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/* Data references and dependences detectors.
Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009
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 "tm.h"
#include "ggc.h"
#include "tree.h"
/* These RTL headers are needed for basic-block.h. */
#include "rtl.h"
#include "basic-block.h"
#include "diagnostic.h"
#include "tree-flow.h"
#include "tree-dump.h"
#include "timevar.h"
#include "cfgloop.h"
#include "tree-data-ref.h"
#include "tree-scalar-evolution.h"
#include "tree-pass.h"
#include "langhooks.h"
static struct datadep_stats
{
int num_dependence_tests;
int num_dependence_dependent;
int num_dependence_independent;
int num_dependence_undetermined;
int num_subscript_tests;
int num_subscript_undetermined;
int num_same_subscript_function;
int num_ziv;
int num_ziv_independent;
int num_ziv_dependent;
int num_ziv_unimplemented;
int num_siv;
int num_siv_independent;
int num_siv_dependent;
int num_siv_unimplemented;
int num_miv;
int num_miv_independent;
int num_miv_dependent;
int num_miv_unimplemented;
} dependence_stats;
static 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, 0));
}
/* Returns true iff A divides B. */
static inline bool
int_divides_p (int a, int b)
{
return ((b % a) == 0);
}
/* Dump into FILE all the data references from DATAREFS. */
void
dump_data_references (FILE *file, VEC (data_reference_p, heap) *datarefs)
{
unsigned int i;
struct data_reference *dr;
for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++)
dump_data_reference (file, dr);
}
/* Dump to STDERR all the dependence relations from DDRS. */
void
debug_data_dependence_relations (VEC (ddr_p, heap) *ddrs)
{
dump_data_dependence_relations (stderr, ddrs);
}
/* Dump into FILE all the dependence relations from DDRS. */
void
dump_data_dependence_relations (FILE *file,
VEC (ddr_p, heap) *ddrs)
{
unsigned int i;
struct data_dependence_relation *ddr;
for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
dump_data_dependence_relation (file, ddr);
}
/* Dump function for a DATA_REFERENCE structure. */
void
dump_data_reference (FILE *outf,
struct data_reference *dr)
{
unsigned int i;
fprintf (outf, "(Data Ref: \n stmt: ");
print_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");
}
/* Dumps the affine function described by FN to the file OUTF. */
static void
dump_affine_function (FILE *outf, affine_fn fn)
{
unsigned i;
tree coef;
print_generic_expr (outf, VEC_index (tree, fn, 0), TDF_SLIM);
for (i = 1; VEC_iterate (tree, fn, i, coef); i++)
{
fprintf (outf, " + ");
print_generic_expr (outf, coef, TDF_SLIM);
fprintf (outf, " * x_%u", i);
}
}
/* Dumps the conflict function CF to the file OUTF. */
static void
dump_conflict_function (FILE *outf, conflict_function *cf)
{
unsigned i;
if (cf->n == NO_DEPENDENCE)
fprintf (outf, "no dependence\n");
else if (cf->n == NOT_KNOWN)
fprintf (outf, "not known\n");
else
{
for (i = 0; i < cf->n; i++)
{
fprintf (outf, "[");
dump_affine_function (outf, cf->fns[i]);
fprintf (outf, "]\n");
}
}
}
/* Dump function for a SUBSCRIPT structure. */
void
dump_subscript (FILE *outf, struct subscript *subscript)
{
conflict_function *cf = SUB_CONFLICTS_IN_A (subscript);
fprintf (outf, "\n (subscript \n");
fprintf (outf, " iterations_that_access_an_element_twice_in_A: ");
dump_conflict_function (outf, cf);
if (CF_NONTRIVIAL_P (cf))
{
tree last_iteration = SUB_LAST_CONFLICT (subscript);
fprintf (outf, " last_conflict: ");
print_generic_stmt (outf, last_iteration, 0);
}
cf = SUB_CONFLICTS_IN_B (subscript);
fprintf (outf, " iterations_that_access_an_element_twice_in_B: ");
dump_conflict_function (outf, cf);
if (CF_NONTRIVIAL_P (cf))
{
tree last_iteration = SUB_LAST_CONFLICT (subscript);
fprintf (outf, " last_conflict: ");
print_generic_stmt (outf, last_iteration, 0);
}
fprintf (outf, " (Subscript distance: ");
print_generic_stmt (outf, SUB_DISTANCE (subscript), 0);
fprintf (outf, " )\n");
fprintf (outf, " )\n");
}
/* Print the classic direction vector DIRV to OUTF. */
void
print_direction_vector (FILE *outf,
lambda_vector dirv,
int length)
{
int eq;
for (eq = 0; eq < length; eq++)
{
enum data_dependence_direction dir = dirv[eq];
switch (dir)
{
case dir_positive:
fprintf (outf, " +");
break;
case dir_negative:
fprintf (outf, " -");
break;
case dir_equal:
fprintf (outf, " =");
break;
case dir_positive_or_equal:
fprintf (outf, " +=");
break;
case dir_positive_or_negative:
fprintf (outf, " +-");
break;
case dir_negative_or_equal:
fprintf (outf, " -=");
break;
case dir_star:
fprintf (outf, " *");
break;
default:
fprintf (outf, "indep");
break;
}
}
fprintf (outf, "\n");
}
/* Print a vector of direction vectors. */
void
print_dir_vectors (FILE *outf, VEC (lambda_vector, heap) *dir_vects,
int length)
{
unsigned j;
lambda_vector v;
for (j = 0; VEC_iterate (lambda_vector, dir_vects, j, v); j++)
print_direction_vector (outf, v, length);
}
/* Print a vector of distance vectors. */
void
print_dist_vectors (FILE *outf, VEC (lambda_vector, heap) *dist_vects,
int length)
{
unsigned j;
lambda_vector v;
for (j = 0; VEC_iterate (lambda_vector, dist_vects, j, v); j++)
print_lambda_vector (outf, v, length);
}
/* Debug version. */
void
debug_data_dependence_relation (struct data_dependence_relation *ddr)
{
dump_data_dependence_relation (stderr, ddr);
}
/* Dump function for a DATA_DEPENDENCE_RELATION structure. */
void
dump_data_dependence_relation (FILE *outf,
struct data_dependence_relation *ddr)
{
struct data_reference *dra, *drb;
fprintf (outf, "(Data Dep: \n");
if (!ddr || DDR_ARE_DEPENDENT (ddr) == chrec_dont_know)
{
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 (i = 0; VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++)
fprintf (outf, "%d ", loopi->num);
fprintf (outf, ")\n");
for (i = 0; i < DDR_NUM_DIST_VECTS (ddr); i++)
{
fprintf (outf, " distance_vector: ");
print_lambda_vector (outf, DDR_DIST_VECT (ddr, i),
DDR_NB_LOOPS (ddr));
}
for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++)
{
fprintf (outf, " direction_vector: ");
print_direction_vector (outf, DDR_DIR_VECT (ddr, i),
DDR_NB_LOOPS (ddr));
}
}
fprintf (outf, ")\n");
}
/* Dump function for a DATA_DEPENDENCE_DIRECTION structure. */
void
dump_data_dependence_direction (FILE *file,
enum data_dependence_direction dir)
{
switch (dir)
{
case dir_positive:
fprintf (file, "+");
break;
case dir_negative:
fprintf (file, "-");
break;
case dir_equal:
fprintf (file, "=");
break;
case dir_positive_or_negative:
fprintf (file, "+-");
break;
case dir_positive_or_equal:
fprintf (file, "+=");
break;
case dir_negative_or_equal:
fprintf (file, "-=");
break;
case dir_star:
fprintf (file, "*");
break;
default:
break;
}
}
/* Dumps the distance and direction vectors in FILE. DDRS contains
the dependence relations, and VECT_SIZE is the size of the
dependence vectors, or in other words the number of loops in the
considered nest. */
void
dump_dist_dir_vectors (FILE *file, VEC (ddr_p, heap) *ddrs)
{
unsigned int i, j;
struct data_dependence_relation *ddr;
lambda_vector v;
for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE && DDR_AFFINE_P (ddr))
{
for (j = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), j, v); j++)
{
fprintf (file, "DISTANCE_V (");
print_lambda_vector (file, v, DDR_NB_LOOPS (ddr));
fprintf (file, ")\n");
}
for (j = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), j, v); j++)
{
fprintf (file, "DIRECTION_V (");
print_direction_vector (file, v, DDR_NB_LOOPS (ddr));
fprintf (file, ")\n");
}
}
fprintf (file, "\n\n");
}
/* Dumps the data dependence relations DDRS in FILE. */
void
dump_ddrs (FILE *file, VEC (ddr_p, heap) *ddrs)
{
unsigned int i;
struct data_dependence_relation *ddr;
for (i = 0; VEC_iterate (ddr_p, ddrs, i, ddr); i++)
dump_data_dependence_relation (file, ddr);
fprintf (file, "\n\n");
}
/* 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);
if (!handled_component_p (op0))
return false;
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_build2 (POINTER_PLUS_EXPR, TREE_TYPE (base),
base, fold_convert (sizetype, 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);
}
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 (automatically_generated_chrec_p (exp))
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 that
contains it. Returns true if analysis succeed or false otherwise. */
bool
dr_analyze_innermost (struct data_reference *dr)
{
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;
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;
}
base = build_fold_addr_expr (base);
if (!simple_iv (loop, loop_containing_stmt (stmt), base, &base_iv, false))
{
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, "failed: evolution of base is not affine.\n");
return false;
}
if (!poffset)
{
offset_iv.base = ssize_int (0);
offset_iv.step = ssize_int (0);
}
else if (!simple_iv (loop, loop_containing_stmt (stmt),
poffset, &offset_iv, false))
{
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, "failed: evolution of offset is not affine.\n");
return false;
}
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 nest NEST. */
static void
dr_analyze_indices (struct data_reference *dr, struct loop *nest)
{
gimple stmt = DR_STMT (dr);
struct loop *loop = loop_containing_stmt (stmt);
VEC (tree, heap) *access_fns = NULL;
tree ref = unshare_expr (DR_REF (dr)), aref = ref, op;
tree base, off, access_fn;
basic_block before_loop = block_before_loop (nest);
while (handled_component_p (aref))
{
if (TREE_CODE (aref) == ARRAY_REF)
{
op = TREE_OPERAND (aref, 1);
access_fn = analyze_scalar_evolution (loop, op);
access_fn = instantiate_scev (before_loop, loop, access_fn);
VEC_safe_push (tree, heap, access_fns, access_fn);
TREE_OPERAND (aref, 1) = build_int_cst (TREE_TYPE (op), 0);
}
aref = TREE_OPERAND (aref, 0);
}
if (INDIRECT_REF_P (aref))
{
op = TREE_OPERAND (aref, 0);
access_fn = analyze_scalar_evolution (loop, op);
access_fn = instantiate_scev (before_loop, loop, access_fn);
base = initial_condition (access_fn);
split_constant_offset (base, &base, &off);
access_fn = chrec_replace_initial_condition (access_fn,
fold_convert (TREE_TYPE (base), off));
TREE_OPERAND (aref, 0) = base;
VEC_safe_push (tree, heap, access_fns, access_fn);
}
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)
{
gimple stmt = DR_STMT (dr);
tree ref = DR_REF (dr);
tree base = get_base_address (ref), addr, smt = NULL_TREE;
ssa_op_iter it;
tree op;
bitmap vops;
if (DECL_P (base))
smt = base;
else if (INDIRECT_REF_P (base))
{
addr = TREE_OPERAND (base, 0);
if (TREE_CODE (addr) == SSA_NAME)
{
smt = symbol_mem_tag (SSA_NAME_VAR (addr));
DR_PTR_INFO (dr) = SSA_NAME_PTR_INFO (addr);
}
}
DR_SYMBOL_TAG (dr) = smt;
vops = BITMAP_ALLOC (NULL);
FOR_EACH_SSA_TREE_OPERAND (op, stmt, it, SSA_OP_VIRTUAL_USES)
{
bitmap_set_bit (vops, DECL_UID (SSA_NAME_VAR (op)));
}
DR_VOPS (dr) = vops;
}
/* Returns true if the address of DR is invariant. */
static bool
dr_address_invariant_p (struct data_reference *dr)
{
unsigned i;
tree idx;
for (i = 0; VEC_iterate (tree, DR_ACCESS_FNS (dr), i, idx); i++)
if (tree_contains_chrecs (idx, NULL))
return false;
return true;
}
/* Frees data reference DR. */
void
free_data_ref (data_reference_p dr)
{
BITMAP_FREE (DR_VOPS (dr));
VEC_free (tree, heap, DR_ACCESS_FNS (dr));
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 of the
loop nest in that the reference should be analyzed. */
struct data_reference *
create_data_ref (struct loop *nest, 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);
dr_analyze_indices (dr, nest);
dr_analyze_alias (dr);
if (dump_file && (dump_flags & TDF_DETAILS))
{
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\tsymbol tag: ");
print_generic_expr (dump_file, DR_SYMBOL_TAG (dr), TDF_SLIM);
fprintf (dump_file, "\n");
}
return dr;
}
/* Returns true if FNA == FNB. */
static bool
affine_function_equal_p (affine_fn fna, affine_fn fnb)
{
unsigned i, n = VEC_length (tree, fna);
if (n != VEC_length (tree, fnb))
return false;
for (i = 0; i < n; i++)
if (!operand_equal_p (VEC_index (tree, fna, i),
VEC_index (tree, fnb, i), 0))
return false;
return true;
}
/* If all the functions in CF are the same, returns one of them,
otherwise returns NULL. */
static affine_fn
common_affine_function (conflict_function *cf)
{
unsigned i;
affine_fn comm;
if (!CF_NONTRIVIAL_P (cf))
return NULL;
comm = cf->fns[0];
for (i = 1; i < cf->n; i++)
if (!affine_function_equal_p (comm, cf->fns[i]))
return NULL;
return comm;
}
/* Returns the base of the affine function FN. */
static tree
affine_function_base (affine_fn fn)
{
return VEC_index (tree, fn, 0);
}
/* Returns true if FN is a constant. */
static bool
affine_function_constant_p (affine_fn fn)
{
unsigned i;
tree coef;
for (i = 1; VEC_iterate (tree, fn, i, coef); i++)
if (!integer_zerop (coef))
return false;
return true;
}
/* Returns true if FN is the zero constant function. */
static bool
affine_function_zero_p (affine_fn fn)
{
return (integer_zerop (affine_function_base (fn))
&& affine_function_constant_p (fn));
}
/* 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 (VEC_length (tree, fnb) > VEC_length (tree, fna))
{
n = VEC_length (tree, fna);
m = VEC_length (tree, fnb);
}
else
{
n = VEC_length (tree, fnb);
m = VEC_length (tree, fna);
}
ret = VEC_alloc (tree, heap, m);
for (i = 0; i < n; i++)
{
tree type = signed_type_for_types (TREE_TYPE (VEC_index (tree, fna, i)),
TREE_TYPE (VEC_index (tree, fnb, i)));
VEC_quick_push (tree, ret,
fold_build2 (op, type,
VEC_index (tree, fna, i),
VEC_index (tree, fnb, i)));
}
for (; VEC_iterate (tree, fna, i, coef); i++)
VEC_quick_push (tree, ret,
fold_build2 (op, signed_type_for (TREE_TYPE (coef)),
coef, integer_zero_node));
for (; VEC_iterate (tree, fnb, i, coef); i++)
VEC_quick_push (tree, ret,
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)
{
VEC_free (tree, heap, fn);
}
/* Determine for each subscript in the data dependence relation DDR
the distance. */
static void
compute_subscript_distance (struct data_dependence_relation *ddr)
{
conflict_function *cf_a, *cf_b;
affine_fn fn_a, fn_b, diff;
if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
{
unsigned int i;
for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
{
struct subscript *subscript;
subscript = DDR_SUBSCRIPT (ddr, i);
cf_a = SUB_CONFLICTS_IN_A (subscript);
cf_b = SUB_CONFLICTS_IN_B (subscript);
fn_a = common_affine_function (cf_a);
fn_b = common_affine_function (cf_b);
if (!fn_a || !fn_b)
{
SUB_DISTANCE (subscript) = chrec_dont_know;
return;
}
diff = affine_fn_minus (fn_a, fn_b);
if (affine_function_constant_p (diff))
SUB_DISTANCE (subscript) = affine_function_base (diff);
else
SUB_DISTANCE (subscript) = chrec_dont_know;
affine_fn_free (diff);
}
}
}
/* Returns the conflict function for "unknown". */
static conflict_function *
conflict_fn_not_known (void)
{
conflict_function *fn = XCNEW (conflict_function);
fn->n = NOT_KNOWN;
return fn;
}
/* Returns the conflict function for "independent". */
static conflict_function *
conflict_fn_no_dependence (void)
{
conflict_function *fn = XCNEW (conflict_function);
fn->n = NO_DEPENDENCE;
return fn;
}
/* 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))
return true;
return !chrec_contains_symbols_defined_in_loop (TREE_OPERAND (obj, 0),
loop->num);
}
/* Returns true if A and B are accesses to different objects, or to different
fields of the same object. */
static bool
disjoint_objects_p (tree a, tree b)
{
tree base_a, base_b;
VEC (tree, heap) *comp_a = NULL, *comp_b = NULL;
bool ret;
base_a = get_base_address (a);
base_b = get_base_address (b);
if (DECL_P (base_a)
&& DECL_P (base_b)
&& base_a != base_b)
return true;
if (!operand_equal_p (base_a, base_b, 0))
return false;
/* Compare the component references of A and B. We must start from the inner
ones, so record them to the vector first. */
while (handled_component_p (a))
{
VEC_safe_push (tree, heap, comp_a, a);
a = TREE_OPERAND (a, 0);
}
while (handled_component_p (b))
{
VEC_safe_push (tree, heap, comp_b, b);
b = TREE_OPERAND (b, 0);
}
ret = false;
while (1)
{
if (VEC_length (tree, comp_a) == 0
|| VEC_length (tree, comp_b) == 0)
break;
a = VEC_pop (tree, comp_a);
b = VEC_pop (tree, comp_b);
/* Real and imaginary part of a variable do not alias. */
if ((TREE_CODE (a) == REALPART_EXPR
&& TREE_CODE (b) == IMAGPART_EXPR)
|| (TREE_CODE (a) == IMAGPART_EXPR
&& TREE_CODE (b) == REALPART_EXPR))
{
ret = true;
break;
}
if (TREE_CODE (a) != TREE_CODE (b))
break;
/* Nothing to do for ARRAY_REFs, as the indices of array_refs in
DR_BASE_OBJECT are always zero. */
if (TREE_CODE (a) == ARRAY_REF)
continue;
else if (TREE_CODE (a) == COMPONENT_REF)
{
if (operand_equal_p (TREE_OPERAND (a, 1), TREE_OPERAND (b, 1), 0))
continue;
/* Different fields of unions may overlap. */
base_a = TREE_OPERAND (a, 0);
if (TREE_CODE (TREE_TYPE (base_a)) == UNION_TYPE)
break;
/* Different fields of structures cannot. */
ret = true;
break;
}
else
break;
}
VEC_free (tree, heap, comp_a);
VEC_free (tree, heap, comp_b);
return ret;
}
/* Returns false if we can prove that data references A and B do not alias,
true otherwise. */
bool
dr_may_alias_p (const struct data_reference *a, const struct data_reference *b)
{
const_tree addr_a = DR_BASE_ADDRESS (a);
const_tree addr_b = DR_BASE_ADDRESS (b);
const_tree type_a, type_b;
const_tree decl_a = NULL_TREE, decl_b = NULL_TREE;
/* If the sets of virtual operands are disjoint, the memory references do not
alias. */
if (!bitmap_intersect_p (DR_VOPS (a), DR_VOPS (b)))
return false;
/* If the accessed objects are disjoint, the memory references do not
alias. */
if (disjoint_objects_p (DR_BASE_OBJECT (a), DR_BASE_OBJECT (b)))
return false;
if (!addr_a || !addr_b)
return true;
/* If the references are based on different static objects, they cannot alias
(PTA should be able to disambiguate such accesses, but often it fails to,
since currently we cannot distinguish between pointer and offset in pointer
arithmetics). */
if (TREE_CODE (addr_a) == ADDR_EXPR
&& TREE_CODE (addr_b) == ADDR_EXPR)
return TREE_OPERAND (addr_a, 0) == TREE_OPERAND (addr_b, 0);
/* An instruction writing through a restricted pointer is "independent" of any
instruction reading or writing through a different restricted pointer,
in the same block/scope. */
type_a = TREE_TYPE (addr_a);
type_b = TREE_TYPE (addr_b);
gcc_assert (POINTER_TYPE_P (type_a) && POINTER_TYPE_P (type_b));
if (TREE_CODE (addr_a) == SSA_NAME)
decl_a = SSA_NAME_VAR (addr_a);
if (TREE_CODE (addr_b) == SSA_NAME)
decl_b = SSA_NAME_VAR (addr_b);
if (TYPE_RESTRICT (type_a) && TYPE_RESTRICT (type_b)
&& (!DR_IS_READ (a) || !DR_IS_READ (b))
&& decl_a && DECL_P (decl_a)
&& decl_b && DECL_P (decl_b)
&& decl_a != decl_b
&& TREE_CODE (DECL_CONTEXT (decl_a)) == FUNCTION_DECL
&& DECL_CONTEXT (decl_a) == DECL_CONTEXT (decl_b))
return false;
return true;
}
static void compute_self_dependence (struct data_dependence_relation *);
/* Initialize a data dependence relation between data accesses A and
B. NB_LOOPS is the number of loops surrounding the references: the
size of the classic distance/direction vectors. */
static struct data_dependence_relation *
initialize_data_dependence_relation (struct data_reference *a,
struct data_reference *b,
VEC (loop_p, heap) *loop_nest)
{
struct data_dependence_relation *res;
unsigned int i;
res = XNEW (struct data_dependence_relation);
DDR_A (res) = a;
DDR_B (res) = b;
DDR_LOOP_NEST (res) = NULL;
DDR_REVERSED_P (res) = false;
DDR_SUBSCRIPTS (res) = NULL;
DDR_DIR_VECTS (res) = NULL;
DDR_DIST_VECTS (res) = NULL;
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))
{
DDR_ARE_DEPENDENT (res) = chrec_known;
return res;
}
/* When the references are exactly the same, don't spend time doing
the data dependence tests, just initialize the ddr and return. */
if (operand_equal_p (DR_REF (a), DR_REF (b), 0))
{
DDR_AFFINE_P (res) = true;
DDR_ARE_DEPENDENT (res) = NULL_TREE;
DDR_SUBSCRIPTS (res) = VEC_alloc (subscript_p, heap, DR_NUM_DIMENSIONS (a));
DDR_LOOP_NEST (res) = loop_nest;
DDR_INNER_LOOP (res) = 0;
DDR_SELF_REFERENCE (res) = true;
compute_self_dependence (res);
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 (!object_address_invariant_in_loop_p (VEC_index (loop_p, loop_nest, 0),
DR_BASE_OBJECT (a)))
{
DDR_ARE_DEPENDENT (res) = chrec_dont_know;
return res;
}
gcc_assert (DR_NUM_DIMENSIONS (a) == DR_NUM_DIMENSIONS (b));
DDR_AFFINE_P (res) = true;
DDR_ARE_DEPENDENT (res) = NULL_TREE;
DDR_SUBSCRIPTS (res) = VEC_alloc (subscript_p, heap, DR_NUM_DIMENSIONS (a));
DDR_LOOP_NEST (res) = loop_nest;
DDR_INNER_LOOP (res) = 0;
DDR_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;
VEC_safe_push (subscript_p, heap, DDR_SUBSCRIPTS (res), subscript);
}
return res;
}
/* Frees memory used by the conflict function F. */
static void
free_conflict_function (conflict_function *f)
{
unsigned i;
if (CF_NONTRIVIAL_P (f))
{
for (i = 0; i < f->n; i++)
affine_fn_free (f->fns[i]);
}
free (f);
}
/* Frees memory used by SUBSCRIPTS. */
static void
free_subscripts (VEC (subscript_p, heap) *subscripts)
{
unsigned i;
subscript_p s;
for (i = 0; VEC_iterate (subscript_p, subscripts, i, s); i++)
{
free_conflict_function (s->conflicting_iterations_in_a);
free_conflict_function (s->conflicting_iterations_in_b);
free (s);
}
VEC_free (subscript_p, heap, subscripts);
}
/* Set DDR_ARE_DEPENDENT to CHREC and finalize the subscript overlap
description. */
static inline void
finalize_ddr_dependent (struct data_dependence_relation *ddr,
tree chrec)
{
if (dump_file && (dump_flags & TDF_DETAILS))
{
fprintf (dump_file, "(dependence classified: ");
print_generic_expr (dump_file, chrec, 0);
fprintf (dump_file, ")\n");
}
DDR_ARE_DEPENDENT (ddr) = chrec;
free_subscripts (DDR_SUBSCRIPTS (ddr));
DDR_SUBSCRIPTS (ddr) = NULL;
}
/* 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 = VEC_alloc (tree, heap, 1);
VEC_quick_push (tree, fn, cst);
return fn;
}
/* Returns affine function with single variable, CST + COEF * x_DIM. */
static affine_fn
affine_fn_univar (tree cst, unsigned dim, tree coef)
{
affine_fn fn = VEC_alloc (tree, heap, dim + 1);
unsigned i;
gcc_assert (dim > 0);
VEC_quick_push (tree, fn, cst);
for (i = 1; i < dim; i++)
VEC_quick_push (tree, fn, integer_zero_node);
VEC_quick_push (tree, fn, coef);
return fn;
}
/* Analyze a ZIV (Zero Index Variable) subscript. *OVERLAPS_A and
*OVERLAPS_B are initialized to the functions that describe the
relation between the elements accessed twice by CHREC_A and
CHREC_B. For k >= 0, the following property is verified:
CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
static void
analyze_ziv_subscript (tree chrec_a,
tree chrec_b,
conflict_function **overlaps_a,
conflict_function **overlaps_b,
tree *last_conflicts)
{
tree 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");
}
/* Sets NIT to the estimated number of executions of the statements in
LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as
large as the number of iterations. If we have no reliable estimate,
the function returns false, otherwise returns true. */
bool
estimated_loop_iterations (struct loop *loop, bool conservative,
double_int *nit)
{
estimate_numbers_of_iterations_loop (loop);
if (conservative)
{
if (!loop->any_upper_bound)
return false;
*nit = loop->nb_iterations_upper_bound;
}
else
{
if (!loop->any_estimate)
return false;
*nit = loop->nb_iterations_estimate;
}
return true;
}
/* Similar to estimated_loop_iterations, but returns the estimate only
if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
on the number of iterations of LOOP could not be derived, returns -1. */
HOST_WIDE_INT
estimated_loop_iterations_int (struct loop *loop, bool conservative)
{
double_int nit;
HOST_WIDE_INT hwi_nit;
if (!estimated_loop_iterations (loop, conservative, &nit))
return -1;
if (!double_int_fits_in_shwi_p (nit))
return -1;
hwi_nit = double_int_to_shwi (nit);
return hwi_nit < 0 ? -1 : hwi_nit;
}
/* Similar to estimated_loop_iterations, but returns the estimate as a tree,
and only if it fits to the int type. If this is not the case, or the
estimate on the number of iterations of LOOP could not be derived, returns
chrec_dont_know. */
static tree
estimated_loop_iterations_tree (struct loop *loop, bool conservative)
{
double_int nit;
tree type;
if (!estimated_loop_iterations (loop, conservative, &nit))
return chrec_dont_know;
type = lang_hooks.types.type_for_size (INT_TYPE_SIZE, true);
if (!double_int_fits_to_tree_p (type, nit))
return chrec_dont_know;
return double_int_to_tree (type, nit);
}
/* Analyze a SIV (Single Index Variable) subscript where CHREC_A is a
constant, and CHREC_B is an affine function. *OVERLAPS_A and
*OVERLAPS_B are initialized to the functions that describe the
relation between the elements accessed twice by CHREC_A and
CHREC_B. For k >= 0, the following property is verified:
CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
static void
analyze_siv_subscript_cst_affine (tree chrec_a,
tree chrec_b,
conflict_function **overlaps_a,
conflict_function **overlaps_b,
tree *last_conflicts)
{
bool value0, value1, value2;
tree 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);
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 = estimated_loop_iterations_int (loop, false);
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 = estimated_loop_iterations_int (loop, false);
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 =
estimated_loop_iterations_int (get_chrec_loop (CHREC_LEFT (chrec_a)),
false);
niter_y = estimated_loop_iterations_int (get_chrec_loop (chrec_a), false);
niter_z = estimated_loop_iterations_int (get_chrec_loop (chrec_b), false);
if (niter_x < 0 || niter_y < 0 || niter_z < 0)
{
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, "overlap steps test failed: no iteration counts.\n");
*overlaps_a = conflict_fn_not_known ();
*overlaps_b = conflict_fn_not_known ();
*last_conflicts = chrec_dont_know;
return;
}
niter = MIN (niter_x, niter_z);
compute_overlap_steps_for_affine_univar (niter, step_x, step_z,
&overlaps_a_xz,
&overlaps_b_xz,
&last_conflicts_xz, 1);
niter = MIN (niter_y, niter_z);
compute_overlap_steps_for_affine_univar (niter, step_y, step_z,
&overlaps_a_yz,
&overlaps_b_yz,
&last_conflicts_yz, 2);
niter = MIN (niter_x, niter_z);
niter = MIN (niter_y, niter);
compute_overlap_steps_for_affine_univar (niter, step_x + step_y, step_z,
&overlaps_a_xyz,
&overlaps_b_xyz,
&last_conflicts_xyz, 3);
xz_p = !integer_zerop (last_conflicts_xz);
yz_p = !integer_zerop (last_conflicts_yz);
xyz_p = !integer_zerop (last_conflicts_xyz);
if (xz_p || yz_p || xyz_p)
{
ova1 = affine_fn_cst (integer_zero_node);
ova2 = affine_fn_cst (integer_zero_node);
ovb = affine_fn_cst (integer_zero_node);
if (xz_p)
{
affine_fn t0 = ova1;
affine_fn t2 = ovb;
ova1 = affine_fn_plus (ova1, overlaps_a_xz);
ovb = affine_fn_plus (ovb, overlaps_b_xz);
affine_fn_free (t0);
affine_fn_free (t2);
*last_conflicts = last_conflicts_xz;
}
if (yz_p)
{
affine_fn t0 = ova2;
affine_fn t2 = ovb;
ova2 = affine_fn_plus (ova2, overlaps_a_yz);
ovb = affine_fn_plus (ovb, overlaps_b_yz);
affine_fn_free (t0);
affine_fn_free (t2);
*last_conflicts = last_conflicts_yz;
}
if (xyz_p)
{
affine_fn t0 = ova1;
affine_fn t2 = ova2;
affine_fn t4 = ovb;
ova1 = affine_fn_plus (ova1, overlaps_a_xyz);
ova2 = affine_fn_plus (ova2, overlaps_a_xyz);
ovb = affine_fn_plus (ovb, overlaps_b_xyz);
affine_fn_free (t0);
affine_fn_free (t2);
affine_fn_free (t4);
*last_conflicts = last_conflicts_xyz;
}
*overlaps_a = conflict_fn (2, ova1, ova2);
*overlaps_b = conflict_fn (1, ovb);
}
else
{
*overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
*overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
*last_conflicts = integer_zero_node;
}
affine_fn_free (overlaps_a_xz);
affine_fn_free (overlaps_b_xz);
affine_fn_free (overlaps_a_yz);
affine_fn_free (overlaps_b_yz);
affine_fn_free (overlaps_a_xyz);
affine_fn_free (overlaps_b_xyz);
}
/* Determines the overlapping elements due to accesses CHREC_A and
CHREC_B, that are affine functions. This function cannot handle
symbolic evolution functions, ie. when initial conditions are
parameters, because it uses lambda matrices of integers. */
static void
analyze_subscript_affine_affine (tree chrec_a,
tree chrec_b,
conflict_function **overlaps_a,
conflict_function **overlaps_b,
tree *last_conflicts)
{
unsigned nb_vars_a, nb_vars_b, dim;
HOST_WIDE_INT init_a, init_b, gamma, gcd_alpha_beta;
lambda_matrix A, U, S;
if (eq_evolutions_p (chrec_a, chrec_b))
{
/* The accessed index overlaps for each iteration in the
loop. */
*overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
*overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
*last_conflicts = chrec_dont_know;
return;
}
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, "(analyze_subscript_affine_affine \n");
/* For determining the initial intersection, we have to solve a
Diophantine equation. This is the most time consuming part.
For answering to the question: "Is there a dependence?" we have
to prove that there exists a solution to the Diophantine
equation, and that the solution is in the iteration domain,
i.e. the solution is positive or zero, and that the solution
happens before the upper bound loop.nb_iterations. Otherwise
there is no dependence. This function outputs a description of
the iterations that hold the intersections. */
nb_vars_a = nb_vars_in_chrec (chrec_a);
nb_vars_b = nb_vars_in_chrec (chrec_b);
dim = nb_vars_a + nb_vars_b;
U = lambda_matrix_new (dim, dim);
A = lambda_matrix_new (dim, 1);
S = lambda_matrix_new (dim, 1);
init_a = 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 = estimated_loop_iterations_int (get_chrec_loop (chrec_a),
false);
niter_b = estimated_loop_iterations_int (get_chrec_loop (chrec_b),
false);
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 = estimated_loop_iterations_int
(get_chrec_loop (chrec_a), false);
HOST_WIDE_INT niter_b = estimated_loop_iterations_int
(get_chrec_loop (chrec_b), false);
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:
if (dump_file && (dump_flags & TDF_DETAILS))
{
fprintf (dump_file, " (overlaps_a = ");
dump_conflict_function (dump_file, *overlaps_a);
fprintf (dump_file, ")\n (overlaps_b = ");
dump_conflict_function (dump_file, *overlaps_b);
fprintf (dump_file, ")\n");
fprintf (dump_file, ")\n");
}
}
/* Returns true when analyze_subscript_affine_affine can be used for
determining the dependence relation between chrec_a and chrec_b,
that contain symbols. This function modifies chrec_a and chrec_b
such that the analysis result is the same, and such that they don't
contain symbols, and then can safely be passed to the analyzer.
Example: The analysis of the following tuples of evolutions produce
the same results: {x+1, +, 1}_1 vs. {x+3, +, 1}_1, and {-2, +, 1}_1
vs. {0, +, 1}_1
{x+1, +, 1}_1 ({2, +, 1}_1) = {x+3, +, 1}_1 ({0, +, 1}_1)
{-2, +, 1}_1 ({2, +, 1}_1) = {0, +, 1}_1 ({0, +, 1}_1)
*/
static bool
can_use_analyze_subscript_affine_affine (tree *chrec_a, tree *chrec_b)
{
tree diff, type, left_a, left_b, right_b;
if (chrec_contains_symbols (CHREC_RIGHT (*chrec_a))
|| chrec_contains_symbols (CHREC_RIGHT (*chrec_b)))
/* FIXME: For the moment not handled. Might be refined later. */
return false;
type = chrec_type (*chrec_a);
left_a = CHREC_LEFT (*chrec_a);
left_b = chrec_convert (type, CHREC_LEFT (*chrec_b), NULL);
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.\n");
*overlaps_a = conflict_fn_not_known ();
*overlaps_b = conflict_fn_not_known ();
*last_conflicts = chrec_dont_know;
dependence_stats.num_siv_unimplemented++;
}
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, ")\n");
}
/* Returns false if we can prove that the greatest common divisor of the steps
of CHREC does not divide CST, false otherwise. */
static bool
gcd_of_steps_may_divide_p (const_tree chrec, const_tree cst)
{
HOST_WIDE_INT cd = 0, val;
tree step;
if (!host_integerp (cst, 0))
return true;
val = tree_low_cst (cst, 0);
while (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
{
step = CHREC_RIGHT (chrec);
if (!host_integerp (step, 0))
return true;
cd = gcd (cd, tree_low_cst (step, 0));
chrec = CHREC_LEFT (chrec);
}
return val % cd == 0;
}
/* Analyze a MIV (Multiple Index Variable) subscript 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)
{
/* FIXME: This is a MIV subscript, not yet handled.
Example: (A[{1, +, 1}_1] vs. A[{1, +, 1}_2]) that comes from
(A[i] vs. A[j]).
In the SIV test we had to solve a Diophantine equation with two
variables. In the MIV case we have to solve a Diophantine
equation with 2*n variables (if the subscript uses n IVs).
*/
tree 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 = estimated_loop_iterations_tree
(get_chrec_loop (chrec_a), true);
dependence_stats.num_miv_dependent++;
}
else if (evolution_function_is_constant_p (difference)
/* For the moment, the following is verified:
evolution_function_is_affine_multivariate_p (chrec_a,
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))
{
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");
fprintf (dump_file, ")\n");
}
}
/* Helper function for uniquely inserting distance vectors. */
static void
save_dist_v (struct data_dependence_relation *ddr, lambda_vector dist_v)
{
unsigned i;
lambda_vector v;
for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, v); i++)
if (lambda_vector_equal (v, dist_v, DDR_NB_LOOPS (ddr)))
return;
VEC_safe_push (lambda_vector, heap, DDR_DIST_VECTS (ddr), dist_v);
}
/* Helper function for uniquely inserting direction vectors. */
static void
save_dir_v (struct data_dependence_relation *ddr, lambda_vector dir_v)
{
unsigned i;
lambda_vector v;
for (i = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), i, v); i++)
if (lambda_vector_equal (v, dir_v, DDR_NB_LOOPS (ddr)))
return;
VEC_safe_push (lambda_vector, heap, DDR_DIR_VECTS (ddr), dir_v);
}
/* Add a distance of 1 on all the loops outer than INDEX. If we
haven't yet determined a distance for this outer loop, push a new
distance vector composed of the previous distance, and a distance
of 1 for this outer loop. Example:
| loop_1
| loop_2
| A[10]
| endloop_2
| endloop_1
Saved vectors are of the form (dist_in_1, dist_in_2). First, we
save (0, 1), then we have to save (1, 0). */
static void
add_outer_distances (struct data_dependence_relation *ddr,
lambda_vector dist_v, int index)
{
/* For each outer loop where init_v is not set, the accesses are
in dependence of distance 1 in the loop. */
while (--index >= 0)
{
lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr));
save_v[index] = 1;
save_dist_v (ddr, save_v);
}
}
/* Return false when fail to represent the data dependence as a
distance vector. INIT_B is set to true when a component has been
added to the distance vector DIST_V. INDEX_CARRY is then set to
the index in DIST_V that carries the dependence. */
static bool
build_classic_dist_vector_1 (struct data_dependence_relation *ddr,
struct data_reference *ddr_a,
struct data_reference *ddr_b,
lambda_vector dist_v, bool *init_b,
int *index_carry)
{
unsigned i;
lambda_vector init_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
{
tree access_fn_a, access_fn_b;
struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
{
non_affine_dependence_relation (ddr);
return false;
}
access_fn_a = DR_ACCESS_FN (ddr_a, i);
access_fn_b = DR_ACCESS_FN (ddr_b, i);
if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC
&& TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC)
{
int dist, index;
int index_a = index_in_loop_nest (CHREC_VARIABLE (access_fn_a),
DDR_LOOP_NEST (ddr));
int index_b = index_in_loop_nest (CHREC_VARIABLE (access_fn_b),
DDR_LOOP_NEST (ddr));
/* The dependence is carried by the outermost loop. Example:
| loop_1
| A[{4, +, 1}_1]
| loop_2
| A[{5, +, 1}_2]
| endloop_2
| endloop_1
In this case, the dependence is carried by loop_1. */
index = index_a < index_b ? index_a : index_b;
*index_carry = MIN (index, *index_carry);
if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
{
non_affine_dependence_relation (ddr);
return false;
}
dist = int_cst_value (SUB_DISTANCE (subscript));
/* This is the subscript coupling test. If we have already
recorded a distance for this loop (a distance coming from
another subscript), it should be the same. For example,
in the following code, there is no dependence:
| loop i = 0, N, 1
| T[i+1][i] = ...
| ... = T[i][i]
| endloop
*/
if (init_v[index] != 0 && dist_v[index] != dist)
{
finalize_ddr_dependent (ddr, chrec_known);
return false;
}
dist_v[index] = dist;