1 /* Data references and dependences detectors.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
3 Contributed by Sebastian Pop <pop@cri.ensmp.fr>
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 3, or (at your option) any later
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING3. If not see
19 <http://www.gnu.org/licenses/>. */
21 /* This pass walks a given loop structure searching for array
22 references. The information about the array accesses is recorded
23 in DATA_REFERENCE structures.
25 The basic test for determining the dependences is:
26 given two access functions chrec1 and chrec2 to a same array, and
27 x and y two vectors from the iteration domain, the same element of
28 the array is accessed twice at iterations x and y if and only if:
29 | chrec1 (x) == chrec2 (y).
31 The goals of this analysis are:
33 - to determine the independence: the relation between two
34 independent accesses is qualified with the chrec_known (this
35 information allows a loop parallelization),
37 - when two data references access the same data, to qualify the
38 dependence relation with classic dependence representations:
42 - loop carried level dependence
43 - polyhedron dependence
44 or with the chains of recurrences based representation,
46 - to define a knowledge base for storing the data dependence
49 - to define an interface to access this data.
54 - subscript: given two array accesses a subscript is the tuple
55 composed of the access functions for a given dimension. Example:
56 Given A[f1][f2][f3] and B[g1][g2][g3], there are three subscripts:
57 (f1, g1), (f2, g2), (f3, g3).
59 - Diophantine equation: an equation whose coefficients and
60 solutions are integer constants, for example the equation
62 has an integer solution x = 1 and y = -1.
66 - "Advanced Compilation for High Performance Computing" by Randy
67 Allen and Ken Kennedy.
68 http://citeseer.ist.psu.edu/goff91practical.html
70 - "Loop Transformations for Restructuring Compilers - The Foundations"
78 #include "coretypes.h"
83 /* These RTL headers are needed for basic-block.h. */
85 #include "basic-block.h"
86 #include "diagnostic.h"
87 #include "tree-flow.h"
88 #include "tree-dump.h"
91 #include "tree-chrec.h"
92 #include "tree-data-ref.h"
93 #include "tree-scalar-evolution.h"
94 #include "tree-pass.h"
95 #include "langhooks.h"
97 static struct datadep_stats
99 int num_dependence_tests;
100 int num_dependence_dependent;
101 int num_dependence_independent;
102 int num_dependence_undetermined;
104 int num_subscript_tests;
105 int num_subscript_undetermined;
106 int num_same_subscript_function;
109 int num_ziv_independent;
110 int num_ziv_dependent;
111 int num_ziv_unimplemented;
114 int num_siv_independent;
115 int num_siv_dependent;
116 int num_siv_unimplemented;
119 int num_miv_independent;
120 int num_miv_dependent;
121 int num_miv_unimplemented;
124 static bool subscript_dependence_tester_1 (struct data_dependence_relation *,
125 struct data_reference *,
126 struct data_reference *,
128 /* Returns true iff A divides B. */
131 tree_fold_divides_p (const_tree a, const_tree b)
133 gcc_assert (TREE_CODE (a) == INTEGER_CST);
134 gcc_assert (TREE_CODE (b) == INTEGER_CST);
135 return integer_zerop (int_const_binop (TRUNC_MOD_EXPR, b, a, 0));
138 /* Returns true iff A divides B. */
141 int_divides_p (int a, int b)
143 return ((b % a) == 0);
148 /* Dump into FILE all the data references from DATAREFS. */
151 dump_data_references (FILE *file, VEC (data_reference_p, heap) *datarefs)
154 struct data_reference *dr;
156 for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++)
157 dump_data_reference (file, dr);
160 /* Dump into FILE all the dependence relations from DDRS. */
163 dump_data_dependence_relations (FILE *file,
164 VEC (ddr_p, heap) *ddrs)
167 struct data_dependence_relation *ddr;
169 for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
170 dump_data_dependence_relation (file, ddr);
173 /* Dump function for a DATA_REFERENCE structure. */
176 dump_data_reference (FILE *outf,
177 struct data_reference *dr)
181 fprintf (outf, "(Data Ref: \n stmt: ");
182 print_generic_stmt (outf, DR_STMT (dr), 0);
183 fprintf (outf, " ref: ");
184 print_generic_stmt (outf, DR_REF (dr), 0);
185 fprintf (outf, " base_object: ");
186 print_generic_stmt (outf, DR_BASE_OBJECT (dr), 0);
188 for (i = 0; i < DR_NUM_DIMENSIONS (dr); i++)
190 fprintf (outf, " Access function %d: ", i);
191 print_generic_stmt (outf, DR_ACCESS_FN (dr, i), 0);
193 fprintf (outf, ")\n");
196 /* Dumps the affine function described by FN to the file OUTF. */
199 dump_affine_function (FILE *outf, affine_fn fn)
204 print_generic_expr (outf, VEC_index (tree, fn, 0), TDF_SLIM);
205 for (i = 1; VEC_iterate (tree, fn, i, coef); i++)
207 fprintf (outf, " + ");
208 print_generic_expr (outf, coef, TDF_SLIM);
209 fprintf (outf, " * x_%u", i);
213 /* Dumps the conflict function CF to the file OUTF. */
216 dump_conflict_function (FILE *outf, conflict_function *cf)
220 if (cf->n == NO_DEPENDENCE)
221 fprintf (outf, "no dependence\n");
222 else if (cf->n == NOT_KNOWN)
223 fprintf (outf, "not known\n");
226 for (i = 0; i < cf->n; i++)
229 dump_affine_function (outf, cf->fns[i]);
230 fprintf (outf, "]\n");
235 /* Dump function for a SUBSCRIPT structure. */
238 dump_subscript (FILE *outf, struct subscript *subscript)
240 conflict_function *cf = SUB_CONFLICTS_IN_A (subscript);
242 fprintf (outf, "\n (subscript \n");
243 fprintf (outf, " iterations_that_access_an_element_twice_in_A: ");
244 dump_conflict_function (outf, cf);
245 if (CF_NONTRIVIAL_P (cf))
247 tree last_iteration = SUB_LAST_CONFLICT (subscript);
248 fprintf (outf, " last_conflict: ");
249 print_generic_stmt (outf, last_iteration, 0);
252 cf = SUB_CONFLICTS_IN_B (subscript);
253 fprintf (outf, " iterations_that_access_an_element_twice_in_B: ");
254 dump_conflict_function (outf, cf);
255 if (CF_NONTRIVIAL_P (cf))
257 tree last_iteration = SUB_LAST_CONFLICT (subscript);
258 fprintf (outf, " last_conflict: ");
259 print_generic_stmt (outf, last_iteration, 0);
262 fprintf (outf, " (Subscript distance: ");
263 print_generic_stmt (outf, SUB_DISTANCE (subscript), 0);
264 fprintf (outf, " )\n");
265 fprintf (outf, " )\n");
268 /* Print the classic direction vector DIRV to OUTF. */
271 print_direction_vector (FILE *outf,
277 for (eq = 0; eq < length; eq++)
279 enum data_dependence_direction dir = dirv[eq];
284 fprintf (outf, " +");
287 fprintf (outf, " -");
290 fprintf (outf, " =");
292 case dir_positive_or_equal:
293 fprintf (outf, " +=");
295 case dir_positive_or_negative:
296 fprintf (outf, " +-");
298 case dir_negative_or_equal:
299 fprintf (outf, " -=");
302 fprintf (outf, " *");
305 fprintf (outf, "indep");
309 fprintf (outf, "\n");
312 /* Print a vector of direction vectors. */
315 print_dir_vectors (FILE *outf, VEC (lambda_vector, heap) *dir_vects,
321 for (j = 0; VEC_iterate (lambda_vector, dir_vects, j, v); j++)
322 print_direction_vector (outf, v, length);
325 /* Print a vector of distance vectors. */
328 print_dist_vectors (FILE *outf, VEC (lambda_vector, heap) *dist_vects,
334 for (j = 0; VEC_iterate (lambda_vector, dist_vects, j, v); j++)
335 print_lambda_vector (outf, v, length);
341 debug_data_dependence_relation (struct data_dependence_relation *ddr)
343 dump_data_dependence_relation (stderr, ddr);
346 /* Dump function for a DATA_DEPENDENCE_RELATION structure. */
349 dump_data_dependence_relation (FILE *outf,
350 struct data_dependence_relation *ddr)
352 struct data_reference *dra, *drb;
356 fprintf (outf, "(Data Dep: \n");
357 if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know)
358 fprintf (outf, " (don't know)\n");
360 else if (DDR_ARE_DEPENDENT (ddr) == chrec_known)
361 fprintf (outf, " (no dependence)\n");
363 else if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
368 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
370 fprintf (outf, " access_fn_A: ");
371 print_generic_stmt (outf, DR_ACCESS_FN (dra, i), 0);
372 fprintf (outf, " access_fn_B: ");
373 print_generic_stmt (outf, DR_ACCESS_FN (drb, i), 0);
374 dump_subscript (outf, DDR_SUBSCRIPT (ddr, i));
377 fprintf (outf, " inner loop index: %d\n", DDR_INNER_LOOP (ddr));
378 fprintf (outf, " loop nest: (");
379 for (i = 0; VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++)
380 fprintf (outf, "%d ", loopi->num);
381 fprintf (outf, ")\n");
383 for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++)
385 fprintf (outf, " distance_vector: ");
386 print_lambda_vector (outf, DDR_DIST_VECT (ddr, i),
390 for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++)
392 fprintf (outf, " direction_vector: ");
393 print_direction_vector (outf, DDR_DIR_VECT (ddr, i),
398 fprintf (outf, ")\n");
401 /* Dump function for a DATA_DEPENDENCE_DIRECTION structure. */
404 dump_data_dependence_direction (FILE *file,
405 enum data_dependence_direction dir)
421 case dir_positive_or_negative:
422 fprintf (file, "+-");
425 case dir_positive_or_equal:
426 fprintf (file, "+=");
429 case dir_negative_or_equal:
430 fprintf (file, "-=");
442 /* Dumps the distance and direction vectors in FILE. DDRS contains
443 the dependence relations, and VECT_SIZE is the size of the
444 dependence vectors, or in other words the number of loops in the
448 dump_dist_dir_vectors (FILE *file, VEC (ddr_p, heap) *ddrs)
451 struct data_dependence_relation *ddr;
454 for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
455 if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE && DDR_AFFINE_P (ddr))
457 for (j = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), j, v); j++)
459 fprintf (file, "DISTANCE_V (");
460 print_lambda_vector (file, v, DDR_NB_LOOPS (ddr));
461 fprintf (file, ")\n");
464 for (j = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), j, v); j++)
466 fprintf (file, "DIRECTION_V (");
467 print_direction_vector (file, v, DDR_NB_LOOPS (ddr));
468 fprintf (file, ")\n");
472 fprintf (file, "\n\n");
475 /* Dumps the data dependence relations DDRS in FILE. */
478 dump_ddrs (FILE *file, VEC (ddr_p, heap) *ddrs)
481 struct data_dependence_relation *ddr;
483 for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
484 dump_data_dependence_relation (file, ddr);
486 fprintf (file, "\n\n");
489 /* Expresses EXP as VAR + OFF, where off is a constant. The type of OFF
490 will be ssizetype. */
493 split_constant_offset (tree exp, tree *var, tree *off)
495 tree type = TREE_TYPE (exp), otype;
502 otype = TREE_TYPE (exp);
503 code = TREE_CODE (exp);
508 *var = build_int_cst (type, 0);
509 *off = fold_convert (ssizetype, exp);
512 case POINTER_PLUS_EXPR:
517 split_constant_offset (TREE_OPERAND (exp, 0), &var0, &off0);
518 split_constant_offset (TREE_OPERAND (exp, 1), &var1, &off1);
519 *var = fold_convert (type, fold_build2 (TREE_CODE (exp), otype,
521 *off = size_binop (code, off0, off1);
525 off1 = TREE_OPERAND (exp, 1);
526 if (TREE_CODE (off1) != INTEGER_CST)
529 split_constant_offset (TREE_OPERAND (exp, 0), &var0, &off0);
530 *var = fold_convert (type, fold_build2 (MULT_EXPR, otype,
532 *off = size_binop (MULT_EXPR, off0, fold_convert (ssizetype, off1));
537 tree op, base, poffset;
538 HOST_WIDE_INT pbitsize, pbitpos;
539 enum machine_mode pmode;
540 int punsignedp, pvolatilep;
542 op = TREE_OPERAND (exp, 0);
543 if (!handled_component_p (op))
546 base = get_inner_reference (op, &pbitsize, &pbitpos, &poffset,
547 &pmode, &punsignedp, &pvolatilep, false);
549 if (pbitpos % BITS_PER_UNIT != 0)
551 base = build_fold_addr_expr (base);
552 off0 = ssize_int (pbitpos / BITS_PER_UNIT);
556 split_constant_offset (poffset, &poffset, &off1);
557 off0 = size_binop (PLUS_EXPR, off0, off1);
558 if (POINTER_TYPE_P (TREE_TYPE (base)))
559 base = fold_build2 (POINTER_PLUS_EXPR, TREE_TYPE (base),
560 base, fold_convert (sizetype, poffset));
562 base = fold_build2 (PLUS_EXPR, TREE_TYPE (base), base,
563 fold_convert (TREE_TYPE (base), poffset));
566 var0 = fold_convert (type, base);
568 /* If variable length types are involved, punt, otherwise casts
569 might be converted into ARRAY_REFs in gimplify_conversion.
570 To compute that ARRAY_REF's element size TYPE_SIZE_UNIT, which
571 possibly no longer appears in current GIMPLE, might resurface.
572 This perhaps could run
573 if (TREE_CODE (var0) == NOP_EXPR
574 || TREE_CODE (var0) == CONVERT_EXPR)
576 gimplify_conversion (&var0);
577 // Attempt to fill in any within var0 found ARRAY_REF's
578 // element size from corresponding op embedded ARRAY_REF,
579 // if unsuccessful, just punt.
581 while (POINTER_TYPE_P (type))
582 type = TREE_TYPE (type);
583 if (int_size_in_bytes (type) < 0)
593 tree def_stmt = SSA_NAME_DEF_STMT (exp);
594 if (TREE_CODE (def_stmt) == GIMPLE_MODIFY_STMT)
596 tree def_stmt_rhs = GIMPLE_STMT_OPERAND (def_stmt, 1);
598 if (!TREE_SIDE_EFFECTS (def_stmt_rhs)
599 && EXPR_P (def_stmt_rhs)
600 && !REFERENCE_CLASS_P (def_stmt_rhs)
601 && !get_call_expr_in (def_stmt_rhs))
603 split_constant_offset (def_stmt_rhs, &var0, &off0);
604 var0 = fold_convert (type, var0);
617 *off = ssize_int (0);
620 /* Returns the address ADDR of an object in a canonical shape (without nop
621 casts, and with type of pointer to the object). */
624 canonicalize_base_object_address (tree addr)
630 /* The base address may be obtained by casting from integer, in that case
632 if (!POINTER_TYPE_P (TREE_TYPE (addr)))
635 if (TREE_CODE (addr) != ADDR_EXPR)
638 return build_fold_addr_expr (TREE_OPERAND (addr, 0));
641 /* Analyzes the behavior of the memory reference DR in the innermost loop that
645 dr_analyze_innermost (struct data_reference *dr)
647 tree stmt = DR_STMT (dr);
648 struct loop *loop = loop_containing_stmt (stmt);
649 tree ref = DR_REF (dr);
650 HOST_WIDE_INT pbitsize, pbitpos;
652 enum machine_mode pmode;
653 int punsignedp, pvolatilep;
654 affine_iv base_iv, offset_iv;
655 tree init, dinit, step;
657 if (dump_file && (dump_flags & TDF_DETAILS))
658 fprintf (dump_file, "analyze_innermost: ");
660 base = get_inner_reference (ref, &pbitsize, &pbitpos, &poffset,
661 &pmode, &punsignedp, &pvolatilep, false);
662 gcc_assert (base != NULL_TREE);
664 if (pbitpos % BITS_PER_UNIT != 0)
666 if (dump_file && (dump_flags & TDF_DETAILS))
667 fprintf (dump_file, "failed: bit offset alignment.\n");
671 base = build_fold_addr_expr (base);
672 if (!simple_iv (loop, stmt, base, &base_iv, false))
674 if (dump_file && (dump_flags & TDF_DETAILS))
675 fprintf (dump_file, "failed: evolution of base is not affine.\n");
680 offset_iv.base = ssize_int (0);
681 offset_iv.step = ssize_int (0);
683 else if (!simple_iv (loop, stmt, poffset, &offset_iv, false))
685 if (dump_file && (dump_flags & TDF_DETAILS))
686 fprintf (dump_file, "failed: evolution of offset is not affine.\n");
690 init = ssize_int (pbitpos / BITS_PER_UNIT);
691 split_constant_offset (base_iv.base, &base_iv.base, &dinit);
692 init = size_binop (PLUS_EXPR, init, dinit);
693 split_constant_offset (offset_iv.base, &offset_iv.base, &dinit);
694 init = size_binop (PLUS_EXPR, init, dinit);
696 step = size_binop (PLUS_EXPR,
697 fold_convert (ssizetype, base_iv.step),
698 fold_convert (ssizetype, offset_iv.step));
700 DR_BASE_ADDRESS (dr) = canonicalize_base_object_address (base_iv.base);
702 DR_OFFSET (dr) = fold_convert (ssizetype, offset_iv.base);
706 DR_ALIGNED_TO (dr) = size_int (highest_pow2_factor (offset_iv.base));
708 if (dump_file && (dump_flags & TDF_DETAILS))
709 fprintf (dump_file, "success.\n");
712 /* Determines the base object and the list of indices of memory reference
713 DR, analyzed in loop nest NEST. */
716 dr_analyze_indices (struct data_reference *dr, struct loop *nest)
718 tree stmt = DR_STMT (dr);
719 struct loop *loop = loop_containing_stmt (stmt);
720 VEC (tree, heap) *access_fns = NULL;
721 tree ref = unshare_expr (DR_REF (dr)), aref = ref, op;
722 tree base, off, access_fn;
724 while (handled_component_p (aref))
726 if (TREE_CODE (aref) == ARRAY_REF)
728 op = TREE_OPERAND (aref, 1);
729 access_fn = analyze_scalar_evolution (loop, op);
730 access_fn = resolve_mixers (nest, access_fn);
731 VEC_safe_push (tree, heap, access_fns, access_fn);
733 TREE_OPERAND (aref, 1) = build_int_cst (TREE_TYPE (op), 0);
736 aref = TREE_OPERAND (aref, 0);
739 if (INDIRECT_REF_P (aref))
741 op = TREE_OPERAND (aref, 0);
742 access_fn = analyze_scalar_evolution (loop, op);
743 access_fn = resolve_mixers (nest, access_fn);
744 base = initial_condition (access_fn);
745 split_constant_offset (base, &base, &off);
746 access_fn = chrec_replace_initial_condition (access_fn,
747 fold_convert (TREE_TYPE (base), off));
749 TREE_OPERAND (aref, 0) = base;
750 VEC_safe_push (tree, heap, access_fns, access_fn);
753 DR_BASE_OBJECT (dr) = ref;
754 DR_ACCESS_FNS (dr) = access_fns;
757 /* Extracts the alias analysis information from the memory reference DR. */
760 dr_analyze_alias (struct data_reference *dr)
762 tree stmt = DR_STMT (dr);
763 tree ref = DR_REF (dr);
764 tree base = get_base_address (ref), addr, smt = NULL_TREE;
771 else if (INDIRECT_REF_P (base))
773 addr = TREE_OPERAND (base, 0);
774 if (TREE_CODE (addr) == SSA_NAME)
776 smt = symbol_mem_tag (SSA_NAME_VAR (addr));
777 DR_PTR_INFO (dr) = SSA_NAME_PTR_INFO (addr);
781 DR_SYMBOL_TAG (dr) = smt;
782 if (smt && var_can_have_subvars (smt))
783 DR_SUBVARS (dr) = get_subvars_for_var (smt);
785 vops = BITMAP_ALLOC (NULL);
786 FOR_EACH_SSA_TREE_OPERAND (op, stmt, it, SSA_OP_VIRTUAL_USES)
788 bitmap_set_bit (vops, DECL_UID (SSA_NAME_VAR (op)));
794 /* Returns true if the address of DR is invariant. */
797 dr_address_invariant_p (struct data_reference *dr)
802 for (i = 0; VEC_iterate (tree, DR_ACCESS_FNS (dr), i, idx); i++)
803 if (tree_contains_chrecs (idx, NULL))
809 /* Frees data reference DR. */
812 free_data_ref (data_reference_p dr)
814 BITMAP_FREE (DR_VOPS (dr));
815 VEC_free (tree, heap, DR_ACCESS_FNS (dr));
819 /* Analyzes memory reference MEMREF accessed in STMT. The reference
820 is read if IS_READ is true, write otherwise. Returns the
821 data_reference description of MEMREF. NEST is the outermost loop of the
822 loop nest in that the reference should be analyzed. */
824 struct data_reference *
825 create_data_ref (struct loop *nest, tree memref, tree stmt, bool is_read)
827 struct data_reference *dr;
829 if (dump_file && (dump_flags & TDF_DETAILS))
831 fprintf (dump_file, "Creating dr for ");
832 print_generic_expr (dump_file, memref, TDF_SLIM);
833 fprintf (dump_file, "\n");
836 dr = XCNEW (struct data_reference);
838 DR_REF (dr) = memref;
839 DR_IS_READ (dr) = is_read;
841 dr_analyze_innermost (dr);
842 dr_analyze_indices (dr, nest);
843 dr_analyze_alias (dr);
845 if (dump_file && (dump_flags & TDF_DETAILS))
847 fprintf (dump_file, "\tbase_address: ");
848 print_generic_expr (dump_file, DR_BASE_ADDRESS (dr), TDF_SLIM);
849 fprintf (dump_file, "\n\toffset from base address: ");
850 print_generic_expr (dump_file, DR_OFFSET (dr), TDF_SLIM);
851 fprintf (dump_file, "\n\tconstant offset from base address: ");
852 print_generic_expr (dump_file, DR_INIT (dr), TDF_SLIM);
853 fprintf (dump_file, "\n\tstep: ");
854 print_generic_expr (dump_file, DR_STEP (dr), TDF_SLIM);
855 fprintf (dump_file, "\n\taligned to: ");
856 print_generic_expr (dump_file, DR_ALIGNED_TO (dr), TDF_SLIM);
857 fprintf (dump_file, "\n\tbase_object: ");
858 print_generic_expr (dump_file, DR_BASE_OBJECT (dr), TDF_SLIM);
859 fprintf (dump_file, "\n\tsymbol tag: ");
860 print_generic_expr (dump_file, DR_SYMBOL_TAG (dr), TDF_SLIM);
861 fprintf (dump_file, "\n");
867 /* Returns true if FNA == FNB. */
870 affine_function_equal_p (affine_fn fna, affine_fn fnb)
872 unsigned i, n = VEC_length (tree, fna);
874 if (n != VEC_length (tree, fnb))
877 for (i = 0; i < n; i++)
878 if (!operand_equal_p (VEC_index (tree, fna, i),
879 VEC_index (tree, fnb, i), 0))
885 /* If all the functions in CF are the same, returns one of them,
886 otherwise returns NULL. */
889 common_affine_function (conflict_function *cf)
894 if (!CF_NONTRIVIAL_P (cf))
899 for (i = 1; i < cf->n; i++)
900 if (!affine_function_equal_p (comm, cf->fns[i]))
906 /* Returns the base of the affine function FN. */
909 affine_function_base (affine_fn fn)
911 return VEC_index (tree, fn, 0);
914 /* Returns true if FN is a constant. */
917 affine_function_constant_p (affine_fn fn)
922 for (i = 1; VEC_iterate (tree, fn, i, coef); i++)
923 if (!integer_zerop (coef))
929 /* Returns true if FN is the zero constant function. */
932 affine_function_zero_p (affine_fn fn)
934 return (integer_zerop (affine_function_base (fn))
935 && affine_function_constant_p (fn));
938 /* Returns a signed integer type with the largest precision from TA
942 signed_type_for_types (tree ta, tree tb)
944 if (TYPE_PRECISION (ta) > TYPE_PRECISION (tb))
945 return signed_type_for (ta);
947 return signed_type_for (tb);
950 /* Applies operation OP on affine functions FNA and FNB, and returns the
954 affine_fn_op (enum tree_code op, affine_fn fna, affine_fn fnb)
960 if (VEC_length (tree, fnb) > VEC_length (tree, fna))
962 n = VEC_length (tree, fna);
963 m = VEC_length (tree, fnb);
967 n = VEC_length (tree, fnb);
968 m = VEC_length (tree, fna);
971 ret = VEC_alloc (tree, heap, m);
972 for (i = 0; i < n; i++)
974 tree type = signed_type_for_types (TREE_TYPE (VEC_index (tree, fna, i)),
975 TREE_TYPE (VEC_index (tree, fnb, i)));
977 VEC_quick_push (tree, ret,
978 fold_build2 (op, type,
979 VEC_index (tree, fna, i),
980 VEC_index (tree, fnb, i)));
983 for (; VEC_iterate (tree, fna, i, coef); i++)
984 VEC_quick_push (tree, ret,
985 fold_build2 (op, signed_type_for (TREE_TYPE (coef)),
986 coef, integer_zero_node));
987 for (; VEC_iterate (tree, fnb, i, coef); i++)
988 VEC_quick_push (tree, ret,
989 fold_build2 (op, signed_type_for (TREE_TYPE (coef)),
990 integer_zero_node, coef));
995 /* Returns the sum of affine functions FNA and FNB. */
998 affine_fn_plus (affine_fn fna, affine_fn fnb)
1000 return affine_fn_op (PLUS_EXPR, fna, fnb);
1003 /* Returns the difference of affine functions FNA and FNB. */
1006 affine_fn_minus (affine_fn fna, affine_fn fnb)
1008 return affine_fn_op (MINUS_EXPR, fna, fnb);
1011 /* Frees affine function FN. */
1014 affine_fn_free (affine_fn fn)
1016 VEC_free (tree, heap, fn);
1019 /* Determine for each subscript in the data dependence relation DDR
1023 compute_subscript_distance (struct data_dependence_relation *ddr)
1025 conflict_function *cf_a, *cf_b;
1026 affine_fn fn_a, fn_b, diff;
1028 if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
1032 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
1034 struct subscript *subscript;
1036 subscript = DDR_SUBSCRIPT (ddr, i);
1037 cf_a = SUB_CONFLICTS_IN_A (subscript);
1038 cf_b = SUB_CONFLICTS_IN_B (subscript);
1040 fn_a = common_affine_function (cf_a);
1041 fn_b = common_affine_function (cf_b);
1044 SUB_DISTANCE (subscript) = chrec_dont_know;
1047 diff = affine_fn_minus (fn_a, fn_b);
1049 if (affine_function_constant_p (diff))
1050 SUB_DISTANCE (subscript) = affine_function_base (diff);
1052 SUB_DISTANCE (subscript) = chrec_dont_know;
1054 affine_fn_free (diff);
1059 /* Returns the conflict function for "unknown". */
1061 static conflict_function *
1062 conflict_fn_not_known (void)
1064 conflict_function *fn = XCNEW (conflict_function);
1070 /* Returns the conflict function for "independent". */
1072 static conflict_function *
1073 conflict_fn_no_dependence (void)
1075 conflict_function *fn = XCNEW (conflict_function);
1076 fn->n = NO_DEPENDENCE;
1081 /* Returns true if the address of OBJ is invariant in LOOP. */
1084 object_address_invariant_in_loop_p (const struct loop *loop, const_tree obj)
1086 while (handled_component_p (obj))
1088 if (TREE_CODE (obj) == ARRAY_REF)
1090 /* Index of the ARRAY_REF was zeroed in analyze_indices, thus we only
1091 need to check the stride and the lower bound of the reference. */
1092 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 2),
1094 || chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 3),
1098 else if (TREE_CODE (obj) == COMPONENT_REF)
1100 if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 2),
1104 obj = TREE_OPERAND (obj, 0);
1107 if (!INDIRECT_REF_P (obj))
1110 return !chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 0),
1114 /* Returns true if A and B are accesses to different objects, or to different
1115 fields of the same object. */
1118 disjoint_objects_p (tree a, tree b)
1120 tree base_a, base_b;
1121 VEC (tree, heap) *comp_a = NULL, *comp_b = NULL;
1124 base_a = get_base_address (a);
1125 base_b = get_base_address (b);
1129 && base_a != base_b)
1132 if (!operand_equal_p (base_a, base_b, 0))
1135 /* Compare the component references of A and B. We must start from the inner
1136 ones, so record them to the vector first. */
1137 while (handled_component_p (a))
1139 VEC_safe_push (tree, heap, comp_a, a);
1140 a = TREE_OPERAND (a, 0);
1142 while (handled_component_p (b))
1144 VEC_safe_push (tree, heap, comp_b, b);
1145 b = TREE_OPERAND (b, 0);
1151 if (VEC_length (tree, comp_a) == 0
1152 || VEC_length (tree, comp_b) == 0)
1155 a = VEC_pop (tree, comp_a);
1156 b = VEC_pop (tree, comp_b);
1158 /* Real and imaginary part of a variable do not alias. */
1159 if ((TREE_CODE (a) == REALPART_EXPR
1160 && TREE_CODE (b) == IMAGPART_EXPR)
1161 || (TREE_CODE (a) == IMAGPART_EXPR
1162 && TREE_CODE (b) == REALPART_EXPR))
1168 if (TREE_CODE (a) != TREE_CODE (b))
1171 /* Nothing to do for ARRAY_REFs, as the indices of array_refs in
1172 DR_BASE_OBJECT are always zero. */
1173 if (TREE_CODE (a) == ARRAY_REF)
1175 else if (TREE_CODE (a) == COMPONENT_REF)
1177 if (operand_equal_p (TREE_OPERAND (a, 1), TREE_OPERAND (b, 1), 0))
1180 /* Different fields of unions may overlap. */
1181 base_a = TREE_OPERAND (a, 0);
1182 if (TREE_CODE (TREE_TYPE (base_a)) == UNION_TYPE)
1185 /* Different fields of structures cannot. */
1193 VEC_free (tree, heap, comp_a);
1194 VEC_free (tree, heap, comp_b);
1199 /* Returns false if we can prove that data references A and B do not alias,
1203 dr_may_alias_p (const struct data_reference *a, const struct data_reference *b)
1205 const_tree addr_a = DR_BASE_ADDRESS (a);
1206 const_tree addr_b = DR_BASE_ADDRESS (b);
1207 const_tree type_a, type_b;
1208 const_tree decl_a = NULL_TREE, decl_b = NULL_TREE;
1210 /* If the sets of virtual operands are disjoint, the memory references do not
1212 if (!bitmap_intersect_p (DR_VOPS (a), DR_VOPS (b)))
1215 /* If the accessed objects are disjoint, the memory references do not
1217 if (disjoint_objects_p (DR_BASE_OBJECT (a), DR_BASE_OBJECT (b)))
1220 if (!addr_a || !addr_b)
1223 /* If the references are based on different static objects, they cannot alias
1224 (PTA should be able to disambiguate such accesses, but often it fails to,
1225 since currently we cannot distinguish between pointer and offset in pointer
1227 if (TREE_CODE (addr_a) == ADDR_EXPR
1228 && TREE_CODE (addr_b) == ADDR_EXPR)
1229 return TREE_OPERAND (addr_a, 0) == TREE_OPERAND (addr_b, 0);
1231 /* An instruction writing through a restricted pointer is "independent" of any
1232 instruction reading or writing through a different restricted pointer,
1233 in the same block/scope. */
1235 type_a = TREE_TYPE (addr_a);
1236 type_b = TREE_TYPE (addr_b);
1237 gcc_assert (POINTER_TYPE_P (type_a) && POINTER_TYPE_P (type_b));
1239 if (TREE_CODE (addr_a) == SSA_NAME)
1240 decl_a = SSA_NAME_VAR (addr_a);
1241 if (TREE_CODE (addr_b) == SSA_NAME)
1242 decl_b = SSA_NAME_VAR (addr_b);
1244 if (TYPE_RESTRICT (type_a) && TYPE_RESTRICT (type_b)
1245 && (!DR_IS_READ (a) || !DR_IS_READ (b))
1246 && decl_a && DECL_P (decl_a)
1247 && decl_b && DECL_P (decl_b)
1249 && TREE_CODE (DECL_CONTEXT (decl_a)) == FUNCTION_DECL
1250 && DECL_CONTEXT (decl_a) == DECL_CONTEXT (decl_b))
1256 /* Initialize a data dependence relation between data accesses A and
1257 B. NB_LOOPS is the number of loops surrounding the references: the
1258 size of the classic distance/direction vectors. */
1260 static struct data_dependence_relation *
1261 initialize_data_dependence_relation (struct data_reference *a,
1262 struct data_reference *b,
1263 VEC (loop_p, heap) *loop_nest)
1265 struct data_dependence_relation *res;
1268 res = XNEW (struct data_dependence_relation);
1271 DDR_LOOP_NEST (res) = NULL;
1272 DDR_REVERSED_P (res) = false;
1273 DDR_SUBSCRIPTS (res) = NULL;
1274 DDR_DIR_VECTS (res) = NULL;
1275 DDR_DIST_VECTS (res) = NULL;
1277 if (a == NULL || b == NULL)
1279 DDR_ARE_DEPENDENT (res) = chrec_dont_know;
1283 /* If the data references do not alias, then they are independent. */
1284 if (!dr_may_alias_p (a, b))
1286 DDR_ARE_DEPENDENT (res) = chrec_known;
1290 /* If the references do not access the same object, we do not know
1291 whether they alias or not. */
1292 if (!operand_equal_p (DR_BASE_OBJECT (a), DR_BASE_OBJECT (b), 0))
1294 DDR_ARE_DEPENDENT (res) = chrec_dont_know;
1298 /* If the base of the object is not invariant in the loop nest, we cannot
1299 analyze it. TODO -- in fact, it would suffice to record that there may
1300 be arbitrary dependences in the loops where the base object varies. */
1301 if (!object_address_invariant_in_loop_p (VEC_index (loop_p, loop_nest, 0),
1302 DR_BASE_OBJECT (a)))
1304 DDR_ARE_DEPENDENT (res) = chrec_dont_know;
1308 gcc_assert (DR_NUM_DIMENSIONS (a) == DR_NUM_DIMENSIONS (b));
1310 DDR_AFFINE_P (res) = true;
1311 DDR_ARE_DEPENDENT (res) = NULL_TREE;
1312 DDR_SUBSCRIPTS (res) = VEC_alloc (subscript_p, heap, DR_NUM_DIMENSIONS (a));
1313 DDR_LOOP_NEST (res) = loop_nest;
1314 DDR_INNER_LOOP (res) = 0;
1316 for (i = 0; i < DR_NUM_DIMENSIONS (a); i++)
1318 struct subscript *subscript;
1320 subscript = XNEW (struct subscript);
1321 SUB_CONFLICTS_IN_A (subscript) = conflict_fn_not_known ();
1322 SUB_CONFLICTS_IN_B (subscript) = conflict_fn_not_known ();
1323 SUB_LAST_CONFLICT (subscript) = chrec_dont_know;
1324 SUB_DISTANCE (subscript) = chrec_dont_know;
1325 VEC_safe_push (subscript_p, heap, DDR_SUBSCRIPTS (res), subscript);
1331 /* Frees memory used by the conflict function F. */
1334 free_conflict_function (conflict_function *f)
1338 if (CF_NONTRIVIAL_P (f))
1340 for (i = 0; i < f->n; i++)
1341 affine_fn_free (f->fns[i]);
1346 /* Frees memory used by SUBSCRIPTS. */
1349 free_subscripts (VEC (subscript_p, heap) *subscripts)
1354 for (i = 0; VEC_iterate (subscript_p, subscripts, i, s); i++)
1356 free_conflict_function (s->conflicting_iterations_in_a);
1357 free_conflict_function (s->conflicting_iterations_in_b);
1359 VEC_free (subscript_p, heap, subscripts);
1362 /* Set DDR_ARE_DEPENDENT to CHREC and finalize the subscript overlap
1366 finalize_ddr_dependent (struct data_dependence_relation *ddr,
1369 if (dump_file && (dump_flags & TDF_DETAILS))
1371 fprintf (dump_file, "(dependence classified: ");
1372 print_generic_expr (dump_file, chrec, 0);
1373 fprintf (dump_file, ")\n");
1376 DDR_ARE_DEPENDENT (ddr) = chrec;
1377 free_subscripts (DDR_SUBSCRIPTS (ddr));
1378 DDR_SUBSCRIPTS (ddr) = NULL;
1381 /* The dependence relation DDR cannot be represented by a distance
1385 non_affine_dependence_relation (struct data_dependence_relation *ddr)
1387 if (dump_file && (dump_flags & TDF_DETAILS))
1388 fprintf (dump_file, "(Dependence relation cannot be represented by distance vector.) \n");
1390 DDR_AFFINE_P (ddr) = false;
1395 /* This section contains the classic Banerjee tests. */
1397 /* Returns true iff CHREC_A and CHREC_B are not dependent on any index
1398 variables, i.e., if the ZIV (Zero Index Variable) test is true. */
1401 ziv_subscript_p (const_tree chrec_a, const_tree chrec_b)
1403 return (evolution_function_is_constant_p (chrec_a)
1404 && evolution_function_is_constant_p (chrec_b));
1407 /* Returns true iff CHREC_A and CHREC_B are dependent on an index
1408 variable, i.e., if the SIV (Single Index Variable) test is true. */
1411 siv_subscript_p (const_tree chrec_a, const_tree chrec_b)
1413 if ((evolution_function_is_constant_p (chrec_a)
1414 && evolution_function_is_univariate_p (chrec_b))
1415 || (evolution_function_is_constant_p (chrec_b)
1416 && evolution_function_is_univariate_p (chrec_a)))
1419 if (evolution_function_is_univariate_p (chrec_a)
1420 && evolution_function_is_univariate_p (chrec_b))
1422 switch (TREE_CODE (chrec_a))
1424 case POLYNOMIAL_CHREC:
1425 switch (TREE_CODE (chrec_b))
1427 case POLYNOMIAL_CHREC:
1428 if (CHREC_VARIABLE (chrec_a) != CHREC_VARIABLE (chrec_b))
1443 /* Creates a conflict function with N dimensions. The affine functions
1444 in each dimension follow. */
1446 static conflict_function *
1447 conflict_fn (unsigned n, ...)
1450 conflict_function *ret = XCNEW (conflict_function);
1453 gcc_assert (0 < n && n <= MAX_DIM);
1457 for (i = 0; i < n; i++)
1458 ret->fns[i] = va_arg (ap, affine_fn);
1464 /* Returns constant affine function with value CST. */
1467 affine_fn_cst (tree cst)
1469 affine_fn fn = VEC_alloc (tree, heap, 1);
1470 VEC_quick_push (tree, fn, cst);
1474 /* Returns affine function with single variable, CST + COEF * x_DIM. */
1477 affine_fn_univar (tree cst, unsigned dim, tree coef)
1479 affine_fn fn = VEC_alloc (tree, heap, dim + 1);
1482 gcc_assert (dim > 0);
1483 VEC_quick_push (tree, fn, cst);
1484 for (i = 1; i < dim; i++)
1485 VEC_quick_push (tree, fn, integer_zero_node);
1486 VEC_quick_push (tree, fn, coef);
1490 /* Analyze a ZIV (Zero Index Variable) subscript. *OVERLAPS_A and
1491 *OVERLAPS_B are initialized to the functions that describe the
1492 relation between the elements accessed twice by CHREC_A and
1493 CHREC_B. For k >= 0, the following property is verified:
1495 CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
1498 analyze_ziv_subscript (tree chrec_a,
1500 conflict_function **overlaps_a,
1501 conflict_function **overlaps_b,
1502 tree *last_conflicts)
1504 tree type, difference;
1505 dependence_stats.num_ziv++;
1507 if (dump_file && (dump_flags & TDF_DETAILS))
1508 fprintf (dump_file, "(analyze_ziv_subscript \n");
1510 type = signed_type_for_types (TREE_TYPE (chrec_a), TREE_TYPE (chrec_b));
1511 chrec_a = chrec_convert (type, chrec_a, NULL_TREE);
1512 chrec_b = chrec_convert (type, chrec_b, NULL_TREE);
1513 difference = chrec_fold_minus (type, chrec_a, chrec_b);
1515 switch (TREE_CODE (difference))
1518 if (integer_zerop (difference))
1520 /* The difference is equal to zero: the accessed index
1521 overlaps for each iteration in the loop. */
1522 *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
1523 *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
1524 *last_conflicts = chrec_dont_know;
1525 dependence_stats.num_ziv_dependent++;
1529 /* The accesses do not overlap. */
1530 *overlaps_a = conflict_fn_no_dependence ();
1531 *overlaps_b = conflict_fn_no_dependence ();
1532 *last_conflicts = integer_zero_node;
1533 dependence_stats.num_ziv_independent++;
1538 /* We're not sure whether the indexes overlap. For the moment,
1539 conservatively answer "don't know". */
1540 if (dump_file && (dump_flags & TDF_DETAILS))
1541 fprintf (dump_file, "ziv test failed: difference is non-integer.\n");
1543 *overlaps_a = conflict_fn_not_known ();
1544 *overlaps_b = conflict_fn_not_known ();
1545 *last_conflicts = chrec_dont_know;
1546 dependence_stats.num_ziv_unimplemented++;
1550 if (dump_file && (dump_flags & TDF_DETAILS))
1551 fprintf (dump_file, ")\n");
1554 /* Sets NIT to the estimated number of executions of the statements in
1555 LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as
1556 large as the number of iterations. If we have no reliable estimate,
1557 the function returns false, otherwise returns true. */
1560 estimated_loop_iterations (struct loop *loop, bool conservative,
1563 estimate_numbers_of_iterations_loop (loop);
1566 if (!loop->any_upper_bound)
1569 *nit = loop->nb_iterations_upper_bound;
1573 if (!loop->any_estimate)
1576 *nit = loop->nb_iterations_estimate;
1582 /* Similar to estimated_loop_iterations, but returns the estimate only
1583 if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
1584 on the number of iterations of LOOP could not be derived, returns -1. */
1587 estimated_loop_iterations_int (struct loop *loop, bool conservative)
1590 HOST_WIDE_INT hwi_nit;
1592 if (!estimated_loop_iterations (loop, conservative, &nit))
1595 if (!double_int_fits_in_shwi_p (nit))
1597 hwi_nit = double_int_to_shwi (nit);
1599 return hwi_nit < 0 ? -1 : hwi_nit;
1602 /* Similar to estimated_loop_iterations, but returns the estimate as a tree,
1603 and only if it fits to the int type. If this is not the case, or the
1604 estimate on the number of iterations of LOOP could not be derived, returns
1608 estimated_loop_iterations_tree (struct loop *loop, bool conservative)
1613 if (!estimated_loop_iterations (loop, conservative, &nit))
1614 return chrec_dont_know;
1616 type = lang_hooks.types.type_for_size (INT_TYPE_SIZE, true);
1617 if (!double_int_fits_to_tree_p (type, nit))
1618 return chrec_dont_know;
1620 return double_int_to_tree (type, nit);
1623 /* Analyze a SIV (Single Index Variable) subscript where CHREC_A is a
1624 constant, and CHREC_B is an affine function. *OVERLAPS_A and
1625 *OVERLAPS_B are initialized to the functions that describe the
1626 relation between the elements accessed twice by CHREC_A and
1627 CHREC_B. For k >= 0, the following property is verified:
1629 CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
1632 analyze_siv_subscript_cst_affine (tree chrec_a,
1634 conflict_function **overlaps_a,
1635 conflict_function **overlaps_b,
1636 tree *last_conflicts)
1638 bool value0, value1, value2;
1639 tree type, difference, tmp;
1641 type = signed_type_for_types (TREE_TYPE (chrec_a), TREE_TYPE (chrec_b));
1642 chrec_a = chrec_convert (type, chrec_a, NULL_TREE);
1643 chrec_b = chrec_convert (type, chrec_b, NULL_TREE);
1644 difference = chrec_fold_minus (type, initial_condition (chrec_b), chrec_a);
1646 if (!chrec_is_positive (initial_condition (difference), &value0))
1648 if (dump_file && (dump_flags & TDF_DETAILS))
1649 fprintf (dump_file, "siv test failed: chrec is not positive.\n");
1651 dependence_stats.num_siv_unimplemented++;
1652 *overlaps_a = conflict_fn_not_known ();
1653 *overlaps_b = conflict_fn_not_known ();
1654 *last_conflicts = chrec_dont_know;
1659 if (value0 == false)
1661 if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value1))
1663 if (dump_file && (dump_flags & TDF_DETAILS))
1664 fprintf (dump_file, "siv test failed: chrec not positive.\n");
1666 *overlaps_a = conflict_fn_not_known ();
1667 *overlaps_b = conflict_fn_not_known ();
1668 *last_conflicts = chrec_dont_know;
1669 dependence_stats.num_siv_unimplemented++;
1678 chrec_b = {10, +, 1}
1681 if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference))
1683 HOST_WIDE_INT numiter;
1684 struct loop *loop = get_chrec_loop (chrec_b);
1686 *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
1687 tmp = fold_build2 (EXACT_DIV_EXPR, type,
1688 fold_build1 (ABS_EXPR, type, difference),
1689 CHREC_RIGHT (chrec_b));
1690 *overlaps_b = conflict_fn (1, affine_fn_cst (tmp));
1691 *last_conflicts = integer_one_node;
1694 /* Perform weak-zero siv test to see if overlap is
1695 outside the loop bounds. */
1696 numiter = estimated_loop_iterations_int (loop, false);
1699 && compare_tree_int (tmp, numiter) > 0)
1701 free_conflict_function (*overlaps_a);
1702 free_conflict_function (*overlaps_b);
1703 *overlaps_a = conflict_fn_no_dependence ();
1704 *overlaps_b = conflict_fn_no_dependence ();
1705 *last_conflicts = integer_zero_node;
1706 dependence_stats.num_siv_independent++;
1709 dependence_stats.num_siv_dependent++;
1713 /* When the step does not divide the difference, there are
1717 *overlaps_a = conflict_fn_no_dependence ();
1718 *overlaps_b = conflict_fn_no_dependence ();
1719 *last_conflicts = integer_zero_node;
1720 dependence_stats.num_siv_independent++;
1729 chrec_b = {10, +, -1}
1731 In this case, chrec_a will not overlap with chrec_b. */
1732 *overlaps_a = conflict_fn_no_dependence ();
1733 *overlaps_b = conflict_fn_no_dependence ();
1734 *last_conflicts = integer_zero_node;
1735 dependence_stats.num_siv_independent++;
1742 if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value2))
1744 if (dump_file && (dump_flags & TDF_DETAILS))
1745 fprintf (dump_file, "siv test failed: chrec not positive.\n");
1747 *overlaps_a = conflict_fn_not_known ();
1748 *overlaps_b = conflict_fn_not_known ();
1749 *last_conflicts = chrec_dont_know;
1750 dependence_stats.num_siv_unimplemented++;
1755 if (value2 == false)
1759 chrec_b = {10, +, -1}
1761 if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference))
1763 HOST_WIDE_INT numiter;
1764 struct loop *loop = get_chrec_loop (chrec_b);
1766 *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
1767 tmp = fold_build2 (EXACT_DIV_EXPR, type, difference,
1768 CHREC_RIGHT (chrec_b));
1769 *overlaps_b = conflict_fn (1, affine_fn_cst (tmp));
1770 *last_conflicts = integer_one_node;
1772 /* Perform weak-zero siv test to see if overlap is
1773 outside the loop bounds. */
1774 numiter = estimated_loop_iterations_int (loop, false);
1777 && compare_tree_int (tmp, numiter) > 0)
1779 free_conflict_function (*overlaps_a);
1780 free_conflict_function (*overlaps_b);
1781 *overlaps_a = conflict_fn_no_dependence ();
1782 *overlaps_b = conflict_fn_no_dependence ();
1783 *last_conflicts = integer_zero_node;
1784 dependence_stats.num_siv_independent++;
1787 dependence_stats.num_siv_dependent++;
1791 /* When the step does not divide the difference, there
1795 *overlaps_a = conflict_fn_no_dependence ();
1796 *overlaps_b = conflict_fn_no_dependence ();
1797 *last_conflicts = integer_zero_node;
1798 dependence_stats.num_siv_independent++;
1808 In this case, chrec_a will not overlap with chrec_b. */
1809 *overlaps_a = conflict_fn_no_dependence ();
1810 *overlaps_b = conflict_fn_no_dependence ();
1811 *last_conflicts = integer_zero_node;
1812 dependence_stats.num_siv_independent++;
1820 /* Helper recursive function for initializing the matrix A. Returns
1821 the initial value of CHREC. */
1824 initialize_matrix_A (lambda_matrix A, tree chrec, unsigned index, int mult)
1828 if (TREE_CODE (chrec) != POLYNOMIAL_CHREC)
1829 return int_cst_value (chrec);
1831 A[index][0] = mult * int_cst_value (CHREC_RIGHT (chrec));
1832 return initialize_matrix_A (A, CHREC_LEFT (chrec), index + 1, mult);
1835 #define FLOOR_DIV(x,y) ((x) / (y))
1837 /* Solves the special case of the Diophantine equation:
1838 | {0, +, STEP_A}_x (OVERLAPS_A) = {0, +, STEP_B}_y (OVERLAPS_B)
1840 Computes the descriptions OVERLAPS_A and OVERLAPS_B. NITER is the
1841 number of iterations that loops X and Y run. The overlaps will be
1842 constructed as evolutions in dimension DIM. */
1845 compute_overlap_steps_for_affine_univar (int niter, int step_a, int step_b,
1846 affine_fn *overlaps_a,
1847 affine_fn *overlaps_b,
1848 tree *last_conflicts, int dim)
1850 if (((step_a > 0 && step_b > 0)
1851 || (step_a < 0 && step_b < 0)))
1853 int step_overlaps_a, step_overlaps_b;
1854 int gcd_steps_a_b, last_conflict, tau2;
1856 gcd_steps_a_b = gcd (step_a, step_b);
1857 step_overlaps_a = step_b / gcd_steps_a_b;
1858 step_overlaps_b = step_a / gcd_steps_a_b;
1862 tau2 = FLOOR_DIV (niter, step_overlaps_a);
1863 tau2 = MIN (tau2, FLOOR_DIV (niter, step_overlaps_b));
1864 last_conflict = tau2;
1865 *last_conflicts = build_int_cst (NULL_TREE, last_conflict);
1868 *last_conflicts = chrec_dont_know;
1870 *overlaps_a = affine_fn_univar (integer_zero_node, dim,
1871 build_int_cst (NULL_TREE,
1873 *overlaps_b = affine_fn_univar (integer_zero_node, dim,
1874 build_int_cst (NULL_TREE,
1880 *overlaps_a = affine_fn_cst (integer_zero_node);
1881 *overlaps_b = affine_fn_cst (integer_zero_node);
1882 *last_conflicts = integer_zero_node;
1886 /* Solves the special case of a Diophantine equation where CHREC_A is
1887 an affine bivariate function, and CHREC_B is an affine univariate
1888 function. For example,
1890 | {{0, +, 1}_x, +, 1335}_y = {0, +, 1336}_z
1892 has the following overlapping functions:
1894 | x (t, u, v) = {{0, +, 1336}_t, +, 1}_v
1895 | y (t, u, v) = {{0, +, 1336}_u, +, 1}_v
1896 | z (t, u, v) = {{{0, +, 1}_t, +, 1335}_u, +, 1}_v
1898 FORNOW: This is a specialized implementation for a case occurring in
1899 a common benchmark. Implement the general algorithm. */
1902 compute_overlap_steps_for_affine_1_2 (tree chrec_a, tree chrec_b,
1903 conflict_function **overlaps_a,
1904 conflict_function **overlaps_b,
1905 tree *last_conflicts)
1907 bool xz_p, yz_p, xyz_p;
1908 int step_x, step_y, step_z;
1909 HOST_WIDE_INT niter_x, niter_y, niter_z, niter;
1910 affine_fn overlaps_a_xz, overlaps_b_xz;
1911 affine_fn overlaps_a_yz, overlaps_b_yz;
1912 affine_fn overlaps_a_xyz, overlaps_b_xyz;
1913 affine_fn ova1, ova2, ovb;
1914 tree last_conflicts_xz, last_conflicts_yz, last_conflicts_xyz;
1916 step_x = int_cst_value (CHREC_RIGHT (CHREC_LEFT (chrec_a)));
1917 step_y = int_cst_value (CHREC_RIGHT (chrec_a));
1918 step_z = int_cst_value (CHREC_RIGHT (chrec_b));
1921 estimated_loop_iterations_int (get_chrec_loop (CHREC_LEFT (chrec_a)),
1923 niter_y = estimated_loop_iterations_int (get_chrec_loop (chrec_a), false);
1924 niter_z = estimated_loop_iterations_int (get_chrec_loop (chrec_b), false);
1926 if (niter_x < 0 || niter_y < 0 || niter_z < 0)
1928 if (dump_file && (dump_flags & TDF_DETAILS))
1929 fprintf (dump_file, "overlap steps test failed: no iteration counts.\n");
1931 *overlaps_a = conflict_fn_not_known ();
1932 *overlaps_b = conflict_fn_not_known ();
1933 *last_conflicts = chrec_dont_know;
1937 niter = MIN (niter_x, niter_z);
1938 compute_overlap_steps_for_affine_univar (niter, step_x, step_z,
1941 &last_conflicts_xz, 1);
1942 niter = MIN (niter_y, niter_z);
1943 compute_overlap_steps_for_affine_univar (niter, step_y, step_z,
1946 &last_conflicts_yz, 2);
1947 niter = MIN (niter_x, niter_z);
1948 niter = MIN (niter_y, niter);
1949 compute_overlap_steps_for_affine_univar (niter, step_x + step_y, step_z,
1952 &last_conflicts_xyz, 3);
1954 xz_p = !integer_zerop (last_conflicts_xz);
1955 yz_p = !integer_zerop (last_conflicts_yz);
1956 xyz_p = !integer_zerop (last_conflicts_xyz);
1958 if (xz_p || yz_p || xyz_p)
1960 ova1 = affine_fn_cst (integer_zero_node);
1961 ova2 = affine_fn_cst (integer_zero_node);
1962 ovb = affine_fn_cst (integer_zero_node);
1965 affine_fn t0 = ova1;
1968 ova1 = affine_fn_plus (ova1, overlaps_a_xz);
1969 ovb = affine_fn_plus (ovb, overlaps_b_xz);
1970 affine_fn_free (t0);
1971 affine_fn_free (t2);
1972 *last_conflicts = last_conflicts_xz;
1976 affine_fn t0 = ova2;
1979 ova2 = affine_fn_plus (ova2, overlaps_a_yz);
1980 ovb = affine_fn_plus (ovb, overlaps_b_yz);
1981 affine_fn_free (t0);
1982 affine_fn_free (t2);
1983 *last_conflicts = last_conflicts_yz;
1987 affine_fn t0 = ova1;
1988 affine_fn t2 = ova2;
1991 ova1 = affine_fn_plus (ova1, overlaps_a_xyz);
1992 ova2 = affine_fn_plus (ova2, overlaps_a_xyz);
1993 ovb = affine_fn_plus (ovb, overlaps_b_xyz);
1994 affine_fn_free (t0);
1995 affine_fn_free (t2);
1996 affine_fn_free (t4);
1997 *last_conflicts = last_conflicts_xyz;
1999 *overlaps_a = conflict_fn (2, ova1, ova2);
2000 *overlaps_b = conflict_fn (1, ovb);
2004 *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
2005 *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
2006 *last_conflicts = integer_zero_node;
2009 affine_fn_free (overlaps_a_xz);
2010 affine_fn_free (overlaps_b_xz);
2011 affine_fn_free (overlaps_a_yz);
2012 affine_fn_free (overlaps_b_yz);
2013 affine_fn_free (overlaps_a_xyz);
2014 affine_fn_free (overlaps_b_xyz);
2017 /* Determines the overlapping elements due to accesses CHREC_A and
2018 CHREC_B, that are affine functions. This function cannot handle
2019 symbolic evolution functions, ie. when initial conditions are
2020 parameters, because it uses lambda matrices of integers. */
2023 analyze_subscript_affine_affine (tree chrec_a,
2025 conflict_function **overlaps_a,
2026 conflict_function **overlaps_b,
2027 tree *last_conflicts)
2029 unsigned nb_vars_a, nb_vars_b, dim;
2030 HOST_WIDE_INT init_a, init_b, gamma, gcd_alpha_beta;
2031 lambda_matrix A, U, S;
2033 if (eq_evolutions_p (chrec_a, chrec_b))
2035 /* The accessed index overlaps for each iteration in the
2037 *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
2038 *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
2039 *last_conflicts = chrec_dont_know;
2042 if (dump_file && (dump_flags & TDF_DETAILS))
2043 fprintf (dump_file, "(analyze_subscript_affine_affine \n");
2045 /* For determining the initial intersection, we have to solve a
2046 Diophantine equation. This is the most time consuming part.
2048 For answering to the question: "Is there a dependence?" we have
2049 to prove that there exists a solution to the Diophantine
2050 equation, and that the solution is in the iteration domain,
2051 i.e. the solution is positive or zero, and that the solution
2052 happens before the upper bound loop.nb_iterations. Otherwise
2053 there is no dependence. This function outputs a description of
2054 the iterations that hold the intersections. */
2056 nb_vars_a = nb_vars_in_chrec (chrec_a);
2057 nb_vars_b = nb_vars_in_chrec (chrec_b);
2059 dim = nb_vars_a + nb_vars_b;
2060 U = lambda_matrix_new (dim, dim);
2061 A = lambda_matrix_new (dim, 1);
2062 S = lambda_matrix_new (dim, 1);
2064 init_a = initialize_matrix_A (A, chrec_a, 0, 1);
2065 init_b = initialize_matrix_A (A, chrec_b, nb_vars_a, -1);
2066 gamma = init_b - init_a;
2068 /* Don't do all the hard work of solving the Diophantine equation
2069 when we already know the solution: for example,
2072 | gamma = 3 - 3 = 0.
2073 Then the first overlap occurs during the first iterations:
2074 | {3, +, 1}_1 ({0, +, 4}_x) = {3, +, 4}_2 ({0, +, 1}_x)
2078 if (nb_vars_a == 1 && nb_vars_b == 1)
2080 HOST_WIDE_INT step_a, step_b;
2081 HOST_WIDE_INT niter, niter_a, niter_b;
2084 niter_a = estimated_loop_iterations_int (get_chrec_loop (chrec_a),
2086 niter_b = estimated_loop_iterations_int (get_chrec_loop (chrec_b),
2088 niter = MIN (niter_a, niter_b);
2089 step_a = int_cst_value (CHREC_RIGHT (chrec_a));
2090 step_b = int_cst_value (CHREC_RIGHT (chrec_b));
2092 compute_overlap_steps_for_affine_univar (niter, step_a, step_b,
2095 *overlaps_a = conflict_fn (1, ova);
2096 *overlaps_b = conflict_fn (1, ovb);
2099 else if (nb_vars_a == 2 && nb_vars_b == 1)
2100 compute_overlap_steps_for_affine_1_2
2101 (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts);
2103 else if (nb_vars_a == 1 && nb_vars_b == 2)
2104 compute_overlap_steps_for_affine_1_2
2105 (chrec_b, chrec_a, overlaps_b, overlaps_a, last_conflicts);
2109 if (dump_file && (dump_flags & TDF_DETAILS))
2110 fprintf (dump_file, "affine-affine test failed: too many variables.\n");
2111 *overlaps_a = conflict_fn_not_known ();
2112 *overlaps_b = conflict_fn_not_known ();
2113 *last_conflicts = chrec_dont_know;
2115 goto end_analyze_subs_aa;
2119 lambda_matrix_right_hermite (A, dim, 1, S, U);
2124 lambda_matrix_row_negate (U, dim, 0);
2126 gcd_alpha_beta = S[0][0];
2128 /* Something went wrong: for example in {1, +, 0}_5 vs. {0, +, 0}_5,
2129 but that is a quite strange case. Instead of ICEing, answer
2131 if (gcd_alpha_beta == 0)
2133 *overlaps_a = conflict_fn_not_known ();
2134 *overlaps_b = conflict_fn_not_known ();
2135 *last_conflicts = chrec_dont_know;
2136 goto end_analyze_subs_aa;
2139 /* The classic "gcd-test". */
2140 if (!int_divides_p (gcd_alpha_beta, gamma))
2142 /* The "gcd-test" has determined that there is no integer
2143 solution, i.e. there is no dependence. */
2144 *overlaps_a = conflict_fn_no_dependence ();
2145 *overlaps_b = conflict_fn_no_dependence ();
2146 *last_conflicts = integer_zero_node;
2149 /* Both access functions are univariate. This includes SIV and MIV cases. */
2150 else if (nb_vars_a == 1 && nb_vars_b == 1)
2152 /* Both functions should have the same evolution sign. */
2153 if (((A[0][0] > 0 && -A[1][0] > 0)
2154 || (A[0][0] < 0 && -A[1][0] < 0)))
2156 /* The solutions are given by:
2158 | [GAMMA/GCD_ALPHA_BETA t].[u11 u12] = [x0]
2161 For a given integer t. Using the following variables,
2163 | i0 = u11 * gamma / gcd_alpha_beta
2164 | j0 = u12 * gamma / gcd_alpha_beta
2171 | y0 = j0 + j1 * t. */
2172 HOST_WIDE_INT i0, j0, i1, j1;
2174 i0 = U[0][0] * gamma / gcd_alpha_beta;
2175 j0 = U[0][1] * gamma / gcd_alpha_beta;
2179 if ((i1 == 0 && i0 < 0)
2180 || (j1 == 0 && j0 < 0))
2182 /* There is no solution.
2183 FIXME: The case "i0 > nb_iterations, j0 > nb_iterations"
2184 falls in here, but for the moment we don't look at the
2185 upper bound of the iteration domain. */
2186 *overlaps_a = conflict_fn_no_dependence ();
2187 *overlaps_b = conflict_fn_no_dependence ();
2188 *last_conflicts = integer_zero_node;
2189 goto end_analyze_subs_aa;
2192 if (i1 > 0 && j1 > 0)
2194 HOST_WIDE_INT niter_a = estimated_loop_iterations_int
2195 (get_chrec_loop (chrec_a), false);
2196 HOST_WIDE_INT niter_b = estimated_loop_iterations_int
2197 (get_chrec_loop (chrec_b), false);
2198 HOST_WIDE_INT niter = MIN (niter_a, niter_b);
2200 /* (X0, Y0) is a solution of the Diophantine equation:
2201 "chrec_a (X0) = chrec_b (Y0)". */
2202 HOST_WIDE_INT tau1 = MAX (CEIL (-i0, i1),
2204 HOST_WIDE_INT x0 = i1 * tau1 + i0;
2205 HOST_WIDE_INT y0 = j1 * tau1 + j0;
2207 /* (X1, Y1) is the smallest positive solution of the eq
2208 "chrec_a (X1) = chrec_b (Y1)", i.e. this is where the
2209 first conflict occurs. */
2210 HOST_WIDE_INT min_multiple = MIN (x0 / i1, y0 / j1);
2211 HOST_WIDE_INT x1 = x0 - i1 * min_multiple;
2212 HOST_WIDE_INT y1 = y0 - j1 * min_multiple;
2216 HOST_WIDE_INT tau2 = MIN (FLOOR_DIV (niter - i0, i1),
2217 FLOOR_DIV (niter - j0, j1));
2218 HOST_WIDE_INT last_conflict = tau2 - (x1 - i0)/i1;
2220 /* If the overlap occurs outside of the bounds of the
2221 loop, there is no dependence. */
2222 if (x1 > niter || y1 > niter)
2224 *overlaps_a = conflict_fn_no_dependence ();
2225 *overlaps_b = conflict_fn_no_dependence ();
2226 *last_conflicts = integer_zero_node;
2227 goto end_analyze_subs_aa;
2230 *last_conflicts = build_int_cst (NULL_TREE, last_conflict);
2233 *last_conflicts = chrec_dont_know;
2237 affine_fn_univar (build_int_cst (NULL_TREE, x1),
2239 build_int_cst (NULL_TREE, i1)));
2242 affine_fn_univar (build_int_cst (NULL_TREE, y1),
2244 build_int_cst (NULL_TREE, j1)));
2248 /* FIXME: For the moment, the upper bound of the
2249 iteration domain for i and j is not checked. */
2250 if (dump_file && (dump_flags & TDF_DETAILS))
2251 fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
2252 *overlaps_a = conflict_fn_not_known ();
2253 *overlaps_b = conflict_fn_not_known ();
2254 *last_conflicts = chrec_dont_know;
2259 if (dump_file && (dump_flags & TDF_DETAILS))
2260 fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
2261 *overlaps_a = conflict_fn_not_known ();
2262 *overlaps_b = conflict_fn_not_known ();
2263 *last_conflicts = chrec_dont_know;
2268 if (dump_file && (dump_flags & TDF_DETAILS))
2269 fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
2270 *overlaps_a = conflict_fn_not_known ();
2271 *overlaps_b = conflict_fn_not_known ();
2272 *last_conflicts = chrec_dont_know;
2275 end_analyze_subs_aa:
2276 if (dump_file && (dump_flags & TDF_DETAILS))
2278 fprintf (dump_file, " (overlaps_a = ");
2279 dump_conflict_function (dump_file, *overlaps_a);
2280 fprintf (dump_file, ")\n (overlaps_b = ");
2281 dump_conflict_function (dump_file, *overlaps_b);
2282 fprintf (dump_file, ")\n");
2283 fprintf (dump_file, ")\n");
2287 /* Returns true when analyze_subscript_affine_affine can be used for
2288 determining the dependence relation between chrec_a and chrec_b,
2289 that contain symbols. This function modifies chrec_a and chrec_b
2290 such that the analysis result is the same, and such that they don't
2291 contain symbols, and then can safely be passed to the analyzer.
2293 Example: The analysis of the following tuples of evolutions produce
2294 the same results: {x+1, +, 1}_1 vs. {x+3, +, 1}_1, and {-2, +, 1}_1
2297 {x+1, +, 1}_1 ({2, +, 1}_1) = {x+3, +, 1}_1 ({0, +, 1}_1)
2298 {-2, +, 1}_1 ({2, +, 1}_1) = {0, +, 1}_1 ({0, +, 1}_1)
2302 can_use_analyze_subscript_affine_affine (tree *chrec_a, tree *chrec_b)
2304 tree diff, type, left_a, left_b, right_b;
2306 if (chrec_contains_symbols (CHREC_RIGHT (*chrec_a))
2307 || chrec_contains_symbols (CHREC_RIGHT (*chrec_b)))
2308 /* FIXME: For the moment not handled. Might be refined later. */
2311 type = chrec_type (*chrec_a);
2312 left_a = CHREC_LEFT (*chrec_a);
2313 left_b = chrec_convert (type, CHREC_LEFT (*chrec_b), NULL_TREE);
2314 diff = chrec_fold_minus (type, left_a, left_b);
2316 if (!evolution_function_is_constant_p (diff))
2319 if (dump_file && (dump_flags & TDF_DETAILS))
2320 fprintf (dump_file, "can_use_subscript_aff_aff_for_symbolic \n");
2322 *chrec_a = build_polynomial_chrec (CHREC_VARIABLE (*chrec_a),
2323 diff, CHREC_RIGHT (*chrec_a));
2324 right_b = chrec_convert (type, CHREC_RIGHT (*chrec_b), NULL_TREE);
2325 *chrec_b = build_polynomial_chrec (CHREC_VARIABLE (*chrec_b),
2326 build_int_cst (type, 0),
2331 /* Analyze a SIV (Single Index Variable) subscript. *OVERLAPS_A and
2332 *OVERLAPS_B are initialized to the functions that describe the
2333 relation between the elements accessed twice by CHREC_A and
2334 CHREC_B. For k >= 0, the following property is verified:
2336 CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
2339 analyze_siv_subscript (tree chrec_a,
2341 conflict_function **overlaps_a,
2342 conflict_function **overlaps_b,
2343 tree *last_conflicts)
2345 dependence_stats.num_siv++;
2347 if (dump_file && (dump_flags & TDF_DETAILS))
2348 fprintf (dump_file, "(analyze_siv_subscript \n");
2350 if (evolution_function_is_constant_p (chrec_a)
2351 && evolution_function_is_affine_p (chrec_b))
2352 analyze_siv_subscript_cst_affine (chrec_a, chrec_b,
2353 overlaps_a, overlaps_b, last_conflicts);
2355 else if (evolution_function_is_affine_p (chrec_a)
2356 && evolution_function_is_constant_p (chrec_b))
2357 analyze_siv_subscript_cst_affine (chrec_b, chrec_a,
2358 overlaps_b, overlaps_a, last_conflicts);
2360 else if (evolution_function_is_affine_p (chrec_a)
2361 && evolution_function_is_affine_p (chrec_b))
2363 if (!chrec_contains_symbols (chrec_a)
2364 && !chrec_contains_symbols (chrec_b))
2366 analyze_subscript_affine_affine (chrec_a, chrec_b,
2367 overlaps_a, overlaps_b,
2370 if (CF_NOT_KNOWN_P (*overlaps_a)
2371 || CF_NOT_KNOWN_P (*overlaps_b))
2372 dependence_stats.num_siv_unimplemented++;
2373 else if (CF_NO_DEPENDENCE_P (*overlaps_a)
2374 || CF_NO_DEPENDENCE_P (*overlaps_b))
2375 dependence_stats.num_siv_independent++;
2377 dependence_stats.num_siv_dependent++;
2379 else if (can_use_analyze_subscript_affine_affine (&chrec_a,
2382 analyze_subscript_affine_affine (chrec_a, chrec_b,
2383 overlaps_a, overlaps_b,
2386 if (CF_NOT_KNOWN_P (*overlaps_a)
2387 || CF_NOT_KNOWN_P (*overlaps_b))
2388 dependence_stats.num_siv_unimplemented++;
2389 else if (CF_NO_DEPENDENCE_P (*overlaps_a)
2390 || CF_NO_DEPENDENCE_P (*overlaps_b))
2391 dependence_stats.num_siv_independent++;
2393 dependence_stats.num_siv_dependent++;
2396 goto siv_subscript_dontknow;
2401 siv_subscript_dontknow:;
2402 if (dump_file && (dump_flags & TDF_DETAILS))
2403 fprintf (dump_file, "siv test failed: unimplemented.\n");
2404 *overlaps_a = conflict_fn_not_known ();
2405 *overlaps_b = conflict_fn_not_known ();
2406 *last_conflicts = chrec_dont_know;
2407 dependence_stats.num_siv_unimplemented++;
2410 if (dump_file && (dump_flags & TDF_DETAILS))
2411 fprintf (dump_file, ")\n");
2414 /* Returns false if we can prove that the greatest common divisor of the steps
2415 of CHREC does not divide CST, false otherwise. */
2418 gcd_of_steps_may_divide_p (const_tree chrec, const_tree cst)
2420 HOST_WIDE_INT cd = 0, val;
2423 if (!host_integerp (cst, 0))
2425 val = tree_low_cst (cst, 0);
2427 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
2429 step = CHREC_RIGHT (chrec);
2430 if (!host_integerp (step, 0))
2432 cd = gcd (cd, tree_low_cst (step, 0));
2433 chrec = CHREC_LEFT (chrec);
2436 return val % cd == 0;
2439 /* Analyze a MIV (Multiple Index Variable) subscript with respect to
2440 LOOP_NEST. *OVERLAPS_A and *OVERLAPS_B are initialized to the
2441 functions that describe the relation between the elements accessed
2442 twice by CHREC_A and CHREC_B. For k >= 0, the following property
2445 CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
2448 analyze_miv_subscript (tree chrec_a,
2450 conflict_function **overlaps_a,
2451 conflict_function **overlaps_b,
2452 tree *last_conflicts,
2453 struct loop *loop_nest)
2455 /* FIXME: This is a MIV subscript, not yet handled.
2456 Example: (A[{1, +, 1}_1] vs. A[{1, +, 1}_2]) that comes from
2459 In the SIV test we had to solve a Diophantine equation with two
2460 variables. In the MIV case we have to solve a Diophantine
2461 equation with 2*n variables (if the subscript uses n IVs).
2463 tree type, difference;
2465 dependence_stats.num_miv++;
2466 if (dump_file && (dump_flags & TDF_DETAILS))
2467 fprintf (dump_file, "(analyze_miv_subscript \n");
2469 type = signed_type_for_types (TREE_TYPE (chrec_a), TREE_TYPE (chrec_b));
2470 chrec_a = chrec_convert (type, chrec_a, NULL_TREE);
2471 chrec_b = chrec_convert (type, chrec_b, NULL_TREE);
2472 difference = chrec_fold_minus (type, chrec_a, chrec_b);
2474 if (eq_evolutions_p (chrec_a, chrec_b))
2476 /* Access functions are the same: all the elements are accessed
2477 in the same order. */
2478 *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
2479 *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
2480 *last_conflicts = estimated_loop_iterations_tree
2481 (get_chrec_loop (chrec_a), true);
2482 dependence_stats.num_miv_dependent++;
2485 else if (evolution_function_is_constant_p (difference)
2486 /* For the moment, the following is verified:
2487 evolution_function_is_affine_multivariate_p (chrec_a,
2489 && !gcd_of_steps_may_divide_p (chrec_a, difference))
2491 /* testsuite/.../ssa-chrec-33.c
2492 {{21, +, 2}_1, +, -2}_2 vs. {{20, +, 2}_1, +, -2}_2
2494 The difference is 1, and all the evolution steps are multiples
2495 of 2, consequently there are no overlapping elements. */
2496 *overlaps_a = conflict_fn_no_dependence ();
2497 *overlaps_b = conflict_fn_no_dependence ();
2498 *last_conflicts = integer_zero_node;
2499 dependence_stats.num_miv_independent++;
2502 else if (evolution_function_is_affine_multivariate_p (chrec_a, loop_nest->num)
2503 && !chrec_contains_symbols (chrec_a)
2504 && evolution_function_is_affine_multivariate_p (chrec_b, loop_nest->num)
2505 && !chrec_contains_symbols (chrec_b))
2507 /* testsuite/.../ssa-chrec-35.c
2508 {0, +, 1}_2 vs. {0, +, 1}_3
2509 the overlapping elements are respectively located at iterations:
2510 {0, +, 1}_x and {0, +, 1}_x,
2511 in other words, we have the equality:
2512 {0, +, 1}_2 ({0, +, 1}_x) = {0, +, 1}_3 ({0, +, 1}_x)
2515 {{0, +, 1}_1, +, 2}_2 ({0, +, 1}_x, {0, +, 1}_y) =
2516 {0, +, 1}_1 ({{0, +, 1}_x, +, 2}_y)
2518 {{0, +, 2}_1, +, 3}_2 ({0, +, 1}_y, {0, +, 1}_x) =
2519 {{0, +, 3}_1, +, 2}_2 ({0, +, 1}_x, {0, +, 1}_y)
2521 analyze_subscript_affine_affine (chrec_a, chrec_b,
2522 overlaps_a, overlaps_b, last_conflicts);
2524 if (CF_NOT_KNOWN_P (*overlaps_a)
2525 || CF_NOT_KNOWN_P (*overlaps_b))
2526 dependence_stats.num_miv_unimplemented++;
2527 else if (CF_NO_DEPENDENCE_P (*overlaps_a)
2528 || CF_NO_DEPENDENCE_P (*overlaps_b))
2529 dependence_stats.num_miv_independent++;
2531 dependence_stats.num_miv_dependent++;
2536 /* When the analysis is too difficult, answer "don't know". */
2537 if (dump_file && (dump_flags & TDF_DETAILS))
2538 fprintf (dump_file, "analyze_miv_subscript test failed: unimplemented.\n");
2540 *overlaps_a = conflict_fn_not_known ();
2541 *overlaps_b = conflict_fn_not_known ();
2542 *last_conflicts = chrec_dont_know;
2543 dependence_stats.num_miv_unimplemented++;
2546 if (dump_file && (dump_flags & TDF_DETAILS))
2547 fprintf (dump_file, ")\n");
2550 /* Determines the iterations for which CHREC_A is equal to CHREC_B in
2551 with respect to LOOP_NEST. OVERLAP_ITERATIONS_A and
2552 OVERLAP_ITERATIONS_B are initialized with two functions that
2553 describe the iterations that contain conflicting elements.
2555 Remark: For an integer k >= 0, the following equality is true:
2557 CHREC_A (OVERLAP_ITERATIONS_A (k)) == CHREC_B (OVERLAP_ITERATIONS_B (k)).
2561 analyze_overlapping_iterations (tree chrec_a,
2563 conflict_function **overlap_iterations_a,
2564 conflict_function **overlap_iterations_b,
2565 tree *last_conflicts, struct loop *loop_nest)
2567 unsigned int lnn = loop_nest->num;
2569 dependence_stats.num_subscript_tests++;
2571 if (dump_file && (dump_flags & TDF_DETAILS))
2573 fprintf (dump_file, "(analyze_overlapping_iterations \n");
2574 fprintf (dump_file, " (chrec_a = ");
2575 print_generic_expr (dump_file, chrec_a, 0);
2576 fprintf (dump_file, ")\n (chrec_b = ");
2577 print_generic_expr (dump_file, chrec_b, 0);
2578 fprintf (dump_file, ")\n");
2581 if (chrec_a == NULL_TREE
2582 || chrec_b == NULL_TREE
2583 || chrec_contains_undetermined (chrec_a)
2584 || chrec_contains_undetermined (chrec_b))
2586 dependence_stats.num_subscript_undetermined++;
2588 *overlap_iterations_a = conflict_fn_not_known ();
2589 *overlap_iterations_b = conflict_fn_not_known ();
2592 /* If they are the same chrec, and are affine, they overlap
2593 on every iteration. */
2594 else if (eq_evolutions_p (chrec_a, chrec_b)
2595 && evolution_function_is_affine_multivariate_p (chrec_a, lnn))
2597 dependence_stats.num_same_subscript_function++;
2598 *overlap_iterations_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
2599 *overlap_iterations_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
2600 *last_conflicts = chrec_dont_know;
2603 /* If they aren't the same, and aren't affine, we can't do anything
2605 else if ((chrec_contains_symbols (chrec_a)
2606 || chrec_contains_symbols (chrec_b))
2607 && (!evolution_function_is_affine_multivariate_p (chrec_a, lnn)
2608 || !evolution_function_is_affine_multivariate_p (chrec_b, lnn)))
2610 dependence_stats.num_subscript_undetermined++;
2611 *overlap_iterations_a = conflict_fn_not_known ();
2612 *overlap_iterations_b = conflict_fn_not_known ();
2615 else if (ziv_subscript_p (chrec_a, chrec_b))
2616 analyze_ziv_subscript (chrec_a, chrec_b,
2617 overlap_iterations_a, overlap_iterations_b,
2620 else if (siv_subscript_p (chrec_a, chrec_b))
2621 analyze_siv_subscript (chrec_a, chrec_b,
2622 overlap_iterations_a, overlap_iterations_b,
2626 analyze_miv_subscript (chrec_a, chrec_b,
2627 overlap_iterations_a, overlap_iterations_b,
2628 last_conflicts, loop_nest);
2630 if (dump_file && (dump_flags & TDF_DETAILS))
2632 fprintf (dump_file, " (overlap_iterations_a = ");
2633 dump_conflict_function (dump_file, *overlap_iterations_a);
2634 fprintf (dump_file, ")\n (overlap_iterations_b = ");
2635 dump_conflict_function (dump_file, *overlap_iterations_b);
2636 fprintf (dump_file, ")\n");
2637 fprintf (dump_file, ")\n");
2641 /* Helper function for uniquely inserting distance vectors. */
2644 save_dist_v (struct data_dependence_relation *ddr, lambda_vector dist_v)
2649 for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, v); i++)
2650 if (lambda_vector_equal (v, dist_v, DDR_NB_LOOPS (ddr)))
2653 VEC_safe_push (lambda_vector, heap, DDR_DIST_VECTS (ddr), dist_v);
2656 /* Helper function for uniquely inserting direction vectors. */
2659 save_dir_v (struct data_dependence_relation *ddr, lambda_vector dir_v)
2664 for (i = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), i, v); i++)
2665 if (lambda_vector_equal (v, dir_v, DDR_NB_LOOPS (ddr)))
2668 VEC_safe_push (lambda_vector, heap, DDR_DIR_VECTS (ddr), dir_v);
2671 /* Add a distance of 1 on all the loops outer than INDEX. If we
2672 haven't yet determined a distance for this outer loop, push a new
2673 distance vector composed of the previous distance, and a distance
2674 of 1 for this outer loop. Example:
2682 Saved vectors are of the form (dist_in_1, dist_in_2). First, we
2683 save (0, 1), then we have to save (1, 0). */
2686 add_outer_distances (struct data_dependence_relation *ddr,
2687 lambda_vector dist_v, int index)
2689 /* For each outer loop where init_v is not set, the accesses are
2690 in dependence of distance 1 in the loop. */
2691 while (--index >= 0)
2693 lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2694 lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr));
2696 save_dist_v (ddr, save_v);
2700 /* Return false when fail to represent the data dependence as a
2701 distance vector. INIT_B is set to true when a component has been
2702 added to the distance vector DIST_V. INDEX_CARRY is then set to
2703 the index in DIST_V that carries the dependence. */
2706 build_classic_dist_vector_1 (struct data_dependence_relation *ddr,
2707 struct data_reference *ddr_a,
2708 struct data_reference *ddr_b,
2709 lambda_vector dist_v, bool *init_b,
2713 lambda_vector init_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2715 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
2717 tree access_fn_a, access_fn_b;
2718 struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
2720 if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
2722 non_affine_dependence_relation (ddr);
2726 access_fn_a = DR_ACCESS_FN (ddr_a, i);
2727 access_fn_b = DR_ACCESS_FN (ddr_b, i);
2729 if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC
2730 && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC)
2733 int index_a = index_in_loop_nest (CHREC_VARIABLE (access_fn_a),
2734 DDR_LOOP_NEST (ddr));
2735 int index_b = index_in_loop_nest (CHREC_VARIABLE (access_fn_b),
2736 DDR_LOOP_NEST (ddr));
2738 /* The dependence is carried by the outermost loop. Example:
2745 In this case, the dependence is carried by loop_1. */
2746 index = index_a < index_b ? index_a : index_b;
2747 *index_carry = MIN (index, *index_carry);
2749 if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
2751 non_affine_dependence_relation (ddr);
2755 dist = int_cst_value (SUB_DISTANCE (subscript));
2757 /* This is the subscript coupling test. If we have already
2758 recorded a distance for this loop (a distance coming from
2759 another subscript), it should be the same. For example,
2760 in the following code, there is no dependence:
2767 if (init_v[index] != 0 && dist_v[index] != dist)
2769 finalize_ddr_dependent (ddr, chrec_known);
2773 dist_v[index] = dist;
2777 else if (!operand_equal_p (access_fn_a, access_fn_b, 0))
2779 /* This can be for example an affine vs. constant dependence
2780 (T[i] vs. T[3]) that is not an affine dependence and is
2781 not representable as a distance vector. */
2782 non_affine_dependence_relation (ddr);
2790 /* Return true when the DDR contains two data references that have the
2791 same access functions. */
2794 same_access_functions (const struct data_dependence_relation *ddr)
2798 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
2799 if (!eq_evolutions_p (DR_ACCESS_FN (DDR_A (ddr), i),
2800 DR_ACCESS_FN (DDR_B (ddr), i)))
2806 /* Return true when the DDR contains only constant access functions. */
2809 constant_access_functions (const struct data_dependence_relation *ddr)
2813 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
2814 if (!evolution_function_is_constant_p (DR_ACCESS_FN (DDR_A (ddr), i))
2815 || !evolution_function_is_constant_p (DR_ACCESS_FN (DDR_B (ddr), i)))
2821 /* Helper function for the case where DDR_A and DDR_B are the same
2822 multivariate access function with a constant step. For an example
2826 add_multivariate_self_dist (struct data_dependence_relation *ddr, tree c_2)
2829 tree c_1 = CHREC_LEFT (c_2);
2830 tree c_0 = CHREC_LEFT (c_1);
2831 lambda_vector dist_v;
2834 /* Polynomials with more than 2 variables are not handled yet. When
2835 the evolution steps are parameters, it is not possible to
2836 represent the dependence using classical distance vectors. */
2837 if (TREE_CODE (c_0) != INTEGER_CST
2838 || TREE_CODE (CHREC_RIGHT (c_1)) != INTEGER_CST
2839 || TREE_CODE (CHREC_RIGHT (c_2)) != INTEGER_CST)
2841 DDR_AFFINE_P (ddr) = false;
2845 x_2 = index_in_loop_nest (CHREC_VARIABLE (c_2), DDR_LOOP_NEST (ddr));
2846 x_1 = index_in_loop_nest (CHREC_VARIABLE (c_1), DDR_LOOP_NEST (ddr));
2848 /* For "{{0, +, 2}_1, +, 3}_2" the distance vector is (3, -2). */
2849 dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2850 v1 = int_cst_value (CHREC_RIGHT (c_1));
2851 v2 = int_cst_value (CHREC_RIGHT (c_2));
2864 save_dist_v (ddr, dist_v);
2866 add_outer_distances (ddr, dist_v, x_1);
2869 /* Helper function for the case where DDR_A and DDR_B are the same
2870 access functions. */
2873 add_other_self_distances (struct data_dependence_relation *ddr)
2875 lambda_vector dist_v;
2877 int index_carry = DDR_NB_LOOPS (ddr);
2879 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
2881 tree access_fun = DR_ACCESS_FN (DDR_A (ddr), i);
2883 if (TREE_CODE (access_fun) == POLYNOMIAL_CHREC)
2885 if (!evolution_function_is_univariate_p (access_fun))
2887 if (DDR_NUM_SUBSCRIPTS (ddr) != 1)
2889 DDR_ARE_DEPENDENT (ddr) = chrec_dont_know;
2893 access_fun = DR_ACCESS_FN (DDR_A (ddr), 0);
2895 if (TREE_CODE (CHREC_LEFT (access_fun)) == POLYNOMIAL_CHREC)
2896 add_multivariate_self_dist (ddr, access_fun);
2898 /* The evolution step is not constant: it varies in
2899 the outer loop, so this cannot be represented by a
2900 distance vector. For example in pr34635.c the
2901 evolution is {0, +, {0, +, 4}_1}_2. */
2902 DDR_AFFINE_P (ddr) = false;
2907 index_carry = MIN (index_carry,
2908 index_in_loop_nest (CHREC_VARIABLE (access_fun),
2909 DDR_LOOP_NEST (ddr)));
2913 dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2914 add_outer_distances (ddr, dist_v, index_carry);
2918 insert_innermost_unit_dist_vector (struct data_dependence_relation *ddr)
2920 lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2922 dist_v[DDR_INNER_LOOP (ddr)] = 1;
2923 save_dist_v (ddr, dist_v);
2926 /* Adds a unit distance vector to DDR when there is a 0 overlap. This
2927 is the case for example when access functions are the same and
2928 equal to a constant, as in:
2935 in which case the distance vectors are (0) and (1). */
2938 add_distance_for_zero_overlaps (struct data_dependence_relation *ddr)
2942 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
2944 subscript_p sub = DDR_SUBSCRIPT (ddr, i);
2945 conflict_function *ca = SUB_CONFLICTS_IN_A (sub);
2946 conflict_function *cb = SUB_CONFLICTS_IN_B (sub);
2948 for (j = 0; j < ca->n; j++)
2949 if (affine_function_zero_p (ca->fns[j]))
2951 insert_innermost_unit_dist_vector (ddr);
2955 for (j = 0; j < cb->n; j++)
2956 if (affine_function_zero_p (cb->fns[j]))
2958 insert_innermost_unit_dist_vector (ddr);
2964 /* Compute the classic per loop distance vector. DDR is the data
2965 dependence relation to build a vector from. Return false when fail
2966 to represent the data dependence as a distance vector. */
2969 build_classic_dist_vector (struct data_dependence_relation *ddr,
2970 struct loop *loop_nest)
2972 bool init_b = false;
2973 int index_carry = DDR_NB_LOOPS (ddr);
2974 lambda_vector dist_v;
2976 if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE)
2979 if (same_access_functions (ddr))
2981 /* Save the 0 vector. */
2982 dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2983 save_dist_v (ddr, dist_v);
2985 if (constant_access_functions (ddr))
2986 add_distance_for_zero_overlaps (ddr);
2988 if (DDR_NB_LOOPS (ddr) > 1)
2989 add_other_self_distances (ddr);
2994 dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
2995 if (!build_classic_dist_vector_1 (ddr, DDR_A (ddr), DDR_B (ddr),
2996 dist_v, &init_b, &index_carry))
2999 /* Save the distance vector if we initialized one. */
3002 /* Verify a basic constraint: classic distance vectors should
3003 always be lexicographically positive.
3005 Data references are collected in the order of execution of
3006 the program, thus for the following loop
3008 | for (i = 1; i < 100; i++)
3009 | for (j = 1; j < 100; j++)
3011 | t = T[j+1][i-1]; // A
3012 | T[j][i] = t + 2; // B
3015 references are collected following the direction of the wind:
3016 A then B. The data dependence tests are performed also
3017 following this order, such that we're looking at the distance
3018 separating the elements accessed by A from the elements later
3019 accessed by B. But in this example, the distance returned by
3020 test_dep (A, B) is lexicographically negative (-1, 1), that
3021 means that the access A occurs later than B with respect to
3022 the outer loop, ie. we're actually looking upwind. In this
3023 case we solve test_dep (B, A) looking downwind to the
3024 lexicographically positive solution, that returns the
3025 distance vector (1, -1). */
3026 if (!lambda_vector_lexico_pos (dist_v, DDR_NB_LOOPS (ddr)))
3028 lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3029 if (!subscript_dependence_tester_1 (ddr, DDR_B (ddr), DDR_A (ddr),
3032 compute_subscript_distance (ddr);
3033 if (!build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr),
3034 save_v, &init_b, &index_carry))
3036 save_dist_v (ddr, save_v);
3037 DDR_REVERSED_P (ddr) = true;
3039 /* In this case there is a dependence forward for all the
3042 | for (k = 1; k < 100; k++)
3043 | for (i = 1; i < 100; i++)
3044 | for (j = 1; j < 100; j++)
3046 | t = T[j+1][i-1]; // A
3047 | T[j][i] = t + 2; // B
3055 if (DDR_NB_LOOPS (ddr) > 1)
3057 add_outer_distances (ddr, save_v, index_carry);
3058 add_outer_distances (ddr, dist_v, index_carry);
3063 lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3064 lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr));
3066 if (DDR_NB_LOOPS (ddr) > 1)
3068 lambda_vector opposite_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3070 if (!subscript_dependence_tester_1 (ddr, DDR_B (ddr),
3071 DDR_A (ddr), loop_nest))
3073 compute_subscript_distance (ddr);
3074 if (!build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr),
3075 opposite_v, &init_b,
3079 save_dist_v (ddr, save_v);
3080 add_outer_distances (ddr, dist_v, index_carry);
3081 add_outer_distances (ddr, opposite_v, index_carry);
3084 save_dist_v (ddr, save_v);
3089 /* There is a distance of 1 on all the outer loops: Example:
3090 there is a dependence of distance 1 on loop_1 for the array A.
3096 add_outer_distances (ddr, dist_v,
3097 lambda_vector_first_nz (dist_v,
3098 DDR_NB_LOOPS (ddr), 0));
3101 if (dump_file && (dump_flags & TDF_DETAILS))
3105 fprintf (dump_file, "(build_classic_dist_vector\n");
3106 for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++)
3108 fprintf (dump_file, " dist_vector = (");
3109 print_lambda_vector (dump_file, DDR_DIST_VECT (ddr, i),
3110 DDR_NB_LOOPS (ddr));
3111 fprintf (dump_file, " )\n");
3113 fprintf (dump_file, ")\n");
3119 /* Return the direction for a given distance.
3120 FIXME: Computing dir this way is suboptimal, since dir can catch
3121 cases that dist is unable to represent. */
3123 static inline enum data_dependence_direction
3124 dir_from_dist (int dist)
3127 return dir_positive;
3129 return dir_negative;
3134 /* Compute the classic per loop direction vector. DDR is the data
3135 dependence relation to build a vector from. */
3138 build_classic_dir_vector (struct data_dependence_relation *ddr)
3141 lambda_vector dist_v;
3143 for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, dist_v); i++)
3145 lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3147 for (j = 0; j < DDR_NB_LOOPS (ddr); j++)
3148 dir_v[j] = dir_from_dist (dist_v[j]);
3150 save_dir_v (ddr, dir_v);
3154 /* Helper function. Returns true when there is a dependence between
3155 data references DRA and DRB. */
3158 subscript_dependence_tester_1 (struct data_dependence_relation *ddr,
3159 struct data_reference *dra,
3160 struct data_reference *drb,
3161 struct loop *loop_nest)
3164 tree last_conflicts;
3165 struct subscript *subscript;
3167 for (i = 0; VEC_iterate (subscript_p, DDR_SUBSCRIPTS (ddr), i, subscript);
3170 conflict_function *overlaps_a, *overlaps_b;
3172 analyze_overlapping_iterations (DR_ACCESS_FN (dra, i),
3173 DR_ACCESS_FN (drb, i),
3174 &overlaps_a, &overlaps_b,
3175 &last_conflicts, loop_nest);
3177 if (CF_NOT_KNOWN_P (overlaps_a)
3178 || CF_NOT_KNOWN_P (overlaps_b))
3180 finalize_ddr_dependent (ddr, chrec_dont_know);
3181 dependence_stats.num_dependence_undetermined++;
3182 free_conflict_function (overlaps_a);
3183 free_conflict_function (overlaps_b);
3187 else if (CF_NO_DEPENDENCE_P (overlaps_a)
3188 || CF_NO_DEPENDENCE_P (overlaps_b))
3190 finalize_ddr_dependent (ddr, chrec_known);
3191 dependence_stats.num_dependence_independent++;
3192 free_conflict_function (overlaps_a);
3193 free_conflict_function (overlaps_b);
3199 SUB_CONFLICTS_IN_A (subscript) = overlaps_a;
3200 SUB_CONFLICTS_IN_B (subscript) = overlaps_b;
3201 SUB_LAST_CONFLICT (subscript) = last_conflicts;
3208 /* Computes the conflicting iterations in LOOP_NEST, and initialize DDR. */
3211 subscript_dependence_tester (struct data_dependence_relation *ddr,
3212 struct loop *loop_nest)
3215 if (dump_file && (dump_flags & TDF_DETAILS))
3216 fprintf (dump_file, "(subscript_dependence_tester \n");
3218 if (subscript_dependence_tester_1 (ddr, DDR_A (ddr), DDR_B (ddr), loop_nest))
3219 dependence_stats.num_dependence_dependent++;
3221 compute_subscript_distance (ddr);
3222 if (build_classic_dist_vector (ddr, loop_nest))
3223 build_classic_dir_vector (ddr);
3225 if (dump_file && (dump_flags & TDF_DETAILS))
3226 fprintf (dump_file, ")\n");
3229 /* Returns true when all the access functions of A are affine or
3230 constant with respect to LOOP_NEST. */
3233 access_functions_are_affine_or_constant_p (const struct data_reference *a,
3234 const struct loop *loop_nest)
3237 VEC(tree,heap) *fns = DR_ACCESS_FNS (a);
3240 for (i = 0; VEC_iterate (tree, fns, i, t); i++)
3241 if (!evolution_function_is_invariant_p (t, loop_nest->num)
3242 && !evolution_function_is_affine_multivariate_p (t, loop_nest->num))
3248 /* Initializes an equation for an OMEGA problem using the information
3249 contained in the ACCESS_FUN. Returns true when the operation
3252 PB is the omega constraint system.
3253 EQ is the number of the equation to be initialized.
3254 OFFSET is used for shifting the variables names in the constraints:
3255 a constrain is composed of 2 * the number of variables surrounding
3256 dependence accesses. OFFSET is set either to 0 for the first n variables,
3257 then it is set to n.
3258 ACCESS_FUN is expected to be an affine chrec. */
3261 init_omega_eq_with_af (omega_pb pb, unsigned eq,
3262 unsigned int offset, tree access_fun,
3263 struct data_dependence_relation *ddr)
3265 switch (TREE_CODE (access_fun))
3267 case POLYNOMIAL_CHREC:
3269 tree left = CHREC_LEFT (access_fun);
3270 tree right = CHREC_RIGHT (access_fun);
3271 int var = CHREC_VARIABLE (access_fun);
3274 if (TREE_CODE (right) != INTEGER_CST)
3277 var_idx = index_in_loop_nest (var, DDR_LOOP_NEST (ddr));
3278 pb->eqs[eq].coef[offset + var_idx + 1] = int_cst_value (right);
3280 /* Compute the innermost loop index. */
3281 DDR_INNER_LOOP (ddr) = MAX (DDR_INNER_LOOP (ddr), var_idx);
3284 pb->eqs[eq].coef[var_idx + DDR_NB_LOOPS (ddr) + 1]
3285 += int_cst_value (right);
3287 switch (TREE_CODE (left))
3289 case POLYNOMIAL_CHREC:
3290 return init_omega_eq_with_af (pb, eq, offset, left, ddr);
3293 pb->eqs[eq].coef[0] += int_cst_value (left);
3302 pb->eqs[eq].coef[0] += int_cst_value (access_fun);
3310 /* As explained in the comments preceding init_omega_for_ddr, we have
3311 to set up a system for each loop level, setting outer loops
3312 variation to zero, and current loop variation to positive or zero.
3313 Save each lexico positive distance vector. */
3316 omega_extract_distance_vectors (omega_pb pb,
3317 struct data_dependence_relation *ddr)
3321 struct loop *loopi, *loopj;
3322 enum omega_result res;
3324 /* Set a new problem for each loop in the nest. The basis is the
3325 problem that we have initialized until now. On top of this we
3326 add new constraints. */
3327 for (i = 0; i <= DDR_INNER_LOOP (ddr)
3328 && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++)
3331 omega_pb copy = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr),
3332 DDR_NB_LOOPS (ddr));
3334 omega_copy_problem (copy, pb);
3336 /* For all the outer loops "loop_j", add "dj = 0". */
3338 j < i && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), j, loopj); j++)
3340 eq = omega_add_zero_eq (copy, omega_black);
3341 copy->eqs[eq].coef[j + 1] = 1;
3344 /* For "loop_i", add "0 <= di". */
3345 geq = omega_add_zero_geq (copy, omega_black);
3346 copy->geqs[geq].coef[i + 1] = 1;
3348 /* Reduce the constraint system, and test that the current
3349 problem is feasible. */
3350 res = omega_simplify_problem (copy);
3351 if (res == omega_false
3352 || res == omega_unknown
3353 || copy->num_geqs > (int) DDR_NB_LOOPS (ddr))
3356 for (eq = 0; eq < copy->num_subs; eq++)
3357 if (copy->subs[eq].key == (int) i + 1)
3359 dist = copy->subs[eq].coef[0];
3365 /* Reinitialize problem... */
3366 omega_copy_problem (copy, pb);
3368 j < i && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), j, loopj); j++)
3370 eq = omega_add_zero_eq (copy, omega_black);
3371 copy->eqs[eq].coef[j + 1] = 1;
3374 /* ..., but this time "di = 1". */
3375 eq = omega_add_zero_eq (copy, omega_black);
3376 copy->eqs[eq].coef[i + 1] = 1;
3377 copy->eqs[eq].coef[0] = -1;
3379 res = omega_simplify_problem (copy);
3380 if (res == omega_false
3381 || res == omega_unknown
3382 || copy->num_geqs > (int) DDR_NB_LOOPS (ddr))
3385 for (eq = 0; eq < copy->num_subs; eq++)
3386 if (copy->subs[eq].key == (int) i + 1)
3388 dist = copy->subs[eq].coef[0];
3394 /* Save the lexicographically positive distance vector. */
3397 lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3398 lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3402 for (eq = 0; eq < copy->num_subs; eq++)
3403 if (copy->subs[eq].key > 0)
3405 dist = copy->subs[eq].coef[0];
3406 dist_v[copy->subs[eq].key - 1] = dist;
3409 for (j = 0; j < DDR_NB_LOOPS (ddr); j++)
3410 dir_v[j] = dir_from_dist (dist_v[j]);
3412 save_dist_v (ddr, dist_v);
3413 save_dir_v (ddr, dir_v);
3417 omega_free_problem (copy);
3421 /* This is called for each subscript of a tuple of data references:
3422 insert an equality for representing the conflicts. */
3425 omega_setup_subscript (tree access_fun_a, tree access_fun_b,
3426 struct data_dependence_relation *ddr,
3427 omega_pb pb, bool *maybe_dependent)
3430 tree type = signed_type_for_types (TREE_TYPE (access_fun_a),
3431 TREE_TYPE (access_fun_b));
3432 tree fun_a = chrec_convert (type, access_fun_a, NULL_TREE);
3433 tree fun_b = chrec_convert (type, access_fun_b, NULL_TREE);
3434 tree difference = chrec_fold_minus (type, fun_a, fun_b);
3436 /* When the fun_a - fun_b is not constant, the dependence is not
3437 captured by the classic distance vector representation. */
3438 if (TREE_CODE (difference) != INTEGER_CST)
3442 if (ziv_subscript_p (fun_a, fun_b) && !integer_zerop (difference))
3444 /* There is no dependence. */
3445 *maybe_dependent = false;
3449 fun_b = chrec_fold_multiply (type, fun_b, integer_minus_one_node);
3451 eq = omega_add_zero_eq (pb, omega_black);
3452 if (!init_omega_eq_with_af (pb, eq, DDR_NB_LOOPS (ddr), fun_a, ddr)
3453 || !init_omega_eq_with_af (pb, eq, 0, fun_b, ddr))
3454 /* There is probably a dependence, but the system of
3455 constraints cannot be built: answer "don't know". */
3459 if (DDR_NB_LOOPS (ddr) != 0 && pb->eqs[eq].coef[0]
3460 && !int_divides_p (lambda_vector_gcd
3461 ((lambda_vector) &(pb->eqs[eq].coef[1]),
3462 2 * DDR_NB_LOOPS (ddr)),
3463 pb->eqs[eq].coef[0]))
3465 /* There is no dependence. */
3466 *maybe_dependent = false;
3473 /* Helper function, same as init_omega_for_ddr but specialized for
3474 data references A and B. */
3477 init_omega_for_ddr_1 (struct data_reference *dra, struct data_reference *drb,
3478 struct data_dependence_relation *ddr,
3479 omega_pb pb, bool *maybe_dependent)
3484 unsigned nb_loops = DDR_NB_LOOPS (ddr);
3486 /* Insert an equality per subscript. */
3487 for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
3489 if (!omega_setup_subscript (DR_ACCESS_FN (dra, i), DR_ACCESS_FN (drb, i),
3490 ddr, pb, maybe_dependent))
3492 else if (*maybe_dependent == false)
3494 /* There is no dependence. */
3495 DDR_ARE_DEPENDENT (ddr) = chrec_known;
3500 /* Insert inequalities: constraints corresponding to the iteration
3501 domain, i.e. the loops surrounding the references "loop_x" and
3502 the distance variables "dx". The layout of the OMEGA
3503 representation is as follows:
3504 - coef[0] is the constant
3505 - coef[1..nb_loops] are the protected variables that will not be
3506 removed by the solver: the "dx"
3507 - coef[nb_loops + 1, 2*nb_loops] are the loop variables: "loop_x".
3509 for (i = 0; i <= DDR_INNER_LOOP (ddr)
3510 && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++)
3512 HOST_WIDE_INT nbi = estimated_loop_iterations_int (loopi, false);
3515 ineq = omega_add_zero_geq (pb, omega_black);
3516 pb->geqs[ineq].coef[i + nb_loops + 1] = 1;
3518 /* 0 <= loop_x + dx */
3519 ineq = omega_add_zero_geq (pb, omega_black);
3520 pb->geqs[ineq].coef[i + nb_loops + 1] = 1;
3521 pb->geqs[ineq].coef[i + 1] = 1;
3525 /* loop_x <= nb_iters */
3526 ineq = omega_add_zero_geq (pb, omega_black);
3527 pb->geqs[ineq].coef[i + nb_loops + 1] = -1;
3528 pb->geqs[ineq].coef[0] = nbi;
3530 /* loop_x + dx <= nb_iters */
3531 ineq = omega_add_zero_geq (pb, omega_black);
3532 pb->geqs[ineq].coef[i + nb_loops + 1] = -1;
3533 pb->geqs[ineq].coef[i + 1] = -1;
3534 pb->geqs[ineq].coef[0] = nbi;
3536 /* A step "dx" bigger than nb_iters is not feasible, so
3537 add "0 <= nb_iters + dx", */
3538 ineq = omega_add_zero_geq (pb, omega_black);
3539 pb->geqs[ineq].coef[i + 1] = 1;
3540 pb->geqs[ineq].coef[0] = nbi;
3541 /* and "dx <= nb_iters". */
3542 ineq = omega_add_zero_geq (pb, omega_black);
3543 pb->geqs[ineq].coef[i + 1] = -1;
3544 pb->geqs[ineq].coef[0] = nbi;
3548 omega_extract_distance_vectors (pb, ddr);
3553 /* Sets up the Omega dependence problem for the data dependence
3554 relation DDR. Returns false when the constraint system cannot be
3555 built, ie. when the test answers "don't know". Returns true
3556 otherwise, and when independence has been proved (using one of the
3557 trivial dependence test), set MAYBE_DEPENDENT to false, otherwise
3558 set MAYBE_DEPENDENT to true.
3560 Example: for setting up the dependence system corresponding to the
3561 conflicting accesses
3566 | ... A[2*j, 2*(i + j)]
3570 the following constraints come from the iteration domain:
3577 where di, dj are the distance variables. The constraints
3578 representing the conflicting elements are:
3581 i + 1 = 2 * (i + di + j + dj)
3583 For asking that the resulting distance vector (di, dj) be
3584 lexicographically positive, we insert the constraint "di >= 0". If
3585 "di = 0" in the solution, we fix that component to zero, and we
3586 look at the inner loops: we set a new problem where all the outer
3587 loop distances are zero, and fix this inner component to be
3588 positive. When one of the components is positive, we save that
3589 distance, and set a new problem where the distance on this loop is
3590 zero, searching for other distances in the inner loops. Here is
3591 the classic example that illustrates that we have to set for each
3592 inner loop a new problem:
3600 we have to save two distances (1, 0) and (0, 1).
3602 Given two array references, refA and refB, we have to set the
3603 dependence problem twice, refA vs. refB and refB vs. refA, and we
3604 cannot do a single test, as refB might occur before refA in the
3605 inner loops, and the contrary when considering outer loops: ex.
3610 | T[{1,+,1}_2][{1,+,1}_1] // refA
3611 | T[{2,+,1}_2][{0,+,1}_1] // refB
3616 refB touches the elements in T before refA, and thus for the same
3617 loop_0 refB precedes refA: ie. the distance vector (0, 1, -1)
3618 but for successive loop_0 iterations, we have (1, -1, 1)
3620 The Omega solver expects the distance variables ("di" in the
3621 previous example) to come first in the constraint system (as
3622 variables to be protected, or "safe" variables), the constraint
3623 system is built using the following layout:
3625 "cst | distance vars | index vars".
3629 init_omega_for_ddr (struct data_dependence_relation *ddr,
3630 bool *maybe_dependent)
3635 *maybe_dependent = true;
3637 if (same_access_functions (ddr))
3640 lambda_vector dir_v;
3642 /* Save the 0 vector. */
3643 save_dist_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr)));
3644 dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
3645 for (j = 0; j < DDR_NB_LOOPS (ddr); j++)
3646 dir_v[j] = dir_equal;
3647 save_dir_v (ddr, dir_v);
3649 /* Save the dependences carried by outer loops. */
3650 pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr));
3651 res = init_omega_for_ddr_1 (DDR_A (ddr), DDR_B (ddr), ddr, pb,
3653 omega_free_problem (pb);
3657 /* Omega expects the protected variables (those that have to be kept
3658 after elimination) to appear first in the constraint system.
3659 These variables are the distance variables. In the following
3660 initialization we declare NB_LOOPS safe variables, and the total
3661 number of variables for the constraint system is 2*NB_LOOPS. */
3662 pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr));
3663 res = init_omega_for_ddr_1 (DDR_A (ddr), DDR_B (ddr), ddr, pb,
3665 omega_free_problem (pb);
3667 /* Stop computation if not decidable, or no dependence. */
3668 if (res == false || *maybe_dependent == false)
3671 pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr));
3672 res = init_omega_for_ddr_1 (DDR_B (ddr), DDR_A (ddr), ddr, pb,
3674 omega_free_problem (pb);
3679 /* Return true when DDR contains the same information as that stored
3680 in DIR_VECTS and in DIST_VECTS, return false otherwise. */
3683 ddr_consistent_p (FILE *file,
3684 struct data_dependence_relation *ddr,
3685 VEC (lambda_vector, heap) *dist_vects,
3686 VEC (lambda_vector, heap) *dir_vects)
3690 /* If dump_file is set, output there. */
3691 if (dump_file && (dump_flags & TDF_DETAILS))
3694 if (VEC_length (lambda_vector, dist_vects) != DDR_NUM_DIST_VECTS (ddr))
3696 lambda_vector b_dist_v;
3697 fprintf (file, "\n(Number of distance vectors differ: Banerjee has %d, Omega has %d.\n",
3698 VEC_length (lambda_vector, dist_vects),
3699 DDR_NUM_DIST_VECTS (ddr));
3701 fprintf (file, "Banerjee dist vectors:\n");
3702 for (i = 0; VEC_iterate (lambda_vector, dist_vects, i, b_dist_v); i++)
3703 print_lambda_vector (file, b_dist_v, DDR_NB_LOOPS (ddr));
3705 fprintf (file, "Omega dist vectors:\n");
3706 for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++)
3707 print_lambda_vector (file, DDR_DIST_VECT (ddr, i), DDR_NB_LOOPS (ddr));
3709 fprintf (file, "data dependence relation:\n");
3710 dump_data_dependence_relation (file, ddr);
3712 fprintf (file, ")\n");
3716 if (VEC_length (lambda_vector, dir_vects) != DDR_NUM_DIR_VECTS (ddr))
3718 fprintf (file, "\n(Number of direction vectors differ: Banerjee has %d, Omega has %d.)\n",
3719 VEC_length (lambda_vector, dir_vects),
3720 DDR_NUM_DIR_VECTS (ddr));
3724 for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++)
3726 lambda_vector a_dist_v;
3727 lambda_vector b_dist_v = DDR_DIST_VECT (ddr, i);
3729 /* Distance vectors are not ordered in the same way in the DDR
3730 and in the DIST_VECTS: search for a matching vector. */
3731 for (j = 0; VEC_iterate (lambda_vector, dist_vects, j, a_dist_v); j++)
3732 if (lambda_vector_equal (a_dist_v, b_dist_v, DDR_NB_LOOPS (ddr)))
3735 if (j == VEC_length (lambda_vector, dist_vects))
3737 fprintf (file, "\n(Dist vectors from the first dependence analyzer:\n");
3738 print_dist_vectors (file, dist_vects, DDR_NB_LOOPS (ddr));
3739 fprintf (file, "not found in Omega dist vectors:\n");
3740 print_dist_vectors (file, DDR_DIST_VECTS (ddr), DDR_NB_LOOPS (ddr));
3741 fprintf (file, "data dependence relation:\n");
3742 dump_data_dependence_relation (file, ddr);
3743 fprintf (file, ")\n");
3747 for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++)
3749 lambda_vector a_dir_v;
3750 lambda_vector b_dir_v = DDR_DIR_VECT (ddr, i);
3752 /* Direction vectors are not ordered in the same way in the DDR
3753 and in the DIR_VECTS: search for a matching vector. */
3754 for (j = 0; VEC_iterate (lambda_vector, dir_vects, j, a_dir_v); j++)
3755 if (lambda_vector_equal (a_dir_v, b_dir_v, DDR_NB_LOOPS (ddr)))
3758 if (j == VEC_length (lambda_vector, dist_vects))
3760 fprintf (file, "\n(Dir vectors from the first dependence analyzer:\n");
3761 print_dir_vectors (file, dir_vects, DDR_NB_LOOPS (ddr));
3762 fprintf (file, "not found in Omega dir vectors:\n");
3763 print_dir_vectors (file, DDR_DIR_VECTS (ddr), DDR_NB_LOOPS (ddr));
3764 fprintf (file, "data dependence relation:\n");
3765 dump_data_dependence_relation (file, ddr);
3766 fprintf (file, ")\n");
3773 /* This computes the affine dependence relation between A and B with
3774 respect to LOOP_NEST. CHREC_KNOWN is used for representing the
3775 independence between two accesses, while CHREC_DONT_KNOW is used
3776 for representing the unknown relation.
3778 Note that it is possible to stop the computation of the dependence
3779 relation the first time we detect a CHREC_KNOWN element for a given
3783 compute_affine_dependence (struct data_dependence_relation *ddr,
3784 struct loop *loop_nest)
3786 struct data_reference *dra = DDR_A (ddr);
3787 struct data_reference *drb = DDR_B (ddr);
3789 if (dump_file && (dump_flags & TDF_DETAILS))
3791 fprintf (dump_file, "(compute_affine_dependence\n");
3792 fprintf (dump_file, " (stmt_a = \n");
3793 print_generic_expr (dump_file, DR_STMT (dra), 0);
3794 fprintf (dump_file, ")\n (stmt_b = \n");
3795 print_generic_expr (dump_file, DR_STMT (drb), 0);
3796 fprintf (dump_file, ")\n");
3799 /* Analyze only when the dependence relation is not yet known. */
3800 if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
3802 dependence_stats.num_dependence_tests++;
3804 if (access_functions_are_affine_or_constant_p (dra, loop_nest)
3805 && access_functions_are_affine_or_constant_p (drb, loop_nest))
3807 if (flag_check_data_deps)
3809 /* Compute the dependences using the first algorithm. */
3810 subscript_dependence_tester (ddr, loop_nest);
3812 if (dump_file && (dump_flags & TDF_DETAILS))
3814 fprintf (dump_file, "\n\nBanerjee Analyzer\n");
3815 dump_data_dependence_relation (dump_file, ddr);
3818 if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
3820 bool maybe_dependent;
3821 VEC (lambda_vector, heap) *dir_vects, *dist_vects;
3823 /* Save the result of the first DD analyzer. */
3824 dist_vects = DDR_DIST_VECTS (ddr);
3825 dir_vects = DDR_DIR_VECTS (ddr);
3827 /* Reset the information. */
3828 DDR_DIST_VECTS (ddr) = NULL;
3829 DDR_DIR_VECTS (ddr) = NULL;
3831 /* Compute the same information using Omega. */
3832 if (!init_omega_for_ddr (ddr, &maybe_dependent))
3833 goto csys_dont_know;
3835 if (dump_file && (dump_flags & TDF_DETAILS))
3837 fprintf (dump_file, "Omega Analyzer\n");
3838 dump_data_dependence_relation (dump_file, ddr);
3841 /* Check that we get the same information. */
3842 if (maybe_dependent)
3843 gcc_assert (ddr_consistent_p (stderr, ddr, dist_vects,
3848 subscript_dependence_tester (ddr, loop_nest);
3851 /* As a last case, if the dependence cannot be determined, or if
3852 the dependence is considered too difficult to determine, answer
3857 dependence_stats.num_dependence_undetermined++;
3859 if (dump_file && (dump_flags & TDF_DETAILS))
3861 fprintf (dump_file, "Data ref a:\n");
3862 dump_data_reference (dump_file, dra);
3863 fprintf (dump_file, "Data ref b:\n");
3864 dump_data_reference (dump_file, drb);
3865 fprintf (dump_file, "affine dependence test not usable: access function not affine or constant.\n");
3867 finalize_ddr_dependent (ddr, chrec_dont_know);
3871 if (dump_file && (dump_flags & TDF_DETAILS))
3872 fprintf (dump_file, ")\n");
3875 /* This computes the dependence relation for the same data
3876 reference into DDR. */
3879 compute_self_dependence (struct data_dependence_relation *ddr)
3882 struct subscript *subscript;
3884 if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE)
3887 for (i = 0; VEC_iterate (subscript_p, DDR_SUBSCRIPTS (ddr), i, subscript);
3890 /* The accessed index overlaps for each iteration. */
3891 SUB_CONFLICTS_IN_A (subscript)
3892 = conflict_fn (1, affine_fn_cst (integer_zero_node));
3893 SUB_CONFLICTS_IN_B (subscript)
3894 = conflict_fn (1, affine_fn_cst (integer_zero_node));
3895 SUB_LAST_CONFLICT (subscript) = chrec_dont_know;
3898 /* The distance vector is the zero vector. */
3899 save_dist_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr)));
3900 save_dir_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr)));
3903 /* Compute in DEPENDENCE_RELATIONS the data dependence graph for all
3904 the data references in DATAREFS, in the LOOP_NEST. When
3905 COMPUTE_SELF_AND_RR is FALSE, don't compute read-read and self
3909 compute_all_dependences (VEC (data_reference_p, heap) *datarefs,
3910 VEC (ddr_p, heap) **dependence_relations,
3911 VEC (loop_p, heap) *loop_nest,
3912 bool compute_self_and_rr)
3914 struct data_dependence_relation *ddr;
3915 struct data_reference *a, *b;
3918 for (i = 0; VEC_iterate (data_reference_p, datarefs, i, a); i++)
3919 for (j = i + 1; VEC_iterate (data_reference_p, datarefs, j, b); j++)
3920 if (!DR_IS_READ (a) || !DR_IS_READ (b) || compute_self_and_rr)
3922 ddr = initialize_data_dependence_relation (a, b, loop_nest);
3923 VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
3924 compute_affine_dependence (ddr, VEC_index (loop_p, loop_nest, 0));
3927 if (compute_self_and_rr)
3928 for (i = 0; VEC_iterate (data_reference_p, datarefs, i, a); i++)
3930 ddr = initialize_data_dependence_relation (a, a, loop_nest);
3931 VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
3932 compute_self_dependence (ddr);
3936 /* Stores the locations of memory references in STMT to REFERENCES. Returns
3937 true if STMT clobbers memory, false otherwise. */
3940 get_references_in_stmt (tree stmt, VEC (data_ref_loc, heap) **references)
3942 bool clobbers_memory = false;
3944 tree *op0, *op1, call;
3948 /* ASM_EXPR and CALL_EXPR may embed arbitrary side effects.
3949 Calls have side-effects, except those to const or pure
3951 call = get_call_expr_in (stmt);
3953 && !(call_expr_flags (call) & (ECF_CONST | ECF_PURE)))
3954 || (TREE_CODE (stmt) == ASM_EXPR
3955 && ASM_VOLATILE_P (stmt)))
3956 clobbers_memory = true;
3958 if (ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
3959 return clobbers_memory;
3961 if (TREE_CODE (stmt) == GIMPLE_MODIFY_STMT)
3963 op0 = &GIMPLE_STMT_OPERAND (stmt, 0);
3964 op1 = &GIMPLE_STMT_OPERAND (stmt, 1);
3967 || (REFERENCE_CLASS_P (*op1) && get_base_address (*op1)))
3969 ref = VEC_safe_push (data_ref_loc, heap, *references, NULL);
3971 ref->is_read = true;
3975 || (REFERENCE_CLASS_P (*op0) && get_base_address (*op0)))
3977 ref = VEC_safe_push (data_ref_loc, heap, *references, NULL);
3979 ref->is_read = false;
3985 unsigned i, n = call_expr_nargs (call);
3987 for (i = 0; i < n; i++)
3989 op0 = &CALL_EXPR_ARG (call, i);
3992 || (REFERENCE_CLASS_P (*op0) && get_base_address (*op0)))
3994 ref = VEC_safe_push (data_ref_loc, heap, *references, NULL);
3996 ref->is_read = true;
4001 return clobbers_memory;
4004 /* Stores the data references in STMT to DATAREFS. If there is an unanalyzable
4005 reference, returns false, otherwise returns true. NEST is the outermost
4006 loop of the loop nest in that the references should be analyzed. */
4009 find_data_references_in_stmt (struct loop *nest, tree stmt,
4010 VEC (data_reference_p, heap) **datarefs)
4013 VEC (data_ref_loc, heap) *references;
4016 data_reference_p dr;
4018 if (get_references_in_stmt (stmt, &references))
4020 VEC_free (data_ref_loc, heap, references);
4024 for (i = 0; VEC_iterate (data_ref_loc, references, i, ref); i++)
4026 dr = create_data_ref (nest, *ref->pos, stmt, ref->is_read);
4027 gcc_assert (dr != NULL);
4029 /* FIXME -- data dependence analysis does not work correctly for objects with
4030 invariant addresses. Let us fail here until the problem is fixed. */
4031 if (dr_address_invariant_p (dr))
4034 if (dump_file && (dump_flags & TDF_DETAILS))
4035 fprintf (dump_file, "\tFAILED as dr address is invariant\n");
4040 VEC_safe_push (data_reference_p, heap, *datarefs, dr);
4042 VEC_free (data_ref_loc, heap, references);
4046 /* Search the data references in LOOP, and record the information into
4047 DATAREFS. Returns chrec_dont_know when failing to analyze a
4048 difficult case, returns NULL_TREE otherwise.
4050 TODO: This function should be made smarter so that it can handle address
4051 arithmetic as if they were array accesses, etc. */
4054 find_data_references_in_loop (struct loop *loop,
4055 VEC (data_reference_p, heap) **datarefs)
4057 basic_block bb, *bbs;
4059 block_stmt_iterator bsi;
4061 bbs = get_loop_body_in_dom_order (loop);
4063 for (i = 0; i < loop->num_nodes; i++)
4067 for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
4069 tree stmt = bsi_stmt (bsi);
4071 if (!find_data_references_in_stmt (loop, stmt, datarefs))
4073 struct data_reference *res;
4074 res = XCNEW (struct data_reference);
4075 VEC_safe_push (data_reference_p, heap, *datarefs, res);
4078 return chrec_dont_know;
4087 /* Recursive helper function. */
4090 find_loop_nest_1 (struct loop *loop, VEC (loop_p, heap) **loop_nest)
4092 /* Inner loops of the nest should not contain siblings. Example:
4093 when there are two consecutive loops,
4104 the dependence relation cannot be captured by the distance
4109 VEC_safe_push (loop_p, heap, *loop_nest, loop);
4111 return find_loop_nest_1 (loop->inner, loop_nest);
4115 /* Return false when the LOOP is not well nested. Otherwise return
4116 true and insert in LOOP_NEST the loops of the nest. LOOP_NEST will
4117 contain the loops from the outermost to the innermost, as they will
4118 appear in the classic distance vector. */
4121 find_loop_nest (struct loop *loop, VEC (loop_p, heap) **loop_nest)
4123 VEC_safe_push (loop_p, heap, *loop_nest, loop);
4125 return find_loop_nest_1 (loop->inner, loop_nest);
4129 /* Given a loop nest LOOP, the following vectors are returned:
4130 DATAREFS is initialized to all the array elements contained in this loop,
4131 DEPENDENCE_RELATIONS contains the relations between the data references.
4132 Compute read-read and self relations if
4133 COMPUTE_SELF_AND_READ_READ_DEPENDENCES is TRUE. */
4136 compute_data_dependences_for_loop (struct loop *loop,
4137 bool compute_self_and_read_read_dependences,
4138 VEC (data_reference_p, heap) **datarefs,
4139 VEC (ddr_p, heap) **dependence_relations)
4141 VEC (loop_p, heap) *vloops = VEC_alloc (loop_p, heap, 3);
4143 memset (&dependence_stats, 0, sizeof (dependence_stats));
4145 /* If the loop nest is not well formed, or one of the data references
4146 is not computable, give up without spending time to compute other
4149 || !find_loop_nest (loop, &vloops)
4150 || find_data_references_in_loop (loop, datarefs) == chrec_dont_know)
4152 struct data_dependence_relation *ddr;
4154 /* Insert a single relation into dependence_relations:
4156 ddr = initialize_data_dependence_relation (NULL, NULL, vloops);
4157 VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
4160 compute_all_dependences (*datarefs, dependence_relations, vloops,
4161 compute_self_and_read_read_dependences);
4163 if (dump_file && (dump_flags & TDF_STATS))
4165 fprintf (dump_file, "Dependence tester statistics:\n");
4167 fprintf (dump_file, "Number of dependence tests: %d\n",
4168 dependence_stats.num_dependence_tests);
4169 fprintf (dump_file, "Number of dependence tests classified dependent: %d\n",
4170 dependence_stats.num_dependence_dependent);
4171 fprintf (dump_file, "Number of dependence tests classified independent: %d\n",
4172 dependence_stats.num_dependence_independent);
4173 fprintf (dump_file, "Number of undetermined dependence tests: %d\n",
4174 dependence_stats.num_dependence_undetermined);
4176 fprintf (dump_file, "Number of subscript tests: %d\n",
4177 dependence_stats.num_subscript_tests);
4178 fprintf (dump_file, "Number of undetermined subscript tests: %d\n",
4179 dependence_stats.num_subscript_undetermined);
4180 fprintf (dump_file, "Number of same subscript function: %d\n",
4181 dependence_stats.num_same_subscript_function);
4183 fprintf (dump_file, "Number of ziv tests: %d\n",
4184 dependence_stats.num_ziv);
4185 fprintf (dump_file, "Number of ziv tests returning dependent: %d\n",
4186 dependence_stats.num_ziv_dependent);
4187 fprintf (dump_file, "Number of ziv tests returning independent: %d\n",
4188 dependence_stats.num_ziv_independent);
4189 fprintf (dump_file, "Number of ziv tests unimplemented: %d\n",
4190 dependence_stats.num_ziv_unimplemented);
4192 fprintf (dump_file, "Number of siv tests: %d\n",
4193 dependence_stats.num_siv);
4194 fprintf (dump_file, "Number of siv tests returning dependent: %d\n",
4195 dependence_stats.num_siv_dependent);
4196 fprintf (dump_file, "Number of siv tests returning independent: %d\n",
4197 dependence_stats.num_siv_independent);
4198 fprintf (dump_file, "Number of siv tests unimplemented: %d\n",
4199 dependence_stats.num_siv_unimplemented);
4201 fprintf (dump_file, "Number of miv tests: %d\n",
4202 dependence_stats.num_miv);
4203 fprintf (dump_file, "Number of miv tests returning dependent: %d\n",
4204 dependence_stats.num_miv_dependent);
4205 fprintf (dump_file, "Number of miv tests returning independent: %d\n",
4206 dependence_stats.num_miv_independent);
4207 fprintf (dump_file, "Number of miv tests unimplemented: %d\n",
4208 dependence_stats.num_miv_unimplemented);
4212 /* Entry point (for testing only). Analyze all the data references
4213 and the dependence relations in LOOP.
4215 The data references are computed first.
4217 A relation on these nodes is represented by a complete graph. Some
4218 of the relations could be of no interest, thus the relations can be
4221 In the following function we compute all the relations. This is
4222 just a first implementation that is here for:
4223 - for showing how to ask for the dependence relations,
4224 - for the debugging the whole dependence graph,
4225 - for the dejagnu testcases and maintenance.
4227 It is possible to ask only for a part of the graph, avoiding to
4228 compute the whole dependence graph. The computed dependences are
4229 stored in a knowledge base (KB) such that later queries don't
4230 recompute the same information. The implementation of this KB is
4231 transparent to the optimizer, and thus the KB can be changed with a
4232 more efficient implementation, or the KB could be disabled. */
4234 analyze_all_data_dependences (struct loop *loop)
4237 int nb_data_refs = 10;
4238 VEC (data_reference_p, heap) *datarefs =
4239 VEC_alloc (data_reference_p, heap, nb_data_refs);
4240 VEC (ddr_p, heap) *dependence_relations =
4241 VEC_alloc (ddr_p, heap, nb_data_refs * nb_data_refs);
4243 /* Compute DDs on the whole function. */
4244 compute_data_dependences_for_loop (loop, false, &datarefs,
4245 &dependence_relations);
4249 dump_data_dependence_relations (dump_file, dependence_relations);
4250 fprintf (dump_file, "\n\n");
4252 if (dump_flags & TDF_DETAILS)
4253 dump_dist_dir_vectors (dump_file, dependence_relations);
4255 if (dump_flags & TDF_STATS)
4257 unsigned nb_top_relations = 0;
4258 unsigned nb_bot_relations = 0;
4259 unsigned nb_basename_differ = 0;
4260 unsigned nb_chrec_relations = 0;
4261 struct data_dependence_relation *ddr;
4263 for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++)
4265 if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr)))
4268 else if (DDR_ARE_DEPENDENT (ddr) == chrec_known)
4270 struct data_reference *a = DDR_A (ddr);
4271 struct data_reference *b = DDR_B (ddr);
4273 if (!bitmap_intersect_p (DR_VOPS (a), DR_VOPS (b)))
4274 nb_basename_differ++;
4280 nb_chrec_relations++;
4283 gather_stats_on_scev_database ();
4287 free_dependence_relations (dependence_relations);
4288 free_data_refs (datarefs);
4291 /* Computes all the data dependences and check that the results of
4292 several analyzers are the same. */
4295 tree_check_data_deps (void)
4298 struct loop *loop_nest;
4300 FOR_EACH_LOOP (li, loop_nest, 0)
4301 analyze_all_data_dependences (loop_nest);
4304 /* Free the memory used by a data dependence relation DDR. */
4307 free_dependence_relation (struct data_dependence_relation *ddr)
4312 if (DDR_SUBSCRIPTS (ddr))
4313 free_subscripts (DDR_SUBSCRIPTS (ddr));
4314 if (DDR_DIST_VECTS (ddr))
4315 VEC_free (lambda_vector, heap, DDR_DIST_VECTS (ddr));
4316 if (DDR_DIR_VECTS (ddr))
4317 VEC_free (lambda_vector, heap, DDR_DIR_VECTS (ddr));
4322 /* Free the memory used by the data dependence relations from
4323 DEPENDENCE_RELATIONS. */
4326 free_dependence_relations (VEC (ddr_p, heap) *dependence_relations)
4329 struct data_dependence_relation *ddr;
4330 VEC (loop_p, heap) *loop_nest = NULL;
4332 for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++)
4336 if (loop_nest == NULL)
4337 loop_nest = DDR_LOOP_NEST (ddr);
4339 gcc_assert (DDR_LOOP_NEST (ddr) == NULL
4340 || DDR_LOOP_NEST (ddr) == loop_nest);
4341 free_dependence_relation (ddr);
4345 VEC_free (loop_p, heap, loop_nest);
4346 VEC_free (ddr_p, heap, dependence_relations);
4349 /* Free the memory used by the data references from DATAREFS. */
4352 free_data_refs (VEC (data_reference_p, heap) *datarefs)
4355 struct data_reference *dr;
4357 for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++)
4359 VEC_free (data_reference_p, heap, datarefs);
4364 /* Returns the index of STMT in RDG. */
4367 find_vertex_for_stmt (const struct graph *rdg, const_tree stmt)
4371 for (i = 0; i < rdg->n_vertices; i++)
4372 if (RDGV_STMT (&(rdg->vertices[i])) == stmt)
4379 /* Creates an edge in RDG for each distance vector from DDR. */
4382 create_rdg_edge_for_ddr (struct graph *rdg, ddr_p ddr)
4385 data_reference_p dra;
4386 data_reference_p drb;
4387 struct graph_edge *e;
4389 if (DDR_REVERSED_P (ddr))
4400 va = find_vertex_for_stmt (rdg, DR_STMT (dra));
4401 vb = find_vertex_for_stmt (rdg, DR_STMT (drb));
4403 e = add_edge (rdg, va, vb);
4404 e->data = XNEW (struct rdg_edge);
4406 /* Determines the type of the data dependence. */
4407 if (DR_IS_READ (dra) && DR_IS_READ (drb))
4408 RDGE_TYPE (e) = input_dd;
4409 else if (!DR_IS_READ (dra) && !DR_IS_READ (drb))
4410 RDGE_TYPE (e) = output_dd;
4411 else if (!DR_IS_READ (dra) && DR_IS_READ (drb))
4412 RDGE_TYPE (e) = flow_dd;
4413 else if (DR_IS_READ (dra) && !DR_IS_READ (drb))
4414 RDGE_TYPE (e) = anti_dd;
4417 /* Creates dependence edges in RDG for all the uses of DEF. IDEF is
4418 the index of DEF in RDG. */
4421 create_rdg_edges_for_scalar (struct graph *rdg, tree def, int idef)
4423 use_operand_p imm_use_p;
4424 imm_use_iterator iterator;
4426 FOR_EACH_IMM_USE_FAST (imm_use_p, iterator, def)
4428 int use = find_vertex_for_stmt (rdg, USE_STMT (imm_use_p));
4429 struct graph_edge *e = add_edge (rdg, idef, use);
4431 e->data = XNEW (struct rdg_edge);
4432 RDGE_TYPE (e) = flow_dd;
4436 /* Creates the edges of the reduced dependence graph RDG. */
4439 create_rdg_edges (struct graph *rdg, VEC (ddr_p, heap) *ddrs)
4442 struct data_dependence_relation *ddr;
4443 def_operand_p def_p;
4446 for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
4447 if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
4448 create_rdg_edge_for_ddr (rdg, ddr);
4450 for (i = 0; i < rdg->n_vertices; i++)
4451 FOR_EACH_PHI_OR_STMT_DEF (def_p, RDGV_STMT (&(rdg->vertices[i])),
4452 iter, SSA_OP_ALL_DEFS)
4453 create_rdg_edges_for_scalar (rdg, DEF_FROM_PTR (def_p), i);
4456 /* Build the vertices of the reduced dependence graph RDG. */
4459 create_rdg_vertices (struct graph *rdg, VEC (tree, heap) *stmts)
4464 for (i = 0; VEC_iterate (tree, stmts, i, s); i++)
4466 struct vertex *v = &(rdg->vertices[i]);
4468 v->data = XNEW (struct rdg_vertex);
4473 /* Initialize STMTS with all the statements and PHI nodes of LOOP. */
4476 stmts_from_loop (struct loop *loop, VEC (tree, heap) **stmts)
4479 basic_block *bbs = get_loop_body_in_dom_order (loop);
4481 for (i = 0; i < loop->num_nodes; i++)
4484 basic_block bb = bbs[i];
4485 block_stmt_iterator bsi;
4487 for (phi = phi_nodes (bb); phi; phi = PHI_CHAIN (phi))
4488 VEC_safe_push (tree, heap, *stmts, phi);
4490 for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
4491 VEC_safe_push (tree, heap, *stmts, bsi_stmt (bsi));
4497 /* Returns true when all the dependences are computable. */
4500 known_dependences_p (VEC (ddr_p, heap) *dependence_relations)
4505 for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++)
4506 if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know)
4512 /* Build a Reduced Dependence Graph with one vertex per statement of the
4513 loop nest and one edge per data dependence or scalar dependence. */
4516 build_rdg (struct loop *loop)
4518 int nb_data_refs = 10;
4519 struct graph *rdg = NULL;
4520 VEC (ddr_p, heap) *dependence_relations;
4521 VEC (data_reference_p, heap) *datarefs;
4522 VEC (tree, heap) *stmts = VEC_alloc (tree, heap, 10);
4524 dependence_relations = VEC_alloc (ddr_p, heap, nb_data_refs * nb_data_refs) ;
4525 datarefs = VEC_alloc (data_reference_p, heap, nb_data_refs);
4526 compute_data_dependences_for_loop (loop,
4529 &dependence_relations);
4531 if (!known_dependences_p (dependence_relations))
4534 stmts_from_loop (loop, &stmts);
4535 rdg = new_graph (VEC_length (tree, stmts));
4536 create_rdg_vertices (rdg, stmts);
4537 create_rdg_edges (rdg, dependence_relations);
4540 free_dependence_relations (dependence_relations);
4541 free_data_refs (datarefs);
4542 VEC_free (tree, heap, stmts);