/* Data references and dependences detectors. Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc. Contributed by Sebastian Pop This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GCC; see the file COPYING. If not, write to the Free Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */ /* This pass walks a given loop structure searching for array references. The information about the array accesses is recorded in DATA_REFERENCE structures. The basic test for determining the dependences is: given two access functions chrec1 and chrec2 to a same array, and x and y two vectors from the iteration domain, the same element of the array is accessed twice at iterations x and y if and only if: | chrec1 (x) == chrec2 (y). The goals of this analysis are: - to determine the independence: the relation between two independent accesses is qualified with the chrec_known (this information allows a loop parallelization), - when two data references access the same data, to qualify the dependence relation with classic dependence representations: - distance vectors - direction vectors - loop carried level dependence - polyhedron dependence or with the chains of recurrences based representation, - to define a knowledge base for storing the data dependence information, - to define an interface to access this data. Definitions: - subscript: given two array accesses a subscript is the tuple composed of the access functions for a given dimension. Example: Given A[f1][f2][f3] and B[g1][g2][g3], there are three subscripts: (f1, g1), (f2, g2), (f3, g3). - Diophantine equation: an equation whose coefficients and solutions are integer constants, for example the equation | 3*x + 2*y = 1 has an integer solution x = 1 and y = -1. References: - "Advanced Compilation for High Performance Computing" by Randy Allen and Ken Kennedy. http://citeseer.ist.psu.edu/goff91practical.html - "Loop Transformations for Restructuring Compilers - The Foundations" by Utpal Banerjee. */ #include "config.h" #include "system.h" #include "coretypes.h" #include "tm.h" #include "ggc.h" #include "tree.h" /* These RTL headers are needed for basic-block.h. */ #include "rtl.h" #include "basic-block.h" #include "diagnostic.h" #include "tree-flow.h" #include "tree-dump.h" #include "timevar.h" #include "cfgloop.h" #include "tree-chrec.h" #include "tree-data-ref.h" #include "tree-scalar-evolution.h" #include "tree-pass.h" #include "langhooks.h" static struct datadep_stats { int num_dependence_tests; int num_dependence_dependent; int num_dependence_independent; int num_dependence_undetermined; int num_subscript_tests; int num_subscript_undetermined; int num_same_subscript_function; int num_ziv; int num_ziv_independent; int num_ziv_dependent; int num_ziv_unimplemented; int num_siv; int num_siv_independent; int num_siv_dependent; int num_siv_unimplemented; int num_miv; int num_miv_independent; int num_miv_dependent; int num_miv_unimplemented; } dependence_stats; static tree object_analysis (tree, tree, bool, struct data_reference **, tree *, tree *, tree *, tree *, tree *, struct ptr_info_def **, subvar_t *); static bool subscript_dependence_tester_1 (struct data_dependence_relation *, struct data_reference *, struct data_reference *); /* Determine if PTR and DECL may alias, the result is put in ALIASED. Return FALSE if there is no symbol memory tag for PTR. */ static bool ptr_decl_may_alias_p (tree ptr, tree decl, struct data_reference *ptr_dr, bool *aliased) { tree tag = NULL_TREE; struct ptr_info_def *pi = DR_PTR_INFO (ptr_dr); gcc_assert (TREE_CODE (ptr) == SSA_NAME && DECL_P (decl)); if (pi) tag = pi->name_mem_tag; if (!tag) tag = symbol_mem_tag (SSA_NAME_VAR (ptr)); if (!tag) tag = DR_MEMTAG (ptr_dr); if (!tag) return false; *aliased = is_aliased_with (tag, decl); return true; } /* Determine if two pointers may alias, the result is put in ALIASED. Return FALSE if there is no symbol memory tag for one of the pointers. */ static bool ptr_ptr_may_alias_p (tree ptr_a, tree ptr_b, struct data_reference *dra, struct data_reference *drb, bool *aliased) { tree tag_a = NULL_TREE, tag_b = NULL_TREE; struct ptr_info_def *pi_a = DR_PTR_INFO (dra); struct ptr_info_def *pi_b = DR_PTR_INFO (drb); bitmap bal1, bal2; if (pi_a && pi_a->name_mem_tag && pi_b && pi_b->name_mem_tag) { tag_a = pi_a->name_mem_tag; tag_b = pi_b->name_mem_tag; } else { tag_a = symbol_mem_tag (SSA_NAME_VAR (ptr_a)); if (!tag_a) tag_a = DR_MEMTAG (dra); if (!tag_a) return false; tag_b = symbol_mem_tag (SSA_NAME_VAR (ptr_b)); if (!tag_b) tag_b = DR_MEMTAG (drb); if (!tag_b) return false; } bal1 = BITMAP_ALLOC (NULL); bitmap_set_bit (bal1, DECL_UID (tag_a)); if (MTAG_P (tag_a) && MTAG_ALIASES (tag_a)) bitmap_ior_into (bal1, MTAG_ALIASES (tag_a)); bal2 = BITMAP_ALLOC (NULL); bitmap_set_bit (bal2, DECL_UID (tag_b)); if (MTAG_P (tag_b) && MTAG_ALIASES (tag_b)) bitmap_ior_into (bal2, MTAG_ALIASES (tag_b)); *aliased = bitmap_intersect_p (bal1, bal2); BITMAP_FREE (bal1); BITMAP_FREE (bal2); return true; } /* Determine if BASE_A and BASE_B may alias, the result is put in ALIASED. Return FALSE if there is no symbol memory tag for one of the symbols. */ static bool may_alias_p (tree base_a, tree base_b, struct data_reference *dra, struct data_reference *drb, bool *aliased) { if (TREE_CODE (base_a) == ADDR_EXPR || TREE_CODE (base_b) == ADDR_EXPR) { if (TREE_CODE (base_a) == ADDR_EXPR && TREE_CODE (base_b) == ADDR_EXPR) { *aliased = (TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0)); return true; } if (TREE_CODE (base_a) == ADDR_EXPR) return ptr_decl_may_alias_p (base_b, TREE_OPERAND (base_a, 0), drb, aliased); else return ptr_decl_may_alias_p (base_a, TREE_OPERAND (base_b, 0), dra, aliased); } return ptr_ptr_may_alias_p (base_a, base_b, dra, drb, aliased); } /* Determine if a pointer (BASE_A) and a record/union access (BASE_B) are not aliased. Return TRUE if they differ. */ static bool record_ptr_differ_p (struct data_reference *dra, struct data_reference *drb) { bool aliased; tree base_a = DR_BASE_OBJECT (dra); tree base_b = DR_BASE_OBJECT (drb); if (TREE_CODE (base_b) != COMPONENT_REF) return false; /* Peel COMPONENT_REFs to get to the base. Do not peel INDIRECT_REFs. For a.b.c.d[i] we will get a, and for a.b->c.d[i] we will get a.b. Probably will be unnecessary with struct alias analysis. */ while (TREE_CODE (base_b) == COMPONENT_REF) base_b = TREE_OPERAND (base_b, 0); /* Compare a record/union access (b.c[i] or p->c[i]) and a pointer ((*q)[i]). */ if (TREE_CODE (base_a) == INDIRECT_REF && ((TREE_CODE (base_b) == VAR_DECL && (ptr_decl_may_alias_p (TREE_OPERAND (base_a, 0), base_b, dra, &aliased) && !aliased)) || (TREE_CODE (base_b) == INDIRECT_REF && (ptr_ptr_may_alias_p (TREE_OPERAND (base_a, 0), TREE_OPERAND (base_b, 0), dra, drb, &aliased) && !aliased)))) return true; else return false; } /* Determine if two record/union accesses are aliased. Return TRUE if they differ. */ static bool record_record_differ_p (struct data_reference *dra, struct data_reference *drb) { bool aliased; tree base_a = DR_BASE_OBJECT (dra); tree base_b = DR_BASE_OBJECT (drb); if (TREE_CODE (base_b) != COMPONENT_REF || TREE_CODE (base_a) != COMPONENT_REF) return false; /* Peel COMPONENT_REFs to get to the base. Do not peel INDIRECT_REFs. For a.b.c.d[i] we will get a, and for a.b->c.d[i] we will get a.b. Probably will be unnecessary with struct alias analysis. */ while (TREE_CODE (base_b) == COMPONENT_REF) base_b = TREE_OPERAND (base_b, 0); while (TREE_CODE (base_a) == COMPONENT_REF) base_a = TREE_OPERAND (base_a, 0); if (TREE_CODE (base_a) == INDIRECT_REF && TREE_CODE (base_b) == INDIRECT_REF && ptr_ptr_may_alias_p (TREE_OPERAND (base_a, 0), TREE_OPERAND (base_b, 0), dra, drb, &aliased) && !aliased) return true; else return false; } /* Determine if an array access (BASE_A) and a record/union access (BASE_B) are not aliased. Return TRUE if they differ. */ static bool record_array_differ_p (struct data_reference *dra, struct data_reference *drb) { bool aliased; tree base_a = DR_BASE_OBJECT (dra); tree base_b = DR_BASE_OBJECT (drb); if (TREE_CODE (base_b) != COMPONENT_REF) return false; /* Peel COMPONENT_REFs to get to the base. Do not peel INDIRECT_REFs. For a.b.c.d[i] we will get a, and for a.b->c.d[i] we will get a.b. Probably will be unnecessary with struct alias analysis. */ while (TREE_CODE (base_b) == COMPONENT_REF) base_b = TREE_OPERAND (base_b, 0); /* Compare a record/union access (b.c[i] or p->c[i]) and an array access (a[i]). In case of p->c[i] use alias analysis to verify that p is not pointing to a. */ if (TREE_CODE (base_a) == VAR_DECL && (TREE_CODE (base_b) == VAR_DECL || (TREE_CODE (base_b) == INDIRECT_REF && (ptr_decl_may_alias_p (TREE_OPERAND (base_b, 0), base_a, drb, &aliased) && !aliased)))) return true; else return false; } /* Determine if an array access (BASE_A) and a pointer (BASE_B) are not aliased. Return TRUE if they differ. */ static bool array_ptr_differ_p (tree base_a, tree base_b, struct data_reference *drb) { bool aliased; /* In case one of the bases is a pointer (a[i] and (*p)[i]), we check with the help of alias analysis that p is not pointing to a. */ if (TREE_CODE (base_a) == VAR_DECL && TREE_CODE (base_b) == INDIRECT_REF && (ptr_decl_may_alias_p (TREE_OPERAND (base_b, 0), base_a, drb, &aliased) && !aliased)) return true; else return false; } /* This is the simplest data dependence test: determines whether the data references A and B access the same array/region. Returns false when the property is not computable at compile time. Otherwise return true, and DIFFER_P will record the result. This utility will not be necessary when alias_sets_conflict_p will be less conservative. */ static bool base_object_differ_p (struct data_reference *a, struct data_reference *b, bool *differ_p) { tree base_a = DR_BASE_OBJECT (a); tree base_b = DR_BASE_OBJECT (b); bool aliased; if (!base_a || !base_b) return false; /* Determine if same base. Example: for the array accesses a[i], b[i] or pointer accesses *a, *b, bases are a, b. */ if (base_a == base_b) { *differ_p = false; return true; } /* For pointer based accesses, (*p)[i], (*q)[j], the bases are (*p) and (*q) */ if (TREE_CODE (base_a) == INDIRECT_REF && TREE_CODE (base_b) == INDIRECT_REF && TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0)) { *differ_p = false; return true; } /* Record/union based accesses - s.a[i], t.b[j]. bases are s.a,t.b. */ if (TREE_CODE (base_a) == COMPONENT_REF && TREE_CODE (base_b) == COMPONENT_REF && TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0) && TREE_OPERAND (base_a, 1) == TREE_OPERAND (base_b, 1)) { *differ_p = false; return true; } /* Determine if different bases. */ /* At this point we know that base_a != base_b. However, pointer accesses of the form x=(*p) and y=(*q), whose bases are p and q, may still be pointing to the same base. In SSAed GIMPLE p and q will be SSA_NAMES in this case. Therefore, here we check if they are really two different declarations. */ if (TREE_CODE (base_a) == VAR_DECL && TREE_CODE (base_b) == VAR_DECL) { *differ_p = true; return true; } /* In case one of the bases is a pointer (a[i] and (*p)[i]), we check with the help of alias analysis that p is not pointing to a. */ if (array_ptr_differ_p (base_a, base_b, b) || array_ptr_differ_p (base_b, base_a, a)) { *differ_p = true; return true; } /* If the bases are pointers ((*q)[i] and (*p)[i]), we check with the help of alias analysis they don't point to the same bases. */ if (TREE_CODE (base_a) == INDIRECT_REF && TREE_CODE (base_b) == INDIRECT_REF && (may_alias_p (TREE_OPERAND (base_a, 0), TREE_OPERAND (base_b, 0), a, b, &aliased) && !aliased)) { *differ_p = true; return true; } /* Compare two record/union bases s.a and t.b: s != t or (a != b and s and t are not unions). */ if (TREE_CODE (base_a) == COMPONENT_REF && TREE_CODE (base_b) == COMPONENT_REF && ((TREE_CODE (TREE_OPERAND (base_a, 0)) == VAR_DECL && TREE_CODE (TREE_OPERAND (base_b, 0)) == VAR_DECL && TREE_OPERAND (base_a, 0) != TREE_OPERAND (base_b, 0)) || (TREE_CODE (TREE_TYPE (TREE_OPERAND (base_a, 0))) == RECORD_TYPE && TREE_CODE (TREE_TYPE (TREE_OPERAND (base_b, 0))) == RECORD_TYPE && TREE_OPERAND (base_a, 1) != TREE_OPERAND (base_b, 1)))) { *differ_p = true; return true; } /* Compare a record/union access (b.c[i] or p->c[i]) and a pointer ((*q)[i]). */ if (record_ptr_differ_p (a, b) || record_ptr_differ_p (b, a)) { *differ_p = true; return true; } /* Compare a record/union access (b.c[i] or p->c[i]) and an array access (a[i]). In case of p->c[i] use alias analysis to verify that p is not pointing to a. */ if (record_array_differ_p (a, b) || record_array_differ_p (b, a)) { *differ_p = true; return true; } /* Compare two record/union accesses (b.c[i] or p->c[i]). */ if (record_record_differ_p (a, b)) { *differ_p = true; return true; } return false; } /* Function base_addr_differ_p. This is the simplest data dependence test: determines whether the data references DRA and DRB access the same array/region. Returns false when the property is not computable at compile time. Otherwise return true, and DIFFER_P will record the result. The algorithm: 1. if (both DRA and DRB are represented as arrays) compare DRA.BASE_OBJECT and DRB.BASE_OBJECT 2. else if (both DRA and DRB are represented as pointers) try to prove that DRA.FIRST_LOCATION == DRB.FIRST_LOCATION 3. else if (DRA and DRB are represented differently or 2. fails) only try to prove that the bases are surely different */ static bool base_addr_differ_p (struct data_reference *dra, struct data_reference *drb, bool *differ_p) { tree addr_a = DR_BASE_ADDRESS (dra); tree addr_b = DR_BASE_ADDRESS (drb); tree type_a, type_b; tree decl_a, decl_b; bool aliased; if (!addr_a || !addr_b) return false; type_a = TREE_TYPE (addr_a); type_b = TREE_TYPE (addr_b); gcc_assert (POINTER_TYPE_P (type_a) && POINTER_TYPE_P (type_b)); /* 1. if (both DRA and DRB are represented as arrays) compare DRA.BASE_OBJECT and DRB.BASE_OBJECT. */ if (DR_TYPE (dra) == ARRAY_REF_TYPE && DR_TYPE (drb) == ARRAY_REF_TYPE) return base_object_differ_p (dra, drb, differ_p); /* 2. else if (both DRA and DRB are represented as pointers) try to prove that DRA.FIRST_LOCATION == DRB.FIRST_LOCATION. */ /* If base addresses are the same, we check the offsets, since the access of the data-ref is described by {base addr + offset} and its access function, i.e., in order to decide whether the bases of data-refs are the same we compare both base addresses and offsets. */ if (DR_TYPE (dra) == POINTER_REF_TYPE && DR_TYPE (drb) == POINTER_REF_TYPE && (addr_a == addr_b || (TREE_CODE (addr_a) == ADDR_EXPR && TREE_CODE (addr_b) == ADDR_EXPR && TREE_OPERAND (addr_a, 0) == TREE_OPERAND (addr_b, 0)))) { /* Compare offsets. */ tree offset_a = DR_OFFSET (dra); tree offset_b = DR_OFFSET (drb); STRIP_NOPS (offset_a); STRIP_NOPS (offset_b); /* FORNOW: we only compare offsets that are MULT_EXPR, i.e., we don't handle PLUS_EXPR. */ if (offset_a == offset_b || (TREE_CODE (offset_a) == MULT_EXPR && TREE_CODE (offset_b) == MULT_EXPR && TREE_OPERAND (offset_a, 0) == TREE_OPERAND (offset_b, 0) && TREE_OPERAND (offset_a, 1) == TREE_OPERAND (offset_b, 1))) { *differ_p = false; return true; } } /* 3. else if (DRA and DRB are represented differently or 2. fails) only try to prove that the bases are surely different. */ /* Apply alias analysis. */ if (may_alias_p (addr_a, addr_b, dra, drb, &aliased) && !aliased) { *differ_p = true; return true; } /* An instruction writing through a restricted pointer is "independent" of any instruction reading or writing through a different restricted pointer, in the same block/scope. */ else if (TYPE_RESTRICT (type_a) && TYPE_RESTRICT (type_b) && (!DR_IS_READ (drb) || !DR_IS_READ (dra)) && TREE_CODE (DR_BASE_ADDRESS (dra)) == SSA_NAME && (decl_a = SSA_NAME_VAR (DR_BASE_ADDRESS (dra))) && TREE_CODE (decl_a) == PARM_DECL && TREE_CODE (DECL_CONTEXT (decl_a)) == FUNCTION_DECL && TREE_CODE (DR_BASE_ADDRESS (drb)) == SSA_NAME && (decl_b = SSA_NAME_VAR (DR_BASE_ADDRESS (drb))) && TREE_CODE (decl_b) == PARM_DECL && TREE_CODE (DECL_CONTEXT (decl_b)) == FUNCTION_DECL && DECL_CONTEXT (decl_a) == DECL_CONTEXT (decl_b)) { *differ_p = true; return true; } return false; } /* Returns true iff A divides B. */ static inline bool tree_fold_divides_p (tree a, tree b) { gcc_assert (TREE_CODE (a) == INTEGER_CST); gcc_assert (TREE_CODE (b) == INTEGER_CST); return integer_zerop (int_const_binop (TRUNC_MOD_EXPR, b, a, 0)); } /* Returns true iff A divides B. */ static inline bool int_divides_p (int a, int b) { return ((b % a) == 0); } /* Dump into FILE all the data references from DATAREFS. */ void dump_data_references (FILE *file, VEC (data_reference_p, heap) *datarefs) { unsigned int i; struct data_reference *dr; for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++) dump_data_reference (file, dr); } /* Dump into FILE all the dependence relations from DDRS. */ void dump_data_dependence_relations (FILE *file, VEC (ddr_p, heap) *ddrs) { unsigned int i; struct data_dependence_relation *ddr; for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++) dump_data_dependence_relation (file, ddr); } /* Dump function for a DATA_REFERENCE structure. */ void dump_data_reference (FILE *outf, struct data_reference *dr) { unsigned int i; fprintf (outf, "(Data Ref: \n stmt: "); print_generic_stmt (outf, DR_STMT (dr), 0); fprintf (outf, " ref: "); print_generic_stmt (outf, DR_REF (dr), 0); fprintf (outf, " base_object: "); print_generic_stmt (outf, DR_BASE_OBJECT (dr), 0); for (i = 0; i < DR_NUM_DIMENSIONS (dr); i++) { fprintf (outf, " Access function %d: ", i); print_generic_stmt (outf, DR_ACCESS_FN (dr, i), 0); } fprintf (outf, ")\n"); } /* Dumps the affine function described by FN to the file OUTF. */ static void dump_affine_function (FILE *outf, affine_fn fn) { unsigned i; tree coef; print_generic_expr (outf, VEC_index (tree, fn, 0), TDF_SLIM); for (i = 1; VEC_iterate (tree, fn, i, coef); i++) { fprintf (outf, " + "); print_generic_expr (outf, coef, TDF_SLIM); fprintf (outf, " * x_%u", i); } } /* Dumps the conflict function CF to the file OUTF. */ static void dump_conflict_function (FILE *outf, conflict_function *cf) { unsigned i; if (cf->n == NO_DEPENDENCE) fprintf (outf, "no dependence\n"); else if (cf->n == NOT_KNOWN) fprintf (outf, "not known\n"); else { for (i = 0; i < cf->n; i++) { fprintf (outf, "["); dump_affine_function (outf, cf->fns[i]); fprintf (outf, "]\n"); } } } /* Dump function for a SUBSCRIPT structure. */ void dump_subscript (FILE *outf, struct subscript *subscript) { conflict_function *cf = SUB_CONFLICTS_IN_A (subscript); fprintf (outf, "\n (subscript \n"); fprintf (outf, " iterations_that_access_an_element_twice_in_A: "); dump_conflict_function (outf, cf); if (CF_NONTRIVIAL_P (cf)) { tree last_iteration = SUB_LAST_CONFLICT (subscript); fprintf (outf, " last_conflict: "); print_generic_stmt (outf, last_iteration, 0); } cf = SUB_CONFLICTS_IN_B (subscript); fprintf (outf, " iterations_that_access_an_element_twice_in_B: "); dump_conflict_function (outf, cf); if (CF_NONTRIVIAL_P (cf)) { tree last_iteration = SUB_LAST_CONFLICT (subscript); fprintf (outf, " last_conflict: "); print_generic_stmt (outf, last_iteration, 0); } fprintf (outf, " (Subscript distance: "); print_generic_stmt (outf, SUB_DISTANCE (subscript), 0); fprintf (outf, " )\n"); fprintf (outf, " )\n"); } /* Print the classic direction vector DIRV to OUTF. */ void print_direction_vector (FILE *outf, lambda_vector dirv, int length) { int eq; for (eq = 0; eq < length; eq++) { enum data_dependence_direction dir = dirv[eq]; switch (dir) { case dir_positive: fprintf (outf, " +"); break; case dir_negative: fprintf (outf, " -"); break; case dir_equal: fprintf (outf, " ="); break; case dir_positive_or_equal: fprintf (outf, " +="); break; case dir_positive_or_negative: fprintf (outf, " +-"); break; case dir_negative_or_equal: fprintf (outf, " -="); break; case dir_star: fprintf (outf, " *"); break; default: fprintf (outf, "indep"); break; } } fprintf (outf, "\n"); } /* Print a vector of direction vectors. */ void print_dir_vectors (FILE *outf, VEC (lambda_vector, heap) *dir_vects, int length) { unsigned j; lambda_vector v; for (j = 0; VEC_iterate (lambda_vector, dir_vects, j, v); j++) print_direction_vector (outf, v, length); } /* Print a vector of distance vectors. */ void print_dist_vectors (FILE *outf, VEC (lambda_vector, heap) *dist_vects, int length) { unsigned j; lambda_vector v; for (j = 0; VEC_iterate (lambda_vector, dist_vects, j, v); j++) print_lambda_vector (outf, v, length); } /* Debug version. */ void debug_data_dependence_relation (struct data_dependence_relation *ddr) { dump_data_dependence_relation (stderr, ddr); } /* Dump function for a DATA_DEPENDENCE_RELATION structure. */ void dump_data_dependence_relation (FILE *outf, struct data_dependence_relation *ddr) { struct data_reference *dra, *drb; dra = DDR_A (ddr); drb = DDR_B (ddr); fprintf (outf, "(Data Dep: \n"); if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know) fprintf (outf, " (don't know)\n"); else if (DDR_ARE_DEPENDENT (ddr) == chrec_known) fprintf (outf, " (no dependence)\n"); else if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE) { unsigned int i; struct loop *loopi; for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) { fprintf (outf, " access_fn_A: "); print_generic_stmt (outf, DR_ACCESS_FN (dra, i), 0); fprintf (outf, " access_fn_B: "); print_generic_stmt (outf, DR_ACCESS_FN (drb, i), 0); dump_subscript (outf, DDR_SUBSCRIPT (ddr, i)); } fprintf (outf, " inner loop index: %d\n", DDR_INNER_LOOP (ddr)); fprintf (outf, " loop nest: ("); for (i = 0; VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++) fprintf (outf, "%d ", loopi->num); fprintf (outf, ")\n"); for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++) { fprintf (outf, " distance_vector: "); print_lambda_vector (outf, DDR_DIST_VECT (ddr, i), DDR_NB_LOOPS (ddr)); } for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++) { fprintf (outf, " direction_vector: "); print_direction_vector (outf, DDR_DIR_VECT (ddr, i), DDR_NB_LOOPS (ddr)); } } fprintf (outf, ")\n"); } /* Dump function for a DATA_DEPENDENCE_DIRECTION structure. */ void dump_data_dependence_direction (FILE *file, enum data_dependence_direction dir) { switch (dir) { case dir_positive: fprintf (file, "+"); break; case dir_negative: fprintf (file, "-"); break; case dir_equal: fprintf (file, "="); break; case dir_positive_or_negative: fprintf (file, "+-"); break; case dir_positive_or_equal: fprintf (file, "+="); break; case dir_negative_or_equal: fprintf (file, "-="); break; case dir_star: fprintf (file, "*"); break; default: break; } } /* Dumps the distance and direction vectors in FILE. DDRS contains the dependence relations, and VECT_SIZE is the size of the dependence vectors, or in other words the number of loops in the considered nest. */ void dump_dist_dir_vectors (FILE *file, VEC (ddr_p, heap) *ddrs) { unsigned int i, j; struct data_dependence_relation *ddr; lambda_vector v; for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++) if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE && DDR_AFFINE_P (ddr)) { for (j = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), j, v); j++) { fprintf (file, "DISTANCE_V ("); print_lambda_vector (file, v, DDR_NB_LOOPS (ddr)); fprintf (file, ")\n"); } for (j = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), j, v); j++) { fprintf (file, "DIRECTION_V ("); print_direction_vector (file, v, DDR_NB_LOOPS (ddr)); fprintf (file, ")\n"); } } fprintf (file, "\n\n"); } /* Dumps the data dependence relations DDRS in FILE. */ void dump_ddrs (FILE *file, VEC (ddr_p, heap) *ddrs) { unsigned int i; struct data_dependence_relation *ddr; for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++) dump_data_dependence_relation (file, ddr); fprintf (file, "\n\n"); } /* Given an ARRAY_REF node REF, records its access functions. Example: given A[i][3], record in ACCESS_FNS the opnd1 function, i.e. the constant "3", then recursively call the function on opnd0, i.e. the ARRAY_REF "A[i]". The function returns the base name: "A". */ static tree analyze_array_indexes (struct loop *loop, VEC(tree,heap) **access_fns, tree ref, tree stmt) { tree opnd0, opnd1; tree access_fn; opnd0 = TREE_OPERAND (ref, 0); opnd1 = TREE_OPERAND (ref, 1); /* The detection of the evolution function for this data access is postponed until the dependence test. This lazy strategy avoids the computation of access functions that are of no interest for the optimizers. */ access_fn = instantiate_parameters (loop, analyze_scalar_evolution (loop, opnd1)); VEC_safe_push (tree, heap, *access_fns, access_fn); /* Recursively record other array access functions. */ if (TREE_CODE (opnd0) == ARRAY_REF) return analyze_array_indexes (loop, access_fns, opnd0, stmt); /* Return the base name of the data access. */ else return opnd0; } /* For a data reference REF contained in the statement STMT, initialize a DATA_REFERENCE structure, and return it. IS_READ flag has to be set to true when REF is in the right hand side of an assignment. */ static struct data_reference * init_array_ref (tree stmt, tree ref, bool is_read) { struct loop *loop = loop_containing_stmt (stmt); VEC(tree,heap) *acc_fns = VEC_alloc (tree, heap, 3); struct data_reference *res = XNEW (struct data_reference);; if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "(init_array_ref \n"); fprintf (dump_file, " (ref = "); print_generic_stmt (dump_file, ref, 0); fprintf (dump_file, ")\n"); } DR_STMT (res) = stmt; DR_REF (res) = ref; DR_BASE_OBJECT (res) = analyze_array_indexes (loop, &acc_fns, ref, stmt); DR_TYPE (res) = ARRAY_REF_TYPE; DR_SET_ACCESS_FNS (res, acc_fns); DR_IS_READ (res) = is_read; DR_BASE_ADDRESS (res) = NULL_TREE; DR_OFFSET (res) = NULL_TREE; DR_INIT (res) = NULL_TREE; DR_STEP (res) = NULL_TREE; DR_OFFSET_MISALIGNMENT (res) = NULL_TREE; DR_MEMTAG (res) = NULL_TREE; DR_PTR_INFO (res) = NULL; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); return res; } /* For a data reference REF contained in the statement STMT, initialize a DATA_REFERENCE structure, and return it. */ static struct data_reference * init_pointer_ref (tree stmt, tree ref, tree access_fn, bool is_read, tree base_address, tree step, struct ptr_info_def *ptr_info) { struct data_reference *res = XNEW (struct data_reference); VEC(tree,heap) *acc_fns = VEC_alloc (tree, heap, 3); if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "(init_pointer_ref \n"); fprintf (dump_file, " (ref = "); print_generic_stmt (dump_file, ref, 0); fprintf (dump_file, ")\n"); } DR_STMT (res) = stmt; DR_REF (res) = ref; DR_BASE_OBJECT (res) = NULL_TREE; DR_TYPE (res) = POINTER_REF_TYPE; DR_SET_ACCESS_FNS (res, acc_fns); VEC_quick_push (tree, DR_ACCESS_FNS (res), access_fn); DR_IS_READ (res) = is_read; DR_BASE_ADDRESS (res) = base_address; DR_OFFSET (res) = NULL_TREE; DR_INIT (res) = NULL_TREE; DR_STEP (res) = step; DR_OFFSET_MISALIGNMENT (res) = NULL_TREE; DR_MEMTAG (res) = NULL_TREE; DR_PTR_INFO (res) = ptr_info; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); return res; } /* Analyze an indirect memory reference, REF, that comes from STMT. IS_READ is true if this is an indirect load, and false if it is an indirect store. Return a new data reference structure representing the indirect_ref, or NULL if we cannot describe the access function. */ static struct data_reference * analyze_indirect_ref (tree stmt, tree ref, bool is_read) { struct loop *loop = loop_containing_stmt (stmt); tree ptr_ref = TREE_OPERAND (ref, 0); tree access_fn = analyze_scalar_evolution (loop, ptr_ref); tree init = initial_condition_in_loop_num (access_fn, loop->num); tree base_address = NULL_TREE, evolution, step = NULL_TREE; struct ptr_info_def *ptr_info = NULL; if (TREE_CODE (ptr_ref) == SSA_NAME) ptr_info = SSA_NAME_PTR_INFO (ptr_ref); STRIP_NOPS (init); if (access_fn == chrec_dont_know || !init || init == chrec_dont_know) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nBad access function of ptr: "); print_generic_expr (dump_file, ref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL; } if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nAccess function of ptr: "); print_generic_expr (dump_file, access_fn, TDF_SLIM); fprintf (dump_file, "\n"); } if (!expr_invariant_in_loop_p (loop, init)) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "\ninitial condition is not loop invariant.\n"); } else { base_address = init; evolution = evolution_part_in_loop_num (access_fn, loop->num); if (evolution != chrec_dont_know) { if (!evolution) step = ssize_int (0); else { if (TREE_CODE (evolution) == INTEGER_CST) step = fold_convert (ssizetype, evolution); else if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "\nnon constant step for ptr access.\n"); } } else if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "\nunknown evolution of ptr.\n"); } return init_pointer_ref (stmt, ref, access_fn, is_read, base_address, step, ptr_info); } /* Function strip_conversions Strip conversions that don't narrow the mode. */ static tree strip_conversion (tree expr) { tree to, ti, oprnd0; while (TREE_CODE (expr) == NOP_EXPR || TREE_CODE (expr) == CONVERT_EXPR) { to = TREE_TYPE (expr); oprnd0 = TREE_OPERAND (expr, 0); ti = TREE_TYPE (oprnd0); if (!INTEGRAL_TYPE_P (to) || !INTEGRAL_TYPE_P (ti)) return NULL_TREE; if (GET_MODE_SIZE (TYPE_MODE (to)) < GET_MODE_SIZE (TYPE_MODE (ti))) return NULL_TREE; expr = oprnd0; } return expr; } /* Function analyze_offset_expr Given an offset expression EXPR received from get_inner_reference, analyze it and create an expression for INITIAL_OFFSET by substituting the variables of EXPR with initial_condition of the corresponding access_fn in the loop. E.g., for i for (j = 3; j < N; j++) a[j].b[i][j] = 0; For a[j].b[i][j], EXPR will be 'i * C_i + j * C_j + C'. 'i' cannot be substituted, since its access_fn in the inner loop is i. 'j' will be substituted with 3. An INITIAL_OFFSET will be 'i * C_i + C`', where C` = 3 * C_j + C. Compute MISALIGN (the misalignment of the data reference initial access from its base). Misalignment can be calculated only if all the variables can be substituted with constants, otherwise, we record maximum possible alignment in ALIGNED_TO. In the above example, since 'i' cannot be substituted, MISALIGN will be NULL_TREE, and the biggest divider of C_i (a power of 2) will be recorded in ALIGNED_TO. STEP is an evolution of the data reference in this loop in bytes. In the above example, STEP is C_j. Return FALSE, if the analysis fails, e.g., there is no access_fn for a variable. In this case, all the outputs (INITIAL_OFFSET, MISALIGN, ALIGNED_TO and STEP) are NULL_TREEs. Otherwise, return TRUE. */ static bool analyze_offset_expr (tree expr, struct loop *loop, tree *initial_offset, tree *misalign, tree *aligned_to, tree *step) { tree oprnd0; tree oprnd1; tree left_offset = ssize_int (0); tree right_offset = ssize_int (0); tree left_misalign = ssize_int (0); tree right_misalign = ssize_int (0); tree left_step = ssize_int (0); tree right_step = ssize_int (0); enum tree_code code; tree init, evolution; tree left_aligned_to = NULL_TREE, right_aligned_to = NULL_TREE; *step = NULL_TREE; *misalign = NULL_TREE; *aligned_to = NULL_TREE; *initial_offset = NULL_TREE; /* Strip conversions that don't narrow the mode. */ expr = strip_conversion (expr); if (!expr) return false; /* Stop conditions: 1. Constant. */ if (TREE_CODE (expr) == INTEGER_CST) { *initial_offset = fold_convert (ssizetype, expr); *misalign = fold_convert (ssizetype, expr); *step = ssize_int (0); return true; } /* 2. Variable. Try to substitute with initial_condition of the corresponding access_fn in the current loop. */ if (SSA_VAR_P (expr)) { tree access_fn = analyze_scalar_evolution (loop, expr); if (access_fn == chrec_dont_know) /* No access_fn. */ return false; init = initial_condition_in_loop_num (access_fn, loop->num); if (!expr_invariant_in_loop_p (loop, init)) /* Not enough information: may be not loop invariant. E.g., for a[b[i]], we get a[D], where D=b[i]. EXPR is D, its initial_condition is D, but it depends on i - loop's induction variable. */ return false; evolution = evolution_part_in_loop_num (access_fn, loop->num); if (evolution && TREE_CODE (evolution) != INTEGER_CST) /* Evolution is not constant. */ return false; if (TREE_CODE (init) == INTEGER_CST) *misalign = fold_convert (ssizetype, init); else /* Not constant, misalignment cannot be calculated. */ *misalign = NULL_TREE; *initial_offset = fold_convert (ssizetype, init); *step = evolution ? fold_convert (ssizetype, evolution) : ssize_int (0); return true; } /* Recursive computation. */ if (!BINARY_CLASS_P (expr)) { /* We expect to get binary expressions (PLUS/MINUS and MULT). */ if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nNot binary expression "); print_generic_expr (dump_file, expr, TDF_SLIM); fprintf (dump_file, "\n"); } return false; } oprnd0 = TREE_OPERAND (expr, 0); oprnd1 = TREE_OPERAND (expr, 1); if (!analyze_offset_expr (oprnd0, loop, &left_offset, &left_misalign, &left_aligned_to, &left_step) || !analyze_offset_expr (oprnd1, loop, &right_offset, &right_misalign, &right_aligned_to, &right_step)) return false; /* The type of the operation: plus, minus or mult. */ code = TREE_CODE (expr); switch (code) { case MULT_EXPR: if (TREE_CODE (right_offset) != INTEGER_CST) /* RIGHT_OFFSET can be not constant. For example, for arrays of variable sized types. FORNOW: We don't support such cases. */ return false; /* Strip conversions that don't narrow the mode. */ left_offset = strip_conversion (left_offset); if (!left_offset) return false; /* Misalignment computation. */ if (SSA_VAR_P (left_offset)) { /* If the left side contains variables that can't be substituted with constants, the misalignment is unknown. However, if the right side is a multiple of some alignment, we know that the expression is aligned to it. Therefore, we record such maximum possible value. */ *misalign = NULL_TREE; *aligned_to = ssize_int (highest_pow2_factor (right_offset)); } else { /* The left operand was successfully substituted with constant. */ if (left_misalign) { /* In case of EXPR '(i * C1 + j) * C2', LEFT_MISALIGN is NULL_TREE. */ *misalign = size_binop (code, left_misalign, right_misalign); if (left_aligned_to && right_aligned_to) *aligned_to = size_binop (MIN_EXPR, left_aligned_to, right_aligned_to); else *aligned_to = left_aligned_to ? left_aligned_to : right_aligned_to; } else *misalign = NULL_TREE; } /* Step calculation. */ /* Multiply the step by the right operand. */ *step = size_binop (MULT_EXPR, left_step, right_offset); break; case PLUS_EXPR: case MINUS_EXPR: /* Combine the recursive calculations for step and misalignment. */ *step = size_binop (code, left_step, right_step); /* Unknown alignment. */ if ((!left_misalign && !left_aligned_to) || (!right_misalign && !right_aligned_to)) { *misalign = NULL_TREE; *aligned_to = NULL_TREE; break; } if (left_misalign && right_misalign) *misalign = size_binop (code, left_misalign, right_misalign); else *misalign = left_misalign ? left_misalign : right_misalign; if (left_aligned_to && right_aligned_to) *aligned_to = size_binop (MIN_EXPR, left_aligned_to, right_aligned_to); else *aligned_to = left_aligned_to ? left_aligned_to : right_aligned_to; break; default: gcc_unreachable (); } /* Compute offset. */ *initial_offset = fold_convert (ssizetype, fold_build2 (code, TREE_TYPE (left_offset), left_offset, right_offset)); return true; } /* Function address_analysis Return the BASE of the address expression EXPR. Also compute the OFFSET from BASE, MISALIGN and STEP. Input: EXPR - the address expression that is being analyzed STMT - the statement that contains EXPR or its original memory reference IS_READ - TRUE if STMT reads from EXPR, FALSE if writes to EXPR DR - data_reference struct for the original memory reference Output: BASE (returned value) - the base of the data reference EXPR. INITIAL_OFFSET - initial offset of EXPR from BASE (an expression) MISALIGN - offset of EXPR from BASE in bytes (a constant) or NULL_TREE if the computation is impossible ALIGNED_TO - maximum alignment of EXPR or NULL_TREE if MISALIGN can be calculated (doesn't depend on variables) STEP - evolution of EXPR in the loop If something unexpected is encountered (an unsupported form of data-ref), then NULL_TREE is returned. */ static tree address_analysis (tree expr, tree stmt, bool is_read, struct data_reference *dr, tree *offset, tree *misalign, tree *aligned_to, tree *step) { tree oprnd0, oprnd1, base_address, offset_expr, base_addr0, base_addr1; tree address_offset = ssize_int (0), address_misalign = ssize_int (0); tree dummy, address_aligned_to = NULL_TREE; struct ptr_info_def *dummy1; subvar_t dummy2; switch (TREE_CODE (expr)) { case PLUS_EXPR: case MINUS_EXPR: /* EXPR is of form {base +/- offset} (or {offset +/- base}). */ oprnd0 = TREE_OPERAND (expr, 0); oprnd1 = TREE_OPERAND (expr, 1); STRIP_NOPS (oprnd0); STRIP_NOPS (oprnd1); /* Recursively try to find the base of the address contained in EXPR. For offset, the returned base will be NULL. */ base_addr0 = address_analysis (oprnd0, stmt, is_read, dr, &address_offset, &address_misalign, &address_aligned_to, step); base_addr1 = address_analysis (oprnd1, stmt, is_read, dr, &address_offset, &address_misalign, &address_aligned_to, step); /* We support cases where only one of the operands contains an address. */ if ((base_addr0 && base_addr1) || (!base_addr0 && !base_addr1)) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\neither more than one address or no addresses in expr "); print_generic_expr (dump_file, expr, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } /* To revert STRIP_NOPS. */ oprnd0 = TREE_OPERAND (expr, 0); oprnd1 = TREE_OPERAND (expr, 1); offset_expr = base_addr0 ? fold_convert (ssizetype, oprnd1) : fold_convert (ssizetype, oprnd0); /* EXPR is of form {base +/- offset} (or {offset +/- base}). If offset is a number, we can add it to the misalignment value calculated for base, otherwise, misalignment is NULL. */ if (TREE_CODE (offset_expr) == INTEGER_CST && address_misalign) { *misalign = size_binop (TREE_CODE (expr), address_misalign, offset_expr); *aligned_to = address_aligned_to; } else { *misalign = NULL_TREE; *aligned_to = NULL_TREE; } /* Combine offset (from EXPR {base + offset}) with the offset calculated for base. */ *offset = size_binop (TREE_CODE (expr), address_offset, offset_expr); return base_addr0 ? base_addr0 : base_addr1; case ADDR_EXPR: base_address = object_analysis (TREE_OPERAND (expr, 0), stmt, is_read, &dr, offset, misalign, aligned_to, step, &dummy, &dummy1, &dummy2); return base_address; case SSA_NAME: if (!POINTER_TYPE_P (TREE_TYPE (expr))) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nnot pointer SSA_NAME "); print_generic_expr (dump_file, expr, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } *aligned_to = ssize_int (TYPE_ALIGN_UNIT (TREE_TYPE (TREE_TYPE (expr)))); *misalign = ssize_int (0); *offset = ssize_int (0); *step = ssize_int (0); return expr; default: return NULL_TREE; } } /* Function object_analysis Create a data-reference structure DR for MEMREF. Return the BASE of the data reference MEMREF if the analysis is possible. Also compute the INITIAL_OFFSET from BASE, MISALIGN and STEP. E.g., for EXPR a.b[i] + 4B, BASE is a, and OFFSET is the overall offset 'a.b[i] + 4B' from a (can be an expression), MISALIGN is an OFFSET instantiated with initial_conditions of access_functions of variables, and STEP is the evolution of the DR_REF in this loop. Function get_inner_reference is used for the above in case of ARRAY_REF and COMPONENT_REF. The structure of the function is as follows: Part 1: Case 1. For handled_component_p refs 1.1 build data-reference structure for MEMREF 1.2 call get_inner_reference 1.2.1 analyze offset expr received from get_inner_reference (fall through with BASE) Case 2. For declarations 2.1 set MEMTAG Case 3. For INDIRECT_REFs 3.1 build data-reference structure for MEMREF 3.2 analyze evolution and initial condition of MEMREF 3.3 set data-reference structure for MEMREF 3.4 call address_analysis to analyze INIT of the access function 3.5 extract memory tag Part 2: Combine the results of object and address analysis to calculate INITIAL_OFFSET, STEP and misalignment info. Input: MEMREF - the memory reference that is being analyzed STMT - the statement that contains MEMREF IS_READ - TRUE if STMT reads from MEMREF, FALSE if writes to MEMREF Output: BASE_ADDRESS (returned value) - the base address of the data reference MEMREF E.g, if MEMREF is a.b[k].c[i][j] the returned base is &a. DR - data_reference struct for MEMREF INITIAL_OFFSET - initial offset of MEMREF from BASE (an expression) MISALIGN - offset of MEMREF from BASE in bytes (a constant) modulo alignment of ALIGNMENT or NULL_TREE if the computation is impossible ALIGNED_TO - maximum alignment of EXPR or NULL_TREE if MISALIGN can be calculated (doesn't depend on variables) STEP - evolution of the DR_REF in the loop MEMTAG - memory tag for aliasing purposes PTR_INFO - NULL or points-to aliasing info from a pointer SSA_NAME SUBVARS - Sub-variables of the variable If the analysis of MEMREF evolution in the loop fails, NULL_TREE is returned, but DR can be created anyway. */ static tree object_analysis (tree memref, tree stmt, bool is_read, struct data_reference **dr, tree *offset, tree *misalign, tree *aligned_to, tree *step, tree *memtag, struct ptr_info_def **ptr_info, subvar_t *subvars) { tree base = NULL_TREE, base_address = NULL_TREE; tree object_offset = ssize_int (0), object_misalign = ssize_int (0); tree object_step = ssize_int (0), address_step = ssize_int (0); tree address_offset = ssize_int (0), address_misalign = ssize_int (0); HOST_WIDE_INT pbitsize, pbitpos; tree poffset, bit_pos_in_bytes; enum machine_mode pmode; int punsignedp, pvolatilep; tree ptr_step = ssize_int (0), ptr_init = NULL_TREE; struct loop *loop = loop_containing_stmt (stmt); struct data_reference *ptr_dr = NULL; tree object_aligned_to = NULL_TREE, address_aligned_to = NULL_TREE; tree comp_ref = NULL_TREE; *ptr_info = NULL; /* Part 1: */ /* Case 1. handled_component_p refs. */ if (handled_component_p (memref)) { /* 1.1 build data-reference structure for MEMREF. */ if (!(*dr)) { if (TREE_CODE (memref) == ARRAY_REF) *dr = init_array_ref (stmt, memref, is_read); else if (TREE_CODE (memref) == COMPONENT_REF) comp_ref = memref; else { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\ndata-ref of unsupported type "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } } /* 1.2 call get_inner_reference. */ /* Find the base and the offset from it. */ base = get_inner_reference (memref, &pbitsize, &pbitpos, &poffset, &pmode, &punsignedp, &pvolatilep, false); if (!base) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nfailed to get inner ref for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } /* 1.2.1 analyze offset expr received from get_inner_reference. */ if (poffset && !analyze_offset_expr (poffset, loop, &object_offset, &object_misalign, &object_aligned_to, &object_step)) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nfailed to compute offset or step for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } /* Add bit position to OFFSET and MISALIGN. */ bit_pos_in_bytes = ssize_int (pbitpos/BITS_PER_UNIT); /* Check that there is no remainder in bits. */ if (pbitpos%BITS_PER_UNIT) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "\nbit offset alignment.\n"); return NULL_TREE; } object_offset = size_binop (PLUS_EXPR, bit_pos_in_bytes, object_offset); if (object_misalign) object_misalign = size_binop (PLUS_EXPR, object_misalign, bit_pos_in_bytes); memref = base; /* To continue analysis of BASE. */ /* fall through */ } /* Part 1: Case 2. Declarations. */ if (DECL_P (memref)) { /* We expect to get a decl only if we already have a DR, or with COMPONENT_REFs of type 'a[i].b'. */ if (!(*dr)) { if (comp_ref && TREE_CODE (TREE_OPERAND (comp_ref, 0)) == ARRAY_REF) { *dr = init_array_ref (stmt, TREE_OPERAND (comp_ref, 0), is_read); if (DR_NUM_DIMENSIONS (*dr) != 1) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\n multidimensional component ref "); print_generic_expr (dump_file, comp_ref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } } else { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nunhandled decl "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } } /* TODO: if during the analysis of INDIRECT_REF we get to an object, put the object in BASE_OBJECT field if we can prove that this is O.K., i.e., the data-ref access is bounded by the bounds of the BASE_OBJECT. (e.g., if the object is an array base 'a', where 'a[N]', we must prove that every access with 'p' (the original INDIRECT_REF based on '&a') in the loop is within the array boundaries - from a[0] to a[N-1]). Otherwise, our alias analysis can be incorrect. Even if an access function based on BASE_OBJECT can't be build, update BASE_OBJECT field to enable us to prove that two data-refs are different (without access function, distance analysis is impossible). */ if (SSA_VAR_P (memref) && var_can_have_subvars (memref)) *subvars = get_subvars_for_var (memref); base_address = build_fold_addr_expr (memref); /* 2.1 set MEMTAG. */ *memtag = memref; } /* Part 1: Case 3. INDIRECT_REFs. */ else if (TREE_CODE (memref) == INDIRECT_REF) { tree ptr_ref = TREE_OPERAND (memref, 0); if (TREE_CODE (ptr_ref) == SSA_NAME) *ptr_info = SSA_NAME_PTR_INFO (ptr_ref); /* 3.1 build data-reference structure for MEMREF. */ ptr_dr = analyze_indirect_ref (stmt, memref, is_read); if (!ptr_dr) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nfailed to create dr for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } /* 3.2 analyze evolution and initial condition of MEMREF. */ ptr_step = DR_STEP (ptr_dr); ptr_init = DR_BASE_ADDRESS (ptr_dr); if (!ptr_init || !ptr_step || !POINTER_TYPE_P (TREE_TYPE (ptr_init))) { *dr = (*dr) ? *dr : ptr_dr; if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nbad pointer access "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } if (integer_zerop (ptr_step) && !(*dr)) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "\nptr is loop invariant.\n"); *dr = ptr_dr; return NULL_TREE; /* If there exists DR for MEMREF, we are analyzing the base of handled component (PTR_INIT), which not necessary has evolution in the loop. */ } object_step = size_binop (PLUS_EXPR, object_step, ptr_step); /* 3.3 set data-reference structure for MEMREF. */ if (!*dr) *dr = ptr_dr; /* 3.4 call address_analysis to analyze INIT of the access function. */ base_address = address_analysis (ptr_init, stmt, is_read, *dr, &address_offset, &address_misalign, &address_aligned_to, &address_step); if (!base_address) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nfailed to analyze address "); print_generic_expr (dump_file, ptr_init, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } /* 3.5 extract memory tag. */ switch (TREE_CODE (base_address)) { case SSA_NAME: *memtag = symbol_mem_tag (SSA_NAME_VAR (base_address)); if (!(*memtag) && TREE_CODE (TREE_OPERAND (memref, 0)) == SSA_NAME) *memtag = symbol_mem_tag (SSA_NAME_VAR (TREE_OPERAND (memref, 0))); break; case ADDR_EXPR: *memtag = TREE_OPERAND (base_address, 0); break; default: if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\nno memtag for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } *memtag = NULL_TREE; break; } } if (!base_address) { /* MEMREF cannot be analyzed. */ if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\ndata-ref of unsupported type "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL_TREE; } if (comp_ref) DR_REF (*dr) = comp_ref; if (SSA_VAR_P (*memtag) && var_can_have_subvars (*memtag)) *subvars = get_subvars_for_var (*memtag); /* Part 2: Combine the results of object and address analysis to calculate INITIAL_OFFSET, STEP and misalignment info. */ *offset = size_binop (PLUS_EXPR, object_offset, address_offset); if ((!object_misalign && !object_aligned_to) || (!address_misalign && !address_aligned_to)) { *misalign = NULL_TREE; *aligned_to = NULL_TREE; } else { if (object_misalign && address_misalign) *misalign = size_binop (PLUS_EXPR, object_misalign, address_misalign); else *misalign = object_misalign ? object_misalign : address_misalign; if (object_aligned_to && address_aligned_to) *aligned_to = size_binop (MIN_EXPR, object_aligned_to, address_aligned_to); else *aligned_to = object_aligned_to ? object_aligned_to : address_aligned_to; } *step = size_binop (PLUS_EXPR, object_step, address_step); return base_address; } /* Function analyze_offset. Extract INVARIANT and CONSTANT parts from OFFSET. */ static bool analyze_offset (tree offset, tree *invariant, tree *constant) { tree op0, op1, constant_0, constant_1, invariant_0, invariant_1; enum tree_code code = TREE_CODE (offset); *invariant = NULL_TREE; *constant = NULL_TREE; /* Not PLUS/MINUS expression - recursion stop condition. */ if (code != PLUS_EXPR && code != MINUS_EXPR) { if (TREE_CODE (offset) == INTEGER_CST) *constant = offset; else *invariant = offset; return true; } op0 = TREE_OPERAND (offset, 0); op1 = TREE_OPERAND (offset, 1); /* Recursive call with the operands. */ if (!analyze_offset (op0, &invariant_0, &constant_0) || !analyze_offset (op1, &invariant_1, &constant_1)) return false; /* Combine the results. Add negation to the subtrahend in case of subtraction. */ if (constant_0 && constant_1) return false; *constant = constant_0 ? constant_0 : constant_1; if (code == MINUS_EXPR && constant_1) *constant = fold_build1 (NEGATE_EXPR, TREE_TYPE (*constant), *constant); if (invariant_0 && invariant_1) *invariant = fold_build2 (code, TREE_TYPE (invariant_0), invariant_0, invariant_1); else { *invariant = invariant_0 ? invariant_0 : invariant_1; if (code == MINUS_EXPR && invariant_1) *invariant = fold_build1 (NEGATE_EXPR, TREE_TYPE (*invariant), *invariant); } return true; } /* Free the memory used by the data reference DR. */ static void free_data_ref (data_reference_p dr) { DR_FREE_ACCESS_FNS (dr); free (dr); } /* Function create_data_ref. Create a data-reference structure for MEMREF. Set its DR_BASE_ADDRESS, DR_OFFSET, DR_INIT, DR_STEP, DR_OFFSET_MISALIGNMENT, DR_ALIGNED_TO, DR_MEMTAG, and DR_POINTSTO_INFO fields. Input: MEMREF - the memory reference that is being analyzed STMT - the statement that contains MEMREF IS_READ - TRUE if STMT reads from MEMREF, FALSE if writes to MEMREF Output: DR (returned value) - data_reference struct for MEMREF */ static struct data_reference * create_data_ref (tree memref, tree stmt, bool is_read) { struct data_reference *dr = NULL; tree base_address, offset, step, misalign, memtag; struct loop *loop = loop_containing_stmt (stmt); tree invariant = NULL_TREE, constant = NULL_TREE; tree type_size, init_cond; struct ptr_info_def *ptr_info; subvar_t subvars = NULL; tree aligned_to, type = NULL_TREE, orig_offset; if (!memref) return NULL; base_address = object_analysis (memref, stmt, is_read, &dr, &offset, &misalign, &aligned_to, &step, &memtag, &ptr_info, &subvars); if (!dr || !base_address) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\ncreate_data_ref: failed to create a dr for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL; } DR_BASE_ADDRESS (dr) = base_address; DR_OFFSET (dr) = offset; DR_INIT (dr) = ssize_int (0); DR_STEP (dr) = step; DR_OFFSET_MISALIGNMENT (dr) = misalign; DR_ALIGNED_TO (dr) = aligned_to; DR_MEMTAG (dr) = memtag; DR_PTR_INFO (dr) = ptr_info; DR_SUBVARS (dr) = subvars; type_size = fold_convert (ssizetype, TYPE_SIZE_UNIT (TREE_TYPE (DR_REF (dr)))); /* Extract CONSTANT and INVARIANT from OFFSET. */ /* Remove cast from OFFSET and restore it for INVARIANT part. */ orig_offset = offset; STRIP_NOPS (offset); if (offset != orig_offset) type = TREE_TYPE (orig_offset); if (!analyze_offset (offset, &invariant, &constant)) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\ncreate_data_ref: failed to analyze dr's"); fprintf (dump_file, " offset for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } return NULL; } if (type && invariant) invariant = fold_convert (type, invariant); /* Put CONSTANT part of OFFSET in DR_INIT and INVARIANT in DR_OFFSET field of DR. */ if (constant) { DR_INIT (dr) = fold_convert (ssizetype, constant); init_cond = fold_build2 (TRUNC_DIV_EXPR, TREE_TYPE (constant), constant, type_size); } else DR_INIT (dr) = init_cond = ssize_int (0); if (invariant) DR_OFFSET (dr) = invariant; else DR_OFFSET (dr) = ssize_int (0); /* Change the access function for INIDIRECT_REFs, according to DR_BASE_ADDRESS. Analyze OFFSET calculated in object_analysis. OFFSET is an expression that can contain loop invariant expressions and constants. We put the constant part in the initial condition of the access function (for data dependence tests), and in DR_INIT of the data-ref. The loop invariant part is put in DR_OFFSET. The evolution part of the access function is STEP calculated in object_analysis divided by the size of data type. */ if (!DR_BASE_OBJECT (dr) || (TREE_CODE (memref) == COMPONENT_REF && DR_NUM_DIMENSIONS (dr) == 1)) { tree access_fn; tree new_step; /* Update access function. */ access_fn = DR_ACCESS_FN (dr, 0); if (automatically_generated_chrec_p (access_fn)) { free_data_ref (dr); return NULL; } new_step = size_binop (TRUNC_DIV_EXPR, fold_convert (ssizetype, step), type_size); init_cond = chrec_convert (chrec_type (access_fn), init_cond, stmt); new_step = chrec_convert (chrec_type (access_fn), new_step, stmt); if (automatically_generated_chrec_p (init_cond) || automatically_generated_chrec_p (new_step)) { free_data_ref (dr); return NULL; } access_fn = chrec_replace_initial_condition (access_fn, init_cond); access_fn = reset_evolution_in_loop (loop->num, access_fn, new_step); VEC_replace (tree, DR_ACCESS_FNS (dr), 0, access_fn); } if (dump_file && (dump_flags & TDF_DETAILS)) { struct ptr_info_def *pi = DR_PTR_INFO (dr); fprintf (dump_file, "\nCreated dr for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n\tbase_address: "); print_generic_expr (dump_file, DR_BASE_ADDRESS (dr), TDF_SLIM); fprintf (dump_file, "\n\toffset from base address: "); print_generic_expr (dump_file, DR_OFFSET (dr), TDF_SLIM); fprintf (dump_file, "\n\tconstant offset from base address: "); print_generic_expr (dump_file, DR_INIT (dr), TDF_SLIM); fprintf (dump_file, "\n\tbase_object: "); print_generic_expr (dump_file, DR_BASE_OBJECT (dr), TDF_SLIM); fprintf (dump_file, "\n\tstep: "); print_generic_expr (dump_file, DR_STEP (dr), TDF_SLIM); fprintf (dump_file, "B\n\tmisalignment from base: "); print_generic_expr (dump_file, DR_OFFSET_MISALIGNMENT (dr), TDF_SLIM); if (DR_OFFSET_MISALIGNMENT (dr)) fprintf (dump_file, "B"); if (DR_ALIGNED_TO (dr)) { fprintf (dump_file, "\n\taligned to: "); print_generic_expr (dump_file, DR_ALIGNED_TO (dr), TDF_SLIM); } fprintf (dump_file, "\n\tmemtag: "); print_generic_expr (dump_file, DR_MEMTAG (dr), TDF_SLIM); fprintf (dump_file, "\n"); if (pi && pi->name_mem_tag) { fprintf (dump_file, "\n\tnametag: "); print_generic_expr (dump_file, pi->name_mem_tag, TDF_SLIM); fprintf (dump_file, "\n"); } } return dr; } /* Returns true if FNA == FNB. */ static bool affine_function_equal_p (affine_fn fna, affine_fn fnb) { unsigned i, n = VEC_length (tree, fna); if (n != VEC_length (tree, fnb)) return false; for (i = 0; i < n; i++) if (!operand_equal_p (VEC_index (tree, fna, i), VEC_index (tree, fnb, i), 0)) return false; return true; } /* If all the functions in CF are the same, returns one of them, otherwise returns NULL. */ static affine_fn common_affine_function (conflict_function *cf) { unsigned i; affine_fn comm; if (!CF_NONTRIVIAL_P (cf)) return NULL; comm = cf->fns[0]; for (i = 1; i < cf->n; i++) if (!affine_function_equal_p (comm, cf->fns[i])) return NULL; return comm; } /* Returns the base of the affine function FN. */ static tree affine_function_base (affine_fn fn) { return VEC_index (tree, fn, 0); } /* Returns true if FN is a constant. */ static bool affine_function_constant_p (affine_fn fn) { unsigned i; tree coef; for (i = 1; VEC_iterate (tree, fn, i, coef); i++) if (!integer_zerop (coef)) return false; return true; } /* Returns true if FN is the zero constant function. */ static bool affine_function_zero_p (affine_fn fn) { return (integer_zerop (affine_function_base (fn)) && affine_function_constant_p (fn)); } /* Applies operation OP on affine functions FNA and FNB, and returns the result. */ static affine_fn affine_fn_op (enum tree_code op, affine_fn fna, affine_fn fnb) { unsigned i, n, m; affine_fn ret; tree coef; if (VEC_length (tree, fnb) > VEC_length (tree, fna)) { n = VEC_length (tree, fna); m = VEC_length (tree, fnb); } else { n = VEC_length (tree, fnb); m = VEC_length (tree, fna); } ret = VEC_alloc (tree, heap, m); for (i = 0; i < n; i++) VEC_quick_push (tree, ret, fold_build2 (op, integer_type_node, VEC_index (tree, fna, i), VEC_index (tree, fnb, i))); for (; VEC_iterate (tree, fna, i, coef); i++) VEC_quick_push (tree, ret, fold_build2 (op, integer_type_node, coef, integer_zero_node)); for (; VEC_iterate (tree, fnb, i, coef); i++) VEC_quick_push (tree, ret, fold_build2 (op, integer_type_node, integer_zero_node, coef)); return ret; } /* Returns the sum of affine functions FNA and FNB. */ static affine_fn affine_fn_plus (affine_fn fna, affine_fn fnb) { return affine_fn_op (PLUS_EXPR, fna, fnb); } /* Returns the difference of affine functions FNA and FNB. */ static affine_fn affine_fn_minus (affine_fn fna, affine_fn fnb) { return affine_fn_op (MINUS_EXPR, fna, fnb); } /* Frees affine function FN. */ static void affine_fn_free (affine_fn fn) { VEC_free (tree, heap, fn); } /* Determine for each subscript in the data dependence relation DDR the distance. */ static void compute_subscript_distance (struct data_dependence_relation *ddr) { conflict_function *cf_a, *cf_b; affine_fn fn_a, fn_b, diff; if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE) { unsigned int i; for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) { struct subscript *subscript; subscript = DDR_SUBSCRIPT (ddr, i); cf_a = SUB_CONFLICTS_IN_A (subscript); cf_b = SUB_CONFLICTS_IN_B (subscript); fn_a = common_affine_function (cf_a); fn_b = common_affine_function (cf_b); if (!fn_a || !fn_b) { SUB_DISTANCE (subscript) = chrec_dont_know; return; } diff = affine_fn_minus (fn_a, fn_b); if (affine_function_constant_p (diff)) SUB_DISTANCE (subscript) = affine_function_base (diff); else SUB_DISTANCE (subscript) = chrec_dont_know; affine_fn_free (diff); } } } /* Returns the conflict function for "unknown". */ static conflict_function * conflict_fn_not_known (void) { conflict_function *fn = XCNEW (conflict_function); fn->n = NOT_KNOWN; return fn; } /* Returns the conflict function for "independent". */ static conflict_function * conflict_fn_no_dependence (void) { conflict_function *fn = XCNEW (conflict_function); fn->n = NO_DEPENDENCE; return fn; } /* Initialize a data dependence relation between data accesses A and B. NB_LOOPS is the number of loops surrounding the references: the size of the classic distance/direction vectors. */ static struct data_dependence_relation * initialize_data_dependence_relation (struct data_reference *a, struct data_reference *b, VEC (loop_p, heap) *loop_nest) { struct data_dependence_relation *res; bool differ_p, known_dependence; unsigned int i; res = XNEW (struct data_dependence_relation); DDR_A (res) = a; DDR_B (res) = b; DDR_LOOP_NEST (res) = NULL; if (a == NULL || b == NULL) { DDR_ARE_DEPENDENT (res) = chrec_dont_know; return res; } /* When A and B are arrays and their dimensions differ, we directly initialize the relation to "there is no dependence": chrec_known. */ if (DR_BASE_OBJECT (a) && DR_BASE_OBJECT (b) && DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b)) { DDR_ARE_DEPENDENT (res) = chrec_known; return res; } if (DR_BASE_ADDRESS (a) && DR_BASE_ADDRESS (b)) known_dependence = base_addr_differ_p (a, b, &differ_p); else known_dependence = base_object_differ_p (a, b, &differ_p); if (!known_dependence) { /* Can't determine whether the data-refs access the same memory region. */ DDR_ARE_DEPENDENT (res) = chrec_dont_know; return res; } if (differ_p) { DDR_ARE_DEPENDENT (res) = chrec_known; return res; } DDR_AFFINE_P (res) = true; DDR_ARE_DEPENDENT (res) = NULL_TREE; DDR_SUBSCRIPTS (res) = VEC_alloc (subscript_p, heap, DR_NUM_DIMENSIONS (a)); DDR_LOOP_NEST (res) = loop_nest; DDR_INNER_LOOP (res) = 0; DDR_DIR_VECTS (res) = NULL; DDR_DIST_VECTS (res) = NULL; for (i = 0; i < DR_NUM_DIMENSIONS (a); i++) { struct subscript *subscript; subscript = XNEW (struct subscript); SUB_CONFLICTS_IN_A (subscript) = conflict_fn_not_known (); SUB_CONFLICTS_IN_B (subscript) = conflict_fn_not_known (); SUB_LAST_CONFLICT (subscript) = chrec_dont_know; SUB_DISTANCE (subscript) = chrec_dont_know; VEC_safe_push (subscript_p, heap, DDR_SUBSCRIPTS (res), subscript); } return res; } /* Frees memory used by the conflict function F. */ static void free_conflict_function (conflict_function *f) { unsigned i; if (CF_NONTRIVIAL_P (f)) { for (i = 0; i < f->n; i++) affine_fn_free (f->fns[i]); } free (f); } /* Frees memory used by SUBSCRIPTS. */ static void free_subscripts (VEC (subscript_p, heap) *subscripts) { unsigned i; subscript_p s; for (i = 0; VEC_iterate (subscript_p, subscripts, i, s); i++) { free_conflict_function (s->conflicting_iterations_in_a); free_conflict_function (s->conflicting_iterations_in_b); } VEC_free (subscript_p, heap, subscripts); } /* Set DDR_ARE_DEPENDENT to CHREC and finalize the subscript overlap description. */ static inline void finalize_ddr_dependent (struct data_dependence_relation *ddr, tree chrec) { if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "(dependence classified: "); print_generic_expr (dump_file, chrec, 0); fprintf (dump_file, ")\n"); } DDR_ARE_DEPENDENT (ddr) = chrec; free_subscripts (DDR_SUBSCRIPTS (ddr)); } /* The dependence relation DDR cannot be represented by a distance vector. */ static inline void non_affine_dependence_relation (struct data_dependence_relation *ddr) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(Dependence relation cannot be represented by distance vector.) \n"); DDR_AFFINE_P (ddr) = false; } /* This section contains the classic Banerjee tests. */ /* Returns true iff CHREC_A and CHREC_B are not dependent on any index variables, i.e., if the ZIV (Zero Index Variable) test is true. */ static inline bool ziv_subscript_p (tree chrec_a, tree chrec_b) { return (evolution_function_is_constant_p (chrec_a) && evolution_function_is_constant_p (chrec_b)); } /* Returns true iff CHREC_A and CHREC_B are dependent on an index variable, i.e., if the SIV (Single Index Variable) test is true. */ static bool siv_subscript_p (tree chrec_a, tree chrec_b) { if ((evolution_function_is_constant_p (chrec_a) && evolution_function_is_univariate_p (chrec_b)) || (evolution_function_is_constant_p (chrec_b) && evolution_function_is_univariate_p (chrec_a))) return true; if (evolution_function_is_univariate_p (chrec_a) && evolution_function_is_univariate_p (chrec_b)) { switch (TREE_CODE (chrec_a)) { case POLYNOMIAL_CHREC: switch (TREE_CODE (chrec_b)) { case POLYNOMIAL_CHREC: if (CHREC_VARIABLE (chrec_a) != CHREC_VARIABLE (chrec_b)) return false; default: return true; } default: return true; } } return false; } /* Creates a conflict function with N dimensions. The affine functions in each dimension follow. */ static conflict_function * conflict_fn (unsigned n, ...) { unsigned i; conflict_function *ret = XCNEW (conflict_function); va_list ap; gcc_assert (0 < n && n <= MAX_DIM); va_start(ap, n); ret->n = n; for (i = 0; i < n; i++) ret->fns[i] = va_arg (ap, affine_fn); va_end(ap); return ret; } /* Returns constant affine function with value CST. */ static affine_fn affine_fn_cst (tree cst) { affine_fn fn = VEC_alloc (tree, heap, 1); VEC_quick_push (tree, fn, cst); return fn; } /* Returns affine function with single variable, CST + COEF * x_DIM. */ static affine_fn affine_fn_univar (tree cst, unsigned dim, tree coef) { affine_fn fn = VEC_alloc (tree, heap, dim + 1); unsigned i; gcc_assert (dim > 0); VEC_quick_push (tree, fn, cst); for (i = 1; i < dim; i++) VEC_quick_push (tree, fn, integer_zero_node); VEC_quick_push (tree, fn, coef); return fn; } /* Analyze a ZIV (Zero Index Variable) subscript. *OVERLAPS_A and *OVERLAPS_B are initialized to the functions that describe the relation between the elements accessed twice by CHREC_A and CHREC_B. For k >= 0, the following property is verified: CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */ static void analyze_ziv_subscript (tree chrec_a, tree chrec_b, conflict_function **overlaps_a, conflict_function **overlaps_b, tree *last_conflicts) { tree difference; dependence_stats.num_ziv++; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(analyze_ziv_subscript \n"); chrec_a = chrec_convert (integer_type_node, chrec_a, NULL_TREE); chrec_b = chrec_convert (integer_type_node, chrec_b, NULL_TREE); difference = chrec_fold_minus (integer_type_node, chrec_a, chrec_b); switch (TREE_CODE (difference)) { case INTEGER_CST: if (integer_zerop (difference)) { /* The difference is equal to zero: the accessed index overlaps for each iteration in the loop. */ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node)); *last_conflicts = chrec_dont_know; dependence_stats.num_ziv_dependent++; } else { /* The accesses do not overlap. */ *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_ziv_independent++; } break; default: /* We're not sure whether the indexes overlap. For the moment, conservatively answer "don't know". */ if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "ziv test failed: difference is non-integer.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; dependence_stats.num_ziv_unimplemented++; break; } if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); } /* Sets NIT to the estimated number of executions of the statements in LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as large as the number of iterations. If we have no reliable estimate, the function returns false, otherwise returns true. */ bool estimated_loop_iterations (struct loop *loop, bool conservative, double_int *nit) { estimate_numbers_of_iterations_loop (loop); if (conservative) { if (!loop->any_upper_bound) return false; *nit = loop->nb_iterations_upper_bound; } else { if (!loop->any_estimate) return false; *nit = loop->nb_iterations_estimate; } return true; } /* Similar to estimated_loop_iterations, but returns the estimate only if it fits to HOST_WIDE_INT. If this is not the case, or the estimate on the number of iterations of LOOP could not be derived, returns -1. */ HOST_WIDE_INT estimated_loop_iterations_int (struct loop *loop, bool conservative) { double_int nit; HOST_WIDE_INT hwi_nit; if (!estimated_loop_iterations (loop, conservative, &nit)) return -1; if (!double_int_fits_in_shwi_p (nit)) return -1; hwi_nit = double_int_to_shwi (nit); return hwi_nit < 0 ? -1 : hwi_nit; } /* Similar to estimated_loop_iterations, but returns the estimate as a tree, and only if it fits to the int type. If this is not the case, or the estimate on the number of iterations of LOOP could not be derived, returns chrec_dont_know. */ static tree estimated_loop_iterations_tree (struct loop *loop, bool conservative) { double_int nit; tree type; if (!estimated_loop_iterations (loop, conservative, &nit)) return chrec_dont_know; type = lang_hooks.types.type_for_size (INT_TYPE_SIZE, true); if (!double_int_fits_to_tree_p (type, nit)) return chrec_dont_know; return double_int_to_tree (type, nit); } /* Analyze a SIV (Single Index Variable) subscript where CHREC_A is a constant, and CHREC_B is an affine function. *OVERLAPS_A and *OVERLAPS_B are initialized to the functions that describe the relation between the elements accessed twice by CHREC_A and CHREC_B. For k >= 0, the following property is verified: CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */ static void analyze_siv_subscript_cst_affine (tree chrec_a, tree chrec_b, conflict_function **overlaps_a, conflict_function **overlaps_b, tree *last_conflicts) { bool value0, value1, value2; tree difference, tmp; chrec_a = chrec_convert (integer_type_node, chrec_a, NULL_TREE); chrec_b = chrec_convert (integer_type_node, chrec_b, NULL_TREE); difference = chrec_fold_minus (integer_type_node, initial_condition (chrec_b), chrec_a); if (!chrec_is_positive (initial_condition (difference), &value0)) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "siv test failed: chrec is not positive.\n"); dependence_stats.num_siv_unimplemented++; *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; return; } else { if (value0 == false) { if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value1)) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "siv test failed: chrec not positive.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; dependence_stats.num_siv_unimplemented++; return; } else { if (value1 == true) { /* Example: chrec_a = 12 chrec_b = {10, +, 1} */ if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference)) { HOST_WIDE_INT numiter; struct loop *loop = get_chrec_loop (chrec_b); *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); tmp = fold_build2 (EXACT_DIV_EXPR, integer_type_node, fold_build1 (ABS_EXPR, integer_type_node, difference), CHREC_RIGHT (chrec_b)); *overlaps_b = conflict_fn (1, affine_fn_cst (tmp)); *last_conflicts = integer_one_node; /* Perform weak-zero siv test to see if overlap is outside the loop bounds. */ numiter = estimated_loop_iterations_int (loop, true); if (numiter >= 0 && compare_tree_int (tmp, numiter) > 0) { free_conflict_function (*overlaps_a); free_conflict_function (*overlaps_b); *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_siv_independent++; return; } dependence_stats.num_siv_dependent++; return; } /* When the step does not divide the difference, there are no overlaps. */ else { *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_siv_independent++; return; } } else { /* Example: chrec_a = 12 chrec_b = {10, +, -1} In this case, chrec_a will not overlap with chrec_b. */ *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_siv_independent++; return; } } } else { if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value2)) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "siv test failed: chrec not positive.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; dependence_stats.num_siv_unimplemented++; return; } else { if (value2 == false) { /* Example: chrec_a = 3 chrec_b = {10, +, -1} */ if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference)) { HOST_WIDE_INT numiter; struct loop *loop = get_chrec_loop (chrec_b); *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); tmp = fold_build2 (EXACT_DIV_EXPR, integer_type_node, difference, CHREC_RIGHT (chrec_b)); *overlaps_b = conflict_fn (1, affine_fn_cst (tmp)); *last_conflicts = integer_one_node; /* Perform weak-zero siv test to see if overlap is outside the loop bounds. */ numiter = estimated_loop_iterations_int (loop, true); if (numiter >= 0 && compare_tree_int (tmp, numiter) > 0) { free_conflict_function (*overlaps_a); free_conflict_function (*overlaps_b); *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_siv_independent++; return; } dependence_stats.num_siv_dependent++; return; } /* When the step does not divide the difference, there are no overlaps. */ else { *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_siv_independent++; return; } } else { /* Example: chrec_a = 3 chrec_b = {4, +, 1} In this case, chrec_a will not overlap with chrec_b. */ *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_siv_independent++; return; } } } } } /* Helper recursive function for initializing the matrix A. Returns the initial value of CHREC. */ static int initialize_matrix_A (lambda_matrix A, tree chrec, unsigned index, int mult) { gcc_assert (chrec); if (TREE_CODE (chrec) != POLYNOMIAL_CHREC) return int_cst_value (chrec); A[index][0] = mult * int_cst_value (CHREC_RIGHT (chrec)); return initialize_matrix_A (A, CHREC_LEFT (chrec), index + 1, mult); } #define FLOOR_DIV(x,y) ((x) / (y)) /* Solves the special case of the Diophantine equation: | {0, +, STEP_A}_x (OVERLAPS_A) = {0, +, STEP_B}_y (OVERLAPS_B) Computes the descriptions OVERLAPS_A and OVERLAPS_B. NITER is the number of iterations that loops X and Y run. The overlaps will be constructed as evolutions in dimension DIM. */ static void compute_overlap_steps_for_affine_univar (int niter, int step_a, int step_b, affine_fn *overlaps_a, affine_fn *overlaps_b, tree *last_conflicts, int dim) { if (((step_a > 0 && step_b > 0) || (step_a < 0 && step_b < 0))) { int step_overlaps_a, step_overlaps_b; int gcd_steps_a_b, last_conflict, tau2; gcd_steps_a_b = gcd (step_a, step_b); step_overlaps_a = step_b / gcd_steps_a_b; step_overlaps_b = step_a / gcd_steps_a_b; tau2 = FLOOR_DIV (niter, step_overlaps_a); tau2 = MIN (tau2, FLOOR_DIV (niter, step_overlaps_b)); last_conflict = tau2; *overlaps_a = affine_fn_univar (integer_zero_node, dim, build_int_cst (NULL_TREE, step_overlaps_a)); *overlaps_b = affine_fn_univar (integer_zero_node, dim, build_int_cst (NULL_TREE, step_overlaps_b)); *last_conflicts = build_int_cst (NULL_TREE, last_conflict); } else { *overlaps_a = affine_fn_cst (integer_zero_node); *overlaps_b = affine_fn_cst (integer_zero_node); *last_conflicts = integer_zero_node; } } /* Solves the special case of a Diophantine equation where CHREC_A is an affine bivariate function, and CHREC_B is an affine univariate function. For example, | {{0, +, 1}_x, +, 1335}_y = {0, +, 1336}_z has the following overlapping functions: | x (t, u, v) = {{0, +, 1336}_t, +, 1}_v | y (t, u, v) = {{0, +, 1336}_u, +, 1}_v | z (t, u, v) = {{{0, +, 1}_t, +, 1335}_u, +, 1}_v FORNOW: This is a specialized implementation for a case occurring in a common benchmark. Implement the general algorithm. */ static void compute_overlap_steps_for_affine_1_2 (tree chrec_a, tree chrec_b, conflict_function **overlaps_a, conflict_function **overlaps_b, tree *last_conflicts) { bool xz_p, yz_p, xyz_p; int step_x, step_y, step_z; HOST_WIDE_INT niter_x, niter_y, niter_z, niter; affine_fn overlaps_a_xz, overlaps_b_xz; affine_fn overlaps_a_yz, overlaps_b_yz; affine_fn overlaps_a_xyz, overlaps_b_xyz; affine_fn ova1, ova2, ovb; tree last_conflicts_xz, last_conflicts_yz, last_conflicts_xyz; step_x = int_cst_value (CHREC_RIGHT (CHREC_LEFT (chrec_a))); step_y = int_cst_value (CHREC_RIGHT (chrec_a)); step_z = int_cst_value (CHREC_RIGHT (chrec_b)); niter_x = estimated_loop_iterations_int (get_chrec_loop (CHREC_LEFT (chrec_a)), true); niter_y = estimated_loop_iterations_int (get_chrec_loop (chrec_a), true); niter_z = estimated_loop_iterations_int (get_chrec_loop (chrec_b), true); if (niter_x < 0 || niter_y < 0 || niter_z < 0) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "overlap steps test failed: no iteration counts.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; return; } niter = MIN (niter_x, niter_z); compute_overlap_steps_for_affine_univar (niter, step_x, step_z, &overlaps_a_xz, &overlaps_b_xz, &last_conflicts_xz, 1); niter = MIN (niter_y, niter_z); compute_overlap_steps_for_affine_univar (niter, step_y, step_z, &overlaps_a_yz, &overlaps_b_yz, &last_conflicts_yz, 2); niter = MIN (niter_x, niter_z); niter = MIN (niter_y, niter); compute_overlap_steps_for_affine_univar (niter, step_x + step_y, step_z, &overlaps_a_xyz, &overlaps_b_xyz, &last_conflicts_xyz, 3); xz_p = !integer_zerop (last_conflicts_xz); yz_p = !integer_zerop (last_conflicts_yz); xyz_p = !integer_zerop (last_conflicts_xyz); if (xz_p || yz_p || xyz_p) { ova1 = affine_fn_cst (integer_zero_node); ova2 = affine_fn_cst (integer_zero_node); ovb = affine_fn_cst (integer_zero_node); if (xz_p) { affine_fn t0 = ova1; affine_fn t2 = ovb; ova1 = affine_fn_plus (ova1, overlaps_a_xz); ovb = affine_fn_plus (ovb, overlaps_b_xz); affine_fn_free (t0); affine_fn_free (t2); *last_conflicts = last_conflicts_xz; } if (yz_p) { affine_fn t0 = ova2; affine_fn t2 = ovb; ova2 = affine_fn_plus (ova2, overlaps_a_yz); ovb = affine_fn_plus (ovb, overlaps_b_yz); affine_fn_free (t0); affine_fn_free (t2); *last_conflicts = last_conflicts_yz; } if (xyz_p) { affine_fn t0 = ova1; affine_fn t2 = ova2; affine_fn t4 = ovb; ova1 = affine_fn_plus (ova1, overlaps_a_xyz); ova2 = affine_fn_plus (ova2, overlaps_a_xyz); ovb = affine_fn_plus (ovb, overlaps_b_xyz); affine_fn_free (t0); affine_fn_free (t2); affine_fn_free (t4); *last_conflicts = last_conflicts_xyz; } *overlaps_a = conflict_fn (2, ova1, ova2); *overlaps_b = conflict_fn (1, ovb); } else { *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node)); *last_conflicts = integer_zero_node; } affine_fn_free (overlaps_a_xz); affine_fn_free (overlaps_b_xz); affine_fn_free (overlaps_a_yz); affine_fn_free (overlaps_b_yz); affine_fn_free (overlaps_a_xyz); affine_fn_free (overlaps_b_xyz); } /* Determines the overlapping elements due to accesses CHREC_A and CHREC_B, that are affine functions. This function cannot handle symbolic evolution functions, ie. when initial conditions are parameters, because it uses lambda matrices of integers. */ static void analyze_subscript_affine_affine (tree chrec_a, tree chrec_b, conflict_function **overlaps_a, conflict_function **overlaps_b, tree *last_conflicts) { unsigned nb_vars_a, nb_vars_b, dim; int init_a, init_b, gamma, gcd_alpha_beta; int tau1, tau2; lambda_matrix A, U, S; if (eq_evolutions_p (chrec_a, chrec_b)) { /* The accessed index overlaps for each iteration in the loop. */ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node)); *last_conflicts = chrec_dont_know; return; } if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(analyze_subscript_affine_affine \n"); /* For determining the initial intersection, we have to solve a Diophantine equation. This is the most time consuming part. For answering to the question: "Is there a dependence?" we have to prove that there exists a solution to the Diophantine equation, and that the solution is in the iteration domain, i.e. the solution is positive or zero, and that the solution happens before the upper bound loop.nb_iterations. Otherwise there is no dependence. This function outputs a description of the iterations that hold the intersections. */ nb_vars_a = nb_vars_in_chrec (chrec_a); nb_vars_b = nb_vars_in_chrec (chrec_b); dim = nb_vars_a + nb_vars_b; U = lambda_matrix_new (dim, dim); A = lambda_matrix_new (dim, 1); S = lambda_matrix_new (dim, 1); init_a = initialize_matrix_A (A, chrec_a, 0, 1); init_b = initialize_matrix_A (A, chrec_b, nb_vars_a, -1); gamma = init_b - init_a; /* Don't do all the hard work of solving the Diophantine equation when we already know the solution: for example, | {3, +, 1}_1 | {3, +, 4}_2 | gamma = 3 - 3 = 0. Then the first overlap occurs during the first iterations: | {3, +, 1}_1 ({0, +, 4}_x) = {3, +, 4}_2 ({0, +, 1}_x) */ if (gamma == 0) { if (nb_vars_a == 1 && nb_vars_b == 1) { int step_a, step_b; HOST_WIDE_INT niter, niter_a, niter_b; affine_fn ova, ovb; niter_a = estimated_loop_iterations_int (get_chrec_loop (chrec_a), true); niter_b = estimated_loop_iterations_int (get_chrec_loop (chrec_b), true); if (niter_a < 0 || niter_b < 0) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: missing iteration counts.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; goto end_analyze_subs_aa; } niter = MIN (niter_a, niter_b); step_a = int_cst_value (CHREC_RIGHT (chrec_a)); step_b = int_cst_value (CHREC_RIGHT (chrec_b)); compute_overlap_steps_for_affine_univar (niter, step_a, step_b, &ova, &ovb, last_conflicts, 1); *overlaps_a = conflict_fn (1, ova); *overlaps_b = conflict_fn (1, ovb); } else if (nb_vars_a == 2 && nb_vars_b == 1) compute_overlap_steps_for_affine_1_2 (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts); else if (nb_vars_a == 1 && nb_vars_b == 2) compute_overlap_steps_for_affine_1_2 (chrec_b, chrec_a, overlaps_b, overlaps_a, last_conflicts); else { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: too many variables.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; } goto end_analyze_subs_aa; } /* U.A = S */ lambda_matrix_right_hermite (A, dim, 1, S, U); if (S[0][0] < 0) { S[0][0] *= -1; lambda_matrix_row_negate (U, dim, 0); } gcd_alpha_beta = S[0][0]; /* Something went wrong: for example in {1, +, 0}_5 vs. {0, +, 0}_5, but that is a quite strange case. Instead of ICEing, answer don't know. */ if (gcd_alpha_beta == 0) { *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; goto end_analyze_subs_aa; } /* The classic "gcd-test". */ if (!int_divides_p (gcd_alpha_beta, gamma)) { /* The "gcd-test" has determined that there is no integer solution, i.e. there is no dependence. */ *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; } /* Both access functions are univariate. This includes SIV and MIV cases. */ else if (nb_vars_a == 1 && nb_vars_b == 1) { /* Both functions should have the same evolution sign. */ if (((A[0][0] > 0 && -A[1][0] > 0) || (A[0][0] < 0 && -A[1][0] < 0))) { /* The solutions are given by: | | [GAMMA/GCD_ALPHA_BETA t].[u11 u12] = [x0] | [u21 u22] [y0] For a given integer t. Using the following variables, | i0 = u11 * gamma / gcd_alpha_beta | j0 = u12 * gamma / gcd_alpha_beta | i1 = u21 | j1 = u22 the solutions are: | x0 = i0 + i1 * t, | y0 = j0 + j1 * t. */ int i0, j0, i1, j1; /* X0 and Y0 are the first iterations for which there is a dependence. X0, Y0 are two solutions of the Diophantine equation: chrec_a (X0) = chrec_b (Y0). */ int x0, y0; int niter, niter_a, niter_b; niter_a = estimated_loop_iterations_int (get_chrec_loop (chrec_a), true); niter_b = estimated_loop_iterations_int (get_chrec_loop (chrec_b), true); if (niter_a < 0 || niter_b < 0) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: missing iteration counts.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; goto end_analyze_subs_aa; } niter = MIN (niter_a, niter_b); i0 = U[0][0] * gamma / gcd_alpha_beta; j0 = U[0][1] * gamma / gcd_alpha_beta; i1 = U[1][0]; j1 = U[1][1]; if ((i1 == 0 && i0 < 0) || (j1 == 0 && j0 < 0)) { /* There is no solution. FIXME: The case "i0 > nb_iterations, j0 > nb_iterations" falls in here, but for the moment we don't look at the upper bound of the iteration domain. */ *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; } else { if (i1 > 0) { tau1 = CEIL (-i0, i1); tau2 = FLOOR_DIV (niter - i0, i1); if (j1 > 0) { int last_conflict, min_multiple; tau1 = MAX (tau1, CEIL (-j0, j1)); tau2 = MIN (tau2, FLOOR_DIV (niter - j0, j1)); x0 = i1 * tau1 + i0; y0 = j1 * tau1 + j0; /* At this point (x0, y0) is one of the solutions to the Diophantine equation. The next step has to compute the smallest positive solution: the first conflicts. */ min_multiple = MIN (x0 / i1, y0 / j1); x0 -= i1 * min_multiple; y0 -= j1 * min_multiple; tau1 = (x0 - i0)/i1; last_conflict = tau2 - tau1; /* If the overlap occurs outside of the bounds of the loop, there is no dependence. */ if (x0 > niter || y0 > niter) { *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; } else { *overlaps_a = conflict_fn (1, affine_fn_univar (build_int_cst (NULL_TREE, x0), 1, build_int_cst (NULL_TREE, i1))); *overlaps_b = conflict_fn (1, affine_fn_univar (build_int_cst (NULL_TREE, y0), 1, build_int_cst (NULL_TREE, j1))); *last_conflicts = build_int_cst (NULL_TREE, last_conflict); } } else { /* FIXME: For the moment, the upper bound of the iteration domain for j is not checked. */ if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: unimplemented.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; } } else { /* FIXME: For the moment, the upper bound of the iteration domain for i is not checked. */ if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: unimplemented.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; } } } else { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: unimplemented.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; } } else { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "affine-affine test failed: unimplemented.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; } end_analyze_subs_aa: if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, " (overlaps_a = "); dump_conflict_function (dump_file, *overlaps_a); fprintf (dump_file, ")\n (overlaps_b = "); dump_conflict_function (dump_file, *overlaps_b); fprintf (dump_file, ")\n"); fprintf (dump_file, ")\n"); } } /* Returns true when analyze_subscript_affine_affine can be used for determining the dependence relation between chrec_a and chrec_b, that contain symbols. This function modifies chrec_a and chrec_b such that the analysis result is the same, and such that they don't contain symbols, and then can safely be passed to the analyzer. Example: The analysis of the following tuples of evolutions produce the same results: {x+1, +, 1}_1 vs. {x+3, +, 1}_1, and {-2, +, 1}_1 vs. {0, +, 1}_1 {x+1, +, 1}_1 ({2, +, 1}_1) = {x+3, +, 1}_1 ({0, +, 1}_1) {-2, +, 1}_1 ({2, +, 1}_1) = {0, +, 1}_1 ({0, +, 1}_1) */ static bool can_use_analyze_subscript_affine_affine (tree *chrec_a, tree *chrec_b) { tree diff, type, left_a, left_b, right_b; if (chrec_contains_symbols (CHREC_RIGHT (*chrec_a)) || chrec_contains_symbols (CHREC_RIGHT (*chrec_b))) /* FIXME: For the moment not handled. Might be refined later. */ return false; type = chrec_type (*chrec_a); left_a = CHREC_LEFT (*chrec_a); left_b = chrec_convert (type, CHREC_LEFT (*chrec_b), NULL_TREE); diff = chrec_fold_minus (type, left_a, left_b); if (!evolution_function_is_constant_p (diff)) return false; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "can_use_subscript_aff_aff_for_symbolic \n"); *chrec_a = build_polynomial_chrec (CHREC_VARIABLE (*chrec_a), diff, CHREC_RIGHT (*chrec_a)); right_b = chrec_convert (type, CHREC_RIGHT (*chrec_b), NULL_TREE); *chrec_b = build_polynomial_chrec (CHREC_VARIABLE (*chrec_b), build_int_cst (type, 0), right_b); return true; } /* Analyze a SIV (Single Index Variable) subscript. *OVERLAPS_A and *OVERLAPS_B are initialized to the functions that describe the relation between the elements accessed twice by CHREC_A and CHREC_B. For k >= 0, the following property is verified: CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */ static void analyze_siv_subscript (tree chrec_a, tree chrec_b, conflict_function **overlaps_a, conflict_function **overlaps_b, tree *last_conflicts) { dependence_stats.num_siv++; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(analyze_siv_subscript \n"); if (evolution_function_is_constant_p (chrec_a) && evolution_function_is_affine_p (chrec_b)) analyze_siv_subscript_cst_affine (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts); else if (evolution_function_is_affine_p (chrec_a) && evolution_function_is_constant_p (chrec_b)) analyze_siv_subscript_cst_affine (chrec_b, chrec_a, overlaps_b, overlaps_a, last_conflicts); else if (evolution_function_is_affine_p (chrec_a) && evolution_function_is_affine_p (chrec_b)) { if (!chrec_contains_symbols (chrec_a) && !chrec_contains_symbols (chrec_b)) { analyze_subscript_affine_affine (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts); if (CF_NOT_KNOWN_P (*overlaps_a) || CF_NOT_KNOWN_P (*overlaps_b)) dependence_stats.num_siv_unimplemented++; else if (CF_NO_DEPENDENCE_P (*overlaps_a) || CF_NO_DEPENDENCE_P (*overlaps_b)) dependence_stats.num_siv_independent++; else dependence_stats.num_siv_dependent++; } else if (can_use_analyze_subscript_affine_affine (&chrec_a, &chrec_b)) { analyze_subscript_affine_affine (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts); /* FIXME: The number of iterations is a symbolic expression. Compute it properly. */ *last_conflicts = chrec_dont_know; if (CF_NOT_KNOWN_P (*overlaps_a) || CF_NOT_KNOWN_P (*overlaps_b)) dependence_stats.num_siv_unimplemented++; else if (CF_NO_DEPENDENCE_P (*overlaps_a) || CF_NO_DEPENDENCE_P (*overlaps_b)) dependence_stats.num_siv_independent++; else dependence_stats.num_siv_dependent++; } else goto siv_subscript_dontknow; } else { siv_subscript_dontknow:; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "siv test failed: unimplemented.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; dependence_stats.num_siv_unimplemented++; } if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); } /* Returns false if we can prove that the greatest common divisor of the steps of CHREC does not divide CST, false otherwise. */ static bool gcd_of_steps_may_divide_p (tree chrec, tree cst) { HOST_WIDE_INT cd = 0, val; tree step; if (!host_integerp (cst, 0)) return true; val = tree_low_cst (cst, 0); while (TREE_CODE (chrec) == POLYNOMIAL_CHREC) { step = CHREC_RIGHT (chrec); if (!host_integerp (step, 0)) return true; cd = gcd (cd, tree_low_cst (step, 0)); chrec = CHREC_LEFT (chrec); } return val % cd == 0; } /* Analyze a MIV (Multiple Index Variable) subscript. *OVERLAPS_A and *OVERLAPS_B are initialized to the functions that describe the relation between the elements accessed twice by CHREC_A and CHREC_B. For k >= 0, the following property is verified: CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */ static void analyze_miv_subscript (tree chrec_a, tree chrec_b, conflict_function **overlaps_a, conflict_function **overlaps_b, tree *last_conflicts) { /* FIXME: This is a MIV subscript, not yet handled. Example: (A[{1, +, 1}_1] vs. A[{1, +, 1}_2]) that comes from (A[i] vs. A[j]). In the SIV test we had to solve a Diophantine equation with two variables. In the MIV case we have to solve a Diophantine equation with 2*n variables (if the subscript uses n IVs). */ tree difference; dependence_stats.num_miv++; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(analyze_miv_subscript \n"); chrec_a = chrec_convert (integer_type_node, chrec_a, NULL_TREE); chrec_b = chrec_convert (integer_type_node, chrec_b, NULL_TREE); difference = chrec_fold_minus (integer_type_node, chrec_a, chrec_b); if (eq_evolutions_p (chrec_a, chrec_b)) { /* Access functions are the same: all the elements are accessed in the same order. */ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node)); *last_conflicts = estimated_loop_iterations_tree (get_chrec_loop (chrec_a), true); dependence_stats.num_miv_dependent++; } else if (evolution_function_is_constant_p (difference) /* For the moment, the following is verified: evolution_function_is_affine_multivariate_p (chrec_a) */ && !gcd_of_steps_may_divide_p (chrec_a, difference)) { /* testsuite/.../ssa-chrec-33.c {{21, +, 2}_1, +, -2}_2 vs. {{20, +, 2}_1, +, -2}_2 The difference is 1, and all the evolution steps are multiples of 2, consequently there are no overlapping elements. */ *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; dependence_stats.num_miv_independent++; } else if (evolution_function_is_affine_multivariate_p (chrec_a) && !chrec_contains_symbols (chrec_a) && evolution_function_is_affine_multivariate_p (chrec_b) && !chrec_contains_symbols (chrec_b)) { /* testsuite/.../ssa-chrec-35.c {0, +, 1}_2 vs. {0, +, 1}_3 the overlapping elements are respectively located at iterations: {0, +, 1}_x and {0, +, 1}_x, in other words, we have the equality: {0, +, 1}_2 ({0, +, 1}_x) = {0, +, 1}_3 ({0, +, 1}_x) Other examples: {{0, +, 1}_1, +, 2}_2 ({0, +, 1}_x, {0, +, 1}_y) = {0, +, 1}_1 ({{0, +, 1}_x, +, 2}_y) {{0, +, 2}_1, +, 3}_2 ({0, +, 1}_y, {0, +, 1}_x) = {{0, +, 3}_1, +, 2}_2 ({0, +, 1}_x, {0, +, 1}_y) */ analyze_subscript_affine_affine (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts); if (CF_NOT_KNOWN_P (*overlaps_a) || CF_NOT_KNOWN_P (*overlaps_b)) dependence_stats.num_miv_unimplemented++; else if (CF_NO_DEPENDENCE_P (*overlaps_a) || CF_NO_DEPENDENCE_P (*overlaps_b)) dependence_stats.num_miv_independent++; else dependence_stats.num_miv_dependent++; } else { /* When the analysis is too difficult, answer "don't know". */ if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "analyze_miv_subscript test failed: unimplemented.\n"); *overlaps_a = conflict_fn_not_known (); *overlaps_b = conflict_fn_not_known (); *last_conflicts = chrec_dont_know; dependence_stats.num_miv_unimplemented++; } if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); } /* Determines the iterations for which CHREC_A is equal to CHREC_B. OVERLAP_ITERATIONS_A and OVERLAP_ITERATIONS_B are initialized with two functions that describe the iterations that contain conflicting elements. Remark: For an integer k >= 0, the following equality is true: CHREC_A (OVERLAP_ITERATIONS_A (k)) == CHREC_B (OVERLAP_ITERATIONS_B (k)). */ static void analyze_overlapping_iterations (tree chrec_a, tree chrec_b, conflict_function **overlap_iterations_a, conflict_function **overlap_iterations_b, tree *last_conflicts) { dependence_stats.num_subscript_tests++; if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "(analyze_overlapping_iterations \n"); fprintf (dump_file, " (chrec_a = "); print_generic_expr (dump_file, chrec_a, 0); fprintf (dump_file, ")\n (chrec_b = "); print_generic_expr (dump_file, chrec_b, 0); fprintf (dump_file, ")\n"); } if (chrec_a == NULL_TREE || chrec_b == NULL_TREE || chrec_contains_undetermined (chrec_a) || chrec_contains_undetermined (chrec_b)) { dependence_stats.num_subscript_undetermined++; *overlap_iterations_a = conflict_fn_not_known (); *overlap_iterations_b = conflict_fn_not_known (); } /* If they are the same chrec, and are affine, they overlap on every iteration. */ else if (eq_evolutions_p (chrec_a, chrec_b) && evolution_function_is_affine_multivariate_p (chrec_a)) { dependence_stats.num_same_subscript_function++; *overlap_iterations_a = conflict_fn (1, affine_fn_cst (integer_zero_node)); *overlap_iterations_b = conflict_fn (1, affine_fn_cst (integer_zero_node)); *last_conflicts = chrec_dont_know; } /* If they aren't the same, and aren't affine, we can't do anything yet. */ else if ((chrec_contains_symbols (chrec_a) || chrec_contains_symbols (chrec_b)) && (!evolution_function_is_affine_multivariate_p (chrec_a) || !evolution_function_is_affine_multivariate_p (chrec_b))) { dependence_stats.num_subscript_undetermined++; *overlap_iterations_a = conflict_fn_not_known (); *overlap_iterations_b = conflict_fn_not_known (); } else if (ziv_subscript_p (chrec_a, chrec_b)) analyze_ziv_subscript (chrec_a, chrec_b, overlap_iterations_a, overlap_iterations_b, last_conflicts); else if (siv_subscript_p (chrec_a, chrec_b)) analyze_siv_subscript (chrec_a, chrec_b, overlap_iterations_a, overlap_iterations_b, last_conflicts); else analyze_miv_subscript (chrec_a, chrec_b, overlap_iterations_a, overlap_iterations_b, last_conflicts); if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, " (overlap_iterations_a = "); dump_conflict_function (dump_file, *overlap_iterations_a); fprintf (dump_file, ")\n (overlap_iterations_b = "); dump_conflict_function (dump_file, *overlap_iterations_b); fprintf (dump_file, ")\n"); fprintf (dump_file, ")\n"); } } /* Helper function for uniquely inserting distance vectors. */ static void save_dist_v (struct data_dependence_relation *ddr, lambda_vector dist_v) { unsigned i; lambda_vector v; for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, v); i++) if (lambda_vector_equal (v, dist_v, DDR_NB_LOOPS (ddr))) return; VEC_safe_push (lambda_vector, heap, DDR_DIST_VECTS (ddr), dist_v); } /* Helper function for uniquely inserting direction vectors. */ static void save_dir_v (struct data_dependence_relation *ddr, lambda_vector dir_v) { unsigned i; lambda_vector v; for (i = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), i, v); i++) if (lambda_vector_equal (v, dir_v, DDR_NB_LOOPS (ddr))) return; VEC_safe_push (lambda_vector, heap, DDR_DIR_VECTS (ddr), dir_v); } /* Add a distance of 1 on all the loops outer than INDEX. If we haven't yet determined a distance for this outer loop, push a new distance vector composed of the previous distance, and a distance of 1 for this outer loop. Example: | loop_1 | loop_2 | A[10] | endloop_2 | endloop_1 Saved vectors are of the form (dist_in_1, dist_in_2). First, we save (0, 1), then we have to save (1, 0). */ static void add_outer_distances (struct data_dependence_relation *ddr, lambda_vector dist_v, int index) { /* For each outer loop where init_v is not set, the accesses are in dependence of distance 1 in the loop. */ while (--index >= 0) { lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr)); save_v[index] = 1; save_dist_v (ddr, save_v); } } /* Return false when fail to represent the data dependence as a distance vector. INIT_B is set to true when a component has been added to the distance vector DIST_V. INDEX_CARRY is then set to the index in DIST_V that carries the dependence. */ static bool build_classic_dist_vector_1 (struct data_dependence_relation *ddr, struct data_reference *ddr_a, struct data_reference *ddr_b, lambda_vector dist_v, bool *init_b, int *index_carry) { unsigned i; lambda_vector init_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) { tree access_fn_a, access_fn_b; struct subscript *subscript = DDR_SUBSCRIPT (ddr, i); if (chrec_contains_undetermined (SUB_DISTANCE (subscript))) { non_affine_dependence_relation (ddr); return false; } access_fn_a = DR_ACCESS_FN (ddr_a, i); access_fn_b = DR_ACCESS_FN (ddr_b, i); if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC) { int dist, index; int index_a = index_in_loop_nest (CHREC_VARIABLE (access_fn_a), DDR_LOOP_NEST (ddr)); int index_b = index_in_loop_nest (CHREC_VARIABLE (access_fn_b), DDR_LOOP_NEST (ddr)); /* The dependence is carried by the outermost loop. Example: | loop_1 | A[{4, +, 1}_1] | loop_2 | A[{5, +, 1}_2] | endloop_2 | endloop_1 In this case, the dependence is carried by loop_1. */ index = index_a < index_b ? index_a : index_b; *index_carry = MIN (index, *index_carry); if (chrec_contains_undetermined (SUB_DISTANCE (subscript))) { non_affine_dependence_relation (ddr); return false; } dist = int_cst_value (SUB_DISTANCE (subscript)); /* This is the subscript coupling test. If we have already recorded a distance for this loop (a distance coming from another subscript), it should be the same. For example, in the following code, there is no dependence: | loop i = 0, N, 1 | T[i+1][i] = ... | ... = T[i][i] | endloop */ if (init_v[index] != 0 && dist_v[index] != dist) { finalize_ddr_dependent (ddr, chrec_known); return false; } dist_v[index] = dist; init_v[index] = 1; *init_b = true; } else { /* This can be for example an affine vs. constant dependence (T[i] vs. T[3]) that is not an affine dependence and is not representable as a distance vector. */ non_affine_dependence_relation (ddr); return false; } } return true; } /* Return true when the DDR contains two data references that have the same access functions. */ static bool same_access_functions (struct data_dependence_relation *ddr) { unsigned i; for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) if (!eq_evolutions_p (DR_ACCESS_FN (DDR_A (ddr), i), DR_ACCESS_FN (DDR_B (ddr), i))) return false; return true; } /* Return true when the DDR contains only constant access functions. */ static bool constant_access_functions (struct data_dependence_relation *ddr) { unsigned i; for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) if (!evolution_function_is_constant_p (DR_ACCESS_FN (DDR_A (ddr), i)) || !evolution_function_is_constant_p (DR_ACCESS_FN (DDR_B (ddr), i))) return false; return true; } /* Helper function for the case where DDR_A and DDR_B are the same multivariate access function. */ static void add_multivariate_self_dist (struct data_dependence_relation *ddr, tree c_2) { int x_1, x_2; tree c_1 = CHREC_LEFT (c_2); tree c_0 = CHREC_LEFT (c_1); lambda_vector dist_v; int v1, v2, cd; /* Polynomials with more than 2 variables are not handled yet. */ if (TREE_CODE (c_0) != INTEGER_CST) { DDR_ARE_DEPENDENT (ddr) = chrec_dont_know; return; } x_2 = index_in_loop_nest (CHREC_VARIABLE (c_2), DDR_LOOP_NEST (ddr)); x_1 = index_in_loop_nest (CHREC_VARIABLE (c_1), DDR_LOOP_NEST (ddr)); /* For "{{0, +, 2}_1, +, 3}_2" the distance vector is (3, -2). */ dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); v1 = int_cst_value (CHREC_RIGHT (c_1)); v2 = int_cst_value (CHREC_RIGHT (c_2)); cd = gcd (v1, v2); v1 /= cd; v2 /= cd; if (v2 < 0) { v2 = -v2; v1 = -v1; } dist_v[x_1] = v2; dist_v[x_2] = -v1; save_dist_v (ddr, dist_v); add_outer_distances (ddr, dist_v, x_1); } /* Helper function for the case where DDR_A and DDR_B are the same access functions. */ static void add_other_self_distances (struct data_dependence_relation *ddr) { lambda_vector dist_v; unsigned i; int index_carry = DDR_NB_LOOPS (ddr); for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) { tree access_fun = DR_ACCESS_FN (DDR_A (ddr), i); if (TREE_CODE (access_fun) == POLYNOMIAL_CHREC) { if (!evolution_function_is_univariate_p (access_fun)) { if (DDR_NUM_SUBSCRIPTS (ddr) != 1) { DDR_ARE_DEPENDENT (ddr) = chrec_dont_know; return; } add_multivariate_self_dist (ddr, DR_ACCESS_FN (DDR_A (ddr), 0)); return; } index_carry = MIN (index_carry, index_in_loop_nest (CHREC_VARIABLE (access_fun), DDR_LOOP_NEST (ddr))); } } dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); add_outer_distances (ddr, dist_v, index_carry); } static void insert_innermost_unit_dist_vector (struct data_dependence_relation *ddr) { lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); dist_v[DDR_INNER_LOOP (ddr)] = 1; save_dist_v (ddr, dist_v); } /* Adds a unit distance vector to DDR when there is a 0 overlap. This is the case for example when access functions are the same and equal to a constant, as in: | loop_1 | A[3] = ... | ... = A[3] | endloop_1 in which case the distance vectors are (0) and (1). */ static void add_distance_for_zero_overlaps (struct data_dependence_relation *ddr) { unsigned i, j; for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) { subscript_p sub = DDR_SUBSCRIPT (ddr, i); conflict_function *ca = SUB_CONFLICTS_IN_A (sub); conflict_function *cb = SUB_CONFLICTS_IN_B (sub); for (j = 0; j < ca->n; j++) if (affine_function_zero_p (ca->fns[j])) { insert_innermost_unit_dist_vector (ddr); return; } for (j = 0; j < cb->n; j++) if (affine_function_zero_p (cb->fns[j])) { insert_innermost_unit_dist_vector (ddr); return; } } } /* Compute the classic per loop distance vector. DDR is the data dependence relation to build a vector from. Return false when fail to represent the data dependence as a distance vector. */ static bool build_classic_dist_vector (struct data_dependence_relation *ddr) { bool init_b = false; int index_carry = DDR_NB_LOOPS (ddr); lambda_vector dist_v; if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE) return true; if (same_access_functions (ddr)) { /* Save the 0 vector. */ dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); save_dist_v (ddr, dist_v); if (constant_access_functions (ddr)) add_distance_for_zero_overlaps (ddr); if (DDR_NB_LOOPS (ddr) > 1) add_other_self_distances (ddr); return true; } dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); if (!build_classic_dist_vector_1 (ddr, DDR_A (ddr), DDR_B (ddr), dist_v, &init_b, &index_carry)) return false; /* Save the distance vector if we initialized one. */ if (init_b) { /* Verify a basic constraint: classic distance vectors should always be lexicographically positive. Data references are collected in the order of execution of the program, thus for the following loop | for (i = 1; i < 100; i++) | for (j = 1; j < 100; j++) | { | t = T[j+1][i-1]; // A | T[j][i] = t + 2; // B | } references are collected following the direction of the wind: A then B. The data dependence tests are performed also following this order, such that we're looking at the distance separating the elements accessed by A from the elements later accessed by B. But in this example, the distance returned by test_dep (A, B) is lexicographically negative (-1, 1), that means that the access A occurs later than B with respect to the outer loop, ie. we're actually looking upwind. In this case we solve test_dep (B, A) looking downwind to the lexicographically positive solution, that returns the distance vector (1, -1). */ if (!lambda_vector_lexico_pos (dist_v, DDR_NB_LOOPS (ddr))) { lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); subscript_dependence_tester_1 (ddr, DDR_B (ddr), DDR_A (ddr)); compute_subscript_distance (ddr); build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr), save_v, &init_b, &index_carry); save_dist_v (ddr, save_v); /* In this case there is a dependence forward for all the outer loops: | for (k = 1; k < 100; k++) | for (i = 1; i < 100; i++) | for (j = 1; j < 100; j++) | { | t = T[j+1][i-1]; // A | T[j][i] = t + 2; // B | } the vectors are: (0, 1, -1) (1, 1, -1) (1, -1, 1) */ if (DDR_NB_LOOPS (ddr) > 1) { add_outer_distances (ddr, save_v, index_carry); add_outer_distances (ddr, dist_v, index_carry); } } else { lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr)); save_dist_v (ddr, save_v); if (DDR_NB_LOOPS (ddr) > 1) { lambda_vector opposite_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); subscript_dependence_tester_1 (ddr, DDR_B (ddr), DDR_A (ddr)); compute_subscript_distance (ddr); build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr), opposite_v, &init_b, &index_carry); add_outer_distances (ddr, dist_v, index_carry); add_outer_distances (ddr, opposite_v, index_carry); } } } else { /* There is a distance of 1 on all the outer loops: Example: there is a dependence of distance 1 on loop_1 for the array A. | loop_1 | A[5] = ... | endloop */ add_outer_distances (ddr, dist_v, lambda_vector_first_nz (dist_v, DDR_NB_LOOPS (ddr), 0)); } if (dump_file && (dump_flags & TDF_DETAILS)) { unsigned i; fprintf (dump_file, "(build_classic_dist_vector\n"); for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++) { fprintf (dump_file, " dist_vector = ("); print_lambda_vector (dump_file, DDR_DIST_VECT (ddr, i), DDR_NB_LOOPS (ddr)); fprintf (dump_file, " )\n"); } fprintf (dump_file, ")\n"); } return true; } /* Return the direction for a given distance. FIXME: Computing dir this way is suboptimal, since dir can catch cases that dist is unable to represent. */ static inline enum data_dependence_direction dir_from_dist (int dist) { if (dist > 0) return dir_positive; else if (dist < 0) return dir_negative; else return dir_equal; } /* Compute the classic per loop direction vector. DDR is the data dependence relation to build a vector from. */ static void build_classic_dir_vector (struct data_dependence_relation *ddr) { unsigned i, j; lambda_vector dist_v; for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, dist_v); i++) { lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); for (j = 0; j < DDR_NB_LOOPS (ddr); j++) dir_v[j] = dir_from_dist (dist_v[j]); save_dir_v (ddr, dir_v); } } /* Helper function. Returns true when there is a dependence between data references DRA and DRB. */ static bool subscript_dependence_tester_1 (struct data_dependence_relation *ddr, struct data_reference *dra, struct data_reference *drb) { unsigned int i; tree last_conflicts; struct subscript *subscript; for (i = 0; VEC_iterate (subscript_p, DDR_SUBSCRIPTS (ddr), i, subscript); i++) { conflict_function *overlaps_a, *overlaps_b; analyze_overlapping_iterations (DR_ACCESS_FN (dra, i), DR_ACCESS_FN (drb, i), &overlaps_a, &overlaps_b, &last_conflicts); if (CF_NOT_KNOWN_P (overlaps_a) || CF_NOT_KNOWN_P (overlaps_b)) { finalize_ddr_dependent (ddr, chrec_dont_know); dependence_stats.num_dependence_undetermined++; free_conflict_function (overlaps_a); free_conflict_function (overlaps_b); return false; } else if (CF_NO_DEPENDENCE_P (overlaps_a) || CF_NO_DEPENDENCE_P (overlaps_b)) { finalize_ddr_dependent (ddr, chrec_known); dependence_stats.num_dependence_independent++; free_conflict_function (overlaps_a); free_conflict_function (overlaps_b); return false; } else { SUB_CONFLICTS_IN_A (subscript) = overlaps_a; SUB_CONFLICTS_IN_B (subscript) = overlaps_b; SUB_LAST_CONFLICT (subscript) = last_conflicts; } } return true; } /* Computes the conflicting iterations, and initialize DDR. */ static void subscript_dependence_tester (struct data_dependence_relation *ddr) { if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(subscript_dependence_tester \n"); if (subscript_dependence_tester_1 (ddr, DDR_A (ddr), DDR_B (ddr))) dependence_stats.num_dependence_dependent++; compute_subscript_distance (ddr); if (build_classic_dist_vector (ddr)) build_classic_dir_vector (ddr); if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); } /* Returns true when all the access functions of A are affine or constant. */ static bool access_functions_are_affine_or_constant_p (struct data_reference *a) { unsigned int i; VEC(tree,heap) *fns = DR_ACCESS_FNS (a); tree t; for (i = 0; VEC_iterate (tree, fns, i, t); i++) if (!evolution_function_is_constant_p (t) && !evolution_function_is_affine_multivariate_p (t)) return false; return true; } /* Initializes an equation for an OMEGA problem using the information contained in the ACCESS_FUN. Returns true when the operation succeeded. PB is the omega constraint system. EQ is the number of the equation to be initialized. OFFSET is used for shifting the variables names in the constraints: a constrain is composed of 2 * the number of variables surrounding dependence accesses. OFFSET is set either to 0 for the first n variables, then it is set to n. ACCESS_FUN is expected to be an affine chrec. */ static bool init_omega_eq_with_af (omega_pb pb, unsigned eq, unsigned int offset, tree access_fun, struct data_dependence_relation *ddr) { switch (TREE_CODE (access_fun)) { case POLYNOMIAL_CHREC: { tree left = CHREC_LEFT (access_fun); tree right = CHREC_RIGHT (access_fun); int var = CHREC_VARIABLE (access_fun); unsigned var_idx; if (TREE_CODE (right) != INTEGER_CST) return false; var_idx = index_in_loop_nest (var, DDR_LOOP_NEST (ddr)); pb->eqs[eq].coef[offset + var_idx + 1] = int_cst_value (right); /* Compute the innermost loop index. */ DDR_INNER_LOOP (ddr) = MAX (DDR_INNER_LOOP (ddr), var_idx); if (offset == 0) pb->eqs[eq].coef[var_idx + DDR_NB_LOOPS (ddr) + 1] += int_cst_value (right); switch (TREE_CODE (left)) { case POLYNOMIAL_CHREC: return init_omega_eq_with_af (pb, eq, offset, left, ddr); case INTEGER_CST: pb->eqs[eq].coef[0] += int_cst_value (left); return true; default: return false; } } case INTEGER_CST: pb->eqs[eq].coef[0] += int_cst_value (access_fun); return true; default: return false; } } /* As explained in the comments preceding init_omega_for_ddr, we have to set up a system for each loop level, setting outer loops variation to zero, and current loop variation to positive or zero. Save each lexico positive distance vector. */ static void omega_extract_distance_vectors (omega_pb pb, struct data_dependence_relation *ddr) { int eq, geq; unsigned i, j; struct loop *loopi, *loopj; enum omega_result res; /* Set a new problem for each loop in the nest. The basis is the problem that we have initialized until now. On top of this we add new constraints. */ for (i = 0; i <= DDR_INNER_LOOP (ddr) && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++) { int dist = 0; omega_pb copy = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); omega_copy_problem (copy, pb); /* For all the outer loops "loop_j", add "dj = 0". */ for (j = 0; j < i && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), j, loopj); j++) { eq = omega_add_zero_eq (copy, omega_black); copy->eqs[eq].coef[j + 1] = 1; } /* For "loop_i", add "0 <= di". */ geq = omega_add_zero_geq (copy, omega_black); copy->geqs[geq].coef[i + 1] = 1; /* Reduce the constraint system, and test that the current problem is feasible. */ res = omega_simplify_problem (copy); if (res == omega_false || res == omega_unknown || copy->num_geqs > (int) DDR_NB_LOOPS (ddr)) goto next_problem; for (eq = 0; eq < copy->num_subs; eq++) if (copy->subs[eq].key == (int) i + 1) { dist = copy->subs[eq].coef[0]; goto found_dist; } if (dist == 0) { /* Reinitialize problem... */ omega_copy_problem (copy, pb); for (j = 0; j < i && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), j, loopj); j++) { eq = omega_add_zero_eq (copy, omega_black); copy->eqs[eq].coef[j + 1] = 1; } /* ..., but this time "di = 1". */ eq = omega_add_zero_eq (copy, omega_black); copy->eqs[eq].coef[i + 1] = 1; copy->eqs[eq].coef[0] = -1; res = omega_simplify_problem (copy); if (res == omega_false || res == omega_unknown || copy->num_geqs > (int) DDR_NB_LOOPS (ddr)) goto next_problem; for (eq = 0; eq < copy->num_subs; eq++) if (copy->subs[eq].key == (int) i + 1) { dist = copy->subs[eq].coef[0]; goto found_dist; } } found_dist:; /* Save the lexicographically positive distance vector. */ if (dist >= 0) { lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); dist_v[i] = dist; for (eq = 0; eq < copy->num_subs; eq++) if (copy->subs[eq].key > 0) { dist = copy->subs[eq].coef[0]; dist_v[copy->subs[eq].key - 1] = dist; } for (j = 0; j < DDR_NB_LOOPS (ddr); j++) dir_v[j] = dir_from_dist (dist_v[j]); save_dist_v (ddr, dist_v); save_dir_v (ddr, dir_v); } next_problem:; omega_free_problem (copy); } } /* This is called for each subscript of a tuple of data references: insert an equality for representing the conflicts. */ static bool omega_setup_subscript (tree access_fun_a, tree access_fun_b, struct data_dependence_relation *ddr, omega_pb pb, bool *maybe_dependent) { int eq; tree fun_a = chrec_convert (integer_type_node, access_fun_a, NULL_TREE); tree fun_b = chrec_convert (integer_type_node, access_fun_b, NULL_TREE); tree difference = chrec_fold_minus (integer_type_node, fun_a, fun_b); /* When the fun_a - fun_b is not constant, the dependence is not captured by the classic distance vector representation. */ if (TREE_CODE (difference) != INTEGER_CST) return false; /* ZIV test. */ if (ziv_subscript_p (fun_a, fun_b) && !integer_zerop (difference)) { /* There is no dependence. */ *maybe_dependent = false; return true; } fun_b = chrec_fold_multiply (integer_type_node, fun_b, integer_minus_one_node); eq = omega_add_zero_eq (pb, omega_black); if (!init_omega_eq_with_af (pb, eq, DDR_NB_LOOPS (ddr), fun_a, ddr) || !init_omega_eq_with_af (pb, eq, 0, fun_b, ddr)) /* There is probably a dependence, but the system of constraints cannot be built: answer "don't know". */ return false; /* GCD test. */ if (DDR_NB_LOOPS (ddr) != 0 && pb->eqs[eq].coef[0] && !int_divides_p (lambda_vector_gcd ((lambda_vector) &(pb->eqs[eq].coef[1]), 2 * DDR_NB_LOOPS (ddr)), pb->eqs[eq].coef[0])) { /* There is no dependence. */ *maybe_dependent = false; return true; } return true; } /* Helper function, same as init_omega_for_ddr but specialized for data references A and B. */ static bool init_omega_for_ddr_1 (struct data_reference *dra, struct data_reference *drb, struct data_dependence_relation *ddr, omega_pb pb, bool *maybe_dependent) { unsigned i; int ineq; struct loop *loopi; unsigned nb_loops = DDR_NB_LOOPS (ddr); /* Insert an equality per subscript. */ for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) { if (!omega_setup_subscript (DR_ACCESS_FN (dra, i), DR_ACCESS_FN (drb, i), ddr, pb, maybe_dependent)) return false; else if (*maybe_dependent == false) { /* There is no dependence. */ DDR_ARE_DEPENDENT (ddr) = chrec_known; return true; } } /* Insert inequalities: constraints corresponding to the iteration domain, i.e. the loops surrounding the references "loop_x" and the distance variables "dx". The layout of the OMEGA representation is as follows: - coef[0] is the constant - coef[1..nb_loops] are the protected variables that will not be removed by the solver: the "dx" - coef[nb_loops + 1, 2*nb_loops] are the loop variables: "loop_x". */ for (i = 0; i <= DDR_INNER_LOOP (ddr) && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++) { HOST_WIDE_INT nbi = estimated_loop_iterations_int (loopi, true); /* 0 <= loop_x */ ineq = omega_add_zero_geq (pb, omega_black); pb->geqs[ineq].coef[i + nb_loops + 1] = 1; /* 0 <= loop_x + dx */ ineq = omega_add_zero_geq (pb, omega_black); pb->geqs[ineq].coef[i + nb_loops + 1] = 1; pb->geqs[ineq].coef[i + 1] = 1; if (nbi != -1) { /* loop_x <= nb_iters */ ineq = omega_add_zero_geq (pb, omega_black); pb->geqs[ineq].coef[i + nb_loops + 1] = -1; pb->geqs[ineq].coef[0] = nbi; /* loop_x + dx <= nb_iters */ ineq = omega_add_zero_geq (pb, omega_black); pb->geqs[ineq].coef[i + nb_loops + 1] = -1; pb->geqs[ineq].coef[i + 1] = -1; pb->geqs[ineq].coef[0] = nbi; /* A step "dx" bigger than nb_iters is not feasible, so add "0 <= nb_iters + dx", */ ineq = omega_add_zero_geq (pb, omega_black); pb->geqs[ineq].coef[i + 1] = 1; pb->geqs[ineq].coef[0] = nbi; /* and "dx <= nb_iters". */ ineq = omega_add_zero_geq (pb, omega_black); pb->geqs[ineq].coef[i + 1] = -1; pb->geqs[ineq].coef[0] = nbi; } } omega_extract_distance_vectors (pb, ddr); return true; } /* Sets up the Omega dependence problem for the data dependence relation DDR. Returns false when the constraint system cannot be built, ie. when the test answers "don't know". Returns true otherwise, and when independence has been proved (using one of the trivial dependence test), set MAYBE_DEPENDENT to false, otherwise set MAYBE_DEPENDENT to true. Example: for setting up the dependence system corresponding to the conflicting accesses | loop_i | loop_j | A[i, i+1] = ... | ... A[2*j, 2*(i + j)] | endloop_j | endloop_i the following constraints come from the iteration domain: 0 <= i <= Ni 0 <= i + di <= Ni 0 <= j <= Nj 0 <= j + dj <= Nj where di, dj are the distance variables. The constraints representing the conflicting elements are: i = 2 * (j + dj) i + 1 = 2 * (i + di + j + dj) For asking that the resulting distance vector (di, dj) be lexicographically positive, we insert the constraint "di >= 0". If "di = 0" in the solution, we fix that component to zero, and we look at the inner loops: we set a new problem where all the outer loop distances are zero, and fix this inner component to be positive. When one of the components is positive, we save that distance, and set a new problem where the distance on this loop is zero, searching for other distances in the inner loops. Here is the classic example that illustrates that we have to set for each inner loop a new problem: | loop_1 | loop_2 | A[10] | endloop_2 | endloop_1 we have to save two distances (1, 0) and (0, 1). Given two array references, refA and refB, we have to set the dependence problem twice, refA vs. refB and refB vs. refA, and we cannot do a single test, as refB might occur before refA in the inner loops, and the contrary when considering outer loops: ex. | loop_0 | loop_1 | loop_2 | T[{1,+,1}_2][{1,+,1}_1] // refA | T[{2,+,1}_2][{0,+,1}_1] // refB | endloop_2 | endloop_1 | endloop_0 refB touches the elements in T before refA, and thus for the same loop_0 refB precedes refA: ie. the distance vector (0, 1, -1) but for successive loop_0 iterations, we have (1, -1, 1) The Omega solver expects the distance variables ("di" in the previous example) to come first in the constraint system (as variables to be protected, or "safe" variables), the constraint system is built using the following layout: "cst | distance vars | index vars". */ static bool init_omega_for_ddr (struct data_dependence_relation *ddr, bool *maybe_dependent) { omega_pb pb; bool res = false; *maybe_dependent = true; if (same_access_functions (ddr)) { unsigned j; lambda_vector dir_v; /* Save the 0 vector. */ save_dist_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr))); dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); for (j = 0; j < DDR_NB_LOOPS (ddr); j++) dir_v[j] = dir_equal; save_dir_v (ddr, dir_v); /* Save the dependences carried by outer loops. */ pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); res = init_omega_for_ddr_1 (DDR_A (ddr), DDR_B (ddr), ddr, pb, maybe_dependent); omega_free_problem (pb); return res; } /* Omega expects the protected variables (those that have to be kept after elimination) to appear first in the constraint system. These variables are the distance variables. In the following initialization we declare NB_LOOPS safe variables, and the total number of variables for the constraint system is 2*NB_LOOPS. */ pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); res = init_omega_for_ddr_1 (DDR_A (ddr), DDR_B (ddr), ddr, pb, maybe_dependent); omega_free_problem (pb); /* Stop computation if not decidable, or no dependence. */ if (res == false || *maybe_dependent == false) return res; pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); res = init_omega_for_ddr_1 (DDR_B (ddr), DDR_A (ddr), ddr, pb, maybe_dependent); omega_free_problem (pb); return res; } /* Return true when DDR contains the same information as that stored in DIR_VECTS and in DIST_VECTS, return false otherwise. */ static bool ddr_consistent_p (FILE *file, struct data_dependence_relation *ddr, VEC (lambda_vector, heap) *dist_vects, VEC (lambda_vector, heap) *dir_vects) { unsigned int i, j; /* If dump_file is set, output there. */ if (dump_file && (dump_flags & TDF_DETAILS)) file = dump_file; if (VEC_length (lambda_vector, dist_vects) != DDR_NUM_DIST_VECTS (ddr)) { lambda_vector b_dist_v; fprintf (file, "\n(Number of distance vectors differ: Banerjee has %d, Omega has %d.\n", VEC_length (lambda_vector, dist_vects), DDR_NUM_DIST_VECTS (ddr)); fprintf (file, "Banerjee dist vectors:\n"); for (i = 0; VEC_iterate (lambda_vector, dist_vects, i, b_dist_v); i++) print_lambda_vector (file, b_dist_v, DDR_NB_LOOPS (ddr)); fprintf (file, "Omega dist vectors:\n"); for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++) print_lambda_vector (file, DDR_DIST_VECT (ddr, i), DDR_NB_LOOPS (ddr)); fprintf (file, "data dependence relation:\n"); dump_data_dependence_relation (file, ddr); fprintf (file, ")\n"); return false; } if (VEC_length (lambda_vector, dir_vects) != DDR_NUM_DIR_VECTS (ddr)) { fprintf (file, "\n(Number of direction vectors differ: Banerjee has %d, Omega has %d.)\n", VEC_length (lambda_vector, dir_vects), DDR_NUM_DIR_VECTS (ddr)); return false; } for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++) { lambda_vector a_dist_v; lambda_vector b_dist_v = DDR_DIST_VECT (ddr, i); /* Distance vectors are not ordered in the same way in the DDR and in the DIST_VECTS: search for a matching vector. */ for (j = 0; VEC_iterate (lambda_vector, dist_vects, j, a_dist_v); j++) if (lambda_vector_equal (a_dist_v, b_dist_v, DDR_NB_LOOPS (ddr))) break; if (j == VEC_length (lambda_vector, dist_vects)) { fprintf (file, "\n(Dist vectors from the first dependence analyzer:\n"); print_dist_vectors (file, dist_vects, DDR_NB_LOOPS (ddr)); fprintf (file, "not found in Omega dist vectors:\n"); print_dist_vectors (file, DDR_DIST_VECTS (ddr), DDR_NB_LOOPS (ddr)); fprintf (file, "data dependence relation:\n"); dump_data_dependence_relation (file, ddr); fprintf (file, ")\n"); } } for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++) { lambda_vector a_dir_v; lambda_vector b_dir_v = DDR_DIR_VECT (ddr, i); /* Direction vectors are not ordered in the same way in the DDR and in the DIR_VECTS: search for a matching vector. */ for (j = 0; VEC_iterate (lambda_vector, dir_vects, j, a_dir_v); j++) if (lambda_vector_equal (a_dir_v, b_dir_v, DDR_NB_LOOPS (ddr))) break; if (j == VEC_length (lambda_vector, dist_vects)) { fprintf (file, "\n(Dir vectors from the first dependence analyzer:\n"); print_dir_vectors (file, dir_vects, DDR_NB_LOOPS (ddr)); fprintf (file, "not found in Omega dir vectors:\n"); print_dir_vectors (file, DDR_DIR_VECTS (ddr), DDR_NB_LOOPS (ddr)); fprintf (file, "data dependence relation:\n"); dump_data_dependence_relation (file, ddr); fprintf (file, ")\n"); } } return true; } /* This computes the affine dependence relation between A and B. CHREC_KNOWN is used for representing the independence between two accesses, while CHREC_DONT_KNOW is used for representing the unknown relation. Note that it is possible to stop the computation of the dependence relation the first time we detect a CHREC_KNOWN element for a given subscript. */ static void compute_affine_dependence (struct data_dependence_relation *ddr) { struct data_reference *dra = DDR_A (ddr); struct data_reference *drb = DDR_B (ddr); if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "(compute_affine_dependence\n"); fprintf (dump_file, " (stmt_a = \n"); print_generic_expr (dump_file, DR_STMT (dra), 0); fprintf (dump_file, ")\n (stmt_b = \n"); print_generic_expr (dump_file, DR_STMT (drb), 0); fprintf (dump_file, ")\n"); } /* Analyze only when the dependence relation is not yet known. */ if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE) { dependence_stats.num_dependence_tests++; if (access_functions_are_affine_or_constant_p (dra) && access_functions_are_affine_or_constant_p (drb)) { if (flag_check_data_deps) { /* Compute the dependences using the first algorithm. */ subscript_dependence_tester (ddr); if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "\n\nBanerjee Analyzer\n"); dump_data_dependence_relation (dump_file, ddr); } if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE) { bool maybe_dependent; VEC (lambda_vector, heap) *dir_vects, *dist_vects; /* Save the result of the first DD analyzer. */ dist_vects = DDR_DIST_VECTS (ddr); dir_vects = DDR_DIR_VECTS (ddr); /* Reset the information. */ DDR_DIST_VECTS (ddr) = NULL; DDR_DIR_VECTS (ddr) = NULL; /* Compute the same information using Omega. */ if (!init_omega_for_ddr (ddr, &maybe_dependent)) goto csys_dont_know; if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "Omega Analyzer\n"); dump_data_dependence_relation (dump_file, ddr); } /* Check that we get the same information. */ if (maybe_dependent) gcc_assert (ddr_consistent_p (stderr, ddr, dist_vects, dir_vects)); } } else subscript_dependence_tester (ddr); } /* As a last case, if the dependence cannot be determined, or if the dependence is considered too difficult to determine, answer "don't know". */ else { csys_dont_know:; dependence_stats.num_dependence_undetermined++; if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "Data ref a:\n"); dump_data_reference (dump_file, dra); fprintf (dump_file, "Data ref b:\n"); dump_data_reference (dump_file, drb); fprintf (dump_file, "affine dependence test not usable: access function not affine or constant.\n"); } finalize_ddr_dependent (ddr, chrec_dont_know); } } if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, ")\n"); } /* This computes the dependence relation for the same data reference into DDR. */ static void compute_self_dependence (struct data_dependence_relation *ddr) { unsigned int i; struct subscript *subscript; for (i = 0; VEC_iterate (subscript_p, DDR_SUBSCRIPTS (ddr), i, subscript); i++) { /* The accessed index overlaps for each iteration. */ SUB_CONFLICTS_IN_A (subscript) = conflict_fn (1, affine_fn_cst (integer_zero_node)); SUB_CONFLICTS_IN_B (subscript) = conflict_fn (1, affine_fn_cst (integer_zero_node)); SUB_LAST_CONFLICT (subscript) = chrec_dont_know; } /* The distance vector is the zero vector. */ save_dist_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr))); save_dir_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr))); } /* Compute in DEPENDENCE_RELATIONS the data dependence graph for all the data references in DATAREFS, in the LOOP_NEST. When COMPUTE_SELF_AND_RR is FALSE, don't compute read-read and self relations. */ static void compute_all_dependences (VEC (data_reference_p, heap) *datarefs, VEC (ddr_p, heap) **dependence_relations, VEC (loop_p, heap) *loop_nest, bool compute_self_and_rr) { struct data_dependence_relation *ddr; struct data_reference *a, *b; unsigned int i, j; for (i = 0; VEC_iterate (data_reference_p, datarefs, i, a); i++) for (j = i + 1; VEC_iterate (data_reference_p, datarefs, j, b); j++) if (!DR_IS_READ (a) || !DR_IS_READ (b) || compute_self_and_rr) { ddr = initialize_data_dependence_relation (a, b, loop_nest); VEC_safe_push (ddr_p, heap, *dependence_relations, ddr); compute_affine_dependence (ddr); } if (compute_self_and_rr) for (i = 0; VEC_iterate (data_reference_p, datarefs, i, a); i++) { ddr = initialize_data_dependence_relation (a, a, loop_nest); VEC_safe_push (ddr_p, heap, *dependence_relations, ddr); compute_self_dependence (ddr); } } /* Stores the locations of memory references in STMT to REFERENCES. Returns true if STMT clobbers memory, false otherwise. */ bool get_references_in_stmt (tree stmt, VEC (data_ref_loc, heap) **references) { bool clobbers_memory = false; data_ref_loc *ref; tree *op0, *op1, call; *references = NULL; /* ASM_EXPR and CALL_EXPR may embed arbitrary side effects. Calls have side-effects, except those to const or pure functions. */ call = get_call_expr_in (stmt); if ((call && !(call_expr_flags (call) & (ECF_CONST | ECF_PURE))) || (TREE_CODE (stmt) == ASM_EXPR && ASM_VOLATILE_P (stmt))) clobbers_memory = true; if (ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS)) return clobbers_memory; if (TREE_CODE (stmt) == GIMPLE_MODIFY_STMT) { op0 = &GIMPLE_STMT_OPERAND (stmt, 0); op1 = &GIMPLE_STMT_OPERAND (stmt, 1); if (DECL_P (*op1) || REFERENCE_CLASS_P (*op1)) { ref = VEC_safe_push (data_ref_loc, heap, *references, NULL); ref->pos = op1; ref->is_read = true; } if (DECL_P (*op0) || REFERENCE_CLASS_P (*op0)) { ref = VEC_safe_push (data_ref_loc, heap, *references, NULL); ref->pos = op0; ref->is_read = false; } } if (call) { unsigned i, n = call_expr_nargs (call); for (i = 0; i < n; i++) { op0 = &CALL_EXPR_ARG (call, i); if (DECL_P (*op0) || REFERENCE_CLASS_P (*op0)) { ref = VEC_safe_push (data_ref_loc, heap, *references, NULL); ref->pos = op0; ref->is_read = true; } } } return clobbers_memory; } /* Stores the data references in STMT to DATAREFS. If there is an unanalyzable reference, returns false, otherwise returns true. */ static bool find_data_references_in_stmt (tree stmt, VEC (data_reference_p, heap) **datarefs) { unsigned i; VEC (data_ref_loc, heap) *references; data_ref_loc *ref; bool ret = true; data_reference_p dr; if (get_references_in_stmt (stmt, &references)) { VEC_free (data_ref_loc, heap, references); return false; } for (i = 0; VEC_iterate (data_ref_loc, references, i, ref); i++) { dr = create_data_ref (*ref->pos, stmt, ref->is_read); if (dr) VEC_safe_push (data_reference_p, heap, *datarefs, dr); else { ret = false; break; } } VEC_free (data_ref_loc, heap, references); return ret; } /* Search the data references in LOOP, and record the information into DATAREFS. Returns chrec_dont_know when failing to analyze a difficult case, returns NULL_TREE otherwise. TODO: This function should be made smarter so that it can handle address arithmetic as if they were array accesses, etc. */ tree find_data_references_in_loop (struct loop *loop, VEC (data_reference_p, heap) **datarefs) { basic_block bb, *bbs; unsigned int i; block_stmt_iterator bsi; bbs = get_loop_body (loop); for (i = 0; i < loop->num_nodes; i++) { bb = bbs[i]; for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi)) { tree stmt = bsi_stmt (bsi); if (!find_data_references_in_stmt (stmt, datarefs)) { struct data_reference *res; res = XNEW (struct data_reference); DR_STMT (res) = NULL_TREE; DR_REF (res) = NULL_TREE; DR_BASE_OBJECT (res) = NULL; DR_TYPE (res) = ARRAY_REF_TYPE; DR_SET_ACCESS_FNS (res, NULL); DR_BASE_OBJECT (res) = NULL; DR_IS_READ (res) = false; DR_BASE_ADDRESS (res) = NULL_TREE; DR_OFFSET (res) = NULL_TREE; DR_INIT (res) = NULL_TREE; DR_STEP (res) = NULL_TREE; DR_OFFSET_MISALIGNMENT (res) = NULL_TREE; DR_MEMTAG (res) = NULL_TREE; DR_PTR_INFO (res) = NULL; VEC_safe_push (data_reference_p, heap, *datarefs, res); free (bbs); return chrec_dont_know; } } } free (bbs); return NULL_TREE; } /* Recursive helper function. */ static bool find_loop_nest_1 (struct loop *loop, VEC (loop_p, heap) **loop_nest) { /* Inner loops of the nest should not contain siblings. Example: when there are two consecutive loops, | loop_0 | loop_1 | A[{0, +, 1}_1] | endloop_1 | loop_2 | A[{0, +, 1}_2] | endloop_2 | endloop_0 the dependence relation cannot be captured by the distance abstraction. */ if (loop->next) return false; VEC_safe_push (loop_p, heap, *loop_nest, loop); if (loop->inner) return find_loop_nest_1 (loop->inner, loop_nest); return true; } /* Return false when the LOOP is not well nested. Otherwise return true and insert in LOOP_NEST the loops of the nest. LOOP_NEST will contain the loops from the outermost to the innermost, as they will appear in the classic distance vector. */ static bool find_loop_nest (struct loop *loop, VEC (loop_p, heap) **loop_nest) { VEC_safe_push (loop_p, heap, *loop_nest, loop); if (loop->inner) return find_loop_nest_1 (loop->inner, loop_nest); return true; } /* Given a loop nest LOOP, the following vectors are returned: DATAREFS is initialized to all the array elements contained in this loop, DEPENDENCE_RELATIONS contains the relations between the data references. Compute read-read and self relations if COMPUTE_SELF_AND_READ_READ_DEPENDENCES is TRUE. */ void compute_data_dependences_for_loop (struct loop *loop, bool compute_self_and_read_read_dependences, VEC (data_reference_p, heap) **datarefs, VEC (ddr_p, heap) **dependence_relations) { struct loop *loop_nest = loop; VEC (loop_p, heap) *vloops = VEC_alloc (loop_p, heap, 3); memset (&dependence_stats, 0, sizeof (dependence_stats)); /* If the loop nest is not well formed, or one of the data references is not computable, give up without spending time to compute other dependences. */ if (!loop_nest || !find_loop_nest (loop_nest, &vloops) || find_data_references_in_loop (loop, datarefs) == chrec_dont_know) { struct data_dependence_relation *ddr; /* Insert a single relation into dependence_relations: chrec_dont_know. */ ddr = initialize_data_dependence_relation (NULL, NULL, vloops); VEC_safe_push (ddr_p, heap, *dependence_relations, ddr); } else compute_all_dependences (*datarefs, dependence_relations, vloops, compute_self_and_read_read_dependences); if (dump_file && (dump_flags & TDF_STATS)) { fprintf (dump_file, "Dependence tester statistics:\n"); fprintf (dump_file, "Number of dependence tests: %d\n", dependence_stats.num_dependence_tests); fprintf (dump_file, "Number of dependence tests classified dependent: %d\n", dependence_stats.num_dependence_dependent); fprintf (dump_file, "Number of dependence tests classified independent: %d\n", dependence_stats.num_dependence_independent); fprintf (dump_file, "Number of undetermined dependence tests: %d\n", dependence_stats.num_dependence_undetermined); fprintf (dump_file, "Number of subscript tests: %d\n", dependence_stats.num_subscript_tests); fprintf (dump_file, "Number of undetermined subscript tests: %d\n", dependence_stats.num_subscript_undetermined); fprintf (dump_file, "Number of same subscript function: %d\n", dependence_stats.num_same_subscript_function); fprintf (dump_file, "Number of ziv tests: %d\n", dependence_stats.num_ziv); fprintf (dump_file, "Number of ziv tests returning dependent: %d\n", dependence_stats.num_ziv_dependent); fprintf (dump_file, "Number of ziv tests returning independent: %d\n", dependence_stats.num_ziv_independent); fprintf (dump_file, "Number of ziv tests unimplemented: %d\n", dependence_stats.num_ziv_unimplemented); fprintf (dump_file, "Number of siv tests: %d\n", dependence_stats.num_siv); fprintf (dump_file, "Number of siv tests returning dependent: %d\n", dependence_stats.num_siv_dependent); fprintf (dump_file, "Number of siv tests returning independent: %d\n", dependence_stats.num_siv_independent); fprintf (dump_file, "Number of siv tests unimplemented: %d\n", dependence_stats.num_siv_unimplemented); fprintf (dump_file, "Number of miv tests: %d\n", dependence_stats.num_miv); fprintf (dump_file, "Number of miv tests returning dependent: %d\n", dependence_stats.num_miv_dependent); fprintf (dump_file, "Number of miv tests returning independent: %d\n", dependence_stats.num_miv_independent); fprintf (dump_file, "Number of miv tests unimplemented: %d\n", dependence_stats.num_miv_unimplemented); } } /* Entry point (for testing only). Analyze all the data references and the dependence relations in LOOP. The data references are computed first. A relation on these nodes is represented by a complete graph. Some of the relations could be of no interest, thus the relations can be computed on demand. In the following function we compute all the relations. This is just a first implementation that is here for: - for showing how to ask for the dependence relations, - for the debugging the whole dependence graph, - for the dejagnu testcases and maintenance. It is possible to ask only for a part of the graph, avoiding to compute the whole dependence graph. The computed dependences are stored in a knowledge base (KB) such that later queries don't recompute the same information. The implementation of this KB is transparent to the optimizer, and thus the KB can be changed with a more efficient implementation, or the KB could be disabled. */ static void analyze_all_data_dependences (struct loop *loop) { unsigned int i; int nb_data_refs = 10; VEC (data_reference_p, heap) *datarefs = VEC_alloc (data_reference_p, heap, nb_data_refs); VEC (ddr_p, heap) *dependence_relations = VEC_alloc (ddr_p, heap, nb_data_refs * nb_data_refs); /* Compute DDs on the whole function. */ compute_data_dependences_for_loop (loop, false, &datarefs, &dependence_relations); if (dump_file) { dump_data_dependence_relations (dump_file, dependence_relations); fprintf (dump_file, "\n\n"); if (dump_flags & TDF_DETAILS) dump_dist_dir_vectors (dump_file, dependence_relations); if (dump_flags & TDF_STATS) { unsigned nb_top_relations = 0; unsigned nb_bot_relations = 0; unsigned nb_basename_differ = 0; unsigned nb_chrec_relations = 0; struct data_dependence_relation *ddr; for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++) { if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr))) nb_top_relations++; else if (DDR_ARE_DEPENDENT (ddr) == chrec_known) { struct data_reference *a = DDR_A (ddr); struct data_reference *b = DDR_B (ddr); bool differ_p; if ((DR_BASE_OBJECT (a) && DR_BASE_OBJECT (b) && DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b)) || (base_object_differ_p (a, b, &differ_p) && differ_p)) nb_basename_differ++; else nb_bot_relations++; } else nb_chrec_relations++; } gather_stats_on_scev_database (); } } free_dependence_relations (dependence_relations); free_data_refs (datarefs); } /* Computes all the data dependences and check that the results of several analyzers are the same. */ void tree_check_data_deps (void) { loop_iterator li; struct loop *loop_nest; FOR_EACH_LOOP (li, loop_nest, 0) analyze_all_data_dependences (loop_nest); } /* Free the memory used by a data dependence relation DDR. */ void free_dependence_relation (struct data_dependence_relation *ddr) { if (ddr == NULL) return; if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE && DDR_SUBSCRIPTS (ddr)) free_subscripts (DDR_SUBSCRIPTS (ddr)); free (ddr); } /* Free the memory used by the data dependence relations from DEPENDENCE_RELATIONS. */ void free_dependence_relations (VEC (ddr_p, heap) *dependence_relations) { unsigned int i; struct data_dependence_relation *ddr; VEC (loop_p, heap) *loop_nest = NULL; for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++) { if (ddr == NULL) continue; if (loop_nest == NULL) loop_nest = DDR_LOOP_NEST (ddr); else gcc_assert (DDR_LOOP_NEST (ddr) == NULL || DDR_LOOP_NEST (ddr) == loop_nest); free_dependence_relation (ddr); } if (loop_nest) VEC_free (loop_p, heap, loop_nest); VEC_free (ddr_p, heap, dependence_relations); } /* Free the memory used by the data references from DATAREFS. */ void free_data_refs (VEC (data_reference_p, heap) *datarefs) { unsigned int i; struct data_reference *dr; for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++) free_data_ref (dr); VEC_free (data_reference_p, heap, datarefs); }