diff options
author | Ben Cheng <bccheng@google.com> | 2014-03-25 22:37:19 -0700 |
---|---|---|
committer | Ben Cheng <bccheng@google.com> | 2014-03-25 22:37:19 -0700 |
commit | 1bc5aee63eb72b341f506ad058502cd0361f0d10 (patch) | |
tree | c607e8252f3405424ff15bc2d00aa38dadbb2518 /gcc-4.9/gcc/tree-data-ref.c | |
parent | 283a0bf58fcf333c58a2a92c3ebbc41fb9eb1fdb (diff) | |
download | toolchain_gcc-1bc5aee63eb72b341f506ad058502cd0361f0d10.tar.gz toolchain_gcc-1bc5aee63eb72b341f506ad058502cd0361f0d10.tar.bz2 toolchain_gcc-1bc5aee63eb72b341f506ad058502cd0361f0d10.zip |
Initial checkin of GCC 4.9.0 from trunk (r208799).
Change-Id: I48a3c08bb98542aa215912a75f03c0890e497dba
Diffstat (limited to 'gcc-4.9/gcc/tree-data-ref.c')
-rw-r--r-- | gcc-4.9/gcc/tree-data-ref.c | 4833 |
1 files changed, 4833 insertions, 0 deletions
diff --git a/gcc-4.9/gcc/tree-data-ref.c b/gcc-4.9/gcc/tree-data-ref.c new file mode 100644 index 000000000..01d0a7a79 --- /dev/null +++ b/gcc-4.9/gcc/tree-data-ref.c @@ -0,0 +1,4833 @@ +/* Data references and dependences detectors. + Copyright (C) 2003-2014 Free Software Foundation, Inc. + Contributed by Sebastian Pop <pop@cri.ensmp.fr> + +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 +<http://www.gnu.org/licenses/>. */ + +/* 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 "tree.h" +#include "expr.h" +#include "gimple-pretty-print.h" +#include "basic-block.h" +#include "tree-ssa-alias.h" +#include "internal-fn.h" +#include "gimple-expr.h" +#include "is-a.h" +#include "gimple.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 "langhooks.h" +#include "tree-affine.h" +#include "params.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 *, + struct data_reference *, + struct data_reference *, + 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); +} + + + +/* Dump into FILE all the data references from DATAREFS. */ + +static void +dump_data_references (FILE *file, vec<data_reference_p> 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<data_reference_p> &ref) +{ + dump_data_references (stderr, ref); +} + +DEBUG_FUNCTION void +debug (vec<data_reference_p> *ptr) +{ + if (ptr) + debug (*ptr); + else + fprintf (stderr, "<nil>\n"); +} + + +/* Dump into STDERR all the data references from DATAREFS. */ + +DEBUG_FUNCTION void +debug_data_references (vec<data_reference_p> 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, 0); + fprintf (outf, "# ref: "); + print_generic_stmt (outf, DR_REF (dr), 0); + fprintf (outf, "# base_object: "); + print_generic_stmt (outf, DR_BASE_OBJECT (dr), 0); + + for (i = 0; i < DR_NUM_DIMENSIONS (dr); i++) + { + fprintf (outf, "# Access function %d: ", i); + print_generic_stmt (outf, DR_ACCESS_FN (dr, i), 0); + } + fprintf (outf, "#)\n"); +} + +/* 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, "<nil>\n"); +} + + +/* Dumps the affine function described by FN to the file OUTF. */ + +static void +dump_affine_function (FILE *outf, affine_fn fn) +{ + unsigned i; + tree coef; + + print_generic_expr (outf, 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. */ + +static 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. */ + +static 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, 0); + } + + 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, 0); + } + + fprintf (outf, "\n (Subscript distance: "); + print_generic_expr (outf, SUB_DISTANCE (subscript), 0); + fprintf (outf, " ))\n"); +} + +/* Print the classic direction vector DIRV to OUTF. */ + +static 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. */ + +static void +print_dir_vectors (FILE *outf, vec<lambda_vector> 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. */ + +static inline void +print_lambda_vector (FILE * outfile, lambda_vector vector, int n) +{ + int i; + + for (i = 0; i < n; i++) + fprintf (outfile, "%3d ", vector[i]); + fprintf (outfile, "\n"); +} + +/* Print a vector of distance vectors. */ + +static void +print_dist_vectors (FILE *outf, vec<lambda_vector> 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. */ + +static 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; + + for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) + { + fprintf (outf, " access_fn_A: "); + print_generic_stmt (outf, DR_ACCESS_FN (dra, i), 0); + fprintf (outf, " access_fn_B: "); + print_generic_stmt (outf, DR_ACCESS_FN (drb, i), 0); + dump_subscript (outf, DDR_SUBSCRIPT (ddr, i)); + } + + fprintf (outf, " inner loop index: %d\n", DDR_INNER_LOOP (ddr)); + fprintf (outf, " loop nest: ("); + FOR_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. */ + +void +dump_data_dependence_relations (FILE *file, + vec<ddr_p> 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<ddr_p> &ref) +{ + dump_data_dependence_relations (stderr, ref); +} + +DEBUG_FUNCTION void +debug (vec<ddr_p> *ptr) +{ + if (ptr) + debug (*ptr); + else + fprintf (stderr, "<nil>\n"); +} + + +/* Dump to STDERR all the dependence relations from DDRS. */ + +DEBUG_FUNCTION void +debug_data_dependence_relations (vec<ddr_p> 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. */ + +static void +dump_dist_dir_vectors (FILE *file, vec<ddr_p> 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. */ + +static void +dump_ddrs (FILE *file, vec<ddr_p> 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<ddr_p> ddrs) +{ + dump_ddrs (stderr, ddrs); +} + +/* 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) +{ + 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); + split_constant_offset (op1, &var1, &off1); + *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); + *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; + HOST_WIDE_INT pbitsize, pbitpos; + enum machine_mode pmode; + int punsignedp, pvolatilep; + + op0 = TREE_OPERAND (op0, 0); + base = get_inner_reference (op0, &pbitsize, &pbitpos, &poffset, + &pmode, &punsignedp, &pvolatilep, false); + + if (pbitpos % BITS_PER_UNIT != 0) + return false; + base = build_fold_addr_expr (base); + off0 = ssize_int (pbitpos / BITS_PER_UNIT); + + if (poffset) + { + split_constant_offset (poffset, &poffset, &off1); + 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: + { + gimple def_stmt = SSA_NAME_DEF_STMT (op0); + enum tree_code subcode; + + if (gimple_code (def_stmt) != GIMPLE_ASSIGN) + return false; + + var0 = gimple_assign_rhs1 (def_stmt); + subcode = gimple_assign_rhs_code (def_stmt); + var1 = gimple_assign_rhs2 (def_stmt); + + return split_constant_offset_1 (type, var0, subcode, var1, var, off); + } + 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_UNDEFINED (itype))) + && TYPE_PRECISION (type) >= TYPE_PRECISION (itype) + && (POINTER_TYPE_P (type) || INTEGRAL_TYPE_P (type))) + { + split_constant_offset (op0, &var0, off); + *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. */ + +void +split_constant_offset (tree exp, tree *var, tree *off) +{ + tree type = TREE_TYPE (exp), otype, op0, op1, e, o; + enum tree_code code; + + *var = exp; + *off = ssize_int (0); + STRIP_NOPS (exp); + + if (tree_is_chrec (exp) + || get_gimple_rhs_class (TREE_CODE (exp)) == GIMPLE_TERNARY_RHS) + return; + + otype = TREE_TYPE (exp); + code = TREE_CODE (exp); + extract_ops_from_tree (exp, &code, &op0, &op1); + if (split_constant_offset_1 (otype, op0, code, op1, &e, &o)) + { + *var = fold_convert (type, e); + *off = o; + } +} + +/* 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)); +} + +/* Analyzes the behavior of the memory reference DR in the innermost loop or + basic block that contains it. Returns true if analysis succeed or false + otherwise. */ + +bool +dr_analyze_innermost (struct data_reference *dr, struct loop *nest) +{ + gimple stmt = DR_STMT (dr); + struct loop *loop = loop_containing_stmt (stmt); + tree ref = DR_REF (dr); + HOST_WIDE_INT pbitsize, pbitpos; + tree base, poffset; + enum machine_mode pmode; + int punsignedp, 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, &pvolatilep, false); + gcc_assert (base != NULL_TREE); + + if (pbitpos % BITS_PER_UNIT != 0) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, "failed: bit offset alignment.\n"); + return false; + } + + if (TREE_CODE (base) == MEM_REF) + { + if (!integer_zerop (TREE_OPERAND (base, 1))) + { + double_int moff = mem_ref_offset (base); + tree mofft = double_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_containing_stmt (stmt), base, &base_iv, + nest ? true : false)) + { + if (nest) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, "failed: evolution of base is not" + " affine.\n"); + return false; + } + else + { + base_iv.base = base; + base_iv.step = ssize_int (0); + base_iv.no_overflow = true; + } + } + } + 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_containing_stmt (stmt), + poffset, &offset_iv, + nest ? true : false)) + { + if (nest) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, "failed: evolution of offset is not" + " affine.\n"); + return false; + } + else + { + offset_iv.base = poffset; + offset_iv.step = ssize_int (0); + } + } + } + + init = ssize_int (pbitpos / BITS_PER_UNIT); + split_constant_offset (base_iv.base, &base_iv.base, &dinit); + init = size_binop (PLUS_EXPR, init, 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)); + + DR_BASE_ADDRESS (dr) = canonicalize_base_object_address (base_iv.base); + + DR_OFFSET (dr) = fold_convert (ssizetype, offset_iv.base); + DR_INIT (dr) = init; + DR_STEP (dr) = step; + + DR_ALIGNED_TO (dr) = size_int (highest_pow2_factor (offset_iv.base)); + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, "success.\n"); + + return true; +} + +/* Determines the base object and the list of indices of memory reference + DR, analyzed in LOOP and instantiated in loop nest NEST. */ + +static void +dr_analyze_indices (struct data_reference *dr, loop_p nest, loop_p loop) +{ + vec<tree> access_fns = vNULL; + tree ref, op; + tree base, off, access_fn; + basic_block before_loop; + + /* 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); + before_loop = block_before_loop (nest); + + /* 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. */ + 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 (before_loop, 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 (before_loop, 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); + /* 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); + } + 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. */ + ref = fold_build2_loc (EXPR_LOCATION (ref), + MEM_REF, TREE_TYPE (ref), + base, memoff); + 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); +} + +/* Analyzes memory reference MEMREF accessed in STMT. The reference + is read if IS_READ is true, write otherwise. Returns 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 (loop_p nest, loop_p loop, tree memref, gimple stmt, + bool is_read) +{ + 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_analyze_innermost (dr, nest); + 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\taligned to: "); + print_generic_expr (dump_file, DR_ALIGNED_TO (dr), TDF_SLIM); + 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; +} + +/* 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) + { + /* Index of the ARRAY_REF was zeroed in analyze_indices, thus we only + need to check the stride and the lower bound of the reference. */ + if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 2), + loop->num) + || chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 3), + 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; + double_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, double_int_minus_one); + aff_combination_add (&off2, &off1); + if (aff_comb_cannot_overlap_p (&off2, size1, size2)) + return false; + } + + /* If we had an evolution in a 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)) + { + if (TREE_CODE (addr_b) == MEM_REF + && DR_UNCONSTRAINED_BASE (b)) + 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)) + 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); +} + +/* 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_p> loop_nest) +{ + struct data_dependence_relation *res; + unsigned int i; + + res = XNEW (struct data_dependence_relation); + DDR_A (res) = a; + DDR_B (res) = b; + DDR_LOOP_NEST (res).create (0); + DDR_REVERSED_P (res) = false; + 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; + } + + /* The case where the references are exactly the same. */ + if (operand_equal_p (DR_REF (a), DR_REF (b), 0)) + { + if (loop_nest.exists () + && !object_address_invariant_in_loop_p (loop_nest[0], + DR_BASE_OBJECT (a))) + { + DDR_ARE_DEPENDENT (res) = chrec_dont_know; + return res; + } + DDR_AFFINE_P (res) = true; + DDR_ARE_DEPENDENT (res) = NULL_TREE; + DDR_SUBSCRIPTS (res).create (DR_NUM_DIMENSIONS (a)); + DDR_LOOP_NEST (res) = loop_nest; + DDR_INNER_LOOP (res) = 0; + DDR_SELF_REFERENCE (res) = true; + for (i = 0; i < DR_NUM_DIMENSIONS (a); i++) + { + struct subscript *subscript; + + subscript = XNEW (struct subscript); + SUB_CONFLICTS_IN_A (subscript) = conflict_fn_not_known (); + SUB_CONFLICTS_IN_B (subscript) = conflict_fn_not_known (); + SUB_LAST_CONFLICT (subscript) = chrec_dont_know; + SUB_DISTANCE (subscript) = chrec_dont_know; + DDR_SUBSCRIPTS (res).safe_push (subscript); + } + return res; + } + + /* If the references do not access the same object, we do not know + whether they alias or not. */ + if (!operand_equal_p (DR_BASE_OBJECT (a), DR_BASE_OBJECT (b), 0)) + { + DDR_ARE_DEPENDENT (res) = chrec_dont_know; + return res; + } + + /* If the base of the object is not invariant in the loop nest, we cannot + analyze it. TODO -- in fact, it would suffice to record that there may + be arbitrary dependences in the loops where the base object varies. */ + if (loop_nest.exists () + && !object_address_invariant_in_loop_p (loop_nest[0], + DR_BASE_OBJECT (a))) + { + DDR_ARE_DEPENDENT (res) = chrec_dont_know; + return res; + } + + /* If the number of dimensions of the access to not agree we can have + a pointer access to a component of the array element type and an + array access while the base-objects are still the same. Punt. */ + if (DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b)) + { + DDR_ARE_DEPENDENT (res) = chrec_dont_know; + return res; + } + + DDR_AFFINE_P (res) = true; + DDR_ARE_DEPENDENT (res) = NULL_TREE; + DDR_SUBSCRIPTS (res).create (DR_NUM_DIMENSIONS (a)); + DDR_LOOP_NEST (res) = loop_nest; + DDR_INNER_LOOP (res) = 0; + DDR_SELF_REFERENCE (res) = false; + + for (i = 0; i < DR_NUM_DIMENSIONS (a); i++) + { + struct subscript *subscript; + + subscript = XNEW (struct subscript); + SUB_CONFLICTS_IN_A (subscript) = conflict_fn_not_known (); + SUB_CONFLICTS_IN_B (subscript) = conflict_fn_not_known (); + SUB_LAST_CONFLICT (subscript) = chrec_dont_know; + SUB_DISTANCE (subscript) = chrec_dont_know; + 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<subscript_p> 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; + + default: + return true; + } + + default: + return true; + } + } + + return false; +} + +/* Creates a conflict function with N dimensions. The affine functions + in each dimension follow. */ + +static conflict_function * +conflict_fn (unsigned n, ...) +{ + unsigned i; + conflict_function *ret = XCNEW (conflict_function); + va_list ap; + + gcc_assert (0 < n && n <= MAX_DIM); + va_start (ap, n); + + ret->n = n; + for (i = 0; i < n; i++) + ret->fns[i] = va_arg (ap, affine_fn); + va_end (ap); + + return ret; +} + +/* Returns constant affine function with value CST. */ + +static affine_fn +affine_fn_cst (tree cst) +{ + affine_fn fn; + 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) +{ + double_int nit; + + if (!max_stmt_executions (loop, &nit)) + return chrec_dont_know; + + if (!double_int_fits_to_tree_p (unsigned_type_node, nit)) + return chrec_dont_know; + + return double_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 (!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 (!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: + gcc_assert (TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST); + + 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 NOP_EXPR: + { + 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 (int niter, int step_a, int step_b, + affine_fn *overlaps_a, + affine_fn *overlaps_b, + tree *last_conflicts, int dim) +{ + if (((step_a > 0 && step_b > 0) + || (step_a < 0 && step_b < 0))) + { + int step_overlaps_a, step_overlaps_b; + int gcd_steps_a_b, last_conflict, tau2; + + gcd_steps_a_b = gcd (step_a, step_b); + step_overlaps_a = step_b / gcd_steps_a_b; + step_overlaps_b = step_a / gcd_steps_a_b; + + 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; + 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 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, int const1) +{ + int i; + + if (const1 == 0) + return; + + for (i = 0; i < n; i++) + mat[r2][i] += const1 * mat[r1][i]; +} + +/* Swap rows R1 and R2 in matrix MAT. */ + +static void +lambda_matrix_row_exchange (lambda_matrix mat, int r1, int r2) +{ + lambda_vector row; + + row = mat[r1]; + mat[r1] = mat[r2]; + mat[r2] = row; +} + +/* 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, 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) + { + int sigma, factor, a, b; + + a = S[i-1][j]; + b = S[i][j]; + sigma = (a * b < 0) ? -1: 1; + a = abs (a); + b = abs (b); + factor = sigma * (a / b); + + lambda_matrix_row_add (S, n, i, i-1, -factor); + lambda_matrix_row_exchange (S, i, i-1); + + lambda_matrix_row_add (U, m, i, i-1, -factor); + lambda_matrix_row_exchange (U, i, 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 - i0, i1), + FLOOR_DIV (niter - 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 || y1 >= niter) + { + *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) + /* For the moment, the following is verified: + 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_multivariate_p (chrec_a, loop_nest->num) + && !chrec_contains_symbols (chrec_a) + && evolution_function_is_affine_multivariate_p (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, 0); + fprintf (dump_file, ")\n (chrec_b = "); + print_generic_expr (dump_file, chrec_b, 0); + fprintf (dump_file, ")\n"); + } + + if (chrec_a == NULL_TREE + || chrec_b == NULL_TREE + || chrec_contains_undetermined (chrec_a) + || chrec_contains_undetermined (chrec_b)) + { + dependence_stats.num_subscript_undetermined++; + + *overlap_iterations_a = conflict_fn_not_known (); + *overlap_iterations_b = conflict_fn_not_known (); + } + + /* If they are the same chrec, and are affine, they overlap + on every iteration. */ + else if (eq_evolutions_p (chrec_a, chrec_b) + && (evolution_function_is_affine_multivariate_p (chrec_a, 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. INIT_B is set to true when a component has been + added to the distance vector DIST_V. INDEX_CARRY is then set to + the index in DIST_V that carries the dependence. */ + +static bool +build_classic_dist_vector_1 (struct data_dependence_relation *ddr, + struct data_reference *ddr_a, + struct data_reference *ddr_b, + lambda_vector dist_v, bool *init_b, + int *index_carry) +{ + unsigned i; + lambda_vector init_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); + + for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) + { + tree access_fn_a, access_fn_b; + struct subscript *subscript = DDR_SUBSCRIPT (ddr, i); + + if (chrec_contains_undetermined (SUB_DISTANCE (subscript))) + { + non_affine_dependence_relation (ddr); + return false; + } + + access_fn_a = DR_ACCESS_FN (ddr_a, i); + access_fn_b = DR_ACCESS_FN (ddr_b, i); + + if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC + && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC) + { + int dist, index; + int 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; + + for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) + if (!evolution_function_is_constant_p (DR_ACCESS_FN (DDR_A (ddr), i)) + || !evolution_function_is_constant_p (DR_ACCESS_FN (DDR_B (ddr), i))) + return false; + + return true; +} + +/* Helper function for the case where DDR_A and DDR_B are the same + multivariate access function 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; + 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); + + for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) + { + tree access_fun = DR_ACCESS_FN (DDR_A (ddr), i); + + if (TREE_CODE (access_fun) == POLYNOMIAL_CHREC) + { + if (!evolution_function_is_univariate_p (access_fun)) + { + if (DDR_NUM_SUBSCRIPTS (ddr) != 1) + { + DDR_ARE_DEPENDENT (ddr) = chrec_dont_know; + return; + } + + access_fun = DR_ACCESS_FN (DDR_A (ddr), 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; + } + } +} + +/* 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, DDR_A (ddr), DDR_B (ddr), + dist_v, &init_b, &index_carry)) + return false; + + /* Save the distance vector if we initialized one. */ + if (init_b) + { + /* Verify a basic constraint: classic distance vectors should + always be lexicographically positive. + + Data references are collected in the order of execution of + the program, thus for the following loop + + | for (i = 1; i < 100; i++) + | for (j = 1; j < 100; j++) + | { + | t = T[j+1][i-1]; // A + | T[j][i] = t + 2; // B + | } + + references are collected following the direction of the wind: + A then B. The data dependence tests are performed also + following this order, such that we're looking at the distance + separating the elements accessed by A from the elements later + accessed by B. But in this example, the distance returned by + test_dep (A, B) is lexicographically negative (-1, 1), that + means that the access A occurs later than B with respect to + the outer loop, ie. we're actually looking upwind. In this + case we solve test_dep (B, A) looking downwind to the + lexicographically positive solution, that returns the + distance vector (1, -1). */ + if (!lambda_vector_lexico_pos (dist_v, DDR_NB_LOOPS (ddr))) + { + lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); + if (!subscript_dependence_tester_1 (ddr, DDR_B (ddr), DDR_A (ddr), + loop_nest)) + return false; + compute_subscript_distance (ddr); + if (!build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr), + 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, DDR_B (ddr), + DDR_A (ddr), loop_nest)) + return false; + compute_subscript_distance (ddr); + if (!build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr), + 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 + data references DRA and DRB. */ + +static bool +subscript_dependence_tester_1 (struct data_dependence_relation *ddr, + struct data_reference *dra, + struct data_reference *drb, + 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 (DR_ACCESS_FN (dra, i), + DR_ACCESS_FN (drb, i), + &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, DDR_A (ddr), DDR_B (ddr), 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<tree> 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; +} + +/* Initializes an equation for an OMEGA problem using the information + contained in the ACCESS_FUN. Returns true when the operation + succeeded. + + PB is the omega constraint system. + EQ is the number of the equation to be initialized. + OFFSET is used for shifting the variables names in the constraints: + a constrain is composed of 2 * the number of variables surrounding + dependence accesses. OFFSET is set either to 0 for the first n variables, + then it is set to n. + ACCESS_FUN is expected to be an affine chrec. */ + +static bool +init_omega_eq_with_af (omega_pb pb, unsigned eq, + unsigned int offset, tree access_fun, + struct data_dependence_relation *ddr) +{ + switch (TREE_CODE (access_fun)) + { + case POLYNOMIAL_CHREC: + { + tree left = CHREC_LEFT (access_fun); + tree right = CHREC_RIGHT (access_fun); + int var = CHREC_VARIABLE (access_fun); + unsigned var_idx; + + if (TREE_CODE (right) != INTEGER_CST) + return false; + + var_idx = index_in_loop_nest (var, DDR_LOOP_NEST (ddr)); + pb->eqs[eq].coef[offset + var_idx + 1] = int_cst_value (right); + + /* Compute the innermost loop index. */ + DDR_INNER_LOOP (ddr) = MAX (DDR_INNER_LOOP (ddr), var_idx); + + if (offset == 0) + pb->eqs[eq].coef[var_idx + DDR_NB_LOOPS (ddr) + 1] + += int_cst_value (right); + + switch (TREE_CODE (left)) + { + case POLYNOMIAL_CHREC: + return init_omega_eq_with_af (pb, eq, offset, left, ddr); + + case INTEGER_CST: + pb->eqs[eq].coef[0] += int_cst_value (left); + return true; + + default: + return false; + } + } + + case INTEGER_CST: + pb->eqs[eq].coef[0] += int_cst_value (access_fun); + return true; + + default: + return false; + } +} + +/* As explained in the comments preceding init_omega_for_ddr, we have + to set up a system for each loop level, setting outer loops + variation to zero, and current loop variation to positive or zero. + Save each lexico positive distance vector. */ + +static void +omega_extract_distance_vectors (omega_pb pb, + struct data_dependence_relation *ddr) +{ + int eq, geq; + unsigned i, j; + struct loop *loopi, *loopj; + enum omega_result res; + + /* Set a new problem for each loop in the nest. The basis is the + problem that we have initialized until now. On top of this we + add new constraints. */ + for (i = 0; i <= DDR_INNER_LOOP (ddr) + && DDR_LOOP_NEST (ddr).iterate (i, &loopi); i++) + { + int dist = 0; + omega_pb copy = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), + DDR_NB_LOOPS (ddr)); + + omega_copy_problem (copy, pb); + + /* For all the outer loops "loop_j", add "dj = 0". */ + for (j = 0; j < i && DDR_LOOP_NEST (ddr).iterate (j, &loopj); j++) + { + eq = omega_add_zero_eq (copy, omega_black); + copy->eqs[eq].coef[j + 1] = 1; + } + + /* For "loop_i", add "0 <= di". */ + geq = omega_add_zero_geq (copy, omega_black); + copy->geqs[geq].coef[i + 1] = 1; + + /* Reduce the constraint system, and test that the current + problem is feasible. */ + res = omega_simplify_problem (copy); + if (res == omega_false + || res == omega_unknown + || copy->num_geqs > (int) DDR_NB_LOOPS (ddr)) + goto next_problem; + + for (eq = 0; eq < copy->num_subs; eq++) + if (copy->subs[eq].key == (int) i + 1) + { + dist = copy->subs[eq].coef[0]; + goto found_dist; + } + + if (dist == 0) + { + /* Reinitialize problem... */ + omega_copy_problem (copy, pb); + for (j = 0; j < i && DDR_LOOP_NEST (ddr).iterate (j, &loopj); j++) + { + eq = omega_add_zero_eq (copy, omega_black); + copy->eqs[eq].coef[j + 1] = 1; + } + + /* ..., but this time "di = 1". */ + eq = omega_add_zero_eq (copy, omega_black); + copy->eqs[eq].coef[i + 1] = 1; + copy->eqs[eq].coef[0] = -1; + + res = omega_simplify_problem (copy); + if (res == omega_false + || res == omega_unknown + || copy->num_geqs > (int) DDR_NB_LOOPS (ddr)) + goto next_problem; + + for (eq = 0; eq < copy->num_subs; eq++) + if (copy->subs[eq].key == (int) i + 1) + { + dist = copy->subs[eq].coef[0]; + goto found_dist; + } + } + + found_dist:; + /* Save the lexicographically positive distance vector. */ + if (dist >= 0) + { + lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); + lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); + + dist_v[i] = dist; + + for (eq = 0; eq < copy->num_subs; eq++) + if (copy->subs[eq].key > 0) + { + dist = copy->subs[eq].coef[0]; + dist_v[copy->subs[eq].key - 1] = dist; + } + + for (j = 0; j < DDR_NB_LOOPS (ddr); j++) + dir_v[j] = dir_from_dist (dist_v[j]); + + save_dist_v (ddr, dist_v); + save_dir_v (ddr, dir_v); + } + + next_problem:; + omega_free_problem (copy); + } +} + +/* This is called for each subscript of a tuple of data references: + insert an equality for representing the conflicts. */ + +static bool +omega_setup_subscript (tree access_fun_a, tree access_fun_b, + struct data_dependence_relation *ddr, + omega_pb pb, bool *maybe_dependent) +{ + int eq; + tree type = signed_type_for_types (TREE_TYPE (access_fun_a), + TREE_TYPE (access_fun_b)); + tree fun_a = chrec_convert (type, access_fun_a, NULL); + tree fun_b = chrec_convert (type, access_fun_b, NULL); + tree difference = chrec_fold_minus (type, fun_a, fun_b); + tree minus_one; + + /* When the fun_a - fun_b is not constant, the dependence is not + captured by the classic distance vector representation. */ + if (TREE_CODE (difference) != INTEGER_CST) + return false; + + /* ZIV test. */ + if (ziv_subscript_p (fun_a, fun_b) && !integer_zerop (difference)) + { + /* There is no dependence. */ + *maybe_dependent = false; + return true; + } + + minus_one = build_int_cst (type, -1); + fun_b = chrec_fold_multiply (type, fun_b, minus_one); + + eq = omega_add_zero_eq (pb, omega_black); + if (!init_omega_eq_with_af (pb, eq, DDR_NB_LOOPS (ddr), fun_a, ddr) + || !init_omega_eq_with_af (pb, eq, 0, fun_b, ddr)) + /* There is probably a dependence, but the system of + constraints cannot be built: answer "don't know". */ + return false; + + /* GCD test. */ + if (DDR_NB_LOOPS (ddr) != 0 && pb->eqs[eq].coef[0] + && !int_divides_p (lambda_vector_gcd + ((lambda_vector) &(pb->eqs[eq].coef[1]), + 2 * DDR_NB_LOOPS (ddr)), + pb->eqs[eq].coef[0])) + { + /* There is no dependence. */ + *maybe_dependent = false; + return true; + } + + return true; +} + +/* Helper function, same as init_omega_for_ddr but specialized for + data references A and B. */ + +static bool +init_omega_for_ddr_1 (struct data_reference *dra, struct data_reference *drb, + struct data_dependence_relation *ddr, + omega_pb pb, bool *maybe_dependent) +{ + unsigned i; + int ineq; + struct loop *loopi; + unsigned nb_loops = DDR_NB_LOOPS (ddr); + + /* Insert an equality per subscript. */ + for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++) + { + if (!omega_setup_subscript (DR_ACCESS_FN (dra, i), DR_ACCESS_FN (drb, i), + ddr, pb, maybe_dependent)) + return false; + else if (*maybe_dependent == false) + { + /* There is no dependence. */ + DDR_ARE_DEPENDENT (ddr) = chrec_known; + return true; + } + } + + /* Insert inequalities: constraints corresponding to the iteration + domain, i.e. the loops surrounding the references "loop_x" and + the distance variables "dx". The layout of the OMEGA + representation is as follows: + - coef[0] is the constant + - coef[1..nb_loops] are the protected variables that will not be + removed by the solver: the "dx" + - coef[nb_loops + 1, 2*nb_loops] are the loop variables: "loop_x". + */ + for (i = 0; i <= DDR_INNER_LOOP (ddr) + && DDR_LOOP_NEST (ddr).iterate (i, &loopi); i++) + { + HOST_WIDE_INT nbi = max_stmt_executions_int (loopi); + + /* 0 <= loop_x */ + ineq = omega_add_zero_geq (pb, omega_black); + pb->geqs[ineq].coef[i + nb_loops + 1] = 1; + + /* 0 <= loop_x + dx */ + ineq = omega_add_zero_geq (pb, omega_black); + pb->geqs[ineq].coef[i + nb_loops + 1] = 1; + pb->geqs[ineq].coef[i + 1] = 1; + + if (nbi != -1) + { + /* loop_x <= nb_iters */ + ineq = omega_add_zero_geq (pb, omega_black); + pb->geqs[ineq].coef[i + nb_loops + 1] = -1; + pb->geqs[ineq].coef[0] = nbi; + + /* loop_x + dx <= nb_iters */ + ineq = omega_add_zero_geq (pb, omega_black); + pb->geqs[ineq].coef[i + nb_loops + 1] = -1; + pb->geqs[ineq].coef[i + 1] = -1; + pb->geqs[ineq].coef[0] = nbi; + + /* A step "dx" bigger than nb_iters is not feasible, so + add "0 <= nb_iters + dx", */ + ineq = omega_add_zero_geq (pb, omega_black); + pb->geqs[ineq].coef[i + 1] = 1; + pb->geqs[ineq].coef[0] = nbi; + /* and "dx <= nb_iters". */ + ineq = omega_add_zero_geq (pb, omega_black); + pb->geqs[ineq].coef[i + 1] = -1; + pb->geqs[ineq].coef[0] = nbi; + } + } + + omega_extract_distance_vectors (pb, ddr); + + return true; +} + +/* Sets up the Omega dependence problem for the data dependence + relation DDR. Returns false when the constraint system cannot be + built, ie. when the test answers "don't know". Returns true + otherwise, and when independence has been proved (using one of the + trivial dependence test), set MAYBE_DEPENDENT to false, otherwise + set MAYBE_DEPENDENT to true. + + Example: for setting up the dependence system corresponding to the + conflicting accesses + + | loop_i + | loop_j + | A[i, i+1] = ... + | ... A[2*j, 2*(i + j)] + | endloop_j + | endloop_i + + the following constraints come from the iteration domain: + + 0 <= i <= Ni + 0 <= i + di <= Ni + 0 <= j <= Nj + 0 <= j + dj <= Nj + + where di, dj are the distance variables. The constraints + representing the conflicting elements are: + + i = 2 * (j + dj) + i + 1 = 2 * (i + di + j + dj) + + For asking that the resulting distance vector (di, dj) be + lexicographically positive, we insert the constraint "di >= 0". If + "di = 0" in the solution, we fix that component to zero, and we + look at the inner loops: we set a new problem where all the outer + loop distances are zero, and fix this inner component to be + positive. When one of the components is positive, we save that + distance, and set a new problem where the distance on this loop is + zero, searching for other distances in the inner loops. Here is + the classic example that illustrates that we have to set for each + inner loop a new problem: + + | loop_1 + | loop_2 + | A[10] + | endloop_2 + | endloop_1 + + we have to save two distances (1, 0) and (0, 1). + + Given two array references, refA and refB, we have to set the + dependence problem twice, refA vs. refB and refB vs. refA, and we + cannot do a single test, as refB might occur before refA in the + inner loops, and the contrary when considering outer loops: ex. + + | loop_0 + | loop_1 + | loop_2 + | T[{1,+,1}_2][{1,+,1}_1] // refA + | T[{2,+,1}_2][{0,+,1}_1] // refB + | endloop_2 + | endloop_1 + | endloop_0 + + refB touches the elements in T before refA, and thus for the same + loop_0 refB precedes refA: ie. the distance vector (0, 1, -1) + but for successive loop_0 iterations, we have (1, -1, 1) + + The Omega solver expects the distance variables ("di" in the + previous example) to come first in the constraint system (as + variables to be protected, or "safe" variables), the constraint + system is built using the following layout: + + "cst | distance vars | index vars". +*/ + +static bool +init_omega_for_ddr (struct data_dependence_relation *ddr, + bool *maybe_dependent) +{ + omega_pb pb; + bool res = false; + + *maybe_dependent = true; + + if (same_access_functions (ddr)) + { + unsigned j; + lambda_vector dir_v; + + /* Save the 0 vector. */ + save_dist_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr))); + dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr)); + for (j = 0; j < DDR_NB_LOOPS (ddr); j++) + dir_v[j] = dir_equal; + save_dir_v (ddr, dir_v); + + /* Save the dependences carried by outer loops. */ + pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); + res = init_omega_for_ddr_1 (DDR_A (ddr), DDR_B (ddr), ddr, pb, + maybe_dependent); + omega_free_problem (pb); + return res; + } + + /* Omega expects the protected variables (those that have to be kept + after elimination) to appear first in the constraint system. + These variables are the distance variables. In the following + initialization we declare NB_LOOPS safe variables, and the total + number of variables for the constraint system is 2*NB_LOOPS. */ + pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); + res = init_omega_for_ddr_1 (DDR_A (ddr), DDR_B (ddr), ddr, pb, + maybe_dependent); + omega_free_problem (pb); + + /* Stop computation if not decidable, or no dependence. */ + if (res == false || *maybe_dependent == false) + return res; + + pb = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr), DDR_NB_LOOPS (ddr)); + res = init_omega_for_ddr_1 (DDR_B (ddr), DDR_A (ddr), ddr, pb, + maybe_dependent); + omega_free_problem (pb); + + return res; +} + +/* Return true when DDR contains the same information as that stored + in DIR_VECTS and in DIST_VECTS, return false otherwise. */ + +static bool +ddr_consistent_p (FILE *file, + struct data_dependence_relation *ddr, + vec<lambda_vector> dist_vects, + vec<lambda_vector> dir_vects) +{ + unsigned int i, j; + + /* If dump_file is set, output there. */ + if (dump_file && (dump_flags & TDF_DETAILS)) + file = dump_file; + + if (dist_vects.length () != DDR_NUM_DIST_VECTS (ddr)) + { + lambda_vector b_dist_v; + fprintf (file, "\n(Number of distance vectors differ: Banerjee has %d, Omega has %d.\n", + dist_vects.length (), + DDR_NUM_DIST_VECTS (ddr)); + + fprintf (file, "Banerjee dist vectors:\n"); + FOR_EACH_VEC_ELT (dist_vects, i, b_dist_v) + print_lambda_vector (file, b_dist_v, DDR_NB_LOOPS (ddr)); + + fprintf (file, "Omega dist vectors:\n"); + for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++) + print_lambda_vector (file, DDR_DIST_VECT (ddr, i), DDR_NB_LOOPS (ddr)); + + fprintf (file, "data dependence relation:\n"); + dump_data_dependence_relation (file, ddr); + + fprintf (file, ")\n"); + return false; + } + + if (dir_vects.length () != DDR_NUM_DIR_VECTS (ddr)) + { + fprintf (file, "\n(Number of direction vectors differ: Banerjee has %d, Omega has %d.)\n", + dir_vects.length (), + DDR_NUM_DIR_VECTS (ddr)); + return false; + } + + for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++) + { + lambda_vector a_dist_v; + lambda_vector b_dist_v = DDR_DIST_VECT (ddr, i); + + /* Distance vectors are not ordered in the same way in the DDR + and in the DIST_VECTS: search for a matching vector. */ + FOR_EACH_VEC_ELT (dist_vects, j, a_dist_v) + if (lambda_vector_equal (a_dist_v, b_dist_v, DDR_NB_LOOPS (ddr))) + break; + + if (j == dist_vects.length ()) + { + fprintf (file, "\n(Dist vectors from the first dependence analyzer:\n"); + print_dist_vectors (file, dist_vects, DDR_NB_LOOPS (ddr)); + fprintf (file, "not found in Omega dist vectors:\n"); + print_dist_vectors (file, DDR_DIST_VECTS (ddr), DDR_NB_LOOPS (ddr)); + fprintf (file, "data dependence relation:\n"); + dump_data_dependence_relation (file, ddr); + fprintf (file, ")\n"); + } + } + + for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++) + { + lambda_vector a_dir_v; + lambda_vector b_dir_v = DDR_DIR_VECT (ddr, i); + + /* Direction vectors are not ordered in the same way in the DDR + and in the DIR_VECTS: search for a matching vector. */ + FOR_EACH_VEC_ELT (dir_vects, j, a_dir_v) + if (lambda_vector_equal (a_dir_v, b_dir_v, DDR_NB_LOOPS (ddr))) + break; + + if (j == dist_vects.length ()) + { + fprintf (file, "\n(Dir vectors from the first dependence analyzer:\n"); + print_dir_vectors (file, dir_vects, DDR_NB_LOOPS (ddr)); + fprintf (file, "not found in Omega dir vectors:\n"); + print_dir_vectors (file, DDR_DIR_VECTS (ddr), DDR_NB_LOOPS (ddr)); + fprintf (file, "data dependence relation:\n"); + dump_data_dependence_relation (file, ddr); + fprintf (file, ")\n"); + } + } + + return true; +} + +/* This computes the affine dependence relation between A and B 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); + + if (flag_check_data_deps) + { + /* Dump the dependences from the first algorithm. */ + if (dump_file && (dump_flags & TDF_DETAILS)) + { + fprintf (dump_file, "\n\nBanerjee Analyzer\n"); + dump_data_dependence_relation (dump_file, ddr); + } + + if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE) + { + bool maybe_dependent; + vec<lambda_vector> dir_vects, dist_vects; + + /* Save the result of the first DD analyzer. */ + dist_vects = DDR_DIST_VECTS (ddr); + dir_vects = DDR_DIR_VECTS (ddr); + + /* Reset the information. */ + DDR_DIST_VECTS (ddr).create (0); + DDR_DIR_VECTS (ddr).create (0); + + /* Compute the same information using Omega. */ + if (!init_omega_for_ddr (ddr, &maybe_dependent)) + goto csys_dont_know; + + if (dump_file && (dump_flags & TDF_DETAILS)) + { + fprintf (dump_file, "Omega Analyzer\n"); + dump_data_dependence_relation (dump_file, ddr); + } + + /* Check that we get the same information. */ + if (maybe_dependent) + gcc_assert (ddr_consistent_p (stderr, ddr, dist_vects, + dir_vects)); + } + } + } + + /* As a last case, if the dependence cannot be determined, or if + the dependence is considered too difficult to determine, answer + "don't know". */ + else + { + csys_dont_know:; + dependence_stats.num_dependence_undetermined++; + + if (dump_file && (dump_flags & TDF_DETAILS)) + { + fprintf (dump_file, "Data ref a:\n"); + dump_data_reference (dump_file, dra); + fprintf (dump_file, "Data ref b:\n"); + dump_data_reference (dump_file, drb); + fprintf (dump_file, "affine dependence test not usable: access function not affine or constant.\n"); + } + finalize_ddr_dependent (ddr, chrec_dont_know); + } + } + + if (dump_file && (dump_flags & TDF_DETAILS)) + { + 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<data_reference_p> datarefs, + vec<ddr_p> *dependence_relations, + vec<loop_p> 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. */ + +typedef struct data_ref_loc_d +{ + /* The memory reference. */ + tree ref; + + /* True if the memory reference is read. */ + bool is_read; +} data_ref_loc; + + +/* 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<data_ref_loc, va_heap> *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 (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)) + { + ref.ref = op1; + ref.is_read = true; + references->safe_push (ref); + } + } + else if (stmt_code == GIMPLE_CALL) + { + unsigned i, n; + + 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; + case IFN_MASK_STORE: + ref.ref = fold_build2 (MEM_REF, + ref.is_read + ? TREE_TYPE (gimple_call_lhs (stmt)) + : TREE_TYPE (gimple_call_arg (stmt, 3)), + gimple_call_arg (stmt, 0), + gimple_call_arg (stmt, 1)); + 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; + 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; + references->safe_push (ref); + } + return clobbers_memory; +} + +/* 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. */ + +bool +find_data_references_in_stmt (struct loop *nest, gimple stmt, + vec<data_reference_p> *datarefs) +{ + unsigned i; + auto_vec<data_ref_loc, 2> 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_containing_stmt (stmt), + ref->ref, stmt, ref->is_read); + gcc_assert (dr != NULL); + datarefs->safe_push (dr); + } + references.release (); + return ret; +} + +/* 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 (loop_p nest, loop_p loop, gimple stmt, + vec<data_reference_p> *datarefs) +{ + unsigned i; + auto_vec<data_ref_loc, 2> 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); + gcc_assert (dr != NULL); + datarefs->safe_push (dr); + } + + references.release (); + 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<data_reference_p> *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<data_reference_p> *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; +} + +/* Recursive helper function. */ + +static bool +find_loop_nest_1 (struct loop *loop, vec<loop_p> *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_p> *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_p> *loop_nest, + vec<data_reference_p> *datarefs, + vec<ddr_p> *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; +} + +/* Returns true when the data dependences for the basic block BB have been + computed, false otherwise. + DATAREFS is initialized to all the array elements contained in this basic + block, 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_bb (basic_block bb, + bool compute_self_and_read_read_dependences, + vec<data_reference_p> *datarefs, + vec<ddr_p> *dependence_relations) +{ + if (find_data_references_in_bb (NULL, bb, datarefs) == chrec_dont_know) + return false; + + return compute_all_dependences (*datarefs, dependence_relations, vNULL, + compute_self_and_read_read_dependences); +} + +/* Entry point (for testing only). Analyze all the data references + and the dependence relations in LOOP. + + The data references are computed first. + + A relation on these nodes is represented by a complete graph. Some + of the relations could be of no interest, thus the relations can be + computed on demand. + + In the following function we compute all the relations. This is + just a first implementation that is here for: + - for showing how to ask for the dependence relations, + - for the debugging the whole dependence graph, + - for the dejagnu testcases and maintenance. + + It is possible to ask only for a part of the graph, avoiding to + compute the whole dependence graph. The computed dependences are + stored in a knowledge base (KB) such that later queries don't + recompute the same information. The implementation of this KB is + transparent to the optimizer, and thus the KB can be changed with a + more efficient implementation, or the KB could be disabled. */ +static void +analyze_all_data_dependences (struct loop *loop) +{ + unsigned int i; + int nb_data_refs = 10; + vec<data_reference_p> datarefs; + datarefs.create (nb_data_refs); + vec<ddr_p> dependence_relations; + dependence_relations.create (nb_data_refs * nb_data_refs); + vec<loop_p> loop_nest; + loop_nest.create (3); + + /* Compute DDs on the whole function. */ + compute_data_dependences_for_loop (loop, false, &loop_nest, &datarefs, + &dependence_relations); + + if (dump_file) + { + dump_data_dependence_relations (dump_file, dependence_relations); + fprintf (dump_file, "\n\n"); + + if (dump_flags & TDF_DETAILS) + dump_dist_dir_vectors (dump_file, dependence_relations); + + if (dump_flags & TDF_STATS) + { + unsigned nb_top_relations = 0; + unsigned nb_bot_relations = 0; + unsigned nb_chrec_relations = 0; + struct data_dependence_relation *ddr; + + FOR_EACH_VEC_ELT (dependence_relations, i, ddr) + { + if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr))) + nb_top_relations++; + + else if (DDR_ARE_DEPENDENT (ddr) == chrec_known) + nb_bot_relations++; + + else + nb_chrec_relations++; + } + + gather_stats_on_scev_database (); + } + } + + loop_nest.release (); + free_dependence_relations (dependence_relations); + free_data_refs (datarefs); +} + +/* Computes all the data dependences and check that the results of + several analyzers are the same. */ + +void +tree_check_data_deps (void) +{ + struct loop *loop_nest; + + FOR_EACH_LOOP (loop_nest, 0) + analyze_all_data_dependences (loop_nest); +} + +/* Free the memory used by a data dependence relation DDR. */ + +void +free_dependence_relation (struct data_dependence_relation *ddr) +{ + if (ddr == NULL) + return; + + if (DDR_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<ddr_p> 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<data_reference_p> datarefs) +{ + unsigned int i; + struct data_reference *dr; + + FOR_EACH_VEC_ELT (datarefs, i, dr) + free_data_ref (dr); + datarefs.release (); +} |