/* Data references and dependences detectors. Copyright (C) 2003-2018 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 3, 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 COPYING3. If not see . */ /* 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 "backend.h" #include "rtl.h" #include "tree.h" #include "gimple.h" #include "gimple-pretty-print.h" #include "alias.h" #include "fold-const.h" #include "expr.h" #include "gimple-iterator.h" #include "tree-ssa-loop-niter.h" #include "tree-ssa-loop.h" #include "tree-ssa.h" #include "cfgloop.h" #include "tree-data-ref.h" #include "tree-scalar-evolution.h" #include "dumpfile.h" #include "tree-affine.h" #include "params.h" #include "builtins.h" #include "tree-eh.h" #include "ssa.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 bool subscript_dependence_tester_1 (struct data_dependence_relation *, unsigned int, unsigned int, struct loop *); /* Returns true iff A divides B. */ static inline bool tree_fold_divides_p (const_tree a, const_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)); } /* Returns true iff A divides B. */ static inline bool int_divides_p (int a, int b) { return ((b % a) == 0); } /* Return true if reference REF contains a union access. */ static bool ref_contains_union_access_p (tree ref) { while (handled_component_p (ref)) { ref = TREE_OPERAND (ref, 0); if (TREE_CODE (TREE_TYPE (ref)) == UNION_TYPE || TREE_CODE (TREE_TYPE (ref)) == QUAL_UNION_TYPE) return true; } return false; } /* Dump into FILE all the data references from DATAREFS. */ static void dump_data_references (FILE *file, vec datarefs) { unsigned int i; struct data_reference *dr; FOR_EACH_VEC_ELT (datarefs, i, dr) dump_data_reference (file, dr); } /* Unified dump into FILE all the data references from DATAREFS. */ DEBUG_FUNCTION void debug (vec &ref) { dump_data_references (stderr, ref); } DEBUG_FUNCTION void debug (vec *ptr) { if (ptr) debug (*ptr); else fprintf (stderr, "\n"); } /* Dump into STDERR all the data references from DATAREFS. */ DEBUG_FUNCTION void debug_data_references (vec datarefs) { dump_data_references (stderr, datarefs); } /* Print to STDERR the data_reference DR. */ DEBUG_FUNCTION void debug_data_reference (struct data_reference *dr) { dump_data_reference (stderr, dr); } /* 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"); fprintf (outf, "# bb: %d \n", gimple_bb (DR_STMT (dr))->index); fprintf (outf, "# stmt: "); print_gimple_stmt (outf, DR_STMT (dr), 0); fprintf (outf, "# ref: "); print_generic_stmt (outf, DR_REF (dr)); fprintf (outf, "# base_object: "); print_generic_stmt (outf, DR_BASE_OBJECT (dr)); for (i = 0; i < DR_NUM_DIMENSIONS (dr); i++) { fprintf (outf, "# Access function %d: ", i); print_generic_stmt (outf, DR_ACCESS_FN (dr, i)); } fprintf (outf, "#)\n"); } /* Unified dump function for a DATA_REFERENCE structure. */ DEBUG_FUNCTION void debug (data_reference &ref) { dump_data_reference (stderr, &ref); } DEBUG_FUNCTION void debug (data_reference *ptr) { if (ptr) debug (*ptr); else fprintf (stderr, "\n"); } /* Dumps the affine function described by FN to the file OUTF. */ DEBUG_FUNCTION void dump_affine_function (FILE *outf, affine_fn fn) { unsigned i; tree coef; print_generic_expr (outf, fn[0], TDF_SLIM); for (i = 1; fn.iterate (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. */ DEBUG_FUNCTION void dump_conflict_function (FILE *outf, conflict_function *cf) { unsigned i; if (cf->n == NO_DEPENDENCE) fprintf (outf, "no dependence"); else if (cf->n == NOT_KNOWN) fprintf (outf, "not known"); else { for (i = 0; i < cf->n; i++) { if (i != 0) fprintf (outf, " "); fprintf (outf, "["); dump_affine_function (outf, cf->fns[i]); fprintf (outf, "]"); } } } /* Dump function for a SUBSCRIPT structure. */ DEBUG_FUNCTION 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, "\n last_conflict: "); print_generic_expr (outf, last_iteration); } cf = SUB_CONFLICTS_IN_B (subscript); fprintf (outf, "\n 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, "\n last_conflict: "); print_generic_expr (outf, last_iteration); } fprintf (outf, "\n (Subscript distance: "); print_generic_expr (outf, SUB_DISTANCE (subscript)); fprintf (outf, " ))\n"); } /* Print the classic direction vector DIRV to OUTF. */ DEBUG_FUNCTION void print_direction_vector (FILE *outf, lambda_vector dirv, int length) { int eq; for (eq = 0; eq < length; eq++) { enum data_dependence_direction dir = ((enum data_dependence_direction) 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. */ DEBUG_FUNCTION void print_dir_vectors (FILE *outf, vec dir_vects, int length) { unsigned j; lambda_vector v; FOR_EACH_VEC_ELT (dir_vects, j, v) print_direction_vector (outf, v, length); } /* Print out a vector VEC of length N to OUTFILE. */ DEBUG_FUNCTION void print_lambda_vector (FILE * outfile, lambda_vector vector, int n) { int i; for (i = 0; i < n; i++) fprintf (outfile, "%3d ", (int)vector[i]); fprintf (outfile, "\n"); } /* Print a vector of distance vectors. */ DEBUG_FUNCTION void print_dist_vectors (FILE *outf, vec dist_vects, int length) { unsigned j; lambda_vector v; FOR_EACH_VEC_ELT (dist_vects, j, v) print_lambda_vector (outf, v, length); } /* Dump function for a DATA_DEPENDENCE_RELATION structure. */ DEBUG_FUNCTION void dump_data_dependence_relation (FILE *outf, struct data_dependence_relation *ddr) { struct data_reference *dra, *drb; fprintf (outf, "(Data Dep: \n"); if (!ddr || DDR_ARE_DEPENDENT (ddr) == chrec_dont_know) { if (ddr) { dra = DDR_A (ddr); drb = DDR_B (ddr); if (dra) dump_data_reference (outf, dra); else fprintf (outf, " (nil)\n"); if (drb) dump_data_reference (outf, drb); else fprintf (outf, " (nil)\n"); } fprintf (outf, " (don't know)\n)\n"); return; } dra = DDR_A (ddr); drb = DDR_B (ddr); dump_data_reference (outf, dra); dump_data_reference (outf, drb); 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; subscript *sub; FOR_EACH_VEC_ELT (DDR_SUBSCRIPTS (ddr), i, sub) { fprintf (outf, " access_fn_A: "); print_generic_stmt (outf, SUB_ACCESS_FN (sub, 0)); fprintf (outf, " access_fn_B: "); print_generic_stmt (outf, SUB_ACCESS_FN (sub, 1)); dump_subscript (outf, sub); } fprintf (outf, " inner loop index: %d\n", DDR_INNER_LOOP (ddr)); fprintf (outf, " loop nest: ("); FOR_EACH_VEC_ELT (DDR_LOOP_NEST (ddr), i, loopi) 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"); } /* Debug version. */ DEBUG_FUNCTION void debug_data_dependence_relation (struct data_dependence_relation *ddr) { dump_data_dependence_relation (stderr, ddr); } /* Dump into FILE all the dependence relations from DDRS. */ DEBUG_FUNCTION void dump_data_dependence_relations (FILE *file, vec ddrs) { unsigned int i; struct data_dependence_relation *ddr; FOR_EACH_VEC_ELT (ddrs, i, ddr) dump_data_dependence_relation (file, ddr); } DEBUG_FUNCTION void debug (vec &ref) { dump_data_dependence_relations (stderr, ref); } DEBUG_FUNCTION void debug (vec *ptr) { if (ptr) debug (*ptr); else fprintf (stderr, "\n"); } /* Dump to STDERR all the dependence relations from DDRS. */ DEBUG_FUNCTION void debug_data_dependence_relations (vec ddrs) { dump_data_dependence_relations (stderr, ddrs); } /* 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. */ DEBUG_FUNCTION void dump_dist_dir_vectors (FILE *file, vec ddrs) { unsigned int i, j; struct data_dependence_relation *ddr; lambda_vector v; FOR_EACH_VEC_ELT (ddrs, i, ddr) if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE && DDR_AFFINE_P (ddr)) { FOR_EACH_VEC_ELT (DDR_DIST_VECTS (ddr), j, v) { fprintf (file, "DISTANCE_V ("); print_lambda_vector (file, v, DDR_NB_LOOPS (ddr)); fprintf (file, ")\n"); } FOR_EACH_VEC_ELT (DDR_DIR_VECTS (ddr), j, v) { 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. */ DEBUG_FUNCTION void dump_ddrs (FILE *file, vec ddrs) { unsigned int i; struct data_dependence_relation *ddr; FOR_EACH_VEC_ELT (ddrs, i, ddr) dump_data_dependence_relation (file, ddr); fprintf (file, "\n\n"); } DEBUG_FUNCTION void debug_ddrs (vec ddrs) { dump_ddrs (stderr, ddrs); } static void split_constant_offset (tree exp, tree *var, tree *off, hash_map > &cache); /* Helper function for split_constant_offset. Expresses OP0 CODE OP1 (the type of the result is TYPE) as VAR + OFF, where OFF is a nonzero constant of type ssizetype, and returns true. If we cannot do this with OFF nonzero, OFF and VAR are set to NULL_TREE instead and false is returned. */ static bool split_constant_offset_1 (tree type, tree op0, enum tree_code code, tree op1, tree *var, tree *off, hash_map > &cache) { tree var0, var1; tree off0, off1; enum tree_code ocode = code; *var = NULL_TREE; *off = NULL_TREE; switch (code) { case INTEGER_CST: *var = build_int_cst (type, 0); *off = fold_convert (ssizetype, op0); return true; case POINTER_PLUS_EXPR: ocode = PLUS_EXPR; /* FALLTHROUGH */ case PLUS_EXPR: case MINUS_EXPR: split_constant_offset (op0, &var0, &off0, cache); split_constant_offset (op1, &var1, &off1, cache); *var = fold_build2 (code, type, var0, var1); *off = size_binop (ocode, off0, off1); return true; case MULT_EXPR: if (TREE_CODE (op1) != INTEGER_CST) return false; split_constant_offset (op0, &var0, &off0, cache); *var = fold_build2 (MULT_EXPR, type, var0, op1); *off = size_binop (MULT_EXPR, off0, fold_convert (ssizetype, op1)); return true; case ADDR_EXPR: { tree base, poffset; poly_int64 pbitsize, pbitpos, pbytepos; machine_mode pmode; int punsignedp, preversep, pvolatilep; op0 = TREE_OPERAND (op0, 0); base = get_inner_reference (op0, &pbitsize, &pbitpos, &poffset, &pmode, &punsignedp, &preversep, &pvolatilep); if (!multiple_p (pbitpos, BITS_PER_UNIT, &pbytepos)) return false; base = build_fold_addr_expr (base); off0 = ssize_int (pbytepos); if (poffset) { split_constant_offset (poffset, &poffset, &off1, cache); off0 = size_binop (PLUS_EXPR, off0, off1); if (POINTER_TYPE_P (TREE_TYPE (base))) base = fold_build_pointer_plus (base, poffset); else base = fold_build2 (PLUS_EXPR, TREE_TYPE (base), base, fold_convert (TREE_TYPE (base), poffset)); } var0 = fold_convert (type, base); /* If variable length types are involved, punt, otherwise casts might be converted into ARRAY_REFs in gimplify_conversion. To compute that ARRAY_REF's element size TYPE_SIZE_UNIT, which possibly no longer appears in current GIMPLE, might resurface. This perhaps could run if (CONVERT_EXPR_P (var0)) { gimplify_conversion (&var0); // Attempt to fill in any within var0 found ARRAY_REF's // element size from corresponding op embedded ARRAY_REF, // if unsuccessful, just punt. } */ while (POINTER_TYPE_P (type)) type = TREE_TYPE (type); if (int_size_in_bytes (type) < 0) return false; *var = var0; *off = off0; return true; } case SSA_NAME: { if (SSA_NAME_OCCURS_IN_ABNORMAL_PHI (op0)) return false; gimple *def_stmt = SSA_NAME_DEF_STMT (op0); enum tree_code subcode; if (gimple_code (def_stmt) != GIMPLE_ASSIGN) return false; subcode = gimple_assign_rhs_code (def_stmt); /* We are using a cache to avoid un-CSEing large amounts of code. */ bool use_cache = false; if (!has_single_use (op0) && (subcode == POINTER_PLUS_EXPR || subcode == PLUS_EXPR || subcode == MINUS_EXPR || subcode == MULT_EXPR || subcode == ADDR_EXPR || CONVERT_EXPR_CODE_P (subcode))) { use_cache = true; bool existed; std::pair &e = cache.get_or_insert (op0, &existed); if (existed) { if (integer_zerop (e.second)) return false; *var = e.first; *off = e.second; return true; } e = std::make_pair (op0, ssize_int (0)); } var0 = gimple_assign_rhs1 (def_stmt); var1 = gimple_assign_rhs2 (def_stmt); bool res = split_constant_offset_1 (type, var0, subcode, var1, var, off, cache); if (res && use_cache) *cache.get (op0) = std::make_pair (*var, *off); return res; } CASE_CONVERT: { /* We must not introduce undefined overflow, and we must not change the value. Hence we're okay if the inner type doesn't overflow to start with (pointer or signed), the outer type also is an integer or pointer and the outer precision is at least as large as the inner. */ tree itype = TREE_TYPE (op0); if ((POINTER_TYPE_P (itype) || (INTEGRAL_TYPE_P (itype) && !TYPE_OVERFLOW_TRAPS (itype))) && TYPE_PRECISION (type) >= TYPE_PRECISION (itype) && (POINTER_TYPE_P (type) || INTEGRAL_TYPE_P (type))) { if (INTEGRAL_TYPE_P (itype) && TYPE_OVERFLOW_WRAPS (itype)) { /* Split the unconverted operand and try to prove that wrapping isn't a problem. */ tree tmp_var, tmp_off; split_constant_offset (op0, &tmp_var, &tmp_off, cache); /* See whether we have an SSA_NAME whose range is known to be [A, B]. */ if (TREE_CODE (tmp_var) != SSA_NAME) return false; wide_int var_min, var_max; value_range_kind vr_type = get_range_info (tmp_var, &var_min, &var_max); wide_int var_nonzero = get_nonzero_bits (tmp_var); signop sgn = TYPE_SIGN (itype); if (intersect_range_with_nonzero_bits (vr_type, &var_min, &var_max, var_nonzero, sgn) != VR_RANGE) return false; /* See whether the range of OP0 (i.e. TMP_VAR + TMP_OFF) is known to be [A + TMP_OFF, B + TMP_OFF], with all operations done in ITYPE. The addition must overflow at both ends of the range or at neither. */ wi::overflow_type overflow[2]; unsigned int prec = TYPE_PRECISION (itype); wide_int woff = wi::to_wide (tmp_off, prec); wide_int op0_min = wi::add (var_min, woff, sgn, &overflow[0]); wi::add (var_max, woff, sgn, &overflow[1]); if ((overflow[0] != wi::OVF_NONE) != (overflow[1] != wi::OVF_NONE)) return false; /* Calculate (ssizetype) OP0 - (ssizetype) TMP_VAR. */ widest_int diff = (widest_int::from (op0_min, sgn) - widest_int::from (var_min, sgn)); var0 = tmp_var; *off = wide_int_to_tree (ssizetype, diff); } else split_constant_offset (op0, &var0, off, cache); *var = fold_convert (type, var0); return true; } return false; } default: return false; } } /* Expresses EXP as VAR + OFF, where off is a constant. The type of OFF will be ssizetype. */ static void split_constant_offset (tree exp, tree *var, tree *off, hash_map > &cache) { tree type = TREE_TYPE (exp), op0, op1, e, o; enum tree_code code; *var = exp; *off = ssize_int (0); if (tree_is_chrec (exp) || get_gimple_rhs_class (TREE_CODE (exp)) == GIMPLE_TERNARY_RHS) return; code = TREE_CODE (exp); extract_ops_from_tree (exp, &code, &op0, &op1); if (split_constant_offset_1 (type, op0, code, op1, &e, &o, cache)) { *var = e; *off = o; } } void split_constant_offset (tree exp, tree *var, tree *off) { static hash_map > *cache; if (!cache) cache = new hash_map > (37); split_constant_offset (exp, var, off, *cache); cache->empty (); } /* Returns the address ADDR of an object in a canonical shape (without nop casts, and with type of pointer to the object). */ static tree canonicalize_base_object_address (tree addr) { tree orig = addr; STRIP_NOPS (addr); /* The base address may be obtained by casting from integer, in that case keep the cast. */ if (!POINTER_TYPE_P (TREE_TYPE (addr))) return orig; if (TREE_CODE (addr) != ADDR_EXPR) return addr; return build_fold_addr_expr (TREE_OPERAND (addr, 0)); } /* Analyze the behavior of memory reference REF within STMT. There are two modes: - BB analysis. In this case we simply split the address into base, init and offset components, without reference to any containing loop. The resulting base and offset are general expressions and they can vary arbitrarily from one iteration of the containing loop to the next. The step is always zero. - loop analysis. In this case we analyze the reference both wrt LOOP and on the basis that the reference occurs (is "used") in LOOP; see the comment above analyze_scalar_evolution_in_loop for more information about this distinction. The base, init, offset and step fields are all invariant in LOOP. Perform BB analysis if LOOP is null, or if LOOP is the function's dummy outermost loop. In other cases perform loop analysis. Return true if the analysis succeeded and store the results in DRB if so. BB analysis can only fail for bitfield or reversed-storage accesses. */ opt_result dr_analyze_innermost (innermost_loop_behavior *drb, tree ref, struct loop *loop, const gimple *stmt) { poly_int64 pbitsize, pbitpos; tree base, poffset; machine_mode pmode; int punsignedp, preversep, pvolatilep; affine_iv base_iv, offset_iv; tree init, dinit, step; bool in_loop = (loop && loop->num); if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "analyze_innermost: "); base = get_inner_reference (ref, &pbitsize, &pbitpos, &poffset, &pmode, &punsignedp, &preversep, &pvolatilep); gcc_assert (base != NULL_TREE); poly_int64 pbytepos; if (!multiple_p (pbitpos, BITS_PER_UNIT, &pbytepos)) return opt_result::failure_at (stmt, "failed: bit offset alignment.\n"); if (preversep) return opt_result::failure_at (stmt, "failed: reverse storage order.\n"); /* Calculate the alignment and misalignment for the inner reference. */ unsigned int HOST_WIDE_INT bit_base_misalignment; unsigned int bit_base_alignment; get_object_alignment_1 (base, &bit_base_alignment, &bit_base_misalignment); /* There are no bitfield references remaining in BASE, so the values we got back must be whole bytes. */ gcc_assert (bit_base_alignment % BITS_PER_UNIT == 0 && bit_base_misalignment % BITS_PER_UNIT == 0); unsigned int base_alignment = bit_base_alignment / BITS_PER_UNIT; poly_int64 base_misalignment = bit_base_misalignment / BITS_PER_UNIT; if (TREE_CODE (base) == MEM_REF) { if (!integer_zerop (TREE_OPERAND (base, 1))) { /* Subtract MOFF from the base and add it to POFFSET instead. Adjust the misalignment to reflect the amount we subtracted. */ poly_offset_int moff = mem_ref_offset (base); base_misalignment -= moff.force_shwi (); tree mofft = wide_int_to_tree (sizetype, moff); if (!poffset) poffset = mofft; else poffset = size_binop (PLUS_EXPR, poffset, mofft); } base = TREE_OPERAND (base, 0); } else base = build_fold_addr_expr (base); if (in_loop) { if (!simple_iv (loop, loop, base, &base_iv, true)) return opt_result::failure_at (stmt, "failed: evolution of base is not affine.\n"); } else { base_iv.base = base; base_iv.step = ssize_int (0); base_iv.no_overflow = true; } if (!poffset) { offset_iv.base = ssize_int (0); offset_iv.step = ssize_int (0); } else { if (!in_loop) { offset_iv.base = poffset; offset_iv.step = ssize_int (0); } else if (!simple_iv (loop, loop, poffset, &offset_iv, true)) return opt_result::failure_at (stmt, "failed: evolution of offset is not affine.\n"); } init = ssize_int (pbytepos); /* Subtract any constant component from the base and add it to INIT instead. Adjust the misalignment to reflect the amount we subtracted. */ split_constant_offset (base_iv.base, &base_iv.base, &dinit); init = size_binop (PLUS_EXPR, init, dinit); base_misalignment -= TREE_INT_CST_LOW (dinit); split_constant_offset (offset_iv.base, &offset_iv.base, &dinit); init = size_binop (PLUS_EXPR, init, dinit); step = size_binop (PLUS_EXPR, fold_convert (ssizetype, base_iv.step), fold_convert (ssizetype, offset_iv.step)); base = canonicalize_base_object_address (base_iv.base); /* See if get_pointer_alignment can guarantee a higher alignment than the one we calculated above. */ unsigned int HOST_WIDE_INT alt_misalignment; unsigned int alt_alignment; get_pointer_alignment_1 (base, &alt_alignment, &alt_misalignment); /* As above, these values must be whole bytes. */ gcc_assert (alt_alignment % BITS_PER_UNIT == 0 && alt_misalignment % BITS_PER_UNIT == 0); alt_alignment /= BITS_PER_UNIT; alt_misalignment /= BITS_PER_UNIT; if (base_alignment < alt_alignment) { base_alignment = alt_alignment; base_misalignment = alt_misalignment; } drb->base_address = base; drb->offset = fold_convert (ssizetype, offset_iv.base); drb->init = init; drb->step = step; if (known_misalignment (base_misalignment, base_alignment, &drb->base_misalignment)) drb->base_alignment = base_alignment; else { drb->base_alignment = known_alignment (base_misalignment); drb->base_misalignment = 0; } drb->offset_alignment = highest_pow2_factor (offset_iv.base); drb->step_alignment = highest_pow2_factor (step); if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "success.\n"); return opt_result::success (); } /* Return true if OP is a valid component reference for a DR access function. This accepts a subset of what handled_component_p accepts. */ static bool access_fn_component_p (tree op) { switch (TREE_CODE (op)) { case REALPART_EXPR: case IMAGPART_EXPR: case ARRAY_REF: return true; case COMPONENT_REF: return TREE_CODE (TREE_TYPE (TREE_OPERAND (op, 0))) == RECORD_TYPE; default: return false; } } /* Determines the base object and the list of indices of memory reference DR, analyzed in LOOP and instantiated before NEST. */ static void dr_analyze_indices (struct data_reference *dr, edge nest, loop_p loop) { vec access_fns = vNULL; tree ref, op; tree base, off, access_fn; /* If analyzing a basic-block there are no indices to analyze and thus no access functions. */ if (!nest) { DR_BASE_OBJECT (dr) = DR_REF (dr); DR_ACCESS_FNS (dr).create (0); return; } ref = DR_REF (dr); /* REALPART_EXPR and IMAGPART_EXPR can be handled like accesses into a two element array with a constant index. The base is then just the immediate underlying object. */ if (TREE_CODE (ref) == REALPART_EXPR) { ref = TREE_OPERAND (ref, 0); access_fns.safe_push (integer_zero_node); } else if (TREE_CODE (ref) == IMAGPART_EXPR) { ref = TREE_OPERAND (ref, 0); access_fns.safe_push (integer_one_node); } /* Analyze access functions of dimensions we know to be independent. The list of component references handled here should be kept in sync with access_fn_component_p. */ while (handled_component_p (ref)) { if (TREE_CODE (ref) == ARRAY_REF) { op = TREE_OPERAND (ref, 1); access_fn = analyze_scalar_evolution (loop, op); access_fn = instantiate_scev (nest, loop, access_fn); access_fns.safe_push (access_fn); } else if (TREE_CODE (ref) == COMPONENT_REF && TREE_CODE (TREE_TYPE (TREE_OPERAND (ref, 0))) == RECORD_TYPE) { /* For COMPONENT_REFs of records (but not unions!) use the FIELD_DECL offset as constant access function so we can disambiguate a[i].f1 and a[i].f2. */ tree off = component_ref_field_offset (ref); off = size_binop (PLUS_EXPR, size_binop (MULT_EXPR, fold_convert (bitsizetype, off), bitsize_int (BITS_PER_UNIT)), DECL_FIELD_BIT_OFFSET (TREE_OPERAND (ref, 1))); access_fns.safe_push (off); } else /* If we have an unhandled component we could not translate to an access function stop analyzing. We have determined our base object in this case. */ break; ref = TREE_OPERAND (ref, 0); } /* If the address operand of a MEM_REF base has an evolution in the analyzed nest, add it as an additional independent access-function. */ if (TREE_CODE (ref) == MEM_REF) { op = TREE_OPERAND (ref, 0); access_fn = analyze_scalar_evolution (loop, op); access_fn = instantiate_scev (nest, loop, access_fn); if (TREE_CODE (access_fn) == POLYNOMIAL_CHREC) { tree orig_type; tree memoff = TREE_OPERAND (ref, 1); base = initial_condition (access_fn); orig_type = TREE_TYPE (base); STRIP_USELESS_TYPE_CONVERSION (base); split_constant_offset (base, &base, &off); STRIP_USELESS_TYPE_CONVERSION (base); /* Fold the MEM_REF offset into the evolutions initial value to make more bases comparable. */ if (!integer_zerop (memoff)) { off = size_binop (PLUS_EXPR, off, fold_convert (ssizetype, memoff)); memoff = build_int_cst (TREE_TYPE (memoff), 0); } /* Adjust the offset so it is a multiple of the access type size and thus we separate bases that can possibly be used to produce partial overlaps (which the access_fn machinery cannot handle). */ wide_int rem; if (TYPE_SIZE_UNIT (TREE_TYPE (ref)) && TREE_CODE (TYPE_SIZE_UNIT (TREE_TYPE (ref))) == INTEGER_CST && !integer_zerop (TYPE_SIZE_UNIT (TREE_TYPE (ref)))) rem = wi::mod_trunc (wi::to_wide (off), wi::to_wide (TYPE_SIZE_UNIT (TREE_TYPE (ref))), SIGNED); else /* If we can't compute the remainder simply force the initial condition to zero. */ rem = wi::to_wide (off); off = wide_int_to_tree (ssizetype, wi::to_wide (off) - rem); memoff = wide_int_to_tree (TREE_TYPE (memoff), rem); /* And finally replace the initial condition. */ access_fn = chrec_replace_initial_condition (access_fn, fold_convert (orig_type, off)); /* ??? This is still not a suitable base object for dr_may_alias_p - the base object needs to be an access that covers the object as whole. With an evolution in the pointer this cannot be guaranteed. As a band-aid, mark the access so we can special-case it in dr_may_alias_p. */ tree old = ref; ref = fold_build2_loc (EXPR_LOCATION (ref), MEM_REF, TREE_TYPE (ref), base, memoff); MR_DEPENDENCE_CLIQUE (ref) = MR_DEPENDENCE_CLIQUE (old); MR_DEPENDENCE_BASE (ref) = MR_DEPENDENCE_BASE (old); DR_UNCONSTRAINED_BASE (dr) = true; access_fns.safe_push (access_fn); } } else if (DECL_P (ref)) { /* Canonicalize DR_BASE_OBJECT to MEM_REF form. */ ref = build2 (MEM_REF, TREE_TYPE (ref), build_fold_addr_expr (ref), build_int_cst (reference_alias_ptr_type (ref), 0)); } DR_BASE_OBJECT (dr) = ref; DR_ACCESS_FNS (dr) = access_fns; } /* Extracts the alias analysis information from the memory reference DR. */ static void dr_analyze_alias (struct data_reference *dr) { tree ref = DR_REF (dr); tree base = get_base_address (ref), addr; if (INDIRECT_REF_P (base) || TREE_CODE (base) == MEM_REF) { addr = TREE_OPERAND (base, 0); if (TREE_CODE (addr) == SSA_NAME) DR_PTR_INFO (dr) = SSA_NAME_PTR_INFO (addr); } } /* Frees data reference DR. */ void free_data_ref (data_reference_p dr) { DR_ACCESS_FNS (dr).release (); free (dr); } /* Analyze memory reference MEMREF, which is accessed in STMT. The reference is a read if IS_READ is true, otherwise it is a write. IS_CONDITIONAL_IN_STMT indicates that the reference is conditional within STMT, i.e. that it might not occur even if STMT is executed and runs to completion. Return the data_reference description of MEMREF. NEST is the outermost loop in which the reference should be instantiated, LOOP is the loop in which the data reference should be analyzed. */ struct data_reference * create_data_ref (edge nest, loop_p loop, tree memref, gimple *stmt, bool is_read, bool is_conditional_in_stmt) { struct data_reference *dr; if (dump_file && (dump_flags & TDF_DETAILS)) { fprintf (dump_file, "Creating dr for "); print_generic_expr (dump_file, memref, TDF_SLIM); fprintf (dump_file, "\n"); } dr = XCNEW (struct data_reference); DR_STMT (dr) = stmt; DR_REF (dr) = memref; DR_IS_READ (dr) = is_read; DR_IS_CONDITIONAL_IN_STMT (dr) = is_conditional_in_stmt; dr_analyze_innermost (&DR_INNERMOST (dr), memref, nest != NULL ? loop : NULL, stmt); dr_analyze_indices (dr, nest, loop); dr_analyze_alias (dr); if (dump_file && (dump_flags & TDF_DETAILS)) { unsigned i; fprintf (dump_file, "\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\tstep: "); print_generic_expr (dump_file, DR_STEP (dr), TDF_SLIM); fprintf (dump_file, "\n\tbase alignment: %d", DR_BASE_ALIGNMENT (dr)); fprintf (dump_file, "\n\tbase misalignment: %d", DR_BASE_MISALIGNMENT (dr)); fprintf (dump_file, "\n\toffset alignment: %d", DR_OFFSET_ALIGNMENT (dr)); fprintf (dump_file, "\n\tstep alignment: %d", DR_STEP_ALIGNMENT (dr)); fprintf (dump_file, "\n\tbase_object: "); print_generic_expr (dump_file, DR_BASE_OBJECT (dr), TDF_SLIM); fprintf (dump_file, "\n"); for (i = 0; i < DR_NUM_DIMENSIONS (dr); i++) { fprintf (dump_file, "\tAccess function %d: ", i); print_generic_stmt (dump_file, DR_ACCESS_FN (dr, i), TDF_SLIM); } } return dr; } /* A helper function computes order between two tree epxressions T1 and T2. This is used in comparator functions sorting objects based on the order of tree expressions. The function returns -1, 0, or 1. */ int data_ref_compare_tree (tree t1, tree t2) { int i, cmp; enum tree_code code; char tclass; if (t1 == t2) return 0; if (t1 == NULL) return -1; if (t2 == NULL) return 1; STRIP_USELESS_TYPE_CONVERSION (t1); STRIP_USELESS_TYPE_CONVERSION (t2); if (t1 == t2) return 0; if (TREE_CODE (t1) != TREE_CODE (t2) && ! (CONVERT_EXPR_P (t1) && CONVERT_EXPR_P (t2))) return TREE_CODE (t1) < TREE_CODE (t2) ? -1 : 1; code = TREE_CODE (t1); switch (code) { case INTEGER_CST: return tree_int_cst_compare (t1, t2); case STRING_CST: if (TREE_STRING_LENGTH (t1) != TREE_STRING_LENGTH (t2)) return TREE_STRING_LENGTH (t1) < TREE_STRING_LENGTH (t2) ? -1 : 1; return memcmp (TREE_STRING_POINTER (t1), TREE_STRING_POINTER (t2), TREE_STRING_LENGTH (t1)); case SSA_NAME: if (SSA_NAME_VERSION (t1) != SSA_NAME_VERSION (t2)) return SSA_NAME_VERSION (t1) < SSA_NAME_VERSION (t2) ? -1 : 1; break; default: if (POLY_INT_CST_P (t1)) return compare_sizes_for_sort (wi::to_poly_widest (t1), wi::to_poly_widest (t2)); tclass = TREE_CODE_CLASS (code); /* For decls, compare their UIDs. */ if (tclass == tcc_declaration) { if (DECL_UID (t1) != DECL_UID (t2)) return DECL_UID (t1) < DECL_UID (t2) ? -1 : 1; break; } /* For expressions, compare their operands recursively. */ else if (IS_EXPR_CODE_CLASS (tclass)) { for (i = TREE_OPERAND_LENGTH (t1) - 1; i >= 0; --i) { cmp = data_ref_compare_tree (TREE_OPERAND (t1, i), TREE_OPERAND (t2, i)); if (cmp != 0) return cmp; } } else gcc_unreachable (); } return 0; } /* Return TRUE it's possible to resolve data dependence DDR by runtime alias check. */ opt_result runtime_alias_check_p (ddr_p ddr, struct loop *loop, bool speed_p) { if (dump_enabled_p ()) dump_printf (MSG_NOTE, "consider run-time aliasing test between %T and %T\n", DR_REF (DDR_A (ddr)), DR_REF (DDR_B (ddr))); if (!speed_p) return opt_result::failure_at (DR_STMT (DDR_A (ddr)), "runtime alias check not supported when" " optimizing for size.\n"); /* FORNOW: We don't support versioning with outer-loop in either vectorization or loop distribution. */ if (loop != NULL && loop->inner != NULL) return opt_result::failure_at (DR_STMT (DDR_A (ddr)), "runtime alias check not supported for" " outer loop.\n"); return opt_result::success (); } /* Operator == between two dr_with_seg_len objects. This equality operator is used to make sure two data refs are the same one so that we will consider to combine the aliasing checks of those two pairs of data dependent data refs. */ static bool operator == (const dr_with_seg_len& d1, const dr_with_seg_len& d2) { return (operand_equal_p (DR_BASE_ADDRESS (d1.dr), DR_BASE_ADDRESS (d2.dr), 0) && data_ref_compare_tree (DR_OFFSET (d1.dr), DR_OFFSET (d2.dr)) == 0 && data_ref_compare_tree (DR_INIT (d1.dr), DR_INIT (d2.dr)) == 0 && data_ref_compare_tree (d1.seg_len, d2.seg_len) == 0 && known_eq (d1.access_size, d2.access_size) && d1.align == d2.align); } /* Comparison function for sorting objects of dr_with_seg_len_pair_t so that we can combine aliasing checks in one scan. */ static int comp_dr_with_seg_len_pair (const void *pa_, const void *pb_) { const dr_with_seg_len_pair_t* pa = (const dr_with_seg_len_pair_t *) pa_; const dr_with_seg_len_pair_t* pb = (const dr_with_seg_len_pair_t *) pb_; const dr_with_seg_len &a1 = pa->first, &a2 = pa->second; const dr_with_seg_len &b1 = pb->first, &b2 = pb->second; /* For DR pairs (a, b) and (c, d), we only consider to merge the alias checks if a and c have the same basic address snd step, and b and d have the same address and step. Therefore, if any a&c or b&d don't have the same address and step, we don't care the order of those two pairs after sorting. */ int comp_res; if ((comp_res = data_ref_compare_tree (DR_BASE_ADDRESS (a1.dr), DR_BASE_ADDRESS (b1.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_BASE_ADDRESS (a2.dr), DR_BASE_ADDRESS (b2.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_STEP (a1.dr), DR_STEP (b1.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_STEP (a2.dr), DR_STEP (b2.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_OFFSET (a1.dr), DR_OFFSET (b1.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_INIT (a1.dr), DR_INIT (b1.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_OFFSET (a2.dr), DR_OFFSET (b2.dr))) != 0) return comp_res; if ((comp_res = data_ref_compare_tree (DR_INIT (a2.dr), DR_INIT (b2.dr))) != 0) return comp_res; return 0; } /* Merge alias checks recorded in ALIAS_PAIRS and remove redundant ones. FACTOR is number of iterations that each data reference is accessed. Basically, for each pair of dependent data refs store_ptr_0 & load_ptr_0, we create an expression: ((store_ptr_0 + store_segment_length_0) <= load_ptr_0) || (load_ptr_0 + load_segment_length_0) <= store_ptr_0)) for aliasing checks. However, in some cases we can decrease the number of checks by combining two checks into one. For example, suppose we have another pair of data refs store_ptr_0 & load_ptr_1, and if the following condition is satisfied: load_ptr_0 < load_ptr_1 && load_ptr_1 - load_ptr_0 - load_segment_length_0 < store_segment_length_0 (this condition means, in each iteration of vectorized loop, the accessed memory of store_ptr_0 cannot be between the memory of load_ptr_0 and load_ptr_1.) we then can use only the following expression to finish the alising checks between store_ptr_0 & load_ptr_0 and store_ptr_0 & load_ptr_1: ((store_ptr_0 + store_segment_length_0) <= load_ptr_0) || (load_ptr_1 + load_segment_length_1 <= store_ptr_0)) Note that we only consider that load_ptr_0 and load_ptr_1 have the same basic address. */ void prune_runtime_alias_test_list (vec *alias_pairs, poly_uint64) { /* Sort the collected data ref pairs so that we can scan them once to combine all possible aliasing checks. */ alias_pairs->qsort (comp_dr_with_seg_len_pair); /* Scan the sorted dr pairs and check if we can combine alias checks of two neighboring dr pairs. */ for (size_t i = 1; i < alias_pairs->length (); ++i) { /* Deal with two ddrs (dr_a1, dr_b1) and (dr_a2, dr_b2). */ dr_with_seg_len *dr_a1 = &(*alias_pairs)[i-1].first, *dr_b1 = &(*alias_pairs)[i-1].second, *dr_a2 = &(*alias_pairs)[i].first, *dr_b2 = &(*alias_pairs)[i].second; /* Remove duplicate data ref pairs. */ if (*dr_a1 == *dr_a2 && *dr_b1 == *dr_b2) { if (dump_enabled_p ()) dump_printf (MSG_NOTE, "found equal ranges %T, %T and %T, %T\n", DR_REF (dr_a1->dr), DR_REF (dr_b1->dr), DR_REF (dr_a2->dr), DR_REF (dr_b2->dr)); alias_pairs->ordered_remove (i--); continue; } if (*dr_a1 == *dr_a2 || *dr_b1 == *dr_b2) { /* We consider the case that DR_B1 and DR_B2 are same memrefs, and DR_A1 and DR_A2 are two consecutive memrefs. */ if (*dr_a1 == *dr_a2) { std::swap (dr_a1, dr_b1); std::swap (dr_a2, dr_b2); } poly_int64 init_a1, init_a2; /* Only consider cases in which the distance between the initial DR_A1 and the initial DR_A2 is known at compile time. */ if (!operand_equal_p (DR_BASE_ADDRESS (dr_a1->dr), DR_BASE_ADDRESS (dr_a2->dr), 0) || !operand_equal_p (DR_OFFSET (dr_a1->dr), DR_OFFSET (dr_a2->dr), 0) || !poly_int_tree_p (DR_INIT (dr_a1->dr), &init_a1) || !poly_int_tree_p (DR_INIT (dr_a2->dr), &init_a2)) continue; /* Don't combine if we can't tell which one comes first. */ if (!ordered_p (init_a1, init_a2)) continue; /* Make sure dr_a1 starts left of dr_a2. */ if (maybe_gt (init_a1, init_a2)) { std::swap (*dr_a1, *dr_a2); std::swap (init_a1, init_a2); } /* Work out what the segment length would be if we did combine DR_A1 and DR_A2: - If DR_A1 and DR_A2 have equal lengths, that length is also the combined length. - If DR_A1 and DR_A2 both have negative "lengths", the combined length is the lower bound on those lengths. - If DR_A1 and DR_A2 both have positive lengths, the combined length is the upper bound on those lengths. Other cases are unlikely to give a useful combination. The lengths both have sizetype, so the sign is taken from the step instead. */ if (!operand_equal_p (dr_a1->seg_len, dr_a2->seg_len, 0)) { poly_uint64 seg_len_a1, seg_len_a2; if (!poly_int_tree_p (dr_a1->seg_len, &seg_len_a1) || !poly_int_tree_p (dr_a2->seg_len, &seg_len_a2)) continue; tree indicator_a = dr_direction_indicator (dr_a1->dr); if (TREE_CODE (indicator_a) != INTEGER_CST) continue; tree indicator_b = dr_direction_indicator (dr_a2->dr); if (TREE_CODE (indicator_b) != INTEGER_CST) continue; int sign_a = tree_int_cst_sgn (indicator_a); int sign_b = tree_int_cst_sgn (indicator_b); poly_uint64 new_seg_len; if (sign_a <= 0 && sign_b <= 0) new_seg_len = lower_bound (seg_len_a1, seg_len_a2); else if (sign_a >= 0 && sign_b >= 0) new_seg_len = upper_bound (seg_len_a1, seg_len_a2); else continue; dr_a1->seg_len = build_int_cst (TREE_TYPE (dr_a1->seg_len), new_seg_len); dr_a1->align = MIN (dr_a1->align, known_alignment (new_seg_len)); } /* This is always positive due to the swap above. */ poly_uint64 diff = init_a2 - init_a1; /* The new check will start at DR_A1. Make sure that its access size encompasses the initial DR_A2. */ if (maybe_lt (dr_a1->access_size, diff + dr_a2->access_size)) { dr_a1->access_size = upper_bound (dr_a1->access_size, diff + dr_a2->access_size); unsigned int new_align = known_alignment (dr_a1->access_size); dr_a1->align = MIN (dr_a1->align, new_align); } if (dump_enabled_p ()) dump_printf (MSG_NOTE, "merging ranges for %T, %T and %T, %T\n", DR_REF (dr_a1->dr), DR_REF (dr_b1->dr), DR_REF (dr_a2->dr), DR_REF (dr_b2->dr)); alias_pairs->ordered_remove (i); i--; } } } /* Given LOOP's two data references and segment lengths described by DR_A and DR_B, create expression checking if the two addresses ranges intersect with each other based on index of the two addresses. This can only be done if DR_A and DR_B referring to the same (array) object and the index is the only difference. For example: DR_A DR_B data-ref arr[i] arr[j] base_object arr arr index {i_0, +, 1}_loop {j_0, +, 1}_loop The addresses and their index are like: |<- ADDR_A ->| |<- ADDR_B ->| -------------------------------------------------------> | | | | | | | | | | -------------------------------------------------------> i_0 ... i_0+4 j_0 ... j_0+4 We can create expression based on index rather than address: (i_0 + 4 < j_0 || j_0 + 4 < i_0) Note evolution step of index needs to be considered in comparison. */ static bool create_intersect_range_checks_index (struct loop *loop, tree *cond_expr, const dr_with_seg_len& dr_a, const dr_with_seg_len& dr_b) { if (integer_zerop (DR_STEP (dr_a.dr)) || integer_zerop (DR_STEP (dr_b.dr)) || DR_NUM_DIMENSIONS (dr_a.dr) != DR_NUM_DIMENSIONS (dr_b.dr)) return false; poly_uint64 seg_len1, seg_len2; if (!poly_int_tree_p (dr_a.seg_len, &seg_len1) || !poly_int_tree_p (dr_b.seg_len, &seg_len2)) return false; if (!tree_fits_shwi_p (DR_STEP (dr_a.dr))) return false; if (!operand_equal_p (DR_BASE_OBJECT (dr_a.dr), DR_BASE_OBJECT (dr_b.dr), 0)) return false; if (!operand_equal_p (DR_STEP (dr_a.dr), DR_STEP (dr_b.dr), 0)) return false; gcc_assert (TREE_CODE (DR_STEP (dr_a.dr)) == INTEGER_CST); bool neg_step = tree_int_cst_compare (DR_STEP (dr_a.dr), size_zero_node) < 0; unsigned HOST_WIDE_INT abs_step = tree_to_shwi (DR_STEP (dr_a.dr)); if (neg_step) { abs_step = -abs_step; seg_len1 = -seg_len1; seg_len2 = -seg_len2; } else { /* Include the access size in the length, so that we only have one tree addition below. */ seg_len1 += dr_a.access_size; seg_len2 += dr_b.access_size; } /* Infer the number of iterations with which the memory segment is accessed by DR. In other words, alias is checked if memory segment accessed by DR_A in some iterations intersect with memory segment accessed by DR_B in the same amount iterations. Note segnment length is a linear function of number of iterations with DR_STEP as the coefficient. */ poly_uint64 niter_len1, niter_len2; if (!can_div_trunc_p (seg_len1 + abs_step - 1, abs_step, &niter_len1) || !can_div_trunc_p (seg_len2 + abs_step - 1, abs_step, &niter_len2)) return false; poly_uint64 niter_access1 = 0, niter_access2 = 0; if (neg_step) { /* Divide each access size by the byte step, rounding up. */ if (!can_div_trunc_p (dr_a.access_size - abs_step - 1, abs_step, &niter_access1) || !can_div_trunc_p (dr_b.access_size + abs_step - 1, abs_step, &niter_access2)) return false; } unsigned int i; for (i = 0; i < DR_NUM_DIMENSIONS (dr_a.dr); i++) { tree access1 = DR_ACCESS_FN (dr_a.dr, i); tree access2 = DR_ACCESS_FN (dr_b.dr, i); /* Two indices must be the same if they are not scev, or not scev wrto current loop being vecorized. */ if (TREE_CODE (access1) != POLYNOMIAL_CHREC || TREE_CODE (access2) != POLYNOMIAL_CHREC || CHREC_VARIABLE (access1) != (unsigned)loop->num || CHREC_VARIABLE (access2) != (unsigned)loop->num) { if (operand_equal_p (access1, access2, 0)) continue; return false; } /* The two indices must have the same step. */ if (!operand_equal_p (CHREC_RIGHT (access1), CHREC_RIGHT (access2), 0)) return false; tree idx_step = CHREC_RIGHT (access1); /* Index must have const step, otherwise DR_STEP won't be constant. */ gcc_assert (TREE_CODE (idx_step) == INTEGER_CST); /* Index must evaluate in the same direction as DR. */ gcc_assert (!neg_step || tree_int_cst_sign_bit (idx_step) == 1); tree min1 = CHREC_LEFT (access1); tree min2 = CHREC_LEFT (access2); if (!types_compatible_p (TREE_TYPE (min1), TREE_TYPE (min2))) return false; /* Ideally, alias can be checked against loop's control IV, but we need to prove linear mapping between control IV and reference index. Although that should be true, we check against (array) index of data reference. Like segment length, index length is linear function of the number of iterations with index_step as the coefficient, i.e, niter_len * idx_step. */ tree idx_len1 = fold_build2 (MULT_EXPR, TREE_TYPE (min1), idx_step, build_int_cst (TREE_TYPE (min1), niter_len1)); tree idx_len2 = fold_build2 (MULT_EXPR, TREE_TYPE (min2), idx_step, build_int_cst (TREE_TYPE (min2), niter_len2)); tree max1 = fold_build2 (PLUS_EXPR, TREE_TYPE (min1), min1, idx_len1); tree max2 = fold_build2 (PLUS_EXPR, TREE_TYPE (min2), min2, idx_len2); /* Adjust ranges for negative step. */ if (neg_step) { /* IDX_LEN1 and IDX_LEN2 are negative in this case. */ std::swap (min1, max1); std::swap (min2, max2); /* As with the lengths just calculated, we've measured the access sizes in iterations, so multiply them by the index step. */ tree idx_access1 = fold_build2 (MULT_EXPR, TREE_TYPE (min1), idx_step, build_int_cst (TREE_TYPE (min1), niter_access1)); tree idx_access2 = fold_build2 (MULT_EXPR, TREE_TYPE (min2), idx_step, build_int_cst (TREE_TYPE (min2), niter_access2)); /* MINUS_EXPR because the above values are negative. */ max1 = fold_build2 (MINUS_EXPR, TREE_TYPE (max1), max1, idx_access1); max2 = fold_build2 (MINUS_EXPR, TREE_TYPE (max2), max2, idx_access2); } tree part_cond_expr = fold_build2 (TRUTH_OR_EXPR, boolean_type_node, fold_build2 (LE_EXPR, boolean_type_node, max1, min2), fold_build2 (LE_EXPR, boolean_type_node, max2, min1)); if (*cond_expr) *cond_expr = fold_build2 (TRUTH_AND_EXPR, boolean_type_node, *cond_expr, part_cond_expr); else *cond_expr = part_cond_expr; } return true; } /* If ALIGN is nonzero, set up *SEQ_MIN_OUT and *SEQ_MAX_OUT so that for every address ADDR accessed by D: *SEQ_MIN_OUT <= ADDR (== ADDR & -ALIGN) <= *SEQ_MAX_OUT In this case, every element accessed by D is aligned to at least ALIGN bytes. If ALIGN is zero then instead set *SEG_MAX_OUT so that: *SEQ_MIN_OUT <= ADDR < *SEQ_MAX_OUT. */ static void get_segment_min_max (const dr_with_seg_len &d, tree *seg_min_out, tree *seg_max_out, HOST_WIDE_INT align) { /* Each access has the following pattern: <- |seg_len| -> <--- A: -ve step ---> +-----+-------+-----+-------+-----+ | n-1 | ,.... | 0 | ..... | n-1 | +-----+-------+-----+-------+-----+ <--- B: +ve step ---> <- |seg_len| -> | base address where "n" is the number of scalar iterations covered by the segment. (This should be VF for a particular pair if we know that both steps are the same, otherwise it will be the full number of scalar loop iterations.) A is the range of bytes accessed when the step is negative, B is the range when the step is positive. If the access size is "access_size" bytes, the lowest addressed byte is: base + (step < 0 ? seg_len : 0) [LB] and the highest addressed byte is always below: base + (step < 0 ? 0 : seg_len) + access_size [UB] Thus: LB <= ADDR < UB If ALIGN is nonzero, all three values are aligned to at least ALIGN bytes, so: LB <= ADDR <= UB - ALIGN where "- ALIGN" folds naturally with the "+ access_size" and often cancels it out. We don't try to simplify LB and UB beyond this (e.g. by using MIN and MAX based on whether seg_len rather than the stride is negative) because it is possible for the absolute size of the segment to overflow the range of a ssize_t. Keeping the pointer_plus outside of the cond_expr should allow the cond_exprs to be shared with other alias checks. */ tree indicator = dr_direction_indicator (d.dr); tree neg_step = fold_build2 (LT_EXPR, boolean_type_node, fold_convert (ssizetype, indicator), ssize_int (0)); tree addr_base = fold_build_pointer_plus (DR_BASE_ADDRESS (d.dr), DR_OFFSET (d.dr)); addr_base = fold_build_pointer_plus (addr_base, DR_INIT (d.dr)); tree seg_len = fold_convert (sizetype, rewrite_to_non_trapping_overflow (d.seg_len)); tree min_reach = fold_build3 (COND_EXPR, sizetype, neg_step, seg_len, size_zero_node); tree max_reach = fold_build3 (COND_EXPR, sizetype, neg_step, size_zero_node, seg_len); max_reach = fold_build2 (PLUS_EXPR, sizetype, max_reach, size_int (d.access_size - align)); *seg_min_out = fold_build_pointer_plus (addr_base, min_reach); *seg_max_out = fold_build_pointer_plus (addr_base, max_reach); } /* Given two data references and segment lengths described by DR_A and DR_B, create expression checking if the two addresses ranges intersect with each other: ((DR_A_addr_0 + DR_A_segment_length_0) <= DR_B_addr_0) || (DR_B_addr_0 + DER_B_segment_length_0) <= DR_A_addr_0)) */ static void create_intersect_range_checks (struct loop *loop, tree *cond_expr, const dr_with_seg_len& dr_a, const dr_with_seg_len& dr_b) { *cond_expr = NULL_TREE; if (create_intersect_range_checks_index (loop, cond_expr, dr_a, dr_b)) return; unsigned HOST_WIDE_INT min_align; tree_code cmp_code; if (TREE_CODE (DR_STEP (dr_a.dr)) == INTEGER_CST && TREE_CODE (DR_STEP (dr_b.dr)) == INTEGER_CST) { /* In this case adding access_size to seg_len is likely to give a simple X * step, where X is either the number of scalar iterations or the vectorization factor. We're better off keeping that, rather than subtracting an alignment from it. In this case the maximum values are exclusive and so there is no alias if the maximum of one segment equals the minimum of another. */ min_align = 0; cmp_code = LE_EXPR; } else { /* Calculate the minimum alignment shared by all four pointers, then arrange for this alignment to be subtracted from the exclusive maximum values to get inclusive maximum values. This "- min_align" is cumulative with a "+ access_size" in the calculation of the maximum values. In the best (and common) case, the two cancel each other out, leaving us with an inclusive bound based only on seg_len. In the worst case we're simply adding a smaller number than before. Because the maximum values are inclusive, there is an alias if the maximum value of one segment is equal to the minimum value of the other. */ min_align = MIN (dr_a.align, dr_b.align); cmp_code = LT_EXPR; } tree seg_a_min, seg_a_max, seg_b_min, seg_b_max; get_segment_min_max (dr_a, &seg_a_min, &seg_a_max, min_align); get_segment_min_max (dr_b, &seg_b_min, &seg_b_max, min_align); *cond_expr = fold_build2 (TRUTH_OR_EXPR, boolean_type_node, fold_build2 (cmp_code, boolean_type_node, seg_a_max, seg_b_min), fold_build2 (cmp_code, boolean_type_node, seg_b_max, seg_a_min)); } /* Create a conditional expression that represents the run-time checks for overlapping of address ranges represented by a list of data references pairs passed in ALIAS_PAIRS. Data references are in LOOP. The returned COND_EXPR is the conditional expression to be used in the if statement that controls which version of the loop gets executed at runtime. */ void create_runtime_alias_checks (struct loop *loop, vec *alias_pairs, tree * cond_expr) { tree part_cond_expr; fold_defer_overflow_warnings (); for (size_t i = 0, s = alias_pairs->length (); i < s; ++i) { const dr_with_seg_len& dr_a = (*alias_pairs)[i].first; const dr_with_seg_len& dr_b = (*alias_pairs)[i].second; if (dump_enabled_p ()) dump_printf (MSG_NOTE, "create runtime check for data references %T and %T\n", DR_REF (dr_a.dr), DR_REF (dr_b.dr)); /* Create condition expression for each pair data references. */ create_intersect_range_checks (loop, &part_cond_expr, dr_a, dr_b); if (*cond_expr) *cond_expr = fold_build2 (TRUTH_AND_EXPR, boolean_type_node, *cond_expr, part_cond_expr); else *cond_expr = part_cond_expr; } fold_undefer_and_ignore_overflow_warnings (); } /* Check if OFFSET1 and OFFSET2 (DR_OFFSETs of some data-refs) are identical expressions. */ static bool dr_equal_offsets_p1 (tree offset1, tree offset2) { bool res; STRIP_NOPS (offset1); STRIP_NOPS (offset2); if (offset1 == offset2) return true; if (TREE_CODE (offset1) != TREE_CODE (offset2) || (!BINARY_CLASS_P (offset1) && !UNARY_CLASS_P (offset1))) return false; res = dr_equal_offsets_p1 (TREE_OPERAND (offset1, 0), TREE_OPERAND (offset2, 0)); if (!res || !BINARY_CLASS_P (offset1)) return res; res = dr_equal_offsets_p1 (TREE_OPERAND (offset1, 1), TREE_OPERAND (offset2, 1)); return res; } /* Check if DRA and DRB have equal offsets. */ bool dr_equal_offsets_p (struct data_reference *dra, struct data_reference *drb) { tree offset1, offset2; offset1 = DR_OFFSET (dra); offset2 = DR_OFFSET (drb); return dr_equal_offsets_p1 (offset1, offset2); } /* Returns true if FNA == FNB. */ static bool affine_function_equal_p (affine_fn fna, affine_fn fnb) { unsigned i, n = fna.length (); if (n != fnb.length ()) return false; for (i = 0; i < n; i++) if (!operand_equal_p (fna[i], 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 affine_fn (); comm = cf->fns[0]; for (i = 1; i < cf->n; i++) if (!affine_function_equal_p (comm, cf->fns[i])) return affine_fn (); return comm; } /* Returns the base of the affine function FN. */ static tree affine_function_base (affine_fn fn) { return 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; fn.iterate (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)); } /* Returns a signed integer type with the largest precision from TA and TB. */ static tree signed_type_for_types (tree ta, tree tb) { if (TYPE_PRECISION (ta) > TYPE_PRECISION (tb)) return signed_type_for (ta); else return signed_type_for (tb); } /* 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 (fnb.length () > fna.length ()) { n = fna.length (); m = fnb.length (); } else { n = fnb.length (); m = fna.length (); } ret.create (m); for (i = 0; i < n; i++) { tree type = signed_type_for_types (TREE_TYPE (fna[i]), TREE_TYPE (fnb[i])); ret.quick_push (fold_build2 (op, type, fna[i], fnb[i])); } for (; fna.iterate (i, &coef); i++) ret.quick_push (fold_build2 (op, signed_type_for (TREE_TYPE (coef)), coef, integer_zero_node)); for (; fnb.iterate (i, &coef); i++) ret.quick_push (fold_build2 (op, signed_type_for (TREE_TYPE (coef)), 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) { fn.release (); } /* 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.exists () || !fn_b.exists ()) { 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; } /* Returns true if the address of OBJ is invariant in LOOP. */ static bool object_address_invariant_in_loop_p (const struct loop *loop, const_tree obj) { while (handled_component_p (obj)) { if (TREE_CODE (obj) == ARRAY_REF) { for (int i = 1; i < 4; ++i) if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, i), loop->num)) return false; } else if (TREE_CODE (obj) == COMPONENT_REF) { if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 2), loop->num)) return false; } obj = TREE_OPERAND (obj, 0); } if (!INDIRECT_REF_P (obj) && TREE_CODE (obj) != MEM_REF) return true; return !chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 0), loop->num); } /* Returns false if we can prove that data references A and B do not alias, true otherwise. If LOOP_NEST is false no cross-iteration aliases are considered. */ bool dr_may_alias_p (const struct data_reference *a, const struct data_reference *b, bool loop_nest) { tree addr_a = DR_BASE_OBJECT (a); tree addr_b = DR_BASE_OBJECT (b); /* If we are not processing a loop nest but scalar code we do not need to care about possible cross-iteration dependences and thus can process the full original reference. Do so, similar to how loop invariant motion applies extra offset-based disambiguation. */ if (!loop_nest) { aff_tree off1, off2; poly_widest_int size1, size2; get_inner_reference_aff (DR_REF (a), &off1, &size1); get_inner_reference_aff (DR_REF (b), &off2, &size2); aff_combination_scale (&off1, -1); aff_combination_add (&off2, &off1); if (aff_comb_cannot_overlap_p (&off2, size1, size2)) return false; } if ((TREE_CODE (addr_a) == MEM_REF || TREE_CODE (addr_a) == TARGET_MEM_REF) && (TREE_CODE (addr_b) == MEM_REF || TREE_CODE (addr_b) == TARGET_MEM_REF) && MR_DEPENDENCE_CLIQUE (addr_a) == MR_DEPENDENCE_CLIQUE (addr_b) && MR_DEPENDENCE_BASE (addr_a) != MR_DEPENDENCE_BASE (addr_b)) return false; /* If we had an evolution in a pointer-based MEM_REF BASE_OBJECT we do not know the size of the base-object. So we cannot do any offset/overlap based analysis but have to rely on points-to information only. */ if (TREE_CODE (addr_a) == MEM_REF && (DR_UNCONSTRAINED_BASE (a) || TREE_CODE (TREE_OPERAND (addr_a, 0)) == SSA_NAME)) { /* For true dependences we can apply TBAA. */ if (flag_strict_aliasing && DR_IS_WRITE (a) && DR_IS_READ (b) && !alias_sets_conflict_p (get_alias_set (DR_REF (a)), get_alias_set (DR_REF (b)))) return false; if (TREE_CODE (addr_b) == MEM_REF) return ptr_derefs_may_alias_p (TREE_OPERAND (addr_a, 0), TREE_OPERAND (addr_b, 0)); else return ptr_derefs_may_alias_p (TREE_OPERAND (addr_a, 0), build_fold_addr_expr (addr_b)); } else if (TREE_CODE (addr_b) == MEM_REF && (DR_UNCONSTRAINED_BASE (b) || TREE_CODE (TREE_OPERAND (addr_b, 0)) == SSA_NAME)) { /* For true dependences we can apply TBAA. */ if (flag_strict_aliasing && DR_IS_WRITE (a) && DR_IS_READ (b) && !alias_sets_conflict_p (get_alias_set (DR_REF (a)), get_alias_set (DR_REF (b)))) return false; if (TREE_CODE (addr_a) == MEM_REF) return ptr_derefs_may_alias_p (TREE_OPERAND (addr_a, 0), TREE_OPERAND (addr_b, 0)); else return ptr_derefs_may_alias_p (build_fold_addr_expr (addr_a), TREE_OPERAND (addr_b, 0)); } /* Otherwise DR_BASE_OBJECT is an access that covers the whole object that is being subsetted in the loop nest. */ if (DR_IS_WRITE (a) && DR_IS_WRITE (b)) return refs_output_dependent_p (addr_a, addr_b); else if (DR_IS_READ (a) && DR_IS_WRITE (b)) return refs_anti_dependent_p (addr_a, addr_b); return refs_may_alias_p (addr_a, addr_b); } /* REF_A and REF_B both satisfy access_fn_component_p. Return true if it is meaningful to compare their associated access functions when checking for dependencies. */ static bool access_fn_components_comparable_p (tree ref_a, tree ref_b) { /* Allow pairs of component refs from the following sets: { REALPART_EXPR, IMAGPART_EXPR } { COMPONENT_REF } { ARRAY_REF }. */ tree_code code_a = TREE_CODE (ref_a); tree_code code_b = TREE_CODE (ref_b); if (code_a == IMAGPART_EXPR) code_a = REALPART_EXPR; if (code_b == IMAGPART_EXPR) code_b = REALPART_EXPR; if (code_a != code_b) return false; if (TREE_CODE (ref_a) == COMPONENT_REF) /* ??? We cannot simply use the type of operand #0 of the refs here as the Fortran compiler smuggles type punning into COMPONENT_REFs. Use the DECL_CONTEXT of the FIELD_DECLs instead. */ return (DECL_CONTEXT (TREE_OPERAND (ref_a, 1)) == DECL_CONTEXT (TREE_OPERAND (ref_b, 1))); return types_compatible_p (TREE_TYPE (TREE_OPERAND (ref_a, 0)), TREE_TYPE (TREE_OPERAND (ref_b, 0))); } /* 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. */ struct data_dependence_relation * initialize_data_dependence_relation (struct data_reference *a, struct data_reference *b, vec loop_nest) { struct data_dependence_relation *res; unsigned int i; res = XCNEW (struct data_dependence_relation); DDR_A (res) = a; DDR_B (res) = b; DDR_LOOP_NEST (res).create (0); DDR_SUBSCRIPTS (res).create (0); DDR_DIR_VECTS (res).create (0); DDR_DIST_VECTS (res).create (0); if (a == NULL || b == NULL) { DDR_ARE_DEPENDENT (res) = chrec_dont_know; return res; } /* If the data references do not alias, then they are independent. */ if (!dr_may_alias_p (a, b, loop_nest.exists ())) { DDR_ARE_DEPENDENT (res) = chrec_known; return res; } unsigned int num_dimensions_a = DR_NUM_DIMENSIONS (a); unsigned int num_dimensions_b = DR_NUM_DIMENSIONS (b); if (num_dimensions_a == 0 || num_dimensions_b == 0) { DDR_ARE_DEPENDENT (res) = chrec_dont_know; return res; } /* For unconstrained bases, the root (highest-indexed) subscript describes a variation in the base of the original DR_REF rather than a component access. We have no type that accurately describes the new DR_BASE_OBJECT (whose TREE_TYPE describes the type *after* applying this subscript) so limit the search to the last real component access. E.g. for: void f (int a[][8], int b[][8]) { for (int i = 0; i < 8; ++i) a[i * 2][0] = b[i][0]; } the a and b accesses have a single ARRAY_REF component reference [0] but have two subscripts. */ if (DR_UNCONSTRAINED_BASE (a)) num_dimensions_a -= 1; if (DR_UNCONSTRAINED_BASE (b)) num_dimensions_b -= 1; /* These structures describe sequences of component references in DR_REF (A) and DR_REF (B). Each component reference is tied to a specific access function. */ struct { /* The sequence starts at DR_ACCESS_FN (A, START_A) of A and DR_ACCESS_FN (B, START_B) of B (inclusive) and extends to higher indices. In C notation, these are the indices of the rightmost component references; e.g. for a sequence .b.c.d, the start index is for .d. */ unsigned int start_a; unsigned int start_b; /* The sequence contains LENGTH consecutive access functions from each DR. */ unsigned int length; /* The enclosing objects for the A and B sequences respectively, i.e. the objects to which DR_ACCESS_FN (A, START_A + LENGTH - 1) and DR_ACCESS_FN (B, START_B + LENGTH - 1) are applied. */ tree object_a; tree object_b; } full_seq = {}, struct_seq = {}; /* Before each iteration of the loop: - REF_A is what you get after applying DR_ACCESS_FN (A, INDEX_A) and - REF_B is what you get after applying DR_ACCESS_FN (B, INDEX_B). */ unsigned int index_a = 0; unsigned int index_b = 0; tree ref_a = DR_REF (a); tree ref_b = DR_REF (b); /* Now walk the component references from the final DR_REFs back up to the enclosing base objects. Each component reference corresponds to one access function in the DR, with access function 0 being for the final DR_REF and the highest-indexed access function being the one that is applied to the base of the DR. Look for a sequence of component references whose access functions are comparable (see access_fn_components_comparable_p). If more than one such sequence exists, pick the one nearest the base (which is the leftmost sequence in C notation). Store this sequence in FULL_SEQ. For example, if we have: struct foo { struct bar s; ... } (*a)[10], (*b)[10]; A: a[0][i].s.c.d B: __real b[0][i].s.e[i].f (where d is the same type as the real component of f) then the access functions would be: 0 1 2 3 A: .d .c .s [i] 0 1 2 3 4 5 B: __real .f [i] .e .s [i] The A0/B2 column isn't comparable, since .d is a COMPONENT_REF and [i] is an ARRAY_REF. However, the A1/B3 column contains two COMPONENT_REF accesses for struct bar, so is comparable. Likewise the A2/B4 column contains two COMPONENT_REF accesses for struct foo, so is comparable. The A3/B5 column contains two ARRAY_REFs that index foo[10] arrays, so is again comparable. The sequence is therefore: A: [1, 3] (i.e. [i].s.c) B: [3, 5] (i.e. [i].s.e) Also look for sequences of component references whose access functions are comparable and whose enclosing objects have the same RECORD_TYPE. Store this sequence in STRUCT_SEQ. In the above example, STRUCT_SEQ would be: A: [1, 2] (i.e. s.c) B: [3, 4] (i.e. s.e) */ while (index_a < num_dimensions_a && index_b < num_dimensions_b) { /* REF_A and REF_B must be one of the component access types allowed by dr_analyze_indices. */ gcc_checking_assert (access_fn_component_p (ref_a)); gcc_checking_assert (access_fn_component_p (ref_b)); /* Get the immediately-enclosing objects for REF_A and REF_B, i.e. the references *before* applying DR_ACCESS_FN (A, INDEX_A) and DR_ACCESS_FN (B, INDEX_B). */ tree object_a = TREE_OPERAND (ref_a, 0); tree object_b = TREE_OPERAND (ref_b, 0); tree type_a = TREE_TYPE (object_a); tree type_b = TREE_TYPE (object_b); if (access_fn_components_comparable_p (ref_a, ref_b)) { /* This pair of component accesses is comparable for dependence analysis, so we can include DR_ACCESS_FN (A, INDEX_A) and DR_ACCESS_FN (B, INDEX_B) in the sequence. */ if (full_seq.start_a + full_seq.length != index_a || full_seq.start_b + full_seq.length != index_b) { /* The accesses don't extend the current sequence, so start a new one here. */ full_seq.start_a = index_a; full_seq.start_b = index_b; full_seq.length = 0; } /* Add this pair of references to the sequence. */ full_seq.length += 1; full_seq.object_a = object_a; full_seq.object_b = object_b; /* If the enclosing objects are structures (and thus have the same RECORD_TYPE), record the new sequence in STRUCT_SEQ. */ if (TREE_CODE (type_a) == RECORD_TYPE) struct_seq = full_seq; /* Move to the next containing reference for both A and B. */ ref_a = object_a; ref_b = object_b; index_a += 1; index_b += 1; continue; } /* Try to approach equal type sizes. */ if (!COMPLETE_TYPE_P (type_a) || !COMPLETE_TYPE_P (type_b) || !tree_fits_uhwi_p (TYPE_SIZE_UNIT (type_a)) || !tree_fits_uhwi_p (TYPE_SIZE_UNIT (type_b))) break; unsigned HOST_WIDE_INT size_a = tree_to_uhwi (TYPE_SIZE_UNIT (type_a)); unsigned HOST_WIDE_INT size_b = tree_to_uhwi (TYPE_SIZE_UNIT (type_b)); if (size_a <= size_b) { index_a += 1; ref_a = object_a; } if (size_b <= size_a) { index_b += 1; ref_b = object_b; } } /* See whether FULL_SEQ ends at the base and whether the two bases are equal. We do not care about TBAA or alignment info so we can use OEP_ADDRESS_OF to avoid false negatives. */ tree base_a = DR_BASE_OBJECT (a); tree base_b = DR_BASE_OBJECT (b); bool same_base_p = (full_seq.start_a + full_seq.length == num_dimensions_a && full_seq.start_b + full_seq.length == num_dimensions_b && DR_UNCONSTRAINED_BASE (a) == DR_UNCONSTRAINED_BASE (b) && operand_equal_p (base_a, base_b, OEP_ADDRESS_OF) && types_compatible_p (TREE_TYPE (base_a), TREE_TYPE (base_b)) && (!loop_nest.exists () || (object_address_invariant_in_loop_p (loop_nest[0], base_a)))); /* If the bases are the same, we can include the base variation too. E.g. the b accesses in: for (int i = 0; i < n; ++i) b[i + 4][0] = b[i][0]; have a definite dependence distance of 4, while for: for (int i = 0; i < n; ++i) a[i + 4][0] = b[i][0]; the dependence distance depends on the gap between a and b. If the bases are different then we can only rely on the sequence rooted at a structure access, since arrays are allowed to overlap arbitrarily and change shape arbitrarily. E.g. we treat this as valid code: int a[256]; ... ((int (*)[4][3]) &a[1])[i][0] += ((int (*)[4][3]) &a[2])[i][0]; where two lvalues with the same int[4][3] type overlap, and where both lvalues are distinct from the object's declared type. */ if (same_base_p) { if (DR_UNCONSTRAINED_BASE (a)) full_seq.length += 1; } else full_seq = struct_seq; /* Punt if we didn't find a suitable sequence. */ if (full_seq.length == 0) { DDR_ARE_DEPENDENT (res) = chrec_dont_know; return res; } if (!same_base_p) { /* Partial overlap is possible for different bases when strict aliasing is not in effect. It's also possible if either base involves a union access; e.g. for: struct s1 { int a[2]; }; struct s2 { struct s1 b; int c; }; struct s3 { int d; struct s1 e; }; union u { struct s2 f; struct s3 g; } *p, *q; the s1 at "p->f.b" (base "p->f") partially overlaps the s1 at "p->g.e" (base "p->g") and might partially overlap the s1 at "q->g.e" (base "q->g"). */ if (!flag_strict_aliasing || ref_contains_union_access_p (full_seq.object_a) || ref_contains_union_access_p (full_seq.object_b)) { DDR_ARE_DEPENDENT (res) = chrec_dont_know; return res; } DDR_COULD_BE_INDEPENDENT_P (res) = true; if (!loop_nest.exists () || (object_address_invariant_in_loop_p (loop_nest[0], full_seq.object_a) && object_address_invariant_in_loop_p (loop_nest[0], full_seq.object_b))) { DDR_OBJECT_A (res) = full_seq.object_a; DDR_OBJECT_B (res) = full_seq.object_b; } } DDR_AFFINE_P (res) = true; DDR_ARE_DEPENDENT (res) = NULL_TREE; DDR_SUBSCRIPTS (res).create (full_seq.length); DDR_LOOP_NEST (res) = loop_nest; DDR_INNER_LOOP (res) = 0; DDR_SELF_REFERENCE (res) = false; for (i = 0; i < full_seq.length; ++i) { struct subscript *subscript; subscript = XNEW (struct subscript); SUB_ACCESS_FN (subscript, 0) = DR_ACCESS_FN (a, full_seq.start_a + i); SUB_ACCESS_FN (subscript, 1) = DR_ACCESS_FN (b, full_seq.start_b + i); 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; DDR_SUBSCRIPTS (res).safe_push (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 subscripts) { unsigned i; subscript_p s; FOR_EACH_VEC_ELT (subscripts, i, s) { free_conflict_function (s->conflicting_iterations_in_a); free_conflict_function (s->conflicting_iterations_in_b); free (s); } subscripts.release (); } /* 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) { DDR_ARE_DEPENDENT (ddr) = chrec; free_subscripts (DDR_SUBSCRIPTS (ddr)); DDR_SUBSCRIPTS (ddr).create (0); } /* 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 (const_tree chrec_a, const_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 (const_tree chrec_a, const_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; /* FALLTHRU */ 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 (n > 0 && 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; fn.create (1); fn.quick_push (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; fn.create (dim + 1); unsigned i; gcc_assert (dim > 0); fn.quick_push (cst); for (i = 1; i < dim; i++) fn.quick_push (integer_zero_node); fn.quick_push (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 type, difference; dependence_stats.num_ziv++; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(analyze_ziv_subscript \n"); type = signed_type_for_types (TREE_TYPE (chrec_a), TREE_TYPE (chrec_b)); chrec_a = chrec_convert (type, chrec_a, NULL); chrec_b = chrec_convert (type, chrec_b, NULL); difference = chrec_fold_minus (type, 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"); } /* Similar to max_stmt_executions_int, but returns the bound as a tree, and only if it fits to the int type. If this is not the case, or the bound on the number of iterations of LOOP could not be derived, returns chrec_dont_know. */ static tree max_stmt_executions_tree (struct loop *loop) { widest_int nit; if (!max_stmt_executions (loop, &nit)) return chrec_dont_know; if (!wi::fits_to_tree_p (nit, unsigned_type_node)) return chrec_dont_know; return wide_int_to_tree (unsigned_type_node, nit); } /* Determine whether the CHREC is always positive/negative. If the expression cannot be statically analyzed, return false, otherwise set the answer into VALUE. */ static bool chrec_is_positive (tree chrec, bool *value) { bool value0, value1, value2; tree end_value, nb_iter; switch (TREE_CODE (chrec)) { case POLYNOMIAL_CHREC: if (!chrec_is_positive (CHREC_LEFT (chrec), &value0) || !chrec_is_positive (CHREC_RIGHT (chrec), &value1)) return false; /* FIXME -- overflows. */ if (value0 == value1) { *value = value0; return true; } /* Otherwise the chrec is under the form: "{-197, +, 2}_1", and the proof consists in showing that the sign never changes during the execution of the loop, from 0 to loop->nb_iterations. */ if (!evolution_function_is_affine_p (chrec)) return false; nb_iter = number_of_latch_executions (get_chrec_loop (chrec)); if (chrec_contains_undetermined (nb_iter)) return false; #if 0 /* TODO -- If the test is after the exit, we may decrease the number of iterations by one. */ if (after_exit) nb_iter = chrec_fold_minus (type, nb_iter, build_int_cst (type, 1)); #endif end_value = chrec_apply (CHREC_VARIABLE (chrec), chrec, nb_iter); if (!chrec_is_positive (end_value, &value2)) return false; *value = value0; return value0 == value1; case INTEGER_CST: switch (tree_int_cst_sgn (chrec)) { case -1: *value = false; break; case 1: *value = true; break; default: return false; } return true; default: return false; } } /* 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 type, difference, tmp; type = signed_type_for_types (TREE_TYPE (chrec_a), TREE_TYPE (chrec_b)); chrec_a = chrec_convert (type, chrec_a, NULL); chrec_b = chrec_convert (type, chrec_b, NULL); difference = chrec_fold_minus (type, initial_condition (chrec_b), chrec_a); /* Special case overlap in the first iteration. */ if (integer_zerop (difference)) { *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_one_node; return; } 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 (TREE_CODE (chrec_b) != POLYNOMIAL_CHREC || !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, type, fold_build1 (ABS_EXPR, type, 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 = max_stmt_executions_int (loop); 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 (TREE_CODE (chrec_b) != POLYNOMIAL_CHREC || !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, type, 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 = max_stmt_executions_int (loop); 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 tree initialize_matrix_A (lambda_matrix A, tree chrec, unsigned index, int mult) { gcc_assert (chrec); switch (TREE_CODE (chrec)) { case POLYNOMIAL_CHREC: A[index][0] = mult * int_cst_value (CHREC_RIGHT (chrec)); return initialize_matrix_A (A, CHREC_LEFT (chrec), index + 1, mult); case PLUS_EXPR: case MULT_EXPR: case MINUS_EXPR: { tree op0 = initialize_matrix_A (A, TREE_OPERAND (chrec, 0), index, mult); tree op1 = initialize_matrix_A (A, TREE_OPERAND (chrec, 1), index, mult); return chrec_fold_op (TREE_CODE (chrec), chrec_type (chrec), op0, op1); } CASE_CONVERT: { tree op = initialize_matrix_A (A, TREE_OPERAND (chrec, 0), index, mult); return chrec_convert (chrec_type (chrec), op, NULL); } case BIT_NOT_EXPR: { /* Handle ~X as -1 - X. */ tree op = initialize_matrix_A (A, TREE_OPERAND (chrec, 0), index, mult); return chrec_fold_op (MINUS_EXPR, chrec_type (chrec), build_int_cst (TREE_TYPE (chrec), -1), op); } case INTEGER_CST: return chrec; default: gcc_unreachable (); return NULL_TREE; } } #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 (HOST_WIDE_INT niter, HOST_WIDE_INT step_a, HOST_WIDE_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))) { HOST_WIDE_INT step_overlaps_a, step_overlaps_b; HOST_WIDE_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; if (niter > 0) { tau2 = FLOOR_DIV (niter, step_overlaps_a); tau2 = MIN (tau2, FLOOR_DIV (niter, step_overlaps_b)); last_conflict = tau2; *last_conflicts = build_int_cst (NULL_TREE, last_conflict); } else *last_conflicts = chrec_dont_know; *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)); } 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; HOST_WIDE_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 = max_stmt_executions_int (get_chrec_loop (CHREC_LEFT (chrec_a))); niter_y = max_stmt_executions_int (get_chrec_loop (chrec_a)); niter_z = max_stmt_executions_int (get_chrec_loop (chrec_b)); 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); } /* Copy the elements of vector VEC1 with length SIZE to VEC2. */ static void lambda_vector_copy (lambda_vector vec1, lambda_vector vec2, int size) { memcpy (vec2, vec1, size * sizeof (*vec1)); } /* Copy the elements of M x N matrix MAT1 to MAT2. */ static void lambda_matrix_copy (lambda_matrix mat1, lambda_matrix mat2, int m, int n) { int i; for (i = 0; i < m; i++) lambda_vector_copy (mat1[i], mat2[i], n); } /* Store the N x N identity matrix in MAT. */ static void lambda_matrix_id (lambda_matrix mat, int size) { int i, j; for (i = 0; i < size; i++) for (j = 0; j < size; j++) mat[i][j] = (i == j) ? 1 : 0; } /* Return the index of the first nonzero element of vector VEC1 between START and N. We must have START <= N. Returns N if VEC1 is the zero vector. */ static int lambda_vector_first_nz (lambda_vector vec1, int n, int start) { int j = start; while (j < n && vec1[j] == 0) j++; return j; } /* Add a multiple of row R1 of matrix MAT with N columns to row R2: R2 = R2 + CONST1 * R1. */ static void lambda_matrix_row_add (lambda_matrix mat, int n, int r1, int r2, lambda_int const1) { int i; if (const1 == 0) return; for (i = 0; i < n; i++) mat[r2][i] += const1 * mat[r1][i]; } /* Multiply vector VEC1 of length SIZE by a constant CONST1, and store the result in VEC2. */ static void lambda_vector_mult_const (lambda_vector vec1, lambda_vector vec2, int size, lambda_int const1) { int i; if (const1 == 0) lambda_vector_clear (vec2, size); else for (i = 0; i < size; i++) vec2[i] = const1 * vec1[i]; } /* Negate vector VEC1 with length SIZE and store it in VEC2. */ static void lambda_vector_negate (lambda_vector vec1, lambda_vector vec2, int size) { lambda_vector_mult_const (vec1, vec2, size, -1); } /* Negate row R1 of matrix MAT which has N columns. */ static void lambda_matrix_row_negate (lambda_matrix mat, int n, int r1) { lambda_vector_negate (mat[r1], mat[r1], n); } /* Return true if two vectors are equal. */ static bool lambda_vector_equal (lambda_vector vec1, lambda_vector vec2, int size) { int i; for (i = 0; i < size; i++) if (vec1[i] != vec2[i]) return false; return true; } /* Given an M x N integer matrix A, this function determines an M x M unimodular matrix U, and an M x N echelon matrix S such that "U.A = S". This decomposition is also known as "right Hermite". Ref: Algorithm 2.1 page 33 in "Loop Transformations for Restructuring Compilers" Utpal Banerjee. */ static void lambda_matrix_right_hermite (lambda_matrix A, int m, int n, lambda_matrix S, lambda_matrix U) { int i, j, i0 = 0; lambda_matrix_copy (A, S, m, n); lambda_matrix_id (U, m); for (j = 0; j < n; j++) { if (lambda_vector_first_nz (S[j], m, i0) < m) { ++i0; for (i = m - 1; i >= i0; i--) { while (S[i][j] != 0) { lambda_int sigma, factor, a, b; a = S[i-1][j]; b = S[i][j]; sigma = (a * b < 0) ? -1: 1; a = abs_hwi (a); b = abs_hwi (b); factor = sigma * (a / b); lambda_matrix_row_add (S, n, i, i-1, -factor); std::swap (S[i], S[i-1]); lambda_matrix_row_add (U, m, i, i-1, -factor); std::swap (U[i], U[i-1]); } } } } } /* 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; HOST_WIDE_INT init_a, init_b, gamma, gcd_alpha_beta; lambda_matrix A, U, S; struct obstack scratch_obstack; 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); gcc_obstack_init (&scratch_obstack); dim = nb_vars_a + nb_vars_b; U = lambda_matrix_new (dim, dim, &scratch_obstack); A = lambda_matrix_new (dim, 1, &scratch_obstack); S = lambda_matrix_new (dim, 1, &scratch_obstack); init_a = int_cst_value (initialize_matrix_A (A, chrec_a, 0, 1)); init_b = int_cst_value (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) { HOST_WIDE_INT step_a, step_b; HOST_WIDE_INT niter, niter_a, niter_b; affine_fn ova, ovb; niter_a = max_stmt_executions_int (get_chrec_loop (chrec_a)); niter_b = max_stmt_executions_int (get_chrec_loop (chrec_b)); 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. */ HOST_WIDE_INT i0, j0, i1, j1; 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; goto end_analyze_subs_aa; } if (i1 > 0 && j1 > 0) { HOST_WIDE_INT niter_a = max_stmt_executions_int (get_chrec_loop (chrec_a)); HOST_WIDE_INT niter_b = max_stmt_executions_int (get_chrec_loop (chrec_b)); HOST_WIDE_INT niter = MIN (niter_a, niter_b); /* (X0, Y0) is a solution of the Diophantine equation: "chrec_a (X0) = chrec_b (Y0)". */ HOST_WIDE_INT tau1 = MAX (CEIL (-i0, i1), CEIL (-j0, j1)); HOST_WIDE_INT x0 = i1 * tau1 + i0; HOST_WIDE_INT y0 = j1 * tau1 + j0; /* (X1, Y1) is the smallest positive solution of the eq "chrec_a (X1) = chrec_b (Y1)", i.e. this is where the first conflict occurs. */ HOST_WIDE_INT min_multiple = MIN (x0 / i1, y0 / j1); HOST_WIDE_INT x1 = x0 - i1 * min_multiple; HOST_WIDE_INT y1 = y0 - j1 * min_multiple; if (niter > 0) { HOST_WIDE_INT tau2 = MIN (FLOOR_DIV (niter_a - i0, i1), FLOOR_DIV (niter_b - j0, j1)); HOST_WIDE_INT last_conflict = tau2 - (x1 - i0)/i1; /* If the overlap occurs outside of the bounds of the loop, there is no dependence. */ if (x1 >= niter_a || y1 >= niter_b) { *overlaps_a = conflict_fn_no_dependence (); *overlaps_b = conflict_fn_no_dependence (); *last_conflicts = integer_zero_node; goto end_analyze_subs_aa; } else *last_conflicts = build_int_cst (NULL_TREE, last_conflict); } else *last_conflicts = chrec_dont_know; *overlaps_a = conflict_fn (1, affine_fn_univar (build_int_cst (NULL_TREE, x1), 1, build_int_cst (NULL_TREE, i1))); *overlaps_b = conflict_fn (1, affine_fn_univar (build_int_cst (NULL_TREE, y1), 1, build_int_cst (NULL_TREE, j1))); } else { /* FIXME: For the moment, the upper bound of the iteration domain for i and 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 { 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: obstack_free (&scratch_obstack, NULL); 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"); } } /* 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); 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); *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, int loop_nest_num) { 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_in_loop (chrec_b, loop_nest_num)) analyze_siv_subscript_cst_affine (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts); else if (evolution_function_is_affine_in_loop (chrec_a, loop_nest_num) && 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_in_loop (chrec_a, loop_nest_num) && evolution_function_is_affine_in_loop (chrec_b, loop_nest_num)) { 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); 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"); *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 (const_tree chrec, const_tree cst) { HOST_WIDE_INT cd = 0, val; tree step; if (!tree_fits_shwi_p (cst)) return true; val = tree_to_shwi (cst); while (TREE_CODE (chrec) == POLYNOMIAL_CHREC) { step = CHREC_RIGHT (chrec); if (!tree_fits_shwi_p (step)) return true; cd = gcd (cd, tree_to_shwi (step)); chrec = CHREC_LEFT (chrec); } return val % cd == 0; } /* Analyze a MIV (Multiple Index Variable) subscript with respect to LOOP_NEST. *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, struct loop *loop_nest) { tree type, difference; dependence_stats.num_miv++; if (dump_file && (dump_flags & TDF_DETAILS)) fprintf (dump_file, "(analyze_miv_subscript \n"); type = signed_type_for_types (TREE_TYPE (chrec_a), TREE_TYPE (chrec_b)); chrec_a = chrec_convert (type, chrec_a, NULL); chrec_b = chrec_convert (type, chrec_b, NULL); difference = chrec_fold_minus (type, 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 = max_stmt_executions_tree (get_chrec_loop (chrec_a)); dependence_stats.num_miv_dependent++; } else if (evolution_function_is_constant_p (difference) && evolution_function_is_affine_multivariate_p (chrec_a, loop_nest->num) && !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_in_loop (chrec_a, loop_nest->num) && !chrec_contains_symbols (chrec_a) && evolution_function_is_affine_in_loop (chrec_b, loop_nest->num) && !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 in with respect to LOOP_NEST. 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, struct loop *loop_nest) { unsigned int lnn = loop_nest->num; 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); fprintf (dump_file, ")\n (chrec_b = "); print_generic_expr (dump_file, chrec_b); 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, lnn) || operand_equal_p (chrec_a, chrec_b, 0))) { 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, lnn) || !evolution_function_is_affine_multivariate_p (chrec_b, lnn))) { 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, lnn); else analyze_miv_subscript (chrec_a, chrec_b, overlap_iterations_a, overlap_iterations_b, last_conflicts, loop_nest); 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"); } } /* 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_EACH_VEC_ELT (DDR_DIST_VECTS (ddr), i, v) if (lambda_vector_equal (v, dist_v, DDR_NB_LOOPS (ddr))) return; DDR_DIST_VECTS (ddr).safe_push (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_EACH_VEC_ELT (DDR_DIR_VECTS (ddr), i, v) if (lambda_vector_equal (v, dir_v, DDR_NB_LOOPS (ddr))) return; DDR_DIR_VECTS (ddr).safe_push (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. A_INDEX is the index of the first reference (0 for DDR_A, 1 for DDR_B) and B_INDEX is the index of the second reference. 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, unsigned int a_index, unsigned int b_index, 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 = SUB_ACCESS_FN (subscript, a_index); access_fn_b = SUB_ACCESS_FN (subscript, b_index); if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC) { HOST_WIDE_INT dist; int index; int var_a = CHREC_VARIABLE (access_fn_a); int var_b = CHREC_VARIABLE (access_fn_b); if (var_a != var_b || chrec_contains_undetermined (SUB_DISTANCE (subscript))) { non_affine_dependence_relation (ddr); return false; } dist = int_cst_value (SUB_DISTANCE (subscript)); index = index_in_loop_nest (var_a, DDR_LOOP_NEST (ddr)); *index_carry = MIN (index, *index_carry); /* 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 if (!operand_equal_p (access_fn_a, access_fn_b, 0)) { /* 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 only constant access functions. */ static bool constant_access_functions (const struct data_dependence_relation *ddr) { unsigned i; subscript *sub; FOR_EACH_VEC_ELT (DDR_SUBSCRIPTS (ddr), i, sub) if (!evolution_function_is_constant_p (SUB_ACCESS_FN (sub, 0)) || !evolution_function_is_constant_p (SUB_ACCESS_FN (sub, 1))) return false; return true; } /* Helper function for the case where DDR_A and DDR_B are the same multivariate access function with a constant step. For an example see pr34635-1.c. */ 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; HOST_WIDE_INT v1, v2, cd; /* Polynomials with more than 2 variables are not handled yet. When the evolution steps are parameters, it is not possible to represent the dependence using classical distance vectors. */ if (TREE_CODE (c_0) != INTEGER_CST || TREE_CODE (CHREC_RIGHT (c_1)) != INTEGER_CST || TREE_CODE (CHREC_RIGHT (c_2)) != INTEGER_CST) { DDR_AFFINE_P (ddr) = false; 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); subscript *sub; FOR_EACH_VEC_ELT (DDR_SUBSCRIPTS (ddr), i, sub) { tree access_fun = SUB_ACCESS_FN (sub, 0); 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; } access_fun = SUB_ACCESS_FN (DDR_SUBSCRIPT (ddr, 0), 0); if (TREE_CODE (CHREC_LEFT (access_fun)) == POLYNOMIAL_CHREC) add_multivariate_self_dist (ddr, access_fun); else /* The evolution step is not constant: it varies in the outer loop, so this cannot be represented by a distance vector. For example in pr34635.c the evolution is {0, +, {0, +, 4}_1}_2. */ DDR_AFFINE_P (ddr) = false; 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; } } } /* Return true when the DDR contains two data references that have the same access functions. */ static inline bool same_access_functions (const struct data_dependence_relation *ddr) { unsigned i; subscript *sub; FOR_EACH_VEC_ELT (DDR_SUBSCRIPTS (ddr), i, sub) if (!eq_evolutions_p (SUB_ACCESS_FN (sub, 0), SUB_ACCESS_FN (sub, 1))) return false; return true; } /* 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, struct loop *loop_nest) { bool init_b = false; int index_carry = DDR_NB_LOOPS (ddr); lambda_vector dist_v; if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE) return false; 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, 0, 1, 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)); if (!subscript_dependence_tester_1 (ddr, 1, 0, loop_nest)) return false; compute_subscript_distance (ddr); if (!build_classic_dist_vector_1 (ddr, 1, 0, save_v, &init_b, &index_carry)) return false; save_dist_v (ddr, save_v); DDR_REVERSED_P (ddr) = true; /* 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)); if (DDR_NB_LOOPS (ddr) > 1) { lambda_vector opposite_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); if (!subscript_dependence_tester_1 (ddr, 1, 0, loop_nest)) return false; compute_subscript_distance (ddr); if (!build_classic_dist_vector_1 (ddr, 1, 0, opposite_v, &init_b, &index_carry)) return false; save_dist_v (ddr, save_v); add_outer_distances (ddr, dist_v, index_carry); add_outer_distances (ddr, opposite_v, index_carry); } else save_dist_v (ddr, save_v); } } 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_EACH_VEC_ELT (DDR_DIST_VECTS (ddr), i, dist_v) { 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 the data references. A_INDEX is the index of the first reference (0 for DDR_A, 1 for DDR_B) and B_INDEX is the index of the second reference. */ static bool subscript_dependence_tester_1 (struct data_dependence_relation *ddr, unsigned int a_index, unsigned int b_index, struct loop *loop_nest) { unsigned int i; tree last_conflicts; struct subscript *subscript; tree res = NULL_TREE; for (i = 0; DDR_SUBSCRIPTS (ddr).iterate (i, &subscript); i++) { conflict_function *overlaps_a, *overlaps_b; analyze_overlapping_iterations (SUB_ACCESS_FN (subscript, a_index), SUB_ACCESS_FN (subscript, b_index), &overlaps_a, &overlaps_b, &last_conflicts, loop_nest); if (SUB_CONFLICTS_IN_A (subscript)) free_conflict_function (SUB_CONFLICTS_IN_A (subscript)); if (SUB_CONFLICTS_IN_B (subscript)) free_conflict_function (SUB_CONFLICTS_IN_B (subscript)); SUB_CONFLICTS_IN_A (subscript) = overlaps_a; SUB_CONFLICTS_IN_B (subscript) = overlaps_b; SUB_LAST_CONFLICT (subscript) = last_conflicts; /* If there is any undetermined conflict function we have to give a conservative answer in case we cannot prove that no dependence exists when analyzing another subscript. */ if (CF_NOT_KNOWN_P (overlaps_a) || CF_NOT_KNOWN_P (overlaps_b)) { res = chrec_dont_know; continue; } /* When there is a subscript with no dependence we can stop. */ else if (CF_NO_DEPENDENCE_P (overlaps_a) || CF_NO_DEPENDENCE_P (overlaps_b)) { res = chrec_known; break; } } if (res == NULL_TREE) return true; if (res == chrec_known) dependence_stats.num_dependence_independent++; else dependence_stats.num_dependence_undetermined++; finalize_ddr_dependent (ddr, res); return false; } /* Computes the conflicting iterations in LOOP_NEST, and initialize DDR. */ static void subscript_dependence_tester (struct data_dependence_relation *ddr, struct loop *loop_nest) { if (subscript_dependence_tester_1 (ddr, 0, 1, loop_nest)) dependence_stats.num_dependence_dependent++; compute_subscript_distance (ddr); if (build_classic_dist_vector (ddr, loop_nest)) build_classic_dir_vector (ddr); } /* Returns true when all the access functions of A are affine or constant with respect to LOOP_NEST. */ static bool access_functions_are_affine_or_constant_p (const struct data_reference *a, const struct loop *loop_nest) { unsigned int i; vec fns = DR_ACCESS_FNS (a); tree t; FOR_EACH_VEC_ELT (fns, i, t) if (!evolution_function_is_invariant_p (t, loop_nest->num) && !evolution_function_is_affine_multivariate_p (t, loop_nest->num)) return false; return true; } /* This computes the affine dependence relation between A and B with respect to LOOP_NEST. 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. */ void compute_affine_dependence (struct data_dependence_relation *ddr, struct loop *loop_nest) { 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: "); print_gimple_stmt (dump_file, DR_STMT (dra), 0, TDF_SLIM); fprintf (dump_file, " stmt_b: "); print_gimple_stmt (dump_file, DR_STMT (drb), 0, TDF_SLIM); } /* 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, loop_nest) && access_functions_are_affine_or_constant_p (drb, loop_nest)) subscript_dependence_tester (ddr, loop_nest); /* 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 { 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)) { if (DDR_ARE_DEPENDENT (ddr) == chrec_known) fprintf (dump_file, ") -> no dependence\n"); else if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know) fprintf (dump_file, ") -> dependence analysis failed\n"); else fprintf (dump_file, ")\n"); } } /* 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. Return true when successful, i.e. data references number is small enough to be handled. */ bool compute_all_dependences (vec datarefs, vec *dependence_relations, vec loop_nest, bool compute_self_and_rr) { struct data_dependence_relation *ddr; struct data_reference *a, *b; unsigned int i, j; if ((int) datarefs.length () > PARAM_VALUE (PARAM_LOOP_MAX_DATAREFS_FOR_DATADEPS)) { struct data_dependence_relation *ddr; /* Insert a single relation into dependence_relations: chrec_dont_know. */ ddr = initialize_data_dependence_relation (NULL, NULL, loop_nest); dependence_relations->safe_push (ddr); return false; } FOR_EACH_VEC_ELT (datarefs, i, a) for (j = i + 1; datarefs.iterate (j, &b); j++) if (DR_IS_WRITE (a) || DR_IS_WRITE (b) || compute_self_and_rr) { ddr = initialize_data_dependence_relation (a, b, loop_nest); dependence_relations->safe_push (ddr); if (loop_nest.exists ()) compute_affine_dependence (ddr, loop_nest[0]); } if (compute_self_and_rr) FOR_EACH_VEC_ELT (datarefs, i, a) { ddr = initialize_data_dependence_relation (a, a, loop_nest); dependence_relations->safe_push (ddr); if (loop_nest.exists ()) compute_affine_dependence (ddr, loop_nest[0]); } return true; } /* Describes a location of a memory reference. */ struct data_ref_loc { /* The memory reference. */ tree ref; /* True if the memory reference is read. */ bool is_read; /* True if the data reference is conditional within the containing statement, i.e. if it might not occur even when the statement is executed and runs to completion. */ bool is_conditional_in_stmt; }; /* Stores the locations of memory references in STMT to REFERENCES. Returns true if STMT clobbers memory, false otherwise. */ static bool get_references_in_stmt (gimple *stmt, vec *references) { bool clobbers_memory = false; data_ref_loc ref; tree op0, op1; enum gimple_code stmt_code = gimple_code (stmt); /* ASM_EXPR and CALL_EXPR may embed arbitrary side effects. As we cannot model data-references to not spelled out accesses give up if they may occur. */ if (stmt_code == GIMPLE_CALL && !(gimple_call_flags (stmt) & ECF_CONST)) { /* Allow IFN_GOMP_SIMD_LANE in their own loops. */ if (gimple_call_internal_p (stmt)) switch (gimple_call_internal_fn (stmt)) { case IFN_GOMP_SIMD_LANE: { struct loop *loop = gimple_bb (stmt)->loop_father; tree uid = gimple_call_arg (stmt, 0); gcc_assert (TREE_CODE (uid) == SSA_NAME); if (loop == NULL || loop->simduid != SSA_NAME_VAR (uid)) clobbers_memory = true; break; } case IFN_MASK_LOAD: case IFN_MASK_STORE: break; default: clobbers_memory = true; break; } else clobbers_memory = true; } else if (stmt_code == GIMPLE_ASM && (gimple_asm_volatile_p (as_a (stmt)) || gimple_vuse (stmt))) clobbers_memory = true; if (!gimple_vuse (stmt)) return clobbers_memory; if (stmt_code == GIMPLE_ASSIGN) { tree base; op0 = gimple_assign_lhs (stmt); op1 = gimple_assign_rhs1 (stmt); if (DECL_P (op1) || (REFERENCE_CLASS_P (op1) && (base = get_base_address (op1)) && TREE_CODE (base) != SSA_NAME && !is_gimple_min_invariant (base))) { ref.ref = op1; ref.is_read = true; ref.is_conditional_in_stmt = false; references->safe_push (ref); } } else if (stmt_code == GIMPLE_CALL) { unsigned i, n; tree ptr, type; unsigned int align; ref.is_read = false; if (gimple_call_internal_p (stmt)) switch (gimple_call_internal_fn (stmt)) { case IFN_MASK_LOAD: if (gimple_call_lhs (stmt) == NULL_TREE) break; ref.is_read = true; /* FALLTHRU */ case IFN_MASK_STORE: ptr = build_int_cst (TREE_TYPE (gimple_call_arg (stmt, 1)), 0); align = tree_to_shwi (gimple_call_arg (stmt, 1)); if (ref.is_read) type = TREE_TYPE (gimple_call_lhs (stmt)); else type = TREE_TYPE (gimple_call_arg (stmt, 3)); if (TYPE_ALIGN (type) != align) type = build_aligned_type (type, align); ref.is_conditional_in_stmt = true; ref.ref = fold_build2 (MEM_REF, type, gimple_call_arg (stmt, 0), ptr); references->safe_push (ref); return false; default: break; } op0 = gimple_call_lhs (stmt); n = gimple_call_num_args (stmt); for (i = 0; i < n; i++) { op1 = gimple_call_arg (stmt, i); if (DECL_P (op1) || (REFERENCE_CLASS_P (op1) && get_base_address (op1))) { ref.ref = op1; ref.is_read = true; ref.is_conditional_in_stmt = false; references->safe_push (ref); } } } else return clobbers_memory; if (op0 && (DECL_P (op0) || (REFERENCE_CLASS_P (op0) && get_base_address (op0)))) { ref.ref = op0; ref.is_read = false; ref.is_conditional_in_stmt = false; references->safe_push (ref); } return clobbers_memory; } /* Returns true if the loop-nest has any data reference. */ bool loop_nest_has_data_refs (loop_p loop) { basic_block *bbs = get_loop_body (loop); auto_vec references; for (unsigned i = 0; i < loop->num_nodes; i++) { basic_block bb = bbs[i]; gimple_stmt_iterator bsi; for (bsi = gsi_start_bb (bb); !gsi_end_p (bsi); gsi_next (&bsi)) { gimple *stmt = gsi_stmt (bsi); get_references_in_stmt (stmt, &references); if (references.length ()) { free (bbs); return true; } } } free (bbs); return false; } /* Stores the data references in STMT to DATAREFS. If there is an unanalyzable reference, returns false, otherwise returns true. NEST is the outermost loop of the loop nest in which the references should be analyzed. */ opt_result find_data_references_in_stmt (struct loop *nest, gimple *stmt, vec *datarefs) { unsigned i; auto_vec references; data_ref_loc *ref; data_reference_p dr; if (get_references_in_stmt (stmt, &references)) return opt_result::failure_at (stmt, "statement clobbers memory: %G", stmt); FOR_EACH_VEC_ELT (references, i, ref) { dr = create_data_ref (nest ? loop_preheader_edge (nest) : NULL, loop_containing_stmt (stmt), ref->ref, stmt, ref->is_read, ref->is_conditional_in_stmt); gcc_assert (dr != NULL); datarefs->safe_push (dr); } return opt_result::success (); } /* Stores the data references in STMT to DATAREFS. If there is an unanalyzable reference, returns false, otherwise returns true. NEST is the outermost loop of the loop nest in which the references should be instantiated, LOOP is the loop in which the references should be analyzed. */ bool graphite_find_data_references_in_stmt (edge nest, loop_p loop, gimple *stmt, vec *datarefs) { unsigned i; auto_vec references; data_ref_loc *ref; bool ret = true; data_reference_p dr; if (get_references_in_stmt (stmt, &references)) return false; FOR_EACH_VEC_ELT (references, i, ref) { dr = create_data_ref (nest, loop, ref->ref, stmt, ref->is_read, ref->is_conditional_in_stmt); gcc_assert (dr != NULL); datarefs->safe_push (dr); } 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. */ tree find_data_references_in_bb (struct loop *loop, basic_block bb, vec *datarefs) { gimple_stmt_iterator bsi; for (bsi = gsi_start_bb (bb); !gsi_end_p (bsi); gsi_next (&bsi)) { gimple *stmt = gsi_stmt (bsi); if (!find_data_references_in_stmt (loop, stmt, datarefs)) { struct data_reference *res; res = XCNEW (struct data_reference); datarefs->safe_push (res); return chrec_dont_know; } } return NULL_TREE; } /* 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 *datarefs) { basic_block bb, *bbs; unsigned int i; bbs = get_loop_body_in_dom_order (loop); for (i = 0; i < loop->num_nodes; i++) { bb = bbs[i]; if (find_data_references_in_bb (loop, bb, datarefs) == chrec_dont_know) { free (bbs); return chrec_dont_know; } } free (bbs); return NULL_TREE; } /* Return the alignment in bytes that DRB is guaranteed to have at all times. */ unsigned int dr_alignment (innermost_loop_behavior *drb) { /* Get the alignment of BASE_ADDRESS + INIT. */ unsigned int alignment = drb->base_alignment; unsigned int misalignment = (drb->base_misalignment + TREE_INT_CST_LOW (drb->init)); if (misalignment != 0) alignment = MIN (alignment, misalignment & -misalignment); /* Cap it to the alignment of OFFSET. */ if (!integer_zerop (drb->offset)) alignment = MIN (alignment, drb->offset_alignment); /* Cap it to the alignment of STEP. */ if (!integer_zerop (drb->step)) alignment = MIN (alignment, drb->step_alignment); return alignment; } /* If BASE is a pointer-typed SSA name, try to find the object that it is based on. Return this object X on success and store the alignment in bytes of BASE - &X in *ALIGNMENT_OUT. */ static tree get_base_for_alignment_1 (tree base, unsigned int *alignment_out) { if (TREE_CODE (base) != SSA_NAME || !POINTER_TYPE_P (TREE_TYPE (base))) return NULL_TREE; gimple *def = SSA_NAME_DEF_STMT (base); base = analyze_scalar_evolution (loop_containing_stmt (def), base); /* Peel chrecs and record the minimum alignment preserved by all steps. */ unsigned int alignment = MAX_OFILE_ALIGNMENT / BITS_PER_UNIT; while (TREE_CODE (base) == POLYNOMIAL_CHREC) { unsigned int step_alignment = highest_pow2_factor (CHREC_RIGHT (base)); alignment = MIN (alignment, step_alignment); base = CHREC_LEFT (base); } /* Punt if the expression is too complicated to handle. */ if (tree_contains_chrecs (base, NULL) || !POINTER_TYPE_P (TREE_TYPE (base))) return NULL_TREE; /* The only useful cases are those for which a dereference folds to something other than an INDIRECT_REF. */ tree ref_type = TREE_TYPE (TREE_TYPE (base)); tree ref = fold_indirect_ref_1 (UNKNOWN_LOCATION, ref_type, base); if (!ref) return NULL_TREE; /* Analyze the base to which the steps we peeled were applied. */ poly_int64 bitsize, bitpos, bytepos; machine_mode mode; int unsignedp, reversep, volatilep; tree offset; base = get_inner_reference (ref, &bitsize, &bitpos, &offset, &mode, &unsignedp, &reversep, &volatilep); if (!base || !multiple_p (bitpos, BITS_PER_UNIT, &bytepos)) return NULL_TREE; /* Restrict the alignment to that guaranteed by the offsets. */ unsigned int bytepos_alignment = known_alignment (bytepos); if (bytepos_alignment != 0) alignment = MIN (alignment, bytepos_alignment); if (offset) { unsigned int offset_alignment = highest_pow2_factor (offset); alignment = MIN (alignment, offset_alignment); } *alignment_out = alignment; return base; } /* Return the object whose alignment would need to be changed in order to increase the alignment of ADDR. Store the maximum achievable alignment in *MAX_ALIGNMENT. */ tree get_base_for_alignment (tree addr, unsigned int *max_alignment) { tree base = get_base_for_alignment_1 (addr, max_alignment); if (base) return base; if (TREE_CODE (addr) == ADDR_EXPR) addr = TREE_OPERAND (addr, 0); *max_alignment = MAX_OFILE_ALIGNMENT / BITS_PER_UNIT; return addr; } /* Recursive helper function. */ static bool find_loop_nest_1 (struct loop *loop, vec *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; loop_nest->safe_push (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. */ bool find_loop_nest (struct loop *loop, vec *loop_nest) { loop_nest->safe_push (loop); if (loop->inner) return find_loop_nest_1 (loop->inner, loop_nest); return true; } /* Returns true when the data dependences have been computed, false otherwise. 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. */ bool compute_data_dependences_for_loop (struct loop *loop, bool compute_self_and_read_read_dependences, vec *loop_nest, vec *datarefs, vec *dependence_relations) { bool res = true; 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 || !find_loop_nest (loop, loop_nest) || find_data_references_in_loop (loop, datarefs) == chrec_dont_know || !compute_all_dependences (*datarefs, dependence_relations, *loop_nest, compute_self_and_read_read_dependences)) res = false; 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); } return res; } /* 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_SUBSCRIPTS (ddr).exists ()) free_subscripts (DDR_SUBSCRIPTS (ddr)); DDR_DIST_VECTS (ddr).release (); DDR_DIR_VECTS (ddr).release (); free (ddr); } /* Free the memory used by the data dependence relations from DEPENDENCE_RELATIONS. */ void free_dependence_relations (vec dependence_relations) { unsigned int i; struct data_dependence_relation *ddr; FOR_EACH_VEC_ELT (dependence_relations, i, ddr) if (ddr) free_dependence_relation (ddr); dependence_relations.release (); } /* Free the memory used by the data references from DATAREFS. */ void free_data_refs (vec datarefs) { unsigned int i; struct data_reference *dr; FOR_EACH_VEC_ELT (datarefs, i, dr) free_data_ref (dr); datarefs.release (); } /* Common routine implementing both dr_direction_indicator and dr_zero_step_indicator. Return USEFUL_MIN if the indicator is known to be >= USEFUL_MIN and -1 if the indicator is known to be negative. Return the step as the indicator otherwise. */ static tree dr_step_indicator (struct data_reference *dr, int useful_min) { tree step = DR_STEP (dr); if (!step) return NULL_TREE; STRIP_NOPS (step); /* Look for cases where the step is scaled by a positive constant integer, which will often be the access size. If the multiplication doesn't change the sign (due to overflow effects) then we can test the unscaled value instead. */ if (TREE_CODE (step) == MULT_EXPR && TREE_CODE (TREE_OPERAND (step, 1)) == INTEGER_CST && tree_int_cst_sgn (TREE_OPERAND (step, 1)) > 0) { tree factor = TREE_OPERAND (step, 1); step = TREE_OPERAND (step, 0); /* Strip widening and truncating conversions as well as nops. */ if (CONVERT_EXPR_P (step) && INTEGRAL_TYPE_P (TREE_TYPE (TREE_OPERAND (step, 0)))) step = TREE_OPERAND (step, 0); tree type = TREE_TYPE (step); /* Get the range of step values that would not cause overflow. */ widest_int minv = (wi::to_widest (TYPE_MIN_VALUE (ssizetype)) / wi::to_widest (factor)); widest_int maxv = (wi::to_widest (TYPE_MAX_VALUE (ssizetype)) / wi::to_widest (factor)); /* Get the range of values that the unconverted step actually has. */ wide_int step_min, step_max; if (TREE_CODE (step) != SSA_NAME || get_range_info (step, &step_min, &step_max) != VR_RANGE) { step_min = wi::to_wide (TYPE_MIN_VALUE (type)); step_max = wi::to_wide (TYPE_MAX_VALUE (type)); } /* Check whether the unconverted step has an acceptable range. */ signop sgn = TYPE_SIGN (type); if (wi::les_p (minv, widest_int::from (step_min, sgn)) && wi::ges_p (maxv, widest_int::from (step_max, sgn))) { if (wi::ge_p (step_min, useful_min, sgn)) return ssize_int (useful_min); else if (wi::lt_p (step_max, 0, sgn)) return ssize_int (-1); else return fold_convert (ssizetype, step); } } return DR_STEP (dr); } /* Return a value that is negative iff DR has a negative step. */ tree dr_direction_indicator (struct data_reference *dr) { return dr_step_indicator (dr, 0); } /* Return a value that is zero iff DR has a zero step. */ tree dr_zero_step_indicator (struct data_reference *dr) { return dr_step_indicator (dr, 1); } /* Return true if DR is known to have a nonnegative (but possibly zero) step. */ bool dr_known_forward_stride_p (struct data_reference *dr) { tree indicator = dr_direction_indicator (dr); tree neg_step_val = fold_binary (LT_EXPR, boolean_type_node, fold_convert (ssizetype, indicator), ssize_int (0)); return neg_step_val && integer_zerop (neg_step_val); }