is analyzed on the return walk. */
1402 follow_ssa_edge (struct loop *loop, gimple def, gimple halting_phi,
1403 tree *evolution_of_loop, int limit)
1405 struct loop *def_loop;
1407 if (gimple_nop_p (def))
1410 /* Give up if the path is longer than the MAX that we allow. */
1411 if (limit > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
1414 def_loop = loop_containing_stmt (def);
1416 switch (gimple_code (def))
1419 if (!loop_phi_node_p (def))
1420 /* DEF is a condition-phi-node. Follow the branches, and
1421 record their evolutions. Finally, merge the collected
1422 information and set the approximation to the main
1424 return follow_ssa_edge_in_condition_phi
1425 (loop, def, halting_phi, evolution_of_loop, limit);
1427 /* When the analyzed phi is the halting_phi, the
1428 depth-first search is over: we have found a path from
1429 the halting_phi to itself in the loop. */
1430 if (def == halting_phi)
1433 /* Otherwise, the evolution of the HALTING_PHI depends
1434 on the evolution of another loop-phi-node, i.e. the
1435 evolution function is a higher degree polynomial. */
1436 if (def_loop == loop)
1440 if (flow_loop_nested_p (loop, def_loop))
1441 return follow_ssa_edge_inner_loop_phi
1442 (loop, def, halting_phi, evolution_of_loop, limit + 1);
1448 return follow_ssa_edge_in_rhs (loop, def, halting_phi,
1449 evolution_of_loop, limit);
1452 /* At this level of abstraction, the program is just a set
1453 of GIMPLE_ASSIGNs and PHI_NODEs. In principle there is no
1454 other node to be handled. */
1461 /* Given a LOOP_PHI_NODE, this function determines the evolution
1462 function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop. */
1465 analyze_evolution_in_loop (gimple loop_phi_node,
1468 int i, n = gimple_phi_num_args (loop_phi_node);
1469 tree evolution_function = chrec_not_analyzed_yet;
1470 struct loop *loop = loop_containing_stmt (loop_phi_node);
1473 if (dump_file && (dump_flags & TDF_DETAILS))
1475 fprintf (dump_file, "(analyze_evolution_in_loop \n");
1476 fprintf (dump_file, " (loop_phi_node = ");
1477 print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
1478 fprintf (dump_file, ")\n");
1481 for (i = 0; i < n; i++)
1483 tree arg = PHI_ARG_DEF (loop_phi_node, i);
1488 /* Select the edges that enter the loop body. */
1489 bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1490 if (!flow_bb_inside_loop_p (loop, bb))
1493 if (TREE_CODE (arg) == SSA_NAME)
1495 ssa_chain = SSA_NAME_DEF_STMT (arg);
1497 /* Pass in the initial condition to the follow edge function. */
1499 res = follow_ssa_edge (loop, ssa_chain, loop_phi_node, &ev_fn, 0);
1504 /* When it is impossible to go back on the same
1505 loop_phi_node by following the ssa edges, the
1506 evolution is represented by a peeled chrec, i.e. the
1507 first iteration, EV_FN has the value INIT_COND, then
1508 all the other iterations it has the value of ARG.
1509 For the moment, PEELED_CHREC nodes are not built. */
1511 ev_fn = chrec_dont_know;
1513 /* When there are multiple back edges of the loop (which in fact never
1514 happens currently, but nevertheless), merge their evolutions. */
1515 evolution_function = chrec_merge (evolution_function, ev_fn);
1518 if (dump_file && (dump_flags & TDF_DETAILS))
1520 fprintf (dump_file, " (evolution_function = ");
1521 print_generic_expr (dump_file, evolution_function, 0);
1522 fprintf (dump_file, "))\n");
1525 return evolution_function;
1528 /* Given a loop-phi-node, return the initial conditions of the
1529 variable on entry of the loop. When the CCP has propagated
1530 constants into the loop-phi-node, the initial condition is
1531 instantiated, otherwise the initial condition is kept symbolic.
1532 This analyzer does not analyze the evolution outside the current
1533 loop, and leaves this task to the on-demand tree reconstructor. */
1536 analyze_initial_condition (gimple loop_phi_node)
1539 tree init_cond = chrec_not_analyzed_yet;
1540 struct loop *loop = loop_containing_stmt (loop_phi_node);
1542 if (dump_file && (dump_flags & TDF_DETAILS))
1544 fprintf (dump_file, "(analyze_initial_condition \n");
1545 fprintf (dump_file, " (loop_phi_node = \n");
1546 print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
1547 fprintf (dump_file, ")\n");
1550 n = gimple_phi_num_args (loop_phi_node);
1551 for (i = 0; i < n; i++)
1553 tree branch = PHI_ARG_DEF (loop_phi_node, i);
1554 basic_block bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
1556 /* When the branch is oriented to the loop's body, it does
1557 not contribute to the initial condition. */
1558 if (flow_bb_inside_loop_p (loop, bb))
1561 if (init_cond == chrec_not_analyzed_yet)
1567 if (TREE_CODE (branch) == SSA_NAME)
1569 init_cond = chrec_dont_know;
1573 init_cond = chrec_merge (init_cond, branch);
1576 /* Ooops -- a loop without an entry??? */
1577 if (init_cond == chrec_not_analyzed_yet)
1578 init_cond = chrec_dont_know;
1580 if (dump_file && (dump_flags & TDF_DETAILS))
1582 fprintf (dump_file, " (init_cond = ");
1583 print_generic_expr (dump_file, init_cond, 0);
1584 fprintf (dump_file, "))\n");
1590 /* Analyze the scalar evolution for LOOP_PHI_NODE. */
1593 interpret_loop_phi (struct loop *loop, gimple loop_phi_node)
1596 struct loop *phi_loop = loop_containing_stmt (loop_phi_node);
1599 if (phi_loop != loop)
1601 struct loop *subloop;
1602 tree evolution_fn = analyze_scalar_evolution
1603 (phi_loop, PHI_RESULT (loop_phi_node));
1605 /* Dive one level deeper. */
1606 subloop = superloop_at_depth (phi_loop, loop_depth (loop) + 1);
1608 /* Interpret the subloop. */
1609 res = compute_overall_effect_of_inner_loop (subloop, evolution_fn);
1613 /* Otherwise really interpret the loop phi. */
1614 init_cond = analyze_initial_condition (loop_phi_node);
1615 res = analyze_evolution_in_loop (loop_phi_node, init_cond);
1620 /* This function merges the branches of a condition-phi-node,
1621 contained in the outermost loop, and whose arguments are already
1625 interpret_condition_phi (struct loop *loop, gimple condition_phi)
1627 int i, n = gimple_phi_num_args (condition_phi);
1628 tree res = chrec_not_analyzed_yet;
1630 for (i = 0; i < n; i++)
1634 if (backedge_phi_arg_p (condition_phi, i))
1636 res = chrec_dont_know;
1640 branch_chrec = analyze_scalar_evolution
1641 (loop, PHI_ARG_DEF (condition_phi, i));
1643 res = chrec_merge (res, branch_chrec);
1649 /* Interpret the operation RHS1 OP RHS2. If we didn't
1650 analyze this node before, follow the definitions until ending
1651 either on an analyzed GIMPLE_ASSIGN, or on a loop-phi-node. On the
1652 return path, this function propagates evolutions (ala constant copy
1653 propagation). OPND1 is not a GIMPLE expression because we could
1654 analyze the effect of an inner loop: see interpret_loop_phi. */
1657 interpret_rhs_expr (struct loop *loop, gimple at_stmt,
1658 tree type, tree rhs1, enum tree_code code, tree rhs2)
1660 tree res, chrec1, chrec2;
1662 if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS)
1664 if (is_gimple_min_invariant (rhs1))
1665 return chrec_convert (type, rhs1, at_stmt);
1667 if (code == SSA_NAME)
1668 return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
1671 if (code == ASSERT_EXPR)
1673 rhs1 = ASSERT_EXPR_VAR (rhs1);
1674 return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
1678 return chrec_dont_know;
1683 case POINTER_PLUS_EXPR:
1684 chrec1 = analyze_scalar_evolution (loop, rhs1);
1685 chrec2 = analyze_scalar_evolution (loop, rhs2);
1686 chrec1 = chrec_convert (type, chrec1, at_stmt);
1687 chrec2 = chrec_convert (sizetype, chrec2, at_stmt);
1688 res = chrec_fold_plus (type, chrec1, chrec2);
1692 chrec1 = analyze_scalar_evolution (loop, rhs1);
1693 chrec2 = analyze_scalar_evolution (loop, rhs2);
1694 chrec1 = chrec_convert (type, chrec1, at_stmt);
1695 chrec2 = chrec_convert (type, chrec2, at_stmt);
1696 res = chrec_fold_plus (type, chrec1, chrec2);
1700 chrec1 = analyze_scalar_evolution (loop, rhs1);
1701 chrec2 = analyze_scalar_evolution (loop, rhs2);
1702 chrec1 = chrec_convert (type, chrec1, at_stmt);
1703 chrec2 = chrec_convert (type, chrec2, at_stmt);
1704 res = chrec_fold_minus (type, chrec1, chrec2);
1708 chrec1 = analyze_scalar_evolution (loop, rhs1);
1709 chrec1 = chrec_convert (type, chrec1, at_stmt);
1710 /* TYPE may be integer, real or complex, so use fold_convert. */
1711 res = chrec_fold_multiply (type, chrec1,
1712 fold_convert (type, integer_minus_one_node));
1716 /* Handle ~X as -1 - X. */
1717 chrec1 = analyze_scalar_evolution (loop, rhs1);
1718 chrec1 = chrec_convert (type, chrec1, at_stmt);
1719 res = chrec_fold_minus (type,
1720 fold_convert (type, integer_minus_one_node),
1725 chrec1 = analyze_scalar_evolution (loop, rhs1);
1726 chrec2 = analyze_scalar_evolution (loop, rhs2);
1727 chrec1 = chrec_convert (type, chrec1, at_stmt);
1728 chrec2 = chrec_convert (type, chrec2, at_stmt);
1729 res = chrec_fold_multiply (type, chrec1, chrec2);
1733 chrec1 = analyze_scalar_evolution (loop, rhs1);
1734 res = chrec_convert (type, chrec1, at_stmt);
1738 res = chrec_dont_know;
1745 /* Interpret the expression EXPR. */
1748 interpret_expr (struct loop *loop, gimple at_stmt, tree expr)
1750 enum tree_code code;
1751 tree type = TREE_TYPE (expr), op0, op1;
1753 if (automatically_generated_chrec_p (expr))
1756 if (TREE_CODE (expr) == POLYNOMIAL_CHREC)
1757 return chrec_dont_know;
1759 extract_ops_from_tree (expr, &code, &op0, &op1);
1761 return interpret_rhs_expr (loop, at_stmt, type,
1765 /* Interpret the rhs of the assignment STMT. */
1768 interpret_gimple_assign (struct loop *loop, gimple stmt)
1770 tree type = TREE_TYPE (gimple_assign_lhs (stmt));
1771 enum tree_code code = gimple_assign_rhs_code (stmt);
1773 return interpret_rhs_expr (loop, stmt, type,
1774 gimple_assign_rhs1 (stmt), code,
1775 gimple_assign_rhs2 (stmt));
1780 /* This section contains all the entry points:
1781 - number_of_iterations_in_loop,
1782 - analyze_scalar_evolution,
1783 - instantiate_parameters.
1786 /* Compute and return the evolution function in WRTO_LOOP, the nearest
1787 common ancestor of DEF_LOOP and USE_LOOP. */
1790 compute_scalar_evolution_in_loop (struct loop *wrto_loop,
1791 struct loop *def_loop,
1795 if (def_loop == wrto_loop)
1798 def_loop = superloop_at_depth (def_loop, loop_depth (wrto_loop) + 1);
1799 res = compute_overall_effect_of_inner_loop (def_loop, ev);
1801 return analyze_scalar_evolution_1 (wrto_loop, res, chrec_not_analyzed_yet);
1804 /* Helper recursive function. */
1807 analyze_scalar_evolution_1 (struct loop *loop, tree var, tree res)
1809 tree type = TREE_TYPE (var);
1812 struct loop *def_loop;
1814 if (loop == NULL || TREE_CODE (type) == VECTOR_TYPE)
1815 return chrec_dont_know;
1817 if (TREE_CODE (var) != SSA_NAME)
1818 return interpret_expr (loop, NULL, var);
1820 def = SSA_NAME_DEF_STMT (var);
1821 bb = gimple_bb (def);
1822 def_loop = bb ? bb->loop_father : NULL;
1825 || !flow_bb_inside_loop_p (loop, bb))
1827 /* Keep the symbolic form. */
1832 if (res != chrec_not_analyzed_yet)
1834 if (loop != bb->loop_father)
1835 res = compute_scalar_evolution_in_loop
1836 (find_common_loop (loop, bb->loop_father), bb->loop_father, res);
1841 if (loop != def_loop)
1843 res = analyze_scalar_evolution_1 (def_loop, var, chrec_not_analyzed_yet);
1844 res = compute_scalar_evolution_in_loop (loop, def_loop, res);
1849 switch (gimple_code (def))
1852 res = interpret_gimple_assign (loop, def);
1856 if (loop_phi_node_p (def))
1857 res = interpret_loop_phi (loop, def);
1859 res = interpret_condition_phi (loop, def);
1863 res = chrec_dont_know;
1869 /* Keep the symbolic form. */
1870 if (res == chrec_dont_know)
1873 if (loop == def_loop)
1874 set_scalar_evolution (block_before_loop (loop), var, res);
1879 /* Entry point for the scalar evolution analyzer.
1880 Analyzes and returns the scalar evolution of the ssa_name VAR.
1881 LOOP_NB is the identifier number of the loop in which the variable
1884 Example of use: having a pointer VAR to a SSA_NAME node, STMT a
1885 pointer to the statement that uses this variable, in order to
1886 determine the evolution function of the variable, use the following
1889 unsigned loop_nb = loop_containing_stmt (stmt)->num;
1890 tree chrec_with_symbols = analyze_scalar_evolution (loop_nb, var);
1891 tree chrec_instantiated = instantiate_parameters (loop, chrec_with_symbols);
1895 analyze_scalar_evolution (struct loop *loop, tree var)
1899 if (dump_file && (dump_flags & TDF_DETAILS))
1901 fprintf (dump_file, "(analyze_scalar_evolution \n");
1902 fprintf (dump_file, " (loop_nb = %d)\n", loop->num);
1903 fprintf (dump_file, " (scalar = ");
1904 print_generic_expr (dump_file, var, 0);
1905 fprintf (dump_file, ")\n");
1908 res = get_scalar_evolution (block_before_loop (loop), var);
1909 res = analyze_scalar_evolution_1 (loop, var, res);
1911 if (dump_file && (dump_flags & TDF_DETAILS))
1912 fprintf (dump_file, ")\n");
1917 /* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to
1918 WRTO_LOOP (which should be a superloop of USE_LOOP)
1920 FOLDED_CASTS is set to true if resolve_mixers used
1921 chrec_convert_aggressive (TODO -- not really, we are way too conservative
1922 at the moment in order to keep things simple).
1924 To illustrate the meaning of USE_LOOP and WRTO_LOOP, consider the following
1927 for (i = 0; i < 100; i++) -- loop 1
1929 for (j = 0; j < 100; j++) -- loop 2
1936 for (t = 0; t < 100; t++) -- loop 3
1943 Both k1 and k2 are invariants in loop3, thus
1944 analyze_scalar_evolution_in_loop (loop3, loop3, k1) = k1
1945 analyze_scalar_evolution_in_loop (loop3, loop3, k2) = k2
1947 As they are invariant, it does not matter whether we consider their
1948 usage in loop 3 or loop 2, hence
1949 analyze_scalar_evolution_in_loop (loop2, loop3, k1) =
1950 analyze_scalar_evolution_in_loop (loop2, loop2, k1) = i
1951 analyze_scalar_evolution_in_loop (loop2, loop3, k2) =
1952 analyze_scalar_evolution_in_loop (loop2, loop2, k2) = [0,+,1]_2
1954 Similarly for their evolutions with respect to loop 1. The values of K2
1955 in the use in loop 2 vary independently on loop 1, thus we cannot express
1956 the evolution with respect to loop 1:
1957 analyze_scalar_evolution_in_loop (loop1, loop3, k1) =
1958 analyze_scalar_evolution_in_loop (loop1, loop2, k1) = [0,+,1]_1
1959 analyze_scalar_evolution_in_loop (loop1, loop3, k2) =
1960 analyze_scalar_evolution_in_loop (loop1, loop2, k2) = dont_know
1962 The value of k2 in the use in loop 1 is known, though:
1963 analyze_scalar_evolution_in_loop (loop1, loop1, k1) = [0,+,1]_1
1964 analyze_scalar_evolution_in_loop (loop1, loop1, k2) = 100
1968 analyze_scalar_evolution_in_loop (struct loop *wrto_loop, struct loop *use_loop,
1969 tree version, bool *folded_casts)
1972 tree ev = version, tmp;
1974 /* We cannot just do
1976 tmp = analyze_scalar_evolution (use_loop, version);
1977 ev = resolve_mixers (wrto_loop, tmp);
1979 as resolve_mixers would query the scalar evolution with respect to
1980 wrto_loop. For example, in the situation described in the function
1981 comment, suppose that wrto_loop = loop1, use_loop = loop3 and
1984 analyze_scalar_evolution (use_loop, version) = k2
1986 and resolve_mixers (loop1, k2) finds that the value of k2 in loop 1
1987 is 100, which is a wrong result, since we are interested in the
1990 Instead, we need to proceed from use_loop to wrto_loop loop by loop,
1991 each time checking that there is no evolution in the inner loop. */
1994 *folded_casts = false;
1997 tmp = analyze_scalar_evolution (use_loop, ev);
1998 ev = resolve_mixers (use_loop, tmp);
2000 if (folded_casts && tmp != ev)
2001 *folded_casts = true;
2003 if (use_loop == wrto_loop)
2006 /* If the value of the use changes in the inner loop, we cannot express
2007 its value in the outer loop (we might try to return interval chrec,
2008 but we do not have a user for it anyway) */
2009 if (!no_evolution_in_loop_p (ev, use_loop->num, &val)
2011 return chrec_dont_know;
2013 use_loop = loop_outer (use_loop);
2017 /* Returns from CACHE the value for VERSION instantiated below
2018 INSTANTIATED_BELOW block. */
2021 get_instantiated_value (htab_t cache, basic_block instantiated_below,
2024 struct scev_info_str *info, pattern;
2026 pattern.var = version;
2027 pattern.instantiated_below = instantiated_below;
2028 info = (struct scev_info_str *) htab_find (cache, &pattern);
2036 /* Sets in CACHE the value of VERSION instantiated below basic block
2037 INSTANTIATED_BELOW to VAL. */
2040 set_instantiated_value (htab_t cache, basic_block instantiated_below,
2041 tree version, tree val)
2043 struct scev_info_str *info, pattern;
2046 pattern.var = version;
2047 pattern.instantiated_below = instantiated_below;
2048 slot = htab_find_slot (cache, &pattern, INSERT);
2051 *slot = new_scev_info_str (instantiated_below, version);
2052 info = (struct scev_info_str *) *slot;
2056 /* Return the closed_loop_phi node for VAR. If there is none, return
2060 loop_closed_phi_def (tree var)
2065 gimple_stmt_iterator psi;
2067 if (var == NULL_TREE
2068 || TREE_CODE (var) != SSA_NAME)
2071 loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var));
2072 exit = single_exit (loop);
2076 for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); gsi_next (&psi))
2078 phi = gsi_stmt (psi);
2079 if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var)
2080 return PHI_RESULT (phi);
2086 /* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW
2087 and EVOLUTION_LOOP, that were left under a symbolic form.
2089 CHREC is the scalar evolution to instantiate.
2091 CACHE is the cache of already instantiated values.
2093 FOLD_CONVERSIONS should be set to true when the conversions that
2094 may wrap in signed/pointer type are folded, as long as the value of
2095 the chrec is preserved.
2097 SIZE_EXPR is used for computing the size of the expression to be
2098 instantiated, and to stop if it exceeds some limit. */
2101 instantiate_scev_1 (basic_block instantiate_below,
2102 struct loop *evolution_loop, tree chrec,
2103 bool fold_conversions, htab_t cache, int size_expr)
2105 tree res, op0, op1, op2;
2107 struct loop *def_loop;
2108 tree type = chrec_type (chrec);
2110 /* Give up if the expression is larger than the MAX that we allow. */
2111 if (size_expr++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
2112 return chrec_dont_know;
2114 if (automatically_generated_chrec_p (chrec)
2115 || is_gimple_min_invariant (chrec))
2118 switch (TREE_CODE (chrec))
2121 def_bb = gimple_bb (SSA_NAME_DEF_STMT (chrec));
2123 /* A parameter (or loop invariant and we do not want to include
2124 evolutions in outer loops), nothing to do. */
2126 || loop_depth (def_bb->loop_father) == 0
2127 || dominated_by_p (CDI_DOMINATORS, instantiate_below, def_bb))
2130 /* We cache the value of instantiated variable to avoid exponential
2131 time complexity due to reevaluations. We also store the convenient
2132 value in the cache in order to prevent infinite recursion -- we do
2133 not want to instantiate the SSA_NAME if it is in a mixer
2134 structure. This is used for avoiding the instantiation of
2135 recursively defined functions, such as:
2137 | a_2 -> {0, +, 1, +, a_2}_1 */
2139 res = get_instantiated_value (cache, instantiate_below, chrec);
2143 res = chrec_dont_know;
2144 set_instantiated_value (cache, instantiate_below, chrec, res);
2146 def_loop = find_common_loop (evolution_loop, def_bb->loop_father);
2148 /* If the analysis yields a parametric chrec, instantiate the
2150 res = analyze_scalar_evolution (def_loop, chrec);
2152 /* Don't instantiate loop-closed-ssa phi nodes. */
2153 if (TREE_CODE (res) == SSA_NAME
2154 && (loop_containing_stmt (SSA_NAME_DEF_STMT (res)) == NULL
2155 || (loop_depth (loop_containing_stmt (SSA_NAME_DEF_STMT (res)))
2156 > loop_depth (def_loop))))
2159 res = loop_closed_phi_def (chrec);
2163 if (res == NULL_TREE)
2164 res = chrec_dont_know;
2167 else if (res != chrec_dont_know)
2168 res = instantiate_scev_1 (instantiate_below, evolution_loop, res,
2169 fold_conversions, cache, size_expr);
2171 /* Store the correct value to the cache. */
2172 set_instantiated_value (cache, instantiate_below, chrec, res);
2175 case POLYNOMIAL_CHREC:
2176 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2177 CHREC_LEFT (chrec), fold_conversions, cache,
2179 if (op0 == chrec_dont_know)
2180 return chrec_dont_know;
2182 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2183 CHREC_RIGHT (chrec), fold_conversions, cache,
2185 if (op1 == chrec_dont_know)
2186 return chrec_dont_know;
2188 if (CHREC_LEFT (chrec) != op0
2189 || CHREC_RIGHT (chrec) != op1)
2191 op1 = chrec_convert_rhs (chrec_type (op0), op1, NULL);
2192 chrec = build_polynomial_chrec (CHREC_VARIABLE (chrec), op0, op1);
2196 case POINTER_PLUS_EXPR:
2198 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2199 TREE_OPERAND (chrec, 0), fold_conversions, cache,
2201 if (op0 == chrec_dont_know)
2202 return chrec_dont_know;
2204 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2205 TREE_OPERAND (chrec, 1), fold_conversions, cache,
2207 if (op1 == chrec_dont_know)
2208 return chrec_dont_know;
2210 if (TREE_OPERAND (chrec, 0) != op0
2211 || TREE_OPERAND (chrec, 1) != op1)
2213 op0 = chrec_convert (type, op0, NULL);
2214 op1 = chrec_convert_rhs (type, op1, NULL);
2215 chrec = chrec_fold_plus (type, op0, op1);
2220 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2221 TREE_OPERAND (chrec, 0), fold_conversions, cache,
2223 if (op0 == chrec_dont_know)
2224 return chrec_dont_know;
2226 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2227 TREE_OPERAND (chrec, 1),
2228 fold_conversions, cache, size_expr);
2229 if (op1 == chrec_dont_know)
2230 return chrec_dont_know;
2232 if (TREE_OPERAND (chrec, 0) != op0
2233 || TREE_OPERAND (chrec, 1) != op1)
2235 op0 = chrec_convert (type, op0, NULL);
2236 op1 = chrec_convert (type, op1, NULL);
2237 chrec = chrec_fold_minus (type, op0, op1);
2242 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2243 TREE_OPERAND (chrec, 0),
2244 fold_conversions, cache, size_expr);
2245 if (op0 == chrec_dont_know)
2246 return chrec_dont_know;
2248 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2249 TREE_OPERAND (chrec, 1),
2250 fold_conversions, cache, size_expr);
2251 if (op1 == chrec_dont_know)
2252 return chrec_dont_know;
2254 if (TREE_OPERAND (chrec, 0) != op0
2255 || TREE_OPERAND (chrec, 1) != op1)
2257 op0 = chrec_convert (type, op0, NULL);
2258 op1 = chrec_convert (type, op1, NULL);
2259 chrec = chrec_fold_multiply (type, 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;
2270 if (fold_conversions)
2272 tree tmp = chrec_convert_aggressive (TREE_TYPE (chrec), op0);
2277 if (op0 == TREE_OPERAND (chrec, 0))
2280 /* If we used chrec_convert_aggressive, we can no longer assume that
2281 signed chrecs do not overflow, as chrec_convert does, so avoid
2282 calling it in that case. */
2283 if (fold_conversions)
2284 return fold_convert (TREE_TYPE (chrec), op0);
2286 return chrec_convert (TREE_TYPE (chrec), op0, NULL);
2289 /* Handle ~X as -1 - X. */
2290 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2291 TREE_OPERAND (chrec, 0),
2292 fold_conversions, cache, size_expr);
2293 if (op0 == chrec_dont_know)
2294 return chrec_dont_know;
2296 if (TREE_OPERAND (chrec, 0) != op0)
2298 op0 = chrec_convert (type, op0, NULL);
2299 chrec = chrec_fold_minus (type,
2301 integer_minus_one_node),
2306 case SCEV_NOT_KNOWN:
2307 return chrec_dont_know;
2316 if (VL_EXP_CLASS_P (chrec))
2317 return chrec_dont_know;
2319 switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
2322 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2323 TREE_OPERAND (chrec, 0),
2324 fold_conversions, cache, size_expr);
2325 if (op0 == chrec_dont_know)
2326 return chrec_dont_know;
2328 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2329 TREE_OPERAND (chrec, 1),
2330 fold_conversions, cache, size_expr);
2331 if (op1 == chrec_dont_know)
2332 return chrec_dont_know;
2334 op2 = instantiate_scev_1 (instantiate_below, evolution_loop,
2335 TREE_OPERAND (chrec, 2),
2336 fold_conversions, cache, size_expr);
2337 if (op2 == chrec_dont_know)
2338 return chrec_dont_know;
2340 if (op0 == TREE_OPERAND (chrec, 0)
2341 && op1 == TREE_OPERAND (chrec, 1)
2342 && op2 == TREE_OPERAND (chrec, 2))
2345 return fold_build3 (TREE_CODE (chrec),
2346 TREE_TYPE (chrec), op0, op1, op2);
2349 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2350 TREE_OPERAND (chrec, 0),
2351 fold_conversions, cache, size_expr);
2352 if (op0 == chrec_dont_know)
2353 return chrec_dont_know;
2355 op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
2356 TREE_OPERAND (chrec, 1),
2357 fold_conversions, cache, size_expr);
2358 if (op1 == chrec_dont_know)
2359 return chrec_dont_know;
2361 if (op0 == TREE_OPERAND (chrec, 0)
2362 && op1 == TREE_OPERAND (chrec, 1))
2364 return fold_build2 (TREE_CODE (chrec), TREE_TYPE (chrec), op0, op1);
2367 op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
2368 TREE_OPERAND (chrec, 0),
2369 fold_conversions, cache, size_expr);
2370 if (op0 == chrec_dont_know)
2371 return chrec_dont_know;
2372 if (op0 == TREE_OPERAND (chrec, 0))
2374 return fold_build1 (TREE_CODE (chrec), TREE_TYPE (chrec), op0);
2383 /* Too complicated to handle. */
2384 return chrec_dont_know;
2387 /* Analyze all the parameters of the chrec that were left under a
2388 symbolic form. INSTANTIATE_BELOW is the basic block that stops the
2389 recursive instantiation of parameters: a parameter is a variable
2390 that is defined in a basic block that dominates INSTANTIATE_BELOW or
2391 a function parameter. */
2394 instantiate_scev (basic_block instantiate_below, struct loop *evolution_loop,
2398 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2400 if (dump_file && (dump_flags & TDF_DETAILS))
2402 fprintf (dump_file, "(instantiate_scev \n");
2403 fprintf (dump_file, " (instantiate_below = %d)\n", instantiate_below->index);
2404 fprintf (dump_file, " (evolution_loop = %d)\n", evolution_loop->num);
2405 fprintf (dump_file, " (chrec = ");
2406 print_generic_expr (dump_file, chrec, 0);
2407 fprintf (dump_file, ")\n");
2410 res = instantiate_scev_1 (instantiate_below, evolution_loop, chrec, false,
2413 if (dump_file && (dump_flags & TDF_DETAILS))
2415 fprintf (dump_file, " (res = ");
2416 print_generic_expr (dump_file, res, 0);
2417 fprintf (dump_file, "))\n");
2420 htab_delete (cache);
2425 /* Similar to instantiate_parameters, but does not introduce the
2426 evolutions in outer loops for LOOP invariants in CHREC, and does not
2427 care about causing overflows, as long as they do not affect value
2428 of an expression. */
2431 resolve_mixers (struct loop *loop, tree chrec)
2433 htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
2434 tree ret = instantiate_scev_1 (block_before_loop (loop), loop, chrec, true,
2436 htab_delete (cache);
2440 /* Entry point for the analysis of the number of iterations pass.
2441 This function tries to safely approximate the number of iterations
2442 the loop will run. When this property is not decidable at compile
2443 time, the result is chrec_dont_know. Otherwise the result is
2444 a scalar or a symbolic parameter.
2446 Example of analysis: suppose that the loop has an exit condition:
2448 "if (b > 49) goto end_loop;"
2450 and that in a previous analysis we have determined that the
2451 variable 'b' has an evolution function:
2453 "EF = {23, +, 5}_2".
2455 When we evaluate the function at the point 5, i.e. the value of the
2456 variable 'b' after 5 iterations in the loop, we have EF (5) = 48,
2457 and EF (6) = 53. In this case the value of 'b' on exit is '53' and
2458 the loop body has been executed 6 times. */
2461 number_of_latch_executions (struct loop *loop)
2465 struct tree_niter_desc niter_desc;
2467 /* Determine whether the number_of_iterations_in_loop has already
2469 res = loop->nb_iterations;
2472 res = chrec_dont_know;
2474 if (dump_file && (dump_flags & TDF_DETAILS))
2475 fprintf (dump_file, "(number_of_iterations_in_loop\n");
2477 exit = single_exit (loop);
2481 if (!number_of_iterations_exit (loop, exit, &niter_desc, false))
2484 type = TREE_TYPE (niter_desc.niter);
2485 if (integer_nonzerop (niter_desc.may_be_zero))
2486 res = build_int_cst (type, 0);
2487 else if (integer_zerop (niter_desc.may_be_zero))
2488 res = niter_desc.niter;
2490 res = chrec_dont_know;
2493 return set_nb_iterations_in_loop (loop, res);
2496 /* Returns the number of executions of the exit condition of LOOP,
2497 i.e., the number by one higher than number_of_latch_executions.
2498 Note that unlike number_of_latch_executions, this number does
2499 not necessarily fit in the unsigned variant of the type of
2500 the control variable -- if the number of iterations is a constant,
2501 we return chrec_dont_know if adding one to number_of_latch_executions
2502 overflows; however, in case the number of iterations is symbolic
2503 expression, the caller is responsible for dealing with this
2504 the possible overflow. */
2507 number_of_exit_cond_executions (struct loop *loop)
2509 tree ret = number_of_latch_executions (loop);
2510 tree type = chrec_type (ret);
2512 if (chrec_contains_undetermined (ret))
2515 ret = chrec_fold_plus (type, ret, build_int_cst (type, 1));
2516 if (TREE_CODE (ret) == INTEGER_CST
2517 && TREE_OVERFLOW (ret))
2518 return chrec_dont_know;
2523 /* One of the drivers for testing the scalar evolutions analysis.
2524 This function computes the number of iterations for all the loops
2525 from the EXIT_CONDITIONS array. */
2528 number_of_iterations_for_all_loops (VEC(gimple,heap) **exit_conditions)
2531 unsigned nb_chrec_dont_know_loops = 0;
2532 unsigned nb_static_loops = 0;
2535 for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
2537 tree res = number_of_latch_executions (loop_containing_stmt (cond));
2538 if (chrec_contains_undetermined (res))
2539 nb_chrec_dont_know_loops++;
2546 fprintf (dump_file, "\n(\n");
2547 fprintf (dump_file, "-----------------------------------------\n");
2548 fprintf (dump_file, "%d\tnb_chrec_dont_know_loops\n", nb_chrec_dont_know_loops);
2549 fprintf (dump_file, "%d\tnb_static_loops\n", nb_static_loops);
2550 fprintf (dump_file, "%d\tnb_total_loops\n", number_of_loops ());
2551 fprintf (dump_file, "-----------------------------------------\n");
2552 fprintf (dump_file, ")\n\n");
2554 print_loops (dump_file, 3);
2560 /* Counters for the stats. */
2566 unsigned nb_affine_multivar;
2567 unsigned nb_higher_poly;
2568 unsigned nb_chrec_dont_know;
2569 unsigned nb_undetermined;
2572 /* Reset the counters. */
2575 reset_chrecs_counters (struct chrec_stats *stats)
2577 stats->nb_chrecs = 0;
2578 stats->nb_affine = 0;
2579 stats->nb_affine_multivar = 0;
2580 stats->nb_higher_poly = 0;
2581 stats->nb_chrec_dont_know = 0;
2582 stats->nb_undetermined = 0;
2585 /* Dump the contents of a CHREC_STATS structure. */
2588 dump_chrecs_stats (FILE *file, struct chrec_stats *stats)
2590 fprintf (file, "\n(\n");
2591 fprintf (file, "-----------------------------------------\n");
2592 fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine);
2593 fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar);
2594 fprintf (file, "%d\tdegree greater than 2 polynomials\n",
2595 stats->nb_higher_poly);
2596 fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know);
2597 fprintf (file, "-----------------------------------------\n");
2598 fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs);
2599 fprintf (file, "%d\twith undetermined coefficients\n",
2600 stats->nb_undetermined);
2601 fprintf (file, "-----------------------------------------\n");
2602 fprintf (file, "%d\tchrecs in the scev database\n",
2603 (int) htab_elements (scalar_evolution_info));
2604 fprintf (file, "%d\tsets in the scev database\n", nb_set_scev);
2605 fprintf (file, "%d\tgets in the scev database\n", nb_get_scev);
2606 fprintf (file, "-----------------------------------------\n");
2607 fprintf (file, ")\n\n");
2610 /* Gather statistics about CHREC. */
2613 gather_chrec_stats (tree chrec, struct chrec_stats *stats)
2615 if (dump_file && (dump_flags & TDF_STATS))
2617 fprintf (dump_file, "(classify_chrec ");
2618 print_generic_expr (dump_file, chrec, 0);
2619 fprintf (dump_file, "\n");
2624 if (chrec == NULL_TREE)
2626 stats->nb_undetermined++;
2630 switch (TREE_CODE (chrec))
2632 case POLYNOMIAL_CHREC:
2633 if (evolution_function_is_affine_p (chrec))
2635 if (dump_file && (dump_flags & TDF_STATS))
2636 fprintf (dump_file, " affine_univariate\n");
2639 else if (evolution_function_is_affine_multivariate_p (chrec, 0))
2641 if (dump_file && (dump_flags & TDF_STATS))
2642 fprintf (dump_file, " affine_multivariate\n");
2643 stats->nb_affine_multivar++;
2647 if (dump_file && (dump_flags & TDF_STATS))
2648 fprintf (dump_file, " higher_degree_polynomial\n");
2649 stats->nb_higher_poly++;
2658 if (chrec_contains_undetermined (chrec))
2660 if (dump_file && (dump_flags & TDF_STATS))
2661 fprintf (dump_file, " undetermined\n");
2662 stats->nb_undetermined++;
2665 if (dump_file && (dump_flags & TDF_STATS))
2666 fprintf (dump_file, ")\n");
2669 /* One of the drivers for testing the scalar evolutions analysis.
2670 This function analyzes the scalar evolution of all the scalars
2671 defined as loop phi nodes in one of the loops from the
2672 EXIT_CONDITIONS array.
2674 TODO Optimization: A loop is in canonical form if it contains only
2675 a single scalar loop phi node. All the other scalars that have an
2676 evolution in the loop are rewritten in function of this single
2677 index. This allows the parallelization of the loop. */
2680 analyze_scalar_evolution_for_all_loop_phi_nodes (VEC(gimple,heap) **exit_conditions)
2683 struct chrec_stats stats;
2685 gimple_stmt_iterator psi;
2687 reset_chrecs_counters (&stats);
2689 for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
2695 loop = loop_containing_stmt (cond);
2698 for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
2700 phi = gsi_stmt (psi);
2701 if (is_gimple_reg (PHI_RESULT (phi)))
2703 chrec = instantiate_parameters
2705 analyze_scalar_evolution (loop, PHI_RESULT (phi)));
2707 if (dump_file && (dump_flags & TDF_STATS))
2708 gather_chrec_stats (chrec, &stats);
2713 if (dump_file && (dump_flags & TDF_STATS))
2714 dump_chrecs_stats (dump_file, &stats);
2717 /* Callback for htab_traverse, gathers information on chrecs in the
2721 gather_stats_on_scev_database_1 (void **slot, void *stats)
2723 struct scev_info_str *entry = (struct scev_info_str *) *slot;
2725 gather_chrec_stats (entry->chrec, (struct chrec_stats *) stats);
2730 /* Classify the chrecs of the whole database. */
2733 gather_stats_on_scev_database (void)
2735 struct chrec_stats stats;
2740 reset_chrecs_counters (&stats);
2742 htab_traverse (scalar_evolution_info, gather_stats_on_scev_database_1,
2745 dump_chrecs_stats (dump_file, &stats);
2753 initialize_scalar_evolutions_analyzer (void)
2755 /* The elements below are unique. */
2756 if (chrec_dont_know == NULL_TREE)
2758 chrec_not_analyzed_yet = NULL_TREE;
2759 chrec_dont_know = make_node (SCEV_NOT_KNOWN);
2760 chrec_known = make_node (SCEV_KNOWN);
2761 TREE_TYPE (chrec_dont_know) = void_type_node;
2762 TREE_TYPE (chrec_known) = void_type_node;
2766 /* Initialize the analysis of scalar evolutions for LOOPS. */
2769 scev_initialize (void)
2774 scalar_evolution_info = htab_create_alloc (100,
2781 initialize_scalar_evolutions_analyzer ();
2783 FOR_EACH_LOOP (li, loop, 0)
2785 loop->nb_iterations = NULL_TREE;
2789 /* Cleans up the information cached by the scalar evolutions analysis. */
2797 if (!scalar_evolution_info || !current_loops)
2800 htab_empty (scalar_evolution_info);
2801 FOR_EACH_LOOP (li, loop, 0)
2803 loop->nb_iterations = NULL_TREE;
2807 /* Checks whether use of OP in USE_LOOP behaves as a simple affine iv with
2808 respect to WRTO_LOOP and returns its base and step in IV if possible
2809 (see analyze_scalar_evolution_in_loop for more details on USE_LOOP
2810 and WRTO_LOOP). If ALLOW_NONCONSTANT_STEP is true, we want step to be
2811 invariant in LOOP. Otherwise we require it to be an integer constant.
2813 IV->no_overflow is set to true if we are sure the iv cannot overflow (e.g.
2814 because it is computed in signed arithmetics). Consequently, adding an
2817 for (i = IV->base; ; i += IV->step)
2819 is only safe if IV->no_overflow is false, or TYPE_OVERFLOW_UNDEFINED is
2820 false for the type of the induction variable, or you can prove that i does
2821 not wrap by some other argument. Otherwise, this might introduce undefined
2824 for (i = iv->base; ; i = (type) ((unsigned type) i + (unsigned type) iv->step))
2826 must be used instead. */
2829 simple_iv (struct loop *wrto_loop, struct loop *use_loop, tree op,
2830 affine_iv *iv, bool allow_nonconstant_step)
2835 iv->base = NULL_TREE;
2836 iv->step = NULL_TREE;
2837 iv->no_overflow = false;
2839 type = TREE_TYPE (op);
2840 if (TREE_CODE (type) != INTEGER_TYPE
2841 && TREE_CODE (type) != POINTER_TYPE)
2844 ev = analyze_scalar_evolution_in_loop (wrto_loop, use_loop, op,
2846 if (chrec_contains_undetermined (ev)
2847 || chrec_contains_symbols_defined_in_loop (ev, wrto_loop->num))
2850 if (tree_does_not_contain_chrecs (ev))
2853 iv->step = build_int_cst (TREE_TYPE (ev), 0);
2854 iv->no_overflow = true;
2858 if (TREE_CODE (ev) != POLYNOMIAL_CHREC
2859 || CHREC_VARIABLE (ev) != (unsigned) wrto_loop->num)
2862 iv->step = CHREC_RIGHT (ev);
2863 if ((!allow_nonconstant_step && TREE_CODE (iv->step) != INTEGER_CST)
2864 || tree_contains_chrecs (iv->step, NULL))
2867 iv->base = CHREC_LEFT (ev);
2868 if (tree_contains_chrecs (iv->base, NULL))
2871 iv->no_overflow = !folded_casts && TYPE_OVERFLOW_UNDEFINED (type);
2876 /* Runs the analysis of scalar evolutions. */
2879 scev_analysis (void)
2881 VEC(gimple,heap) *exit_conditions;
2883 exit_conditions = VEC_alloc (gimple, heap, 37);
2884 select_loops_exit_conditions (&exit_conditions);
2886 if (dump_file && (dump_flags & TDF_STATS))
2887 analyze_scalar_evolution_for_all_loop_phi_nodes (&exit_conditions);
2889 number_of_iterations_for_all_loops (&exit_conditions);
2890 VEC_free (gimple, heap, exit_conditions);
2893 /* Finalize the scalar evolution analysis. */
2896 scev_finalize (void)
2898 if (!scalar_evolution_info)
2900 htab_delete (scalar_evolution_info);
2901 scalar_evolution_info = NULL;
2904 /* Returns true if the expression EXPR is considered to be too expensive
2905 for scev_const_prop. */
2908 expression_expensive_p (tree expr)
2910 enum tree_code code;
2912 if (is_gimple_val (expr))
2915 code = TREE_CODE (expr);
2916 if (code == TRUNC_DIV_EXPR
2917 || code == CEIL_DIV_EXPR
2918 || code == FLOOR_DIV_EXPR
2919 || code == ROUND_DIV_EXPR
2920 || code == TRUNC_MOD_EXPR
2921 || code == CEIL_MOD_EXPR
2922 || code == FLOOR_MOD_EXPR
2923 || code == ROUND_MOD_EXPR
2924 || code == EXACT_DIV_EXPR)
2926 /* Division by power of two is usually cheap, so we allow it.
2927 Forbid anything else. */
2928 if (!integer_pow2p (TREE_OPERAND (expr, 1)))
2932 switch (TREE_CODE_CLASS (code))
2935 case tcc_comparison:
2936 if (expression_expensive_p (TREE_OPERAND (expr, 1)))
2941 return expression_expensive_p (TREE_OPERAND (expr, 0));
2948 /* Replace ssa names for that scev can prove they are constant by the
2949 appropriate constants. Also perform final value replacement in loops,
2950 in case the replacement expressions are cheap.
2952 We only consider SSA names defined by phi nodes; rest is left to the
2953 ordinary constant propagation pass. */
2956 scev_const_prop (void)
2959 tree name, type, ev;
2961 struct loop *loop, *ex_loop;
2962 bitmap ssa_names_to_remove = NULL;
2965 gimple_stmt_iterator psi;
2967 if (number_of_loops () <= 1)
2972 loop = bb->loop_father;
2974 for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
2976 phi = gsi_stmt (psi);
2977 name = PHI_RESULT (phi);
2979 if (!is_gimple_reg (name))
2982 type = TREE_TYPE (name);
2984 if (!POINTER_TYPE_P (type)
2985 && !INTEGRAL_TYPE_P (type))
2988 ev = resolve_mixers (loop, analyze_scalar_evolution (loop, name));
2989 if (!is_gimple_min_invariant (ev)
2990 || !may_propagate_copy (name, ev))
2993 /* Replace the uses of the name. */
2995 replace_uses_by (name, ev);
2997 if (!ssa_names_to_remove)
2998 ssa_names_to_remove = BITMAP_ALLOC (NULL);
2999 bitmap_set_bit (ssa_names_to_remove, SSA_NAME_VERSION (name));
3003 /* Remove the ssa names that were replaced by constants. We do not
3004 remove them directly in the previous cycle, since this
3005 invalidates scev cache. */
3006 if (ssa_names_to_remove)
3010 EXECUTE_IF_SET_IN_BITMAP (ssa_names_to_remove, 0, i, bi)
3012 gimple_stmt_iterator psi;
3013 name = ssa_name (i);
3014 phi = SSA_NAME_DEF_STMT (name);
3016 gcc_assert (gimple_code (phi) == GIMPLE_PHI);
3017 psi = gsi_for_stmt (phi);
3018 remove_phi_node (&psi, true);
3021 BITMAP_FREE (ssa_names_to_remove);
3025 /* Now the regular final value replacement. */
3026 FOR_EACH_LOOP (li, loop, LI_FROM_INNERMOST)
3029 tree def, rslt, niter;
3030 gimple_stmt_iterator bsi;
3032 /* If we do not know exact number of iterations of the loop, we cannot
3033 replace the final value. */
3034 exit = single_exit (loop);
3038 niter = number_of_latch_executions (loop);
3039 if (niter == chrec_dont_know)
3042 /* Ensure that it is possible to insert new statements somewhere. */
3043 if (!single_pred_p (exit->dest))
3044 split_loop_exit_edge (exit);
3045 bsi = gsi_after_labels (exit->dest);
3047 ex_loop = superloop_at_depth (loop,
3048 loop_depth (exit->dest->loop_father) + 1);
3050 for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); )
3052 phi = gsi_stmt (psi);
3053 rslt = PHI_RESULT (phi);
3054 def = PHI_ARG_DEF_FROM_EDGE (phi, exit);
3055 if (!is_gimple_reg (def))
3061 if (!POINTER_TYPE_P (TREE_TYPE (def))
3062 && !INTEGRAL_TYPE_P (TREE_TYPE (def)))
3068 def = analyze_scalar_evolution_in_loop (ex_loop, loop, def, NULL);
3069 def = compute_overall_effect_of_inner_loop (ex_loop, def);
3070 if (!tree_does_not_contain_chrecs (def)
3071 || chrec_contains_symbols_defined_in_loop (def, ex_loop->num)
3072 /* Moving the computation from the loop may prolong life range
3073 of some ssa names, which may cause problems if they appear
3074 on abnormal edges. */
3075 || contains_abnormal_ssa_name_p (def)
3076 /* Do not emit expensive expressions. The rationale is that
3077 when someone writes a code like
3079 while (n > 45) n -= 45;
3081 he probably knows that n is not large, and does not want it
3082 to be turned into n %= 45. */
3083 || expression_expensive_p (def))
3089 /* Eliminate the PHI node and replace it by a computation outside
3091 def = unshare_expr (def);
3092 remove_phi_node (&psi, false);
3094 def = force_gimple_operand_gsi (&bsi, def, false, NULL_TREE,
3095 true, GSI_SAME_STMT);
3096 ass = gimple_build_assign (rslt, def);
3097 gsi_insert_before (&bsi, ass, GSI_SAME_STMT);
3103 #include "gt-tree-scalar-evolution.h"