/* Data references and dependences detectors.
- Copyright (C) 2003, 2004 Free Software Foundation, Inc.
- Contributed by Sebastian Pop <s.pop@laposte.net>
+ Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
+ Contributed by Sebastian Pop <pop@cri.ensmp.fr>
This file is part of GCC.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING. If not, write to the Free
-Software Foundation, 59 Temple Place - Suite 330, Boston, MA
-02111-1307, USA. */
+Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
+02110-1301, USA. */
/* This pass walks a given loop structure searching for array
references. The information about the array accesses is recorded
- polyhedron dependence
or with the chains of recurrences based representation,
- - to define a knowledge base for storing the data dependeces
+ - to define a knowledge base for storing the data dependence
information,
- to define an interface to access this data.
#include "system.h"
#include "coretypes.h"
#include "tm.h"
-#include "errors.h"
#include "ggc.h"
#include "tree.h"
#include "tree-data-ref.h"
#include "tree-scalar-evolution.h"
#include "tree-pass.h"
-#include "lambda.h"
+#include "langhooks.h"
-static unsigned int data_ref_id = 0;
+static struct datadep_stats
+{
+ int num_dependence_tests;
+ int num_dependence_dependent;
+ int num_dependence_independent;
+ int num_dependence_undetermined;
+
+ int num_subscript_tests;
+ int num_subscript_undetermined;
+ int num_same_subscript_function;
+
+ int num_ziv;
+ int num_ziv_independent;
+ int num_ziv_dependent;
+ int num_ziv_unimplemented;
+
+ int num_siv;
+ int num_siv_independent;
+ int num_siv_dependent;
+ int num_siv_unimplemented;
+
+ int num_miv;
+ int num_miv_independent;
+ int num_miv_dependent;
+ int num_miv_unimplemented;
+} dependence_stats;
+
+static tree object_analysis (tree, tree, bool, struct data_reference **,
+ tree *, tree *, tree *, tree *, tree *,
+ struct ptr_info_def **, subvar_t *);
+static bool subscript_dependence_tester_1 (struct data_dependence_relation *,
+ struct data_reference *,
+ struct data_reference *);
+
+/* Determine if PTR and DECL may alias, the result is put in ALIASED.
+ Return FALSE if there is no symbol memory tag for PTR. */
-\f
-/* This is the simplest data dependence test: determines whether the
- data references A and B access the same array/region. If can't determine -
- return false; Otherwise, return true, and DIFFER_P will record
- the result. This utility will not be necessary when alias_sets_conflict_p
- will be less conservative. */
+static bool
+ptr_decl_may_alias_p (tree ptr, tree decl,
+ struct data_reference *ptr_dr,
+ bool *aliased)
+{
+ tree tag = NULL_TREE;
+ struct ptr_info_def *pi = DR_PTR_INFO (ptr_dr);
+
+ gcc_assert (TREE_CODE (ptr) == SSA_NAME && DECL_P (decl));
+
+ if (pi)
+ tag = pi->name_mem_tag;
+ if (!tag)
+ tag = symbol_mem_tag (SSA_NAME_VAR (ptr));
+ if (!tag)
+ tag = DR_MEMTAG (ptr_dr);
+ if (!tag)
+ return false;
+
+ *aliased = is_aliased_with (tag, decl);
+ return true;
+}
-bool
-array_base_name_differ_p (struct data_reference *a,
- struct data_reference *b,
- bool *differ_p)
+
+/* Determine if two pointers may alias, the result is put in ALIASED.
+ Return FALSE if there is no symbol memory tag for one of the pointers. */
+
+static bool
+ptr_ptr_may_alias_p (tree ptr_a, tree ptr_b,
+ struct data_reference *dra,
+ struct data_reference *drb,
+ bool *aliased)
+{
+ tree tag_a = NULL_TREE, tag_b = NULL_TREE;
+ struct ptr_info_def *pi_a = DR_PTR_INFO (dra);
+ struct ptr_info_def *pi_b = DR_PTR_INFO (drb);
+ bitmap bal1, bal2;
+
+ if (pi_a && pi_a->name_mem_tag && pi_b && pi_b->name_mem_tag)
+ {
+ tag_a = pi_a->name_mem_tag;
+ tag_b = pi_b->name_mem_tag;
+ }
+ else
+ {
+ tag_a = symbol_mem_tag (SSA_NAME_VAR (ptr_a));
+ if (!tag_a)
+ tag_a = DR_MEMTAG (dra);
+ if (!tag_a)
+ return false;
+
+ tag_b = symbol_mem_tag (SSA_NAME_VAR (ptr_b));
+ if (!tag_b)
+ tag_b = DR_MEMTAG (drb);
+ if (!tag_b)
+ return false;
+ }
+ bal1 = BITMAP_ALLOC (NULL);
+ bitmap_set_bit (bal1, DECL_UID (tag_a));
+ if (MTAG_P (tag_a) && MTAG_ALIASES (tag_a))
+ bitmap_ior_into (bal1, MTAG_ALIASES (tag_a));
+
+ bal2 = BITMAP_ALLOC (NULL);
+ bitmap_set_bit (bal2, DECL_UID (tag_b));
+ if (MTAG_P (tag_b) && MTAG_ALIASES (tag_b))
+ bitmap_ior_into (bal2, MTAG_ALIASES (tag_b));
+ *aliased = bitmap_intersect_p (bal1, bal2);
+
+ BITMAP_FREE (bal1);
+ BITMAP_FREE (bal2);
+ return true;
+}
+
+
+/* Determine if BASE_A and BASE_B may alias, the result is put in ALIASED.
+ Return FALSE if there is no symbol memory tag for one of the symbols. */
+
+static bool
+may_alias_p (tree base_a, tree base_b,
+ struct data_reference *dra,
+ struct data_reference *drb,
+ bool *aliased)
+{
+ if (TREE_CODE (base_a) == ADDR_EXPR || TREE_CODE (base_b) == ADDR_EXPR)
+ {
+ if (TREE_CODE (base_a) == ADDR_EXPR && TREE_CODE (base_b) == ADDR_EXPR)
+ {
+ *aliased = (TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0));
+ return true;
+ }
+ if (TREE_CODE (base_a) == ADDR_EXPR)
+ return ptr_decl_may_alias_p (base_b, TREE_OPERAND (base_a, 0), drb,
+ aliased);
+ else
+ return ptr_decl_may_alias_p (base_a, TREE_OPERAND (base_b, 0), dra,
+ aliased);
+ }
+
+ return ptr_ptr_may_alias_p (base_a, base_b, dra, drb, aliased);
+}
+
+
+/* Determine if a pointer (BASE_A) and a record/union access (BASE_B)
+ are not aliased. Return TRUE if they differ. */
+static bool
+record_ptr_differ_p (struct data_reference *dra,
+ struct data_reference *drb)
+{
+ bool aliased;
+ tree base_a = DR_BASE_OBJECT (dra);
+ tree base_b = DR_BASE_OBJECT (drb);
+
+ if (TREE_CODE (base_b) != COMPONENT_REF)
+ return false;
+
+ /* Peel COMPONENT_REFs to get to the base. Do not peel INDIRECT_REFs.
+ For a.b.c.d[i] we will get a, and for a.b->c.d[i] we will get a.b.
+ Probably will be unnecessary with struct alias analysis. */
+ while (TREE_CODE (base_b) == COMPONENT_REF)
+ base_b = TREE_OPERAND (base_b, 0);
+ /* Compare a record/union access (b.c[i] or p->c[i]) and a pointer
+ ((*q)[i]). */
+ if (TREE_CODE (base_a) == INDIRECT_REF
+ && ((TREE_CODE (base_b) == VAR_DECL
+ && (ptr_decl_may_alias_p (TREE_OPERAND (base_a, 0), base_b, dra,
+ &aliased)
+ && !aliased))
+ || (TREE_CODE (base_b) == INDIRECT_REF
+ && (ptr_ptr_may_alias_p (TREE_OPERAND (base_a, 0),
+ TREE_OPERAND (base_b, 0), dra, drb,
+ &aliased)
+ && !aliased))))
+ return true;
+ else
+ return false;
+}
+
+/* Determine if two record/union accesses are aliased. Return TRUE if they
+ differ. */
+static bool
+record_record_differ_p (struct data_reference *dra,
+ struct data_reference *drb)
{
- tree base_a = DR_BASE_NAME (a);
- tree base_b = DR_BASE_NAME (b);
- tree ta = TREE_TYPE (base_a);
- tree tb = TREE_TYPE (base_b);
+ bool aliased;
+ tree base_a = DR_BASE_OBJECT (dra);
+ tree base_b = DR_BASE_OBJECT (drb);
+
+ if (TREE_CODE (base_b) != COMPONENT_REF
+ || TREE_CODE (base_a) != COMPONENT_REF)
+ return false;
+
+ /* Peel COMPONENT_REFs to get to the base. Do not peel INDIRECT_REFs.
+ For a.b.c.d[i] we will get a, and for a.b->c.d[i] we will get a.b.
+ Probably will be unnecessary with struct alias analysis. */
+ while (TREE_CODE (base_b) == COMPONENT_REF)
+ base_b = TREE_OPERAND (base_b, 0);
+ while (TREE_CODE (base_a) == COMPONENT_REF)
+ base_a = TREE_OPERAND (base_a, 0);
+
+ if (TREE_CODE (base_a) == INDIRECT_REF
+ && TREE_CODE (base_b) == INDIRECT_REF
+ && ptr_ptr_may_alias_p (TREE_OPERAND (base_a, 0),
+ TREE_OPERAND (base_b, 0),
+ dra, drb, &aliased)
+ && !aliased)
+ return true;
+ else
+ return false;
+}
+
+/* Determine if an array access (BASE_A) and a record/union access (BASE_B)
+ are not aliased. Return TRUE if they differ. */
+static bool
+record_array_differ_p (struct data_reference *dra,
+ struct data_reference *drb)
+{
+ bool aliased;
+ tree base_a = DR_BASE_OBJECT (dra);
+ tree base_b = DR_BASE_OBJECT (drb);
+
+ if (TREE_CODE (base_b) != COMPONENT_REF)
+ return false;
+
+ /* Peel COMPONENT_REFs to get to the base. Do not peel INDIRECT_REFs.
+ For a.b.c.d[i] we will get a, and for a.b->c.d[i] we will get a.b.
+ Probably will be unnecessary with struct alias analysis. */
+ while (TREE_CODE (base_b) == COMPONENT_REF)
+ base_b = TREE_OPERAND (base_b, 0);
+
+ /* Compare a record/union access (b.c[i] or p->c[i]) and an array access
+ (a[i]). In case of p->c[i] use alias analysis to verify that p is not
+ pointing to a. */
+ if (TREE_CODE (base_a) == VAR_DECL
+ && (TREE_CODE (base_b) == VAR_DECL
+ || (TREE_CODE (base_b) == INDIRECT_REF
+ && (ptr_decl_may_alias_p (TREE_OPERAND (base_b, 0), base_a, drb,
+ &aliased)
+ && !aliased))))
+ return true;
+ else
+ return false;
+}
+
+
+/* Determine if an array access (BASE_A) and a pointer (BASE_B)
+ are not aliased. Return TRUE if they differ. */
+static bool
+array_ptr_differ_p (tree base_a, tree base_b,
+ struct data_reference *drb)
+{
+ bool aliased;
+
+ /* In case one of the bases is a pointer (a[i] and (*p)[i]), we check with the
+ help of alias analysis that p is not pointing to a. */
+ if (TREE_CODE (base_a) == VAR_DECL && TREE_CODE (base_b) == INDIRECT_REF
+ && (ptr_decl_may_alias_p (TREE_OPERAND (base_b, 0), base_a, drb, &aliased)
+ && !aliased))
+ return true;
+ else
+ return false;
+}
+
+/* This is the simplest data dependence test: determines whether the
+ data references A and B access the same array/region. Returns
+ false when the property is not computable at compile time.
+ Otherwise return true, and DIFFER_P will record the result. This
+ utility will not be necessary when alias_sets_conflict_p will be
+ less conservative. */
+
+static bool
+base_object_differ_p (struct data_reference *a,
+ struct data_reference *b,
+ bool *differ_p)
+{
+ tree base_a = DR_BASE_OBJECT (a);
+ tree base_b = DR_BASE_OBJECT (b);
+ bool aliased;
- /** Determine if same base **/
+ if (!base_a || !base_b)
+ return false;
- /* array accesses: a[i],b[i] or pointer accesses: *a,*b. bases are a,b. */
+ /* Determine if same base. Example: for the array accesses
+ a[i], b[i] or pointer accesses *a, *b, bases are a, b. */
if (base_a == base_b)
{
*differ_p = false;
return true;
}
- /* pointer based accesses - (*p)[i],(*q)[j]. bases are (*p),(*q) */
+ /* For pointer based accesses, (*p)[i], (*q)[j], the bases are (*p)
+ and (*q) */
if (TREE_CODE (base_a) == INDIRECT_REF && TREE_CODE (base_b) == INDIRECT_REF
&& TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0))
{
return true;
}
- /* record/union based accesses - s.a[i], t.b[j]. bases are s.a,t.b. */
+ /* Record/union based accesses - s.a[i], t.b[j]. bases are s.a,t.b. */
if (TREE_CODE (base_a) == COMPONENT_REF && TREE_CODE (base_b) == COMPONENT_REF
&& TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0)
&& TREE_OPERAND (base_a, 1) == TREE_OPERAND (base_b, 1))
}
- /** Determine if different bases **/
+ /* Determine if different bases. */
- /* at this point we know that base_a != base_b. However, pointer accesses
- of the form x=(*p) and y=(*q), which bases are p and q, may still by pointing
- to the same base. In SSAed GIMPLE p and q will be SSA_NAMES in this case.
- Therefore, here we check if it's really two diferent declarations. */
+ /* At this point we know that base_a != base_b. However, pointer
+ accesses of the form x=(*p) and y=(*q), whose bases are p and q,
+ may still be pointing to the same base. In SSAed GIMPLE p and q will
+ be SSA_NAMES in this case. Therefore, here we check if they are
+ really two different declarations. */
if (TREE_CODE (base_a) == VAR_DECL && TREE_CODE (base_b) == VAR_DECL)
{
*differ_p = true;
return true;
}
- /* compare two record/union bases s.a and t.b:
- s != t or (a != b and s and t are not unions) */
+ /* In case one of the bases is a pointer (a[i] and (*p)[i]), we check with the
+ help of alias analysis that p is not pointing to a. */
+ if (array_ptr_differ_p (base_a, base_b, b)
+ || array_ptr_differ_p (base_b, base_a, a))
+ {
+ *differ_p = true;
+ return true;
+ }
+
+ /* If the bases are pointers ((*q)[i] and (*p)[i]), we check with the
+ help of alias analysis they don't point to the same bases. */
+ if (TREE_CODE (base_a) == INDIRECT_REF && TREE_CODE (base_b) == INDIRECT_REF
+ && (may_alias_p (TREE_OPERAND (base_a, 0), TREE_OPERAND (base_b, 0), a, b,
+ &aliased)
+ && !aliased))
+ {
+ *differ_p = true;
+ return true;
+ }
+
+ /* Compare two record/union bases s.a and t.b: s != t or (a != b and
+ s and t are not unions). */
if (TREE_CODE (base_a) == COMPONENT_REF && TREE_CODE (base_b) == COMPONENT_REF
&& ((TREE_CODE (TREE_OPERAND (base_a, 0)) == VAR_DECL
&& TREE_CODE (TREE_OPERAND (base_b, 0)) == VAR_DECL
return true;
}
- /* compare a record/union access and an array access. */
- if ((TREE_CODE (base_a) == VAR_DECL
- && (TREE_CODE (base_b) == COMPONENT_REF
- && TREE_CODE (TREE_OPERAND (base_b, 0)) == VAR_DECL))
- || (TREE_CODE (base_b) == VAR_DECL
- && (TREE_CODE (base_a) == COMPONENT_REF
- && TREE_CODE (TREE_OPERAND (base_a, 0)) == VAR_DECL)))
+ /* Compare a record/union access (b.c[i] or p->c[i]) and a pointer
+ ((*q)[i]). */
+ if (record_ptr_differ_p (a, b) || record_ptr_differ_p (b, a))
{
*differ_p = true;
return true;
}
- if (!alias_sets_conflict_p (get_alias_set (base_a), get_alias_set (base_b)))
+ /* Compare a record/union access (b.c[i] or p->c[i]) and an array access
+ (a[i]). In case of p->c[i] use alias analysis to verify that p is not
+ pointing to a. */
+ if (record_array_differ_p (a, b) || record_array_differ_p (b, a))
{
*differ_p = true;
return true;
}
- /* An insn writing through a restricted pointer is "independent" of any
- insn reading or writing through a different pointer, in the same
- block/scope.
- */
- if ((TREE_CODE (ta) == POINTER_TYPE && TYPE_RESTRICT (ta)
- && !DR_IS_READ(a))
- || (TREE_CODE (tb) == POINTER_TYPE && TYPE_RESTRICT (tb)
- && !DR_IS_READ(b)))
+ /* Compare two record/union accesses (b.c[i] or p->c[i]). */
+ if (record_record_differ_p (a, b))
{
*differ_p = true;
return true;
}
- *differ_p = false; /* Don't know, but be conservative. */
return false;
}
-/* Returns true iff A divides B. */
-
-static inline bool
-tree_fold_divides_p (tree type,
- tree a,
- tree b)
-{
- if (integer_onep (a))
- return true;
-
- /* Determines whether (A == gcd (A, B)). */
- return integer_zerop
- (fold (build (MINUS_EXPR, type, a, tree_fold_gcd (a, b))));
-}
+/* Function base_addr_differ_p.
-/* Bezout: Let A1 and A2 be two integers; there exist two integers U11
- and U12 such that,
-
- | U11 * A1 + U12 * A2 = gcd (A1, A2).
-
- This function computes the greatest common divisor using the
- Blankinship algorithm. The gcd is returned, and the coefficients
- of the unimodular matrix U are (U11, U12, U21, U22) such that,
+ This is the simplest data dependence test: determines whether the
+ data references DRA and DRB access the same array/region. Returns
+ false when the property is not computable at compile time.
+ Otherwise return true, and DIFFER_P will record the result.
- | U.A = S
-
- | (U11 U12) (A1) = (gcd)
- | (U21 U22) (A2) (0)
-
- FIXME: Use lambda_..._hermite for implementing this function.
+ The algorithm:
+ 1. if (both DRA and DRB are represented as arrays)
+ compare DRA.BASE_OBJECT and DRB.BASE_OBJECT
+ 2. else if (both DRA and DRB are represented as pointers)
+ try to prove that DRA.FIRST_LOCATION == DRB.FIRST_LOCATION
+ 3. else if (DRA and DRB are represented differently or 2. fails)
+ only try to prove that the bases are surely different
*/
-static tree
-tree_fold_bezout (tree a1,
- tree a2,
- tree *u11, tree *u12,
- tree *u21, tree *u22)
+static bool
+base_addr_differ_p (struct data_reference *dra,
+ struct data_reference *drb,
+ bool *differ_p)
{
- tree s1, s2;
-
- /* Initialize S with the coefficients of A. */
- s1 = a1;
- s2 = a2;
-
- /* Initialize the U matrix */
- *u11 = integer_one_node;
- *u12 = integer_zero_node;
- *u21 = integer_zero_node;
- *u22 = integer_one_node;
-
- if (integer_zerop (a1)
- || integer_zerop (a2))
- return integer_zero_node;
-
- while (!integer_zerop (s2))
+ tree addr_a = DR_BASE_ADDRESS (dra);
+ tree addr_b = DR_BASE_ADDRESS (drb);
+ tree type_a, type_b;
+ tree decl_a, decl_b;
+ bool aliased;
+
+ if (!addr_a || !addr_b)
+ return false;
+
+ type_a = TREE_TYPE (addr_a);
+ type_b = TREE_TYPE (addr_b);
+
+ gcc_assert (POINTER_TYPE_P (type_a) && POINTER_TYPE_P (type_b));
+
+ /* 1. if (both DRA and DRB are represented as arrays)
+ compare DRA.BASE_OBJECT and DRB.BASE_OBJECT. */
+ if (DR_TYPE (dra) == ARRAY_REF_TYPE && DR_TYPE (drb) == ARRAY_REF_TYPE)
+ return base_object_differ_p (dra, drb, differ_p);
+
+ /* 2. else if (both DRA and DRB are represented as pointers)
+ try to prove that DRA.FIRST_LOCATION == DRB.FIRST_LOCATION. */
+ /* If base addresses are the same, we check the offsets, since the access of
+ the data-ref is described by {base addr + offset} and its access function,
+ i.e., in order to decide whether the bases of data-refs are the same we
+ compare both base addresses and offsets. */
+ if (DR_TYPE (dra) == POINTER_REF_TYPE && DR_TYPE (drb) == POINTER_REF_TYPE
+ && (addr_a == addr_b
+ || (TREE_CODE (addr_a) == ADDR_EXPR && TREE_CODE (addr_b) == ADDR_EXPR
+ && TREE_OPERAND (addr_a, 0) == TREE_OPERAND (addr_b, 0))))
{
- int sign;
- tree z, zu21, zu22, zs2;
-
- sign = tree_int_cst_sgn (s1) * tree_int_cst_sgn (s2);
- z = fold (build (FLOOR_DIV_EXPR, integer_type_node,
- fold (build1 (ABS_EXPR, integer_type_node, s1)),
- fold (build1 (ABS_EXPR, integer_type_node, s2))));
- zu21 = fold (build (MULT_EXPR, integer_type_node, z, *u21));
- zu22 = fold (build (MULT_EXPR, integer_type_node, z, *u22));
- zs2 = fold (build (MULT_EXPR, integer_type_node, z, s2));
+ /* Compare offsets. */
+ tree offset_a = DR_OFFSET (dra);
+ tree offset_b = DR_OFFSET (drb);
- /* row1 -= z * row2. */
- if (sign < 0)
+ STRIP_NOPS (offset_a);
+ STRIP_NOPS (offset_b);
+
+ /* FORNOW: we only compare offsets that are MULT_EXPR, i.e., we don't handle
+ PLUS_EXPR. */
+ if (offset_a == offset_b
+ || (TREE_CODE (offset_a) == MULT_EXPR
+ && TREE_CODE (offset_b) == MULT_EXPR
+ && TREE_OPERAND (offset_a, 0) == TREE_OPERAND (offset_b, 0)
+ && TREE_OPERAND (offset_a, 1) == TREE_OPERAND (offset_b, 1)))
{
- *u11 = fold (build (PLUS_EXPR, integer_type_node, *u11, zu21));
- *u12 = fold (build (PLUS_EXPR, integer_type_node, *u12, zu22));
- s1 = fold (build (PLUS_EXPR, integer_type_node, s1, zs2));
- }
- else if (sign > 0)
- {
- *u11 = fold (build (MINUS_EXPR, integer_type_node, *u11, zu21));
- *u12 = fold (build (MINUS_EXPR, integer_type_node, *u12, zu22));
- s1 = fold (build (MINUS_EXPR, integer_type_node, s1, zs2));
+ *differ_p = false;
+ return true;
}
- else
- /* Should not happen. */
- abort ();
-
- /* Interchange row1 and row2. */
- {
- tree flip;
-
- flip = *u11;
- *u11 = *u21;
- *u21 = flip;
+ }
- flip = *u12;
- *u12 = *u22;
- *u22 = flip;
-
- flip = s1;
- s1 = s2;
- s2 = flip;
- }
+ /* 3. else if (DRA and DRB are represented differently or 2. fails)
+ only try to prove that the bases are surely different. */
+
+ /* Apply alias analysis. */
+ if (may_alias_p (addr_a, addr_b, dra, drb, &aliased) && !aliased)
+ {
+ *differ_p = true;
+ return true;
}
- if (tree_int_cst_sgn (s1) < 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. */
+ else if (TYPE_RESTRICT (type_a)
+ && TYPE_RESTRICT (type_b)
+ && (!DR_IS_READ (drb) || !DR_IS_READ (dra))
+ && TREE_CODE (DR_BASE_ADDRESS (dra)) == SSA_NAME
+ && (decl_a = SSA_NAME_VAR (DR_BASE_ADDRESS (dra)))
+ && TREE_CODE (decl_a) == PARM_DECL
+ && TREE_CODE (DECL_CONTEXT (decl_a)) == FUNCTION_DECL
+ && TREE_CODE (DR_BASE_ADDRESS (drb)) == SSA_NAME
+ && (decl_b = SSA_NAME_VAR (DR_BASE_ADDRESS (drb)))
+ && TREE_CODE (decl_b) == PARM_DECL
+ && TREE_CODE (DECL_CONTEXT (decl_b)) == FUNCTION_DECL
+ && DECL_CONTEXT (decl_a) == DECL_CONTEXT (decl_b))
{
- *u11 = fold (build (MULT_EXPR, integer_type_node, *u11,
- integer_minus_one_node));
- *u12 = fold (build (MULT_EXPR, integer_type_node, *u12,
- integer_minus_one_node));
- s1 = fold (build (MULT_EXPR, integer_type_node, s1, integer_minus_one_node));
+ *differ_p = true;
+ return true;
}
-
- return s1;
+
+ return false;
+}
+
+/* Returns true iff A divides B. */
+
+static inline bool
+tree_fold_divides_p (tree a, tree b)
+{
+ gcc_assert (TREE_CODE (a) == INTEGER_CST);
+ gcc_assert (TREE_CODE (b) == INTEGER_CST);
+ return integer_zerop (int_const_binop (TRUNC_MOD_EXPR, b, a, 0));
+}
+
+/* Returns true iff A divides B. */
+
+static inline bool
+int_divides_p (int a, int b)
+{
+ return ((b % a) == 0);
}
\f
/* Dump into FILE all the data references from DATAREFS. */
void
-dump_data_references (FILE *file,
- varray_type datarefs)
+dump_data_references (FILE *file, VEC (data_reference_p, heap) *datarefs)
{
unsigned int i;
-
- for (i = 0; i < VARRAY_ACTIVE_SIZE (datarefs); i++)
- dump_data_reference (file, VARRAY_GENERIC_PTR (datarefs, i));
+ struct data_reference *dr;
+
+ for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++)
+ dump_data_reference (file, dr);
}
-/* Dump into FILE all the dependence relations from DDR. */
+/* Dump into FILE all the dependence relations from DDRS. */
void
dump_data_dependence_relations (FILE *file,
- varray_type ddr)
+ VEC (ddr_p, heap) *ddrs)
{
unsigned int i;
-
- for (i = 0; i < VARRAY_ACTIVE_SIZE (ddr); i++)
- dump_data_dependence_relation (file, VARRAY_GENERIC_PTR (ddr, 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. */
{
unsigned int i;
- fprintf (outf, "(Data Ref %d: \n stmt: ", DR_ID (dr));
+ fprintf (outf, "(Data Ref: \n stmt: ");
print_generic_stmt (outf, DR_STMT (dr), 0);
fprintf (outf, " ref: ");
print_generic_stmt (outf, DR_REF (dr), 0);
- fprintf (outf, " base_name: ");
- print_generic_stmt (outf, DR_BASE_NAME (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, ")\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)
{
- unsigned int i;
struct data_reference *dra, *drb;
-
+
dra = DDR_A (ddr);
drb = DDR_B (ddr);
-
- if (dra && drb)
- fprintf (outf, "(Data Dep (A = %d, B = %d):", DR_ID (dra), DR_ID (drb));
- else
- fprintf (outf, "(Data Dep:");
-
- if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr)))
+ fprintf (outf, "(Data Dep: \n");
+ if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know)
fprintf (outf, " (don't know)\n");
else if (DDR_ARE_DEPENDENT (ddr) == chrec_known)
fprintf (outf, " (no dependence)\n");
- else
+ else if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
{
+ unsigned int i;
+ struct loop *loopi;
+
for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
{
- tree chrec;
- struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
-
- fprintf (outf, "\n (subscript %d:\n", 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);
-
- chrec = SUB_CONFLICTS_IN_A (subscript);
- fprintf (outf, " iterations_that_access_an_element_twice_in_A: ");
- print_generic_stmt (outf, chrec, 0);
- if (chrec == chrec_known)
- fprintf (outf, " (no dependence)\n");
- else if (chrec_contains_undetermined (chrec))
- fprintf (outf, " (don't know)\n");
- else
- {
- tree last_iteration = SUB_LAST_CONFLICT_IN_A (subscript);
- fprintf (outf, " last_iteration_that_access_an_element_twice_in_A: ");
- print_generic_stmt (outf, last_iteration, 0);
- }
-
- chrec = SUB_CONFLICTS_IN_B (subscript);
- fprintf (outf, " iterations_that_access_an_element_twice_in_B: ");
- print_generic_stmt (outf, chrec, 0);
- if (chrec == chrec_known)
- fprintf (outf, " (no dependence)\n");
- else if (chrec_contains_undetermined (chrec))
- fprintf (outf, " (don't know)\n");
- else
- {
- tree last_iteration = SUB_LAST_CONFLICT_IN_B (subscript);
- fprintf (outf, " last_iteration_that_access_an_element_twice_in_B: ");
- print_generic_stmt (outf, last_iteration, 0);
- }
-
- fprintf (outf, " )\n");
+ dump_subscript (outf, DDR_SUBSCRIPT (ddr, i));
}
-
- fprintf (outf, " (Distance Vector: \n");
- for (i = 0; i < DDR_NUM_SUBSCRIPTS (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++)
{
- struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
-
- fprintf (outf, "(");
- print_generic_stmt (outf, SUB_DISTANCE (subscript), 0);
- fprintf (outf, ")\n");
+ 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");
}
fprintf (outf, ")\n");
}
-
-
/* Dump function for a DATA_DEPENDENCE_DIRECTION structure. */
void
}
}
+/* 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");
+}
+
\f
/* Given an ARRAY_REF node REF, records its access functions.
Example: given A[i][3], record in ACCESS_FNS the opnd1 function,
- ie. the constant "3", then recursively call the function on opnd0,
- ie. the ARRAY_REF "A[i]". The function returns the base name:
- "A". */
+ i.e. the constant "3", then recursively call the function on opnd0,
+ i.e. the ARRAY_REF "A[i]".
+ The function returns the base name: "A". */
static tree
analyze_array_indexes (struct loop *loop,
- varray_type access_fns,
- tree ref)
+ VEC(tree,heap) **access_fns,
+ tree ref, tree stmt)
{
tree opnd0, opnd1;
tree access_fn;
-
+
opnd0 = TREE_OPERAND (ref, 0);
opnd1 = TREE_OPERAND (ref, 1);
-
+
/* The detection of the evolution function for this data access is
postponed until the dependence test. This lazy strategy avoids
the computation of access functions that are of no interest for
the optimizers. */
- access_fn = instantiate_parameters
+ access_fn = instantiate_parameters
(loop, analyze_scalar_evolution (loop, opnd1));
-
- VARRAY_PUSH_TREE (access_fns, access_fn);
+
+ VEC_safe_push (tree, heap, *access_fns, access_fn);
/* Recursively record other array access functions. */
if (TREE_CODE (opnd0) == ARRAY_REF)
- return analyze_array_indexes (loop, access_fns, opnd0);
-
+ return analyze_array_indexes (loop, access_fns, opnd0, stmt);
+
/* Return the base name of the data access. */
else
return opnd0;
}
-/* For a data reference REF contained in the statemet STMT, initialize
+/* For a data reference REF contained in the statement STMT, initialize
a DATA_REFERENCE structure, and return it. IS_READ flag has to be
set to true when REF is in the right hand side of an
assignment. */
-struct data_reference *
-analyze_array (tree stmt, tree ref, bool is_read)
+static struct data_reference *
+init_array_ref (tree stmt, tree ref, bool is_read)
{
- struct data_reference *res;
+ struct loop *loop = loop_containing_stmt (stmt);
+ VEC(tree,heap) *acc_fns = VEC_alloc (tree, heap, 3);
+ struct data_reference *res = XNEW (struct data_reference);;
if (dump_file && (dump_flags & TDF_DETAILS))
{
- fprintf (dump_file, "(analyze_array \n");
+ fprintf (dump_file, "(init_array_ref \n");
fprintf (dump_file, " (ref = ");
print_generic_stmt (dump_file, ref, 0);
fprintf (dump_file, ")\n");
}
-
- res = ggc_alloc (sizeof (struct data_reference));
-
- DR_ID (res) = data_ref_id++;
+
DR_STMT (res) = stmt;
DR_REF (res) = ref;
- VARRAY_TREE_INIT (DR_ACCESS_FNS (res), 3, "access_fns");
- DR_BASE_NAME (res) = analyze_array_indexes
- (loop_containing_stmt (stmt), DR_ACCESS_FNS (res), ref);
+ DR_BASE_OBJECT (res) = analyze_array_indexes (loop, &acc_fns, ref, stmt);
+ DR_TYPE (res) = ARRAY_REF_TYPE;
+ DR_SET_ACCESS_FNS (res, acc_fns);
DR_IS_READ (res) = is_read;
-
+ DR_BASE_ADDRESS (res) = NULL_TREE;
+ DR_OFFSET (res) = NULL_TREE;
+ DR_INIT (res) = NULL_TREE;
+ DR_STEP (res) = NULL_TREE;
+ DR_OFFSET_MISALIGNMENT (res) = NULL_TREE;
+ DR_MEMTAG (res) = NULL_TREE;
+ DR_PTR_INFO (res) = NULL;
+
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, ")\n");
-
+
return res;
}
-/* For a data reference REF contained in the statemet STMT, initialize
+/* For a data reference REF contained in the statement STMT, initialize
a DATA_REFERENCE structure, and return it. */
-struct data_reference *
-init_data_ref (tree stmt,
- tree ref,
- tree base,
- tree access_fn,
- bool is_read)
+static struct data_reference *
+init_pointer_ref (tree stmt, tree ref, tree access_fn, bool is_read,
+ tree base_address, tree step, struct ptr_info_def *ptr_info)
{
- struct data_reference *res;
+ struct data_reference *res = XNEW (struct data_reference);
+ VEC(tree,heap) *acc_fns = VEC_alloc (tree, heap, 3);
if (dump_file && (dump_flags & TDF_DETAILS))
{
- fprintf (dump_file, "(init_data_ref \n");
+ fprintf (dump_file, "(init_pointer_ref \n");
fprintf (dump_file, " (ref = ");
print_generic_stmt (dump_file, ref, 0);
fprintf (dump_file, ")\n");
}
-
- res = ggc_alloc (sizeof (struct data_reference));
-
- DR_ID (res) = data_ref_id++;
+
DR_STMT (res) = stmt;
DR_REF (res) = ref;
- VARRAY_TREE_INIT (DR_ACCESS_FNS (res), 5, "access_fns");
- DR_BASE_NAME (res) = base;
- VARRAY_PUSH_TREE (DR_ACCESS_FNS (res), access_fn);
+ DR_BASE_OBJECT (res) = NULL_TREE;
+ DR_TYPE (res) = POINTER_REF_TYPE;
+ DR_SET_ACCESS_FNS (res, acc_fns);
+ VEC_quick_push (tree, DR_ACCESS_FNS (res), access_fn);
DR_IS_READ (res) = is_read;
-
+ DR_BASE_ADDRESS (res) = base_address;
+ DR_OFFSET (res) = NULL_TREE;
+ DR_INIT (res) = NULL_TREE;
+ DR_STEP (res) = step;
+ DR_OFFSET_MISALIGNMENT (res) = NULL_TREE;
+ DR_MEMTAG (res) = NULL_TREE;
+ DR_PTR_INFO (res) = ptr_info;
+
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, ")\n");
-
+
return res;
}
-\f
-
-/* When there exists a dependence relation, determine its distance
- vector. */
+/* Analyze an indirect memory reference, REF, that comes from STMT.
+ IS_READ is true if this is an indirect load, and false if it is
+ an indirect store.
+ Return a new data reference structure representing the indirect_ref, or
+ NULL if we cannot describe the access function. */
-static void
-compute_distance_vector (struct data_dependence_relation *ddr)
+static struct data_reference *
+analyze_indirect_ref (tree stmt, tree ref, bool is_read)
{
- if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
+ struct loop *loop = loop_containing_stmt (stmt);
+ tree ptr_ref = TREE_OPERAND (ref, 0);
+ tree access_fn = analyze_scalar_evolution (loop, ptr_ref);
+ tree init = initial_condition_in_loop_num (access_fn, loop->num);
+ tree base_address = NULL_TREE, evolution, step = NULL_TREE;
+ struct ptr_info_def *ptr_info = NULL;
+
+ if (TREE_CODE (ptr_ref) == SSA_NAME)
+ ptr_info = SSA_NAME_PTR_INFO (ptr_ref);
+
+ STRIP_NOPS (init);
+ if (access_fn == chrec_dont_know || !init || init == chrec_dont_know)
{
- unsigned int i;
-
- for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
- {
- tree conflicts_a, conflicts_b, difference;
- struct subscript *subscript;
-
- subscript = DDR_SUBSCRIPT (ddr, i);
- conflicts_a = SUB_CONFLICTS_IN_A (subscript);
- conflicts_b = SUB_CONFLICTS_IN_B (subscript);
- difference = chrec_fold_minus
- (integer_type_node, conflicts_b, conflicts_a);
-
- if (evolution_function_is_constant_p (difference))
- SUB_DISTANCE (subscript) = difference;
-
- else
- SUB_DISTANCE (subscript) = chrec_dont_know;
- }
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nBad access function of ptr: ");
+ print_generic_expr (dump_file, ref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL;
}
-}
-
-/* Initialize a ddr. */
-struct data_dependence_relation *
-initialize_data_dependence_relation (struct data_reference *a,
- struct data_reference *b)
-{
- struct data_dependence_relation *res;
- bool differ_p;
-
- res = ggc_alloc (sizeof (struct data_dependence_relation));
- DDR_A (res) = a;
- DDR_B (res) = b;
-
- if (a == NULL || b == NULL
- || DR_BASE_NAME (a) == NULL_TREE
- || DR_BASE_NAME (b) == NULL_TREE)
- DDR_ARE_DEPENDENT (res) = chrec_dont_know;
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nAccess function of ptr: ");
+ print_generic_expr (dump_file, access_fn, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
- /* When the dimensions of A and B differ, we directly initialize
- the relation to "there is no dependence": chrec_known. */
- else if (DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b)
- || (array_base_name_differ_p (a, b, &differ_p) && differ_p))
- DDR_ARE_DEPENDENT (res) = chrec_known;
-
+ if (!expr_invariant_in_loop_p (loop, init))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "\ninitial condition is not loop invariant.\n");
+ }
else
{
- unsigned int i;
- DDR_ARE_DEPENDENT (res) = NULL_TREE;
- DDR_SUBSCRIPTS_VECTOR_INIT (res, DR_NUM_DIMENSIONS (a));
-
- for (i = 0; i < DR_NUM_DIMENSIONS (a); i++)
- {
- struct subscript *subscript;
-
- subscript = ggc_alloc (sizeof (struct subscript));
- SUB_CONFLICTS_IN_A (subscript) = chrec_dont_know;
- SUB_CONFLICTS_IN_B (subscript) = chrec_dont_know;
- SUB_LAST_CONFLICT_IN_A (subscript) = chrec_dont_know;
- SUB_LAST_CONFLICT_IN_B (subscript) = chrec_dont_know;
- SUB_DISTANCE (subscript) = chrec_dont_know;
- SUB_DIRECTION (subscript) = dir_star;
- VARRAY_PUSH_GENERIC_PTR (DDR_SUBSCRIPTS (res), subscript);
+ base_address = init;
+ evolution = evolution_part_in_loop_num (access_fn, loop->num);
+ if (evolution != chrec_dont_know)
+ {
+ if (!evolution)
+ step = ssize_int (0);
+ else
+ {
+ if (TREE_CODE (evolution) == INTEGER_CST)
+ step = fold_convert (ssizetype, evolution);
+ else
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "\nnon constant step for ptr access.\n");
+ }
}
+ else
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "\nunknown evolution of ptr.\n");
}
-
- return res;
+ return init_pointer_ref (stmt, ref, access_fn, is_read, base_address,
+ step, ptr_info);
}
-/* Set DDR_ARE_DEPENDENT to CHREC and finalize the subscript overlap
- description. */
+/* Function strip_conversions
-static inline void
-finalize_ddr_dependent (struct data_dependence_relation *ddr,
- tree chrec)
+ Strip conversions that don't narrow the mode. */
+
+static tree
+strip_conversion (tree expr)
{
- DDR_ARE_DEPENDENT (ddr) = chrec;
- varray_clear (DDR_SUBSCRIPTS (ddr));
+ tree to, ti, oprnd0;
+
+ while (TREE_CODE (expr) == NOP_EXPR || TREE_CODE (expr) == CONVERT_EXPR)
+ {
+ to = TREE_TYPE (expr);
+ oprnd0 = TREE_OPERAND (expr, 0);
+ ti = TREE_TYPE (oprnd0);
+
+ if (!INTEGRAL_TYPE_P (to) || !INTEGRAL_TYPE_P (ti))
+ return NULL_TREE;
+ if (GET_MODE_SIZE (TYPE_MODE (to)) < GET_MODE_SIZE (TYPE_MODE (ti)))
+ return NULL_TREE;
+
+ expr = oprnd0;
+ }
+ return expr;
}
-
\f
-/* This section contains the classic Banerjee tests. */
+/* Function analyze_offset_expr
-/* 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. */
+ Given an offset expression EXPR received from get_inner_reference, analyze
+ it and create an expression for INITIAL_OFFSET by substituting the variables
+ of EXPR with initial_condition of the corresponding access_fn in the loop.
+ E.g.,
+ for i
+ for (j = 3; j < N; j++)
+ a[j].b[i][j] = 0;
+
+ For a[j].b[i][j], EXPR will be 'i * C_i + j * C_j + C'. 'i' cannot be
+ substituted, since its access_fn in the inner loop is i. 'j' will be
+ substituted with 3. An INITIAL_OFFSET will be 'i * C_i + C`', where
+ C` = 3 * C_j + C.
-static inline bool
-ziv_subscript_p (tree chrec_a,
- tree chrec_b)
-{
- return (evolution_function_is_constant_p (chrec_a)
- && evolution_function_is_constant_p (chrec_b));
-}
+ Compute MISALIGN (the misalignment of the data reference initial access from
+ its base). Misalignment can be calculated only if all the variables can be
+ substituted with constants, otherwise, we record maximum possible alignment
+ in ALIGNED_TO. In the above example, since 'i' cannot be substituted, MISALIGN
+ will be NULL_TREE, and the biggest divider of C_i (a power of 2) will be
+ recorded in ALIGNED_TO.
-/* 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. */
+ STEP is an evolution of the data reference in this loop in bytes.
+ In the above example, STEP is C_j.
+
+ Return FALSE, if the analysis fails, e.g., there is no access_fn for a
+ variable. In this case, all the outputs (INITIAL_OFFSET, MISALIGN, ALIGNED_TO
+ and STEP) are NULL_TREEs. Otherwise, return TRUE.
+
+*/
static bool
-siv_subscript_p (tree chrec_a,
- tree chrec_b)
+analyze_offset_expr (tree expr,
+ struct loop *loop,
+ tree *initial_offset,
+ tree *misalign,
+ tree *aligned_to,
+ tree *step)
{
- 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))
+ tree oprnd0;
+ tree oprnd1;
+ tree left_offset = ssize_int (0);
+ tree right_offset = ssize_int (0);
+ tree left_misalign = ssize_int (0);
+ tree right_misalign = ssize_int (0);
+ tree left_step = ssize_int (0);
+ tree right_step = ssize_int (0);
+ enum tree_code code;
+ tree init, evolution;
+ tree left_aligned_to = NULL_TREE, right_aligned_to = NULL_TREE;
+
+ *step = NULL_TREE;
+ *misalign = NULL_TREE;
+ *aligned_to = NULL_TREE;
+ *initial_offset = NULL_TREE;
+
+ /* Strip conversions that don't narrow the mode. */
+ expr = strip_conversion (expr);
+ if (!expr)
+ return false;
+
+ /* Stop conditions:
+ 1. Constant. */
+ if (TREE_CODE (expr) == INTEGER_CST)
{
- switch (TREE_CODE (chrec_a))
+ *initial_offset = fold_convert (ssizetype, expr);
+ *misalign = fold_convert (ssizetype, expr);
+ *step = ssize_int (0);
+ return true;
+ }
+
+ /* 2. Variable. Try to substitute with initial_condition of the corresponding
+ access_fn in the current loop. */
+ if (SSA_VAR_P (expr))
+ {
+ tree access_fn = analyze_scalar_evolution (loop, expr);
+
+ if (access_fn == chrec_dont_know)
+ /* No access_fn. */
+ return false;
+
+ init = initial_condition_in_loop_num (access_fn, loop->num);
+ if (!expr_invariant_in_loop_p (loop, init))
+ /* Not enough information: may be not loop invariant.
+ E.g., for a[b[i]], we get a[D], where D=b[i]. EXPR is D, its
+ initial_condition is D, but it depends on i - loop's induction
+ variable. */
+ return false;
+
+ evolution = evolution_part_in_loop_num (access_fn, loop->num);
+ if (evolution && TREE_CODE (evolution) != INTEGER_CST)
+ /* Evolution is not constant. */
+ return false;
+
+ if (TREE_CODE (init) == INTEGER_CST)
+ *misalign = fold_convert (ssizetype, init);
+ else
+ /* Not constant, misalignment cannot be calculated. */
+ *misalign = NULL_TREE;
+
+ *initial_offset = fold_convert (ssizetype, init);
+
+ *step = evolution ? fold_convert (ssizetype, evolution) : ssize_int (0);
+ return true;
+ }
+
+ /* Recursive computation. */
+ if (!BINARY_CLASS_P (expr))
+ {
+ /* We expect to get binary expressions (PLUS/MINUS and MULT). */
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nNot binary expression ");
+ print_generic_expr (dump_file, expr, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return false;
+ }
+ oprnd0 = TREE_OPERAND (expr, 0);
+ oprnd1 = TREE_OPERAND (expr, 1);
+
+ if (!analyze_offset_expr (oprnd0, loop, &left_offset, &left_misalign,
+ &left_aligned_to, &left_step)
+ || !analyze_offset_expr (oprnd1, loop, &right_offset, &right_misalign,
+ &right_aligned_to, &right_step))
+ return false;
+
+ /* The type of the operation: plus, minus or mult. */
+ code = TREE_CODE (expr);
+ switch (code)
+ {
+ case MULT_EXPR:
+ if (TREE_CODE (right_offset) != INTEGER_CST)
+ /* RIGHT_OFFSET can be not constant. For example, for arrays of variable
+ sized types.
+ FORNOW: We don't support such cases. */
+ return false;
+
+ /* Strip conversions that don't narrow the mode. */
+ left_offset = strip_conversion (left_offset);
+ if (!left_offset)
+ return false;
+ /* Misalignment computation. */
+ if (SSA_VAR_P (left_offset))
{
- case POLYNOMIAL_CHREC:
- switch (TREE_CODE (chrec_b))
+ /* If the left side contains variables that can't be substituted with
+ constants, the misalignment is unknown. However, if the right side
+ is a multiple of some alignment, we know that the expression is
+ aligned to it. Therefore, we record such maximum possible value.
+ */
+ *misalign = NULL_TREE;
+ *aligned_to = ssize_int (highest_pow2_factor (right_offset));
+ }
+ else
+ {
+ /* The left operand was successfully substituted with constant. */
+ if (left_misalign)
{
- case POLYNOMIAL_CHREC:
- if (CHREC_VARIABLE (chrec_a) != CHREC_VARIABLE (chrec_b))
- return false;
-
- default:
- return true;
+ /* In case of EXPR '(i * C1 + j) * C2', LEFT_MISALIGN is
+ NULL_TREE. */
+ *misalign = size_binop (code, left_misalign, right_misalign);
+ if (left_aligned_to && right_aligned_to)
+ *aligned_to = size_binop (MIN_EXPR, left_aligned_to,
+ right_aligned_to);
+ else
+ *aligned_to = left_aligned_to ?
+ left_aligned_to : right_aligned_to;
}
-
- default:
- return true;
+ else
+ *misalign = NULL_TREE;
+ }
+
+ /* Step calculation. */
+ /* Multiply the step by the right operand. */
+ *step = size_binop (MULT_EXPR, left_step, right_offset);
+ break;
+
+ case PLUS_EXPR:
+ case MINUS_EXPR:
+ /* Combine the recursive calculations for step and misalignment. */
+ *step = size_binop (code, left_step, right_step);
+
+ /* Unknown alignment. */
+ if ((!left_misalign && !left_aligned_to)
+ || (!right_misalign && !right_aligned_to))
+ {
+ *misalign = NULL_TREE;
+ *aligned_to = NULL_TREE;
+ break;
}
+
+ if (left_misalign && right_misalign)
+ *misalign = size_binop (code, left_misalign, right_misalign);
+ else
+ *misalign = left_misalign ? left_misalign : right_misalign;
+
+ if (left_aligned_to && right_aligned_to)
+ *aligned_to = size_binop (MIN_EXPR, left_aligned_to, right_aligned_to);
+ else
+ *aligned_to = left_aligned_to ? left_aligned_to : right_aligned_to;
+
+ break;
+
+ default:
+ gcc_unreachable ();
}
-
- return false;
-}
-/* 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:
+ /* Compute offset. */
+ *initial_offset = fold_convert (ssizetype,
+ fold_build2 (code, TREE_TYPE (left_offset),
+ left_offset,
+ right_offset));
+ return true;
+}
- CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+/* Function address_analysis
+
+ Return the BASE of the address expression EXPR.
+ Also compute the OFFSET from BASE, MISALIGN and STEP.
+
+ Input:
+ EXPR - the address expression that is being analyzed
+ STMT - the statement that contains EXPR or its original memory reference
+ IS_READ - TRUE if STMT reads from EXPR, FALSE if writes to EXPR
+ DR - data_reference struct for the original memory reference
+
+ Output:
+ BASE (returned value) - the base of the data reference EXPR.
+ INITIAL_OFFSET - initial offset of EXPR from BASE (an expression)
+ MISALIGN - offset of EXPR from BASE in bytes (a constant) or NULL_TREE if the
+ computation is impossible
+ ALIGNED_TO - maximum alignment of EXPR or NULL_TREE if MISALIGN can be
+ calculated (doesn't depend on variables)
+ STEP - evolution of EXPR in the loop
+
+ If something unexpected is encountered (an unsupported form of data-ref),
+ then NULL_TREE is returned.
+ */
-static void
-analyze_ziv_subscript (tree chrec_a,
- tree chrec_b,
- tree *overlaps_a,
- tree *overlaps_b)
+static tree
+address_analysis (tree expr, tree stmt, bool is_read, struct data_reference *dr,
+ tree *offset, tree *misalign, tree *aligned_to, tree *step)
{
- tree difference;
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, "(analyze_ziv_subscript \n");
-
- difference = chrec_fold_minus (integer_type_node, chrec_a, chrec_b);
-
- switch (TREE_CODE (difference))
+ tree oprnd0, oprnd1, base_address, offset_expr, base_addr0, base_addr1;
+ tree address_offset = ssize_int (0), address_misalign = ssize_int (0);
+ tree dummy, address_aligned_to = NULL_TREE;
+ struct ptr_info_def *dummy1;
+ subvar_t dummy2;
+
+ switch (TREE_CODE (expr))
{
- case INTEGER_CST:
- if (integer_zerop (difference))
+ case PLUS_EXPR:
+ case MINUS_EXPR:
+ /* EXPR is of form {base +/- offset} (or {offset +/- base}). */
+ oprnd0 = TREE_OPERAND (expr, 0);
+ oprnd1 = TREE_OPERAND (expr, 1);
+
+ STRIP_NOPS (oprnd0);
+ STRIP_NOPS (oprnd1);
+
+ /* Recursively try to find the base of the address contained in EXPR.
+ For offset, the returned base will be NULL. */
+ base_addr0 = address_analysis (oprnd0, stmt, is_read, dr, &address_offset,
+ &address_misalign, &address_aligned_to,
+ step);
+
+ base_addr1 = address_analysis (oprnd1, stmt, is_read, dr, &address_offset,
+ &address_misalign, &address_aligned_to,
+ step);
+
+ /* We support cases where only one of the operands contains an
+ address. */
+ if ((base_addr0 && base_addr1) || (!base_addr0 && !base_addr1))
{
- /* The difference is equal to zero: the accessed index
- overlaps for each iteration in the loop. */
- *overlaps_a = integer_zero_node;
- *overlaps_b = integer_zero_node;
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file,
+ "\neither more than one address or no addresses in expr ");
+ print_generic_expr (dump_file, expr, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+
+ /* To revert STRIP_NOPS. */
+ oprnd0 = TREE_OPERAND (expr, 0);
+ oprnd1 = TREE_OPERAND (expr, 1);
+
+ offset_expr = base_addr0 ?
+ fold_convert (ssizetype, oprnd1) : fold_convert (ssizetype, oprnd0);
+
+ /* EXPR is of form {base +/- offset} (or {offset +/- base}). If offset is
+ a number, we can add it to the misalignment value calculated for base,
+ otherwise, misalignment is NULL. */
+ if (TREE_CODE (offset_expr) == INTEGER_CST && address_misalign)
+ {
+ *misalign = size_binop (TREE_CODE (expr), address_misalign,
+ offset_expr);
+ *aligned_to = address_aligned_to;
}
else
{
- /* The accesses do not overlap. */
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
+ *misalign = NULL_TREE;
+ *aligned_to = NULL_TREE;
}
- break;
+
+ /* Combine offset (from EXPR {base + offset}) with the offset calculated
+ for base. */
+ *offset = size_binop (TREE_CODE (expr), address_offset, offset_expr);
+ return base_addr0 ? base_addr0 : base_addr1;
+
+ case ADDR_EXPR:
+ base_address = object_analysis (TREE_OPERAND (expr, 0), stmt, is_read,
+ &dr, offset, misalign, aligned_to, step,
+ &dummy, &dummy1, &dummy2);
+ return base_address;
+
+ case SSA_NAME:
+ if (!POINTER_TYPE_P (TREE_TYPE (expr)))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nnot pointer SSA_NAME ");
+ print_generic_expr (dump_file, expr, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+ *aligned_to = ssize_int (TYPE_ALIGN_UNIT (TREE_TYPE (TREE_TYPE (expr))));
+ *misalign = ssize_int (0);
+ *offset = ssize_int (0);
+ *step = ssize_int (0);
+ return expr;
default:
- /* We're not sure whether the indexes overlap. For the moment,
- conservatively answer "don't know". */
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- break;
+ return NULL_TREE;
}
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, ")\n");
}
-/* 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)). */
+/* Function object_analysis
-static void
-analyze_siv_subscript_cst_affine (tree chrec_a,
- tree chrec_b,
- tree *overlaps_a,
- tree *overlaps_b)
+ Create a data-reference structure DR for MEMREF.
+ Return the BASE of the data reference MEMREF if the analysis is possible.
+ Also compute the INITIAL_OFFSET from BASE, MISALIGN and STEP.
+ E.g., for EXPR a.b[i] + 4B, BASE is a, and OFFSET is the overall offset
+ 'a.b[i] + 4B' from a (can be an expression), MISALIGN is an OFFSET
+ instantiated with initial_conditions of access_functions of variables,
+ and STEP is the evolution of the DR_REF in this loop.
+
+ Function get_inner_reference is used for the above in case of ARRAY_REF and
+ COMPONENT_REF.
+
+ The structure of the function is as follows:
+ Part 1:
+ Case 1. For handled_component_p refs
+ 1.1 build data-reference structure for MEMREF
+ 1.2 call get_inner_reference
+ 1.2.1 analyze offset expr received from get_inner_reference
+ (fall through with BASE)
+ Case 2. For declarations
+ 2.1 set MEMTAG
+ Case 3. For INDIRECT_REFs
+ 3.1 build data-reference structure for MEMREF
+ 3.2 analyze evolution and initial condition of MEMREF
+ 3.3 set data-reference structure for MEMREF
+ 3.4 call address_analysis to analyze INIT of the access function
+ 3.5 extract memory tag
+
+ Part 2:
+ Combine the results of object and address analysis to calculate
+ INITIAL_OFFSET, STEP and misalignment info.
+
+ Input:
+ MEMREF - the memory reference that is being analyzed
+ STMT - the statement that contains MEMREF
+ IS_READ - TRUE if STMT reads from MEMREF, FALSE if writes to MEMREF
+
+ Output:
+ BASE_ADDRESS (returned value) - the base address of the data reference MEMREF
+ E.g, if MEMREF is a.b[k].c[i][j] the returned
+ base is &a.
+ DR - data_reference struct for MEMREF
+ INITIAL_OFFSET - initial offset of MEMREF from BASE (an expression)
+ MISALIGN - offset of MEMREF from BASE in bytes (a constant) modulo alignment of
+ ALIGNMENT or NULL_TREE if the computation is impossible
+ ALIGNED_TO - maximum alignment of EXPR or NULL_TREE if MISALIGN can be
+ calculated (doesn't depend on variables)
+ STEP - evolution of the DR_REF in the loop
+ MEMTAG - memory tag for aliasing purposes
+ PTR_INFO - NULL or points-to aliasing info from a pointer SSA_NAME
+ SUBVARS - Sub-variables of the variable
+
+ If the analysis of MEMREF evolution in the loop fails, NULL_TREE is returned,
+ but DR can be created anyway.
+
+*/
+
+static tree
+object_analysis (tree memref, tree stmt, bool is_read,
+ struct data_reference **dr, tree *offset, tree *misalign,
+ tree *aligned_to, tree *step, tree *memtag,
+ struct ptr_info_def **ptr_info, subvar_t *subvars)
{
- bool value0, value1, value2;
- tree difference = chrec_fold_minus
- (integer_type_node, CHREC_LEFT (chrec_b), chrec_a);
-
- if (!chrec_is_positive (initial_condition (difference), &value0))
- {
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- return;
- }
- else
+ tree base = NULL_TREE, base_address = NULL_TREE;
+ tree object_offset = ssize_int (0), object_misalign = ssize_int (0);
+ tree object_step = ssize_int (0), address_step = ssize_int (0);
+ tree address_offset = ssize_int (0), address_misalign = ssize_int (0);
+ HOST_WIDE_INT pbitsize, pbitpos;
+ tree poffset, bit_pos_in_bytes;
+ enum machine_mode pmode;
+ int punsignedp, pvolatilep;
+ tree ptr_step = ssize_int (0), ptr_init = NULL_TREE;
+ struct loop *loop = loop_containing_stmt (stmt);
+ struct data_reference *ptr_dr = NULL;
+ tree object_aligned_to = NULL_TREE, address_aligned_to = NULL_TREE;
+ tree comp_ref = NULL_TREE;
+
+ *ptr_info = NULL;
+
+ /* Part 1: */
+ /* Case 1. handled_component_p refs. */
+ if (handled_component_p (memref))
{
- if (value0 == false)
+ /* 1.1 build data-reference structure for MEMREF. */
+ if (!(*dr))
+ {
+ if (TREE_CODE (memref) == ARRAY_REF)
+ *dr = init_array_ref (stmt, memref, is_read);
+ else if (TREE_CODE (memref) == COMPONENT_REF)
+ comp_ref = memref;
+ else
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\ndata-ref of unsupported type ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+ }
+
+ /* 1.2 call get_inner_reference. */
+ /* Find the base and the offset from it. */
+ base = get_inner_reference (memref, &pbitsize, &pbitpos, &poffset,
+ &pmode, &punsignedp, &pvolatilep, false);
+ if (!base)
{
- if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value1))
+ if (dump_file && (dump_flags & TDF_DETAILS))
{
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- return;
+ fprintf (dump_file, "\nfailed to get inner ref for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+
+ /* 1.2.1 analyze offset expr received from get_inner_reference. */
+ if (poffset
+ && !analyze_offset_expr (poffset, loop, &object_offset,
+ &object_misalign, &object_aligned_to,
+ &object_step))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nfailed to compute offset or step for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
}
- else
+ return NULL_TREE;
+ }
+
+ /* Add bit position to OFFSET and MISALIGN. */
+
+ bit_pos_in_bytes = ssize_int (pbitpos/BITS_PER_UNIT);
+ /* Check that there is no remainder in bits. */
+ if (pbitpos%BITS_PER_UNIT)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "\nbit offset alignment.\n");
+ return NULL_TREE;
+ }
+ object_offset = size_binop (PLUS_EXPR, bit_pos_in_bytes, object_offset);
+ if (object_misalign)
+ object_misalign = size_binop (PLUS_EXPR, object_misalign,
+ bit_pos_in_bytes);
+
+ memref = base; /* To continue analysis of BASE. */
+ /* fall through */
+ }
+
+ /* Part 1: Case 2. Declarations. */
+ if (DECL_P (memref))
+ {
+ /* We expect to get a decl only if we already have a DR, or with
+ COMPONENT_REFs of type 'a[i].b'. */
+ if (!(*dr))
+ {
+ if (comp_ref && TREE_CODE (TREE_OPERAND (comp_ref, 0)) == ARRAY_REF)
{
- if (value1 == true)
+ *dr = init_array_ref (stmt, TREE_OPERAND (comp_ref, 0), is_read);
+ if (DR_NUM_DIMENSIONS (*dr) != 1)
{
- /* Example:
- chrec_a = 12
- chrec_b = {10, +, 1}
- */
-
- if (tree_fold_divides_p
- (integer_type_node, CHREC_RIGHT (chrec_b), difference))
+ if (dump_file && (dump_flags & TDF_DETAILS))
{
- *overlaps_a = integer_zero_node;
- *overlaps_b = fold
- (build (EXACT_DIV_EXPR, integer_type_node,
- fold (build1 (ABS_EXPR, integer_type_node, difference)),
- CHREC_RIGHT (chrec_b)));
- return;
- }
-
- /* When the step does not divides the difference, there are
- no overlaps. */
- else
- {
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
- return;
+ fprintf (dump_file, "\n multidimensional component ref ");
+ print_generic_expr (dump_file, comp_ref, TDF_SLIM);
+ fprintf (dump_file, "\n");
}
+ return NULL_TREE;
}
-
- else
+ }
+ else
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
{
- /* Example:
- chrec_a = 12
- chrec_b = {10, +, -1}
-
+ fprintf (dump_file, "\nunhandled decl ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+ }
+
+ /* TODO: if during the analysis of INDIRECT_REF we get to an object, put
+ the object in BASE_OBJECT field if we can prove that this is O.K.,
+ i.e., the data-ref access is bounded by the bounds of the BASE_OBJECT.
+ (e.g., if the object is an array base 'a', where 'a[N]', we must prove
+ that every access with 'p' (the original INDIRECT_REF based on '&a')
+ in the loop is within the array boundaries - from a[0] to a[N-1]).
+ Otherwise, our alias analysis can be incorrect.
+ Even if an access function based on BASE_OBJECT can't be build, update
+ BASE_OBJECT field to enable us to prove that two data-refs are
+ different (without access function, distance analysis is impossible).
+ */
+ if (SSA_VAR_P (memref) && var_can_have_subvars (memref))
+ *subvars = get_subvars_for_var (memref);
+ base_address = build_fold_addr_expr (memref);
+ /* 2.1 set MEMTAG. */
+ *memtag = memref;
+ }
+
+ /* Part 1: Case 3. INDIRECT_REFs. */
+ else if (TREE_CODE (memref) == INDIRECT_REF)
+ {
+ tree ptr_ref = TREE_OPERAND (memref, 0);
+ if (TREE_CODE (ptr_ref) == SSA_NAME)
+ *ptr_info = SSA_NAME_PTR_INFO (ptr_ref);
+
+ /* 3.1 build data-reference structure for MEMREF. */
+ ptr_dr = analyze_indirect_ref (stmt, memref, is_read);
+ if (!ptr_dr)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nfailed to create dr for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+
+ /* 3.2 analyze evolution and initial condition of MEMREF. */
+ ptr_step = DR_STEP (ptr_dr);
+ ptr_init = DR_BASE_ADDRESS (ptr_dr);
+ if (!ptr_init || !ptr_step || !POINTER_TYPE_P (TREE_TYPE (ptr_init)))
+ {
+ *dr = (*dr) ? *dr : ptr_dr;
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nbad pointer access ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+
+ if (integer_zerop (ptr_step) && !(*dr))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "\nptr is loop invariant.\n");
+ *dr = ptr_dr;
+ return NULL_TREE;
+
+ /* If there exists DR for MEMREF, we are analyzing the base of
+ handled component (PTR_INIT), which not necessary has evolution in
+ the loop. */
+ }
+ object_step = size_binop (PLUS_EXPR, object_step, ptr_step);
+
+ /* 3.3 set data-reference structure for MEMREF. */
+ if (!*dr)
+ *dr = ptr_dr;
+
+ /* 3.4 call address_analysis to analyze INIT of the access
+ function. */
+ base_address = address_analysis (ptr_init, stmt, is_read, *dr,
+ &address_offset, &address_misalign,
+ &address_aligned_to, &address_step);
+ if (!base_address)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nfailed to analyze address ");
+ print_generic_expr (dump_file, ptr_init, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+
+ /* 3.5 extract memory tag. */
+ switch (TREE_CODE (base_address))
+ {
+ case SSA_NAME:
+ *memtag = symbol_mem_tag (SSA_NAME_VAR (base_address));
+ if (!(*memtag) && TREE_CODE (TREE_OPERAND (memref, 0)) == SSA_NAME)
+ *memtag = symbol_mem_tag (SSA_NAME_VAR (TREE_OPERAND (memref, 0)));
+ break;
+ case ADDR_EXPR:
+ *memtag = TREE_OPERAND (base_address, 0);
+ break;
+ default:
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\nno memtag for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ *memtag = NULL_TREE;
+ break;
+ }
+ }
+
+ if (!base_address)
+ {
+ /* MEMREF cannot be analyzed. */
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\ndata-ref of unsupported type ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL_TREE;
+ }
+
+ if (comp_ref)
+ DR_REF (*dr) = comp_ref;
+
+ if (SSA_VAR_P (*memtag) && var_can_have_subvars (*memtag))
+ *subvars = get_subvars_for_var (*memtag);
+
+ /* Part 2: Combine the results of object and address analysis to calculate
+ INITIAL_OFFSET, STEP and misalignment info. */
+ *offset = size_binop (PLUS_EXPR, object_offset, address_offset);
+
+ if ((!object_misalign && !object_aligned_to)
+ || (!address_misalign && !address_aligned_to))
+ {
+ *misalign = NULL_TREE;
+ *aligned_to = NULL_TREE;
+ }
+ else
+ {
+ if (object_misalign && address_misalign)
+ *misalign = size_binop (PLUS_EXPR, object_misalign, address_misalign);
+ else
+ *misalign = object_misalign ? object_misalign : address_misalign;
+ if (object_aligned_to && address_aligned_to)
+ *aligned_to = size_binop (MIN_EXPR, object_aligned_to,
+ address_aligned_to);
+ else
+ *aligned_to = object_aligned_to ?
+ object_aligned_to : address_aligned_to;
+ }
+ *step = size_binop (PLUS_EXPR, object_step, address_step);
+
+ return base_address;
+}
+
+/* Function analyze_offset.
+
+ Extract INVARIANT and CONSTANT parts from OFFSET.
+
+*/
+static bool
+analyze_offset (tree offset, tree *invariant, tree *constant)
+{
+ tree op0, op1, constant_0, constant_1, invariant_0, invariant_1;
+ enum tree_code code = TREE_CODE (offset);
+
+ *invariant = NULL_TREE;
+ *constant = NULL_TREE;
+
+ /* Not PLUS/MINUS expression - recursion stop condition. */
+ if (code != PLUS_EXPR && code != MINUS_EXPR)
+ {
+ if (TREE_CODE (offset) == INTEGER_CST)
+ *constant = offset;
+ else
+ *invariant = offset;
+ return true;
+ }
+
+ op0 = TREE_OPERAND (offset, 0);
+ op1 = TREE_OPERAND (offset, 1);
+
+ /* Recursive call with the operands. */
+ if (!analyze_offset (op0, &invariant_0, &constant_0)
+ || !analyze_offset (op1, &invariant_1, &constant_1))
+ return false;
+
+ /* Combine the results. Add negation to the subtrahend in case of
+ subtraction. */
+ if (constant_0 && constant_1)
+ return false;
+ *constant = constant_0 ? constant_0 : constant_1;
+ if (code == MINUS_EXPR && constant_1)
+ *constant = fold_build1 (NEGATE_EXPR, TREE_TYPE (*constant), *constant);
+
+ if (invariant_0 && invariant_1)
+ *invariant =
+ fold_build2 (code, TREE_TYPE (invariant_0), invariant_0, invariant_1);
+ else
+ {
+ *invariant = invariant_0 ? invariant_0 : invariant_1;
+ if (code == MINUS_EXPR && invariant_1)
+ *invariant =
+ fold_build1 (NEGATE_EXPR, TREE_TYPE (*invariant), *invariant);
+ }
+ return true;
+}
+
+/* Free the memory used by the data reference DR. */
+
+static void
+free_data_ref (data_reference_p dr)
+{
+ DR_FREE_ACCESS_FNS (dr);
+ free (dr);
+}
+
+/* Function create_data_ref.
+
+ Create a data-reference structure for MEMREF. Set its DR_BASE_ADDRESS,
+ DR_OFFSET, DR_INIT, DR_STEP, DR_OFFSET_MISALIGNMENT, DR_ALIGNED_TO,
+ DR_MEMTAG, and DR_POINTSTO_INFO fields.
+
+ Input:
+ MEMREF - the memory reference that is being analyzed
+ STMT - the statement that contains MEMREF
+ IS_READ - TRUE if STMT reads from MEMREF, FALSE if writes to MEMREF
+
+ Output:
+ DR (returned value) - data_reference struct for MEMREF
+*/
+
+static struct data_reference *
+create_data_ref (tree memref, tree stmt, bool is_read)
+{
+ struct data_reference *dr = NULL;
+ tree base_address, offset, step, misalign, memtag;
+ struct loop *loop = loop_containing_stmt (stmt);
+ tree invariant = NULL_TREE, constant = NULL_TREE;
+ tree type_size, init_cond;
+ struct ptr_info_def *ptr_info;
+ subvar_t subvars = NULL;
+ tree aligned_to, type = NULL_TREE, orig_offset;
+
+ if (!memref)
+ return NULL;
+
+ base_address = object_analysis (memref, stmt, is_read, &dr, &offset,
+ &misalign, &aligned_to, &step, &memtag,
+ &ptr_info, &subvars);
+ if (!dr || !base_address)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\ncreate_data_ref: failed to create a dr for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL;
+ }
+
+ DR_BASE_ADDRESS (dr) = base_address;
+ DR_OFFSET (dr) = offset;
+ DR_INIT (dr) = ssize_int (0);
+ DR_STEP (dr) = step;
+ DR_OFFSET_MISALIGNMENT (dr) = misalign;
+ DR_ALIGNED_TO (dr) = aligned_to;
+ DR_MEMTAG (dr) = memtag;
+ DR_PTR_INFO (dr) = ptr_info;
+ DR_SUBVARS (dr) = subvars;
+
+ type_size = fold_convert (ssizetype, TYPE_SIZE_UNIT (TREE_TYPE (DR_REF (dr))));
+
+ /* Extract CONSTANT and INVARIANT from OFFSET. */
+ /* Remove cast from OFFSET and restore it for INVARIANT part. */
+ orig_offset = offset;
+ STRIP_NOPS (offset);
+ if (offset != orig_offset)
+ type = TREE_TYPE (orig_offset);
+ if (!analyze_offset (offset, &invariant, &constant))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\ncreate_data_ref: failed to analyze dr's");
+ fprintf (dump_file, " offset for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ return NULL;
+ }
+ if (type && invariant)
+ invariant = fold_convert (type, invariant);
+
+ /* Put CONSTANT part of OFFSET in DR_INIT and INVARIANT in DR_OFFSET field
+ of DR. */
+ if (constant)
+ {
+ DR_INIT (dr) = fold_convert (ssizetype, constant);
+ init_cond = fold_build2 (TRUNC_DIV_EXPR, TREE_TYPE (constant),
+ constant, type_size);
+ }
+ else
+ DR_INIT (dr) = init_cond = ssize_int (0);
+
+ if (invariant)
+ DR_OFFSET (dr) = invariant;
+ else
+ DR_OFFSET (dr) = ssize_int (0);
+
+ /* Change the access function for INIDIRECT_REFs, according to
+ DR_BASE_ADDRESS. Analyze OFFSET calculated in object_analysis. OFFSET is
+ an expression that can contain loop invariant expressions and constants.
+ We put the constant part in the initial condition of the access function
+ (for data dependence tests), and in DR_INIT of the data-ref. The loop
+ invariant part is put in DR_OFFSET.
+ The evolution part of the access function is STEP calculated in
+ object_analysis divided by the size of data type.
+ */
+ if (!DR_BASE_OBJECT (dr)
+ || (TREE_CODE (memref) == COMPONENT_REF && DR_NUM_DIMENSIONS (dr) == 1))
+ {
+ tree access_fn;
+ tree new_step;
+
+ /* Update access function. */
+ access_fn = DR_ACCESS_FN (dr, 0);
+ if (automatically_generated_chrec_p (access_fn))
+ {
+ free_data_ref (dr);
+ return NULL;
+ }
+
+ new_step = size_binop (TRUNC_DIV_EXPR,
+ fold_convert (ssizetype, step), type_size);
+
+ init_cond = chrec_convert (chrec_type (access_fn), init_cond, stmt);
+ new_step = chrec_convert (chrec_type (access_fn), new_step, stmt);
+ if (automatically_generated_chrec_p (init_cond)
+ || automatically_generated_chrec_p (new_step))
+ {
+ free_data_ref (dr);
+ return NULL;
+ }
+ access_fn = chrec_replace_initial_condition (access_fn, init_cond);
+ access_fn = reset_evolution_in_loop (loop->num, access_fn, new_step);
+
+ VEC_replace (tree, DR_ACCESS_FNS (dr), 0, access_fn);
+ }
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ struct ptr_info_def *pi = DR_PTR_INFO (dr);
+
+ fprintf (dump_file, "\nCreated dr for ");
+ print_generic_expr (dump_file, memref, TDF_SLIM);
+ fprintf (dump_file, "\n\tbase_address: ");
+ print_generic_expr (dump_file, DR_BASE_ADDRESS (dr), TDF_SLIM);
+ fprintf (dump_file, "\n\toffset from base address: ");
+ print_generic_expr (dump_file, DR_OFFSET (dr), TDF_SLIM);
+ fprintf (dump_file, "\n\tconstant offset from base address: ");
+ print_generic_expr (dump_file, DR_INIT (dr), TDF_SLIM);
+ fprintf (dump_file, "\n\tbase_object: ");
+ print_generic_expr (dump_file, DR_BASE_OBJECT (dr), TDF_SLIM);
+ fprintf (dump_file, "\n\tstep: ");
+ print_generic_expr (dump_file, DR_STEP (dr), TDF_SLIM);
+ fprintf (dump_file, "B\n\tmisalignment from base: ");
+ print_generic_expr (dump_file, DR_OFFSET_MISALIGNMENT (dr), TDF_SLIM);
+ if (DR_OFFSET_MISALIGNMENT (dr))
+ fprintf (dump_file, "B");
+ if (DR_ALIGNED_TO (dr))
+ {
+ fprintf (dump_file, "\n\taligned to: ");
+ print_generic_expr (dump_file, DR_ALIGNED_TO (dr), TDF_SLIM);
+ }
+ fprintf (dump_file, "\n\tmemtag: ");
+ print_generic_expr (dump_file, DR_MEMTAG (dr), TDF_SLIM);
+ fprintf (dump_file, "\n");
+ if (pi && pi->name_mem_tag)
+ {
+ fprintf (dump_file, "\n\tnametag: ");
+ print_generic_expr (dump_file, pi->name_mem_tag, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+ }
+ return dr;
+}
+
+/* Returns true if FNA == FNB. */
+
+static bool
+affine_function_equal_p (affine_fn fna, affine_fn fnb)
+{
+ unsigned i, n = VEC_length (tree, fna);
+
+ if (n != VEC_length (tree, fnb))
+ return false;
+
+ for (i = 0; i < n; i++)
+ if (!operand_equal_p (VEC_index (tree, fna, i),
+ VEC_index (tree, fnb, i), 0))
+ return false;
+
+ return true;
+}
+
+/* If all the functions in CF are the same, returns one of them,
+ otherwise returns NULL. */
+
+static affine_fn
+common_affine_function (conflict_function *cf)
+{
+ unsigned i;
+ affine_fn comm;
+
+ if (!CF_NONTRIVIAL_P (cf))
+ return NULL;
+
+ comm = cf->fns[0];
+
+ for (i = 1; i < cf->n; i++)
+ if (!affine_function_equal_p (comm, cf->fns[i]))
+ return NULL;
+
+ return comm;
+}
+
+/* Returns the base of the affine function FN. */
+
+static tree
+affine_function_base (affine_fn fn)
+{
+ return VEC_index (tree, fn, 0);
+}
+
+/* Returns true if FN is a constant. */
+
+static bool
+affine_function_constant_p (affine_fn fn)
+{
+ unsigned i;
+ tree coef;
+
+ for (i = 1; VEC_iterate (tree, fn, i, coef); i++)
+ if (!integer_zerop (coef))
+ return false;
+
+ return true;
+}
+
+/* Returns true if FN is the zero constant function. */
+
+static bool
+affine_function_zero_p (affine_fn fn)
+{
+ return (integer_zerop (affine_function_base (fn))
+ && affine_function_constant_p (fn));
+}
+
+/* Applies operation OP on affine functions FNA and FNB, and returns the
+ result. */
+
+static affine_fn
+affine_fn_op (enum tree_code op, affine_fn fna, affine_fn fnb)
+{
+ unsigned i, n, m;
+ affine_fn ret;
+ tree coef;
+
+ if (VEC_length (tree, fnb) > VEC_length (tree, fna))
+ {
+ n = VEC_length (tree, fna);
+ m = VEC_length (tree, fnb);
+ }
+ else
+ {
+ n = VEC_length (tree, fnb);
+ m = VEC_length (tree, fna);
+ }
+
+ ret = VEC_alloc (tree, heap, m);
+ for (i = 0; i < n; i++)
+ VEC_quick_push (tree, ret,
+ fold_build2 (op, integer_type_node,
+ VEC_index (tree, fna, i),
+ VEC_index (tree, fnb, i)));
+
+ for (; VEC_iterate (tree, fna, i, coef); i++)
+ VEC_quick_push (tree, ret,
+ fold_build2 (op, integer_type_node,
+ coef, integer_zero_node));
+ for (; VEC_iterate (tree, fnb, i, coef); i++)
+ VEC_quick_push (tree, ret,
+ fold_build2 (op, integer_type_node,
+ integer_zero_node, coef));
+
+ return ret;
+}
+
+/* Returns the sum of affine functions FNA and FNB. */
+
+static affine_fn
+affine_fn_plus (affine_fn fna, affine_fn fnb)
+{
+ return affine_fn_op (PLUS_EXPR, fna, fnb);
+}
+
+/* Returns the difference of affine functions FNA and FNB. */
+
+static affine_fn
+affine_fn_minus (affine_fn fna, affine_fn fnb)
+{
+ return affine_fn_op (MINUS_EXPR, fna, fnb);
+}
+
+/* Frees affine function FN. */
+
+static void
+affine_fn_free (affine_fn fn)
+{
+ VEC_free (tree, heap, fn);
+}
+
+/* Determine for each subscript in the data dependence relation DDR
+ the distance. */
+
+static void
+compute_subscript_distance (struct data_dependence_relation *ddr)
+{
+ conflict_function *cf_a, *cf_b;
+ affine_fn fn_a, fn_b, diff;
+
+ if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
+ {
+ unsigned int i;
+
+ for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
+ {
+ struct subscript *subscript;
+
+ subscript = DDR_SUBSCRIPT (ddr, i);
+ cf_a = SUB_CONFLICTS_IN_A (subscript);
+ cf_b = SUB_CONFLICTS_IN_B (subscript);
+
+ fn_a = common_affine_function (cf_a);
+ fn_b = common_affine_function (cf_b);
+ if (!fn_a || !fn_b)
+ {
+ SUB_DISTANCE (subscript) = chrec_dont_know;
+ return;
+ }
+ diff = affine_fn_minus (fn_a, fn_b);
+
+ if (affine_function_constant_p (diff))
+ SUB_DISTANCE (subscript) = affine_function_base (diff);
+ else
+ SUB_DISTANCE (subscript) = chrec_dont_know;
+
+ affine_fn_free (diff);
+ }
+ }
+}
+
+/* Returns the conflict function for "unknown". */
+
+static conflict_function *
+conflict_fn_not_known (void)
+{
+ conflict_function *fn = XCNEW (conflict_function);
+ fn->n = NOT_KNOWN;
+
+ return fn;
+}
+
+/* Returns the conflict function for "independent". */
+
+static conflict_function *
+conflict_fn_no_dependence (void)
+{
+ conflict_function *fn = XCNEW (conflict_function);
+ fn->n = NO_DEPENDENCE;
+
+ return fn;
+}
+
+/* Initialize a data dependence relation between data accesses A and
+ B. NB_LOOPS is the number of loops surrounding the references: the
+ size of the classic distance/direction vectors. */
+
+static struct data_dependence_relation *
+initialize_data_dependence_relation (struct data_reference *a,
+ struct data_reference *b,
+ VEC (loop_p, heap) *loop_nest)
+{
+ struct data_dependence_relation *res;
+ bool differ_p, known_dependence;
+ unsigned int i;
+
+ res = XNEW (struct data_dependence_relation);
+ DDR_A (res) = a;
+ DDR_B (res) = b;
+ DDR_LOOP_NEST (res) = NULL;
+
+ if (a == NULL || b == NULL)
+ {
+ DDR_ARE_DEPENDENT (res) = chrec_dont_know;
+ return res;
+ }
+
+ /* When A and B are arrays and their dimensions differ, we directly
+ initialize the relation to "there is no dependence": chrec_known. */
+ if (DR_BASE_OBJECT (a) && DR_BASE_OBJECT (b)
+ && DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b))
+ {
+ DDR_ARE_DEPENDENT (res) = chrec_known;
+ return res;
+ }
+
+ if (DR_BASE_ADDRESS (a) && DR_BASE_ADDRESS (b))
+ known_dependence = base_addr_differ_p (a, b, &differ_p);
+ else
+ known_dependence = base_object_differ_p (a, b, &differ_p);
+
+ if (!known_dependence)
+ {
+ /* Can't determine whether the data-refs access the same memory
+ region. */
+ DDR_ARE_DEPENDENT (res) = chrec_dont_know;
+ return res;
+ }
+
+ if (differ_p)
+ {
+ DDR_ARE_DEPENDENT (res) = chrec_known;
+ return res;
+ }
+
+ DDR_AFFINE_P (res) = true;
+ DDR_ARE_DEPENDENT (res) = NULL_TREE;
+ DDR_SUBSCRIPTS (res) = VEC_alloc (subscript_p, heap, DR_NUM_DIMENSIONS (a));
+ DDR_LOOP_NEST (res) = loop_nest;
+ DDR_INNER_LOOP (res) = 0;
+ DDR_DIR_VECTS (res) = NULL;
+ DDR_DIST_VECTS (res) = NULL;
+
+ for (i = 0; i < DR_NUM_DIMENSIONS (a); i++)
+ {
+ struct subscript *subscript;
+
+ subscript = XNEW (struct subscript);
+ SUB_CONFLICTS_IN_A (subscript) = conflict_fn_not_known ();
+ SUB_CONFLICTS_IN_B (subscript) = conflict_fn_not_known ();
+ SUB_LAST_CONFLICT (subscript) = chrec_dont_know;
+ SUB_DISTANCE (subscript) = chrec_dont_know;
+ VEC_safe_push (subscript_p, heap, DDR_SUBSCRIPTS (res), subscript);
+ }
+
+ return res;
+}
+
+/* Frees memory used by the conflict function F. */
+
+static void
+free_conflict_function (conflict_function *f)
+{
+ unsigned i;
+
+ if (CF_NONTRIVIAL_P (f))
+ {
+ for (i = 0; i < f->n; i++)
+ affine_fn_free (f->fns[i]);
+ }
+ free (f);
+}
+
+/* Frees memory used by SUBSCRIPTS. */
+
+static void
+free_subscripts (VEC (subscript_p, heap) *subscripts)
+{
+ unsigned i;
+ subscript_p s;
+
+ for (i = 0; VEC_iterate (subscript_p, subscripts, i, s); i++)
+ {
+ free_conflict_function (s->conflicting_iterations_in_a);
+ free_conflict_function (s->conflicting_iterations_in_b);
+ }
+ VEC_free (subscript_p, heap, subscripts);
+}
+
+/* Set DDR_ARE_DEPENDENT to CHREC and finalize the subscript overlap
+ description. */
+
+static inline void
+finalize_ddr_dependent (struct data_dependence_relation *ddr,
+ tree chrec)
+{
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "(dependence classified: ");
+ print_generic_expr (dump_file, chrec, 0);
+ fprintf (dump_file, ")\n");
+ }
+
+ DDR_ARE_DEPENDENT (ddr) = chrec;
+ free_subscripts (DDR_SUBSCRIPTS (ddr));
+}
+
+/* The dependence relation DDR cannot be represented by a distance
+ vector. */
+
+static inline void
+non_affine_dependence_relation (struct data_dependence_relation *ddr)
+{
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "(Dependence relation cannot be represented by distance vector.) \n");
+
+ DDR_AFFINE_P (ddr) = false;
+}
+
+\f
+
+/* This section contains the classic Banerjee tests. */
+
+/* Returns true iff CHREC_A and CHREC_B are not dependent on any index
+ variables, i.e., if the ZIV (Zero Index Variable) test is true. */
+
+static inline bool
+ziv_subscript_p (tree chrec_a,
+ tree chrec_b)
+{
+ return (evolution_function_is_constant_p (chrec_a)
+ && evolution_function_is_constant_p (chrec_b));
+}
+
+/* Returns true iff CHREC_A and CHREC_B are dependent on an index
+ variable, i.e., if the SIV (Single Index Variable) test is true. */
+
+static bool
+siv_subscript_p (tree chrec_a,
+ tree chrec_b)
+{
+ if ((evolution_function_is_constant_p (chrec_a)
+ && evolution_function_is_univariate_p (chrec_b))
+ || (evolution_function_is_constant_p (chrec_b)
+ && evolution_function_is_univariate_p (chrec_a)))
+ return true;
+
+ if (evolution_function_is_univariate_p (chrec_a)
+ && evolution_function_is_univariate_p (chrec_b))
+ {
+ switch (TREE_CODE (chrec_a))
+ {
+ case POLYNOMIAL_CHREC:
+ switch (TREE_CODE (chrec_b))
+ {
+ case POLYNOMIAL_CHREC:
+ if (CHREC_VARIABLE (chrec_a) != CHREC_VARIABLE (chrec_b))
+ return false;
+
+ default:
+ return true;
+ }
+
+ default:
+ return true;
+ }
+ }
+
+ return false;
+}
+
+/* Creates a conflict function with N dimensions. The affine functions
+ in each dimension follow. */
+
+static conflict_function *
+conflict_fn (unsigned n, ...)
+{
+ unsigned i;
+ conflict_function *ret = XCNEW (conflict_function);
+ va_list ap;
+
+ gcc_assert (0 < n && n <= MAX_DIM);
+ va_start(ap, n);
+
+ ret->n = n;
+ for (i = 0; i < n; i++)
+ ret->fns[i] = va_arg (ap, affine_fn);
+ va_end(ap);
+
+ return ret;
+}
+
+/* Returns constant affine function with value CST. */
+
+static affine_fn
+affine_fn_cst (tree cst)
+{
+ affine_fn fn = VEC_alloc (tree, heap, 1);
+ VEC_quick_push (tree, fn, cst);
+ return fn;
+}
+
+/* Returns affine function with single variable, CST + COEF * x_DIM. */
+
+static affine_fn
+affine_fn_univar (tree cst, unsigned dim, tree coef)
+{
+ affine_fn fn = VEC_alloc (tree, heap, dim + 1);
+ unsigned i;
+
+ gcc_assert (dim > 0);
+ VEC_quick_push (tree, fn, cst);
+ for (i = 1; i < dim; i++)
+ VEC_quick_push (tree, fn, integer_zero_node);
+ VEC_quick_push (tree, fn, coef);
+ return fn;
+}
+
+/* Analyze a ZIV (Zero Index Variable) subscript. *OVERLAPS_A and
+ *OVERLAPS_B are initialized to the functions that describe the
+ relation between the elements accessed twice by CHREC_A and
+ CHREC_B. For k >= 0, the following property is verified:
+
+ CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+
+static void
+analyze_ziv_subscript (tree chrec_a,
+ tree chrec_b,
+ conflict_function **overlaps_a,
+ conflict_function **overlaps_b,
+ tree *last_conflicts)
+{
+ tree difference;
+ dependence_stats.num_ziv++;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "(analyze_ziv_subscript \n");
+
+ chrec_a = chrec_convert (integer_type_node, chrec_a, NULL_TREE);
+ chrec_b = chrec_convert (integer_type_node, chrec_b, NULL_TREE);
+ difference = chrec_fold_minus (integer_type_node, chrec_a, chrec_b);
+
+ switch (TREE_CODE (difference))
+ {
+ case INTEGER_CST:
+ if (integer_zerop (difference))
+ {
+ /* The difference is equal to zero: the accessed index
+ overlaps for each iteration in the loop. */
+ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *last_conflicts = chrec_dont_know;
+ dependence_stats.num_ziv_dependent++;
+ }
+ else
+ {
+ /* The accesses do not overlap. */
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_ziv_independent++;
+ }
+ break;
+
+ default:
+ /* We're not sure whether the indexes overlap. For the moment,
+ conservatively answer "don't know". */
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "ziv test failed: difference is non-integer.\n");
+
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ dependence_stats.num_ziv_unimplemented++;
+ break;
+ }
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, ")\n");
+}
+
+/* Sets NIT to the estimated number of executions of the statements in
+ LOOP. If CONSERVATIVE is true, we must be sure that NIT is at least as
+ large as the number of iterations. If we have no reliable estimate,
+ the function returns false, otherwise returns true. */
+
+bool
+estimated_loop_iterations (struct loop *loop, bool conservative,
+ double_int *nit)
+{
+ estimate_numbers_of_iterations_loop (loop);
+ if (conservative)
+ {
+ if (!loop->any_upper_bound)
+ return false;
+
+ *nit = loop->nb_iterations_upper_bound;
+ }
+ else
+ {
+ if (!loop->any_estimate)
+ return false;
+
+ *nit = loop->nb_iterations_estimate;
+ }
+
+ return true;
+}
+
+/* Similar to estimated_loop_iterations, but returns the estimate only
+ if it fits to HOST_WIDE_INT. If this is not the case, or the estimate
+ on the number of iterations of LOOP could not be derived, returns -1. */
+
+HOST_WIDE_INT
+estimated_loop_iterations_int (struct loop *loop, bool conservative)
+{
+ double_int nit;
+ HOST_WIDE_INT hwi_nit;
+
+ if (!estimated_loop_iterations (loop, conservative, &nit))
+ return -1;
+
+ if (!double_int_fits_in_shwi_p (nit))
+ return -1;
+ hwi_nit = double_int_to_shwi (nit);
+
+ return hwi_nit < 0 ? -1 : hwi_nit;
+}
+
+/* Similar to estimated_loop_iterations, but returns the estimate as a tree,
+ and only if it fits to the int type. If this is not the case, or the
+ estimate on the number of iterations of LOOP could not be derived, returns
+ chrec_dont_know. */
+
+static tree
+estimated_loop_iterations_tree (struct loop *loop, bool conservative)
+{
+ double_int nit;
+ tree type;
+
+ if (!estimated_loop_iterations (loop, conservative, &nit))
+ return chrec_dont_know;
+
+ type = lang_hooks.types.type_for_size (INT_TYPE_SIZE, true);
+ if (!double_int_fits_to_tree_p (type, nit))
+ return chrec_dont_know;
+
+ return double_int_to_tree (type, nit);
+}
+
+/* Analyze a SIV (Single Index Variable) subscript where CHREC_A is a
+ constant, and CHREC_B is an affine function. *OVERLAPS_A and
+ *OVERLAPS_B are initialized to the functions that describe the
+ relation between the elements accessed twice by CHREC_A and
+ CHREC_B. For k >= 0, the following property is verified:
+
+ CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+
+static void
+analyze_siv_subscript_cst_affine (tree chrec_a,
+ tree chrec_b,
+ conflict_function **overlaps_a,
+ conflict_function **overlaps_b,
+ tree *last_conflicts)
+{
+ bool value0, value1, value2;
+ tree difference, tmp;
+
+ chrec_a = chrec_convert (integer_type_node, chrec_a, NULL_TREE);
+ chrec_b = chrec_convert (integer_type_node, chrec_b, NULL_TREE);
+ difference = chrec_fold_minus
+ (integer_type_node, initial_condition (chrec_b), chrec_a);
+
+ if (!chrec_is_positive (initial_condition (difference), &value0))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "siv test failed: chrec is not positive.\n");
+
+ dependence_stats.num_siv_unimplemented++;
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ return;
+ }
+ else
+ {
+ if (value0 == false)
+ {
+ if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value1))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "siv test failed: chrec not positive.\n");
+
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ dependence_stats.num_siv_unimplemented++;
+ return;
+ }
+ else
+ {
+ if (value1 == true)
+ {
+ /* Example:
+ chrec_a = 12
+ chrec_b = {10, +, 1}
+ */
+
+ if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference))
+ {
+ HOST_WIDE_INT numiter;
+ struct loop *loop = get_chrec_loop (chrec_b);
+
+ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ tmp = fold_build2 (EXACT_DIV_EXPR, integer_type_node,
+ fold_build1 (ABS_EXPR,
+ integer_type_node,
+ difference),
+ CHREC_RIGHT (chrec_b));
+ *overlaps_b = conflict_fn (1, affine_fn_cst (tmp));
+ *last_conflicts = integer_one_node;
+
+
+ /* Perform weak-zero siv test to see if overlap is
+ outside the loop bounds. */
+ numiter = estimated_loop_iterations_int (loop, true);
+
+ if (numiter >= 0
+ && compare_tree_int (tmp, numiter) > 0)
+ {
+ free_conflict_function (*overlaps_a);
+ free_conflict_function (*overlaps_b);
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_siv_independent++;
+ return;
+ }
+ dependence_stats.num_siv_dependent++;
+ return;
+ }
+
+ /* When the step does not divide the difference, there are
+ no overlaps. */
+ else
+ {
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_siv_independent++;
+ return;
+ }
+ }
+
+ else
+ {
+ /* Example:
+ chrec_a = 12
+ chrec_b = {10, +, -1}
+
+ In this case, chrec_a will not overlap with chrec_b. */
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_siv_independent++;
+ return;
+ }
+ }
+ }
+ else
+ {
+ if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value2))
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "siv test failed: chrec not positive.\n");
+
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ dependence_stats.num_siv_unimplemented++;
+ return;
+ }
+ else
+ {
+ if (value2 == false)
+ {
+ /* Example:
+ chrec_a = 3
+ chrec_b = {10, +, -1}
+ */
+ if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference))
+ {
+ HOST_WIDE_INT numiter;
+ struct loop *loop = get_chrec_loop (chrec_b);
+
+ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ tmp = fold_build2 (EXACT_DIV_EXPR,
+ integer_type_node, difference,
+ CHREC_RIGHT (chrec_b));
+ *overlaps_b = conflict_fn (1, affine_fn_cst (tmp));
+ *last_conflicts = integer_one_node;
+
+ /* Perform weak-zero siv test to see if overlap is
+ outside the loop bounds. */
+ numiter = estimated_loop_iterations_int (loop, true);
+
+ if (numiter >= 0
+ && compare_tree_int (tmp, numiter) > 0)
+ {
+ free_conflict_function (*overlaps_a);
+ free_conflict_function (*overlaps_b);
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_siv_independent++;
+ return;
+ }
+ dependence_stats.num_siv_dependent++;
+ return;
+ }
+
+ /* When the step does not divide the difference, there
+ are no overlaps. */
+ else
+ {
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_siv_independent++;
+ return;
+ }
+ }
+ else
+ {
+ /* Example:
+ chrec_a = 3
+ chrec_b = {4, +, 1}
+
In this case, chrec_a will not overlap with chrec_b. */
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
+ *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))
+ }
+ }
+}
+
+/* Helper recursive function for initializing the matrix A. Returns
+ the initial value of CHREC. */
+
+static int
+initialize_matrix_A (lambda_matrix A, tree chrec, unsigned index, int mult)
+{
+ gcc_assert (chrec);
+
+ if (TREE_CODE (chrec) != POLYNOMIAL_CHREC)
+ return int_cst_value (chrec);
+
+ A[index][0] = mult * int_cst_value (CHREC_RIGHT (chrec));
+ return initialize_matrix_A (A, CHREC_LEFT (chrec), index + 1, mult);
+}
+
+#define FLOOR_DIV(x,y) ((x) / (y))
+
+/* Solves the special case of the Diophantine equation:
+ | {0, +, STEP_A}_x (OVERLAPS_A) = {0, +, STEP_B}_y (OVERLAPS_B)
+
+ Computes the descriptions OVERLAPS_A and OVERLAPS_B. NITER is the
+ number of iterations that loops X and Y run. The overlaps will be
+ constructed as evolutions in dimension DIM. */
+
+static void
+compute_overlap_steps_for_affine_univar (int niter, int step_a, int step_b,
+ affine_fn *overlaps_a,
+ affine_fn *overlaps_b,
+ tree *last_conflicts, int dim)
+{
+ if (((step_a > 0 && step_b > 0)
+ || (step_a < 0 && step_b < 0)))
+ {
+ int step_overlaps_a, step_overlaps_b;
+ int gcd_steps_a_b, last_conflict, tau2;
+
+ gcd_steps_a_b = gcd (step_a, step_b);
+ step_overlaps_a = step_b / gcd_steps_a_b;
+ step_overlaps_b = step_a / gcd_steps_a_b;
+
+ tau2 = FLOOR_DIV (niter, step_overlaps_a);
+ tau2 = MIN (tau2, FLOOR_DIV (niter, step_overlaps_b));
+ last_conflict = tau2;
+
+ *overlaps_a = affine_fn_univar (integer_zero_node, dim,
+ build_int_cst (NULL_TREE,
+ step_overlaps_a));
+ *overlaps_b = affine_fn_univar (integer_zero_node, dim,
+ build_int_cst (NULL_TREE,
+ step_overlaps_b));
+ *last_conflicts = build_int_cst (NULL_TREE, last_conflict);
+ }
+
+ else
+ {
+ *overlaps_a = affine_fn_cst (integer_zero_node);
+ *overlaps_b = affine_fn_cst (integer_zero_node);
+ *last_conflicts = integer_zero_node;
+ }
+}
+
+/* Solves the special case of a Diophantine equation where CHREC_A is
+ an affine bivariate function, and CHREC_B is an affine univariate
+ function. For example,
+
+ | {{0, +, 1}_x, +, 1335}_y = {0, +, 1336}_z
+
+ has the following overlapping functions:
+
+ | x (t, u, v) = {{0, +, 1336}_t, +, 1}_v
+ | y (t, u, v) = {{0, +, 1336}_u, +, 1}_v
+ | z (t, u, v) = {{{0, +, 1}_t, +, 1335}_u, +, 1}_v
+
+ FORNOW: This is a specialized implementation for a case occurring in
+ a common benchmark. Implement the general algorithm. */
+
+static void
+compute_overlap_steps_for_affine_1_2 (tree chrec_a, tree chrec_b,
+ conflict_function **overlaps_a,
+ conflict_function **overlaps_b,
+ tree *last_conflicts)
+{
+ bool xz_p, yz_p, xyz_p;
+ int step_x, step_y, step_z;
+ HOST_WIDE_INT niter_x, niter_y, niter_z, niter;
+ affine_fn overlaps_a_xz, overlaps_b_xz;
+ affine_fn overlaps_a_yz, overlaps_b_yz;
+ affine_fn overlaps_a_xyz, overlaps_b_xyz;
+ affine_fn ova1, ova2, ovb;
+ tree last_conflicts_xz, last_conflicts_yz, last_conflicts_xyz;
+
+ step_x = int_cst_value (CHREC_RIGHT (CHREC_LEFT (chrec_a)));
+ step_y = int_cst_value (CHREC_RIGHT (chrec_a));
+ step_z = int_cst_value (CHREC_RIGHT (chrec_b));
+
+ niter_x = estimated_loop_iterations_int
+ (get_chrec_loop (CHREC_LEFT (chrec_a)), true);
+ niter_y = estimated_loop_iterations_int (get_chrec_loop (chrec_a), true);
+ niter_z = estimated_loop_iterations_int (get_chrec_loop (chrec_b), true);
+
+ if (niter_x < 0 || niter_y < 0 || niter_z < 0)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "overlap steps test failed: no iteration counts.\n");
+
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ return;
+ }
+
+ niter = MIN (niter_x, niter_z);
+ compute_overlap_steps_for_affine_univar (niter, step_x, step_z,
+ &overlaps_a_xz,
+ &overlaps_b_xz,
+ &last_conflicts_xz, 1);
+ niter = MIN (niter_y, niter_z);
+ compute_overlap_steps_for_affine_univar (niter, step_y, step_z,
+ &overlaps_a_yz,
+ &overlaps_b_yz,
+ &last_conflicts_yz, 2);
+ niter = MIN (niter_x, niter_z);
+ niter = MIN (niter_y, niter);
+ compute_overlap_steps_for_affine_univar (niter, step_x + step_y, step_z,
+ &overlaps_a_xyz,
+ &overlaps_b_xyz,
+ &last_conflicts_xyz, 3);
+
+ xz_p = !integer_zerop (last_conflicts_xz);
+ yz_p = !integer_zerop (last_conflicts_yz);
+ xyz_p = !integer_zerop (last_conflicts_xyz);
+
+ if (xz_p || yz_p || xyz_p)
+ {
+ ova1 = affine_fn_cst (integer_zero_node);
+ ova2 = affine_fn_cst (integer_zero_node);
+ ovb = affine_fn_cst (integer_zero_node);
+ if (xz_p)
+ {
+ affine_fn t0 = ova1;
+ affine_fn t2 = ovb;
+
+ ova1 = affine_fn_plus (ova1, overlaps_a_xz);
+ ovb = affine_fn_plus (ovb, overlaps_b_xz);
+ affine_fn_free (t0);
+ affine_fn_free (t2);
+ *last_conflicts = last_conflicts_xz;
+ }
+ if (yz_p)
+ {
+ affine_fn t0 = ova2;
+ affine_fn t2 = ovb;
+
+ ova2 = affine_fn_plus (ova2, overlaps_a_yz);
+ ovb = affine_fn_plus (ovb, overlaps_b_yz);
+ affine_fn_free (t0);
+ affine_fn_free (t2);
+ *last_conflicts = last_conflicts_yz;
+ }
+ if (xyz_p)
+ {
+ affine_fn t0 = ova1;
+ affine_fn t2 = ova2;
+ affine_fn t4 = ovb;
+
+ ova1 = affine_fn_plus (ova1, overlaps_a_xyz);
+ ova2 = affine_fn_plus (ova2, overlaps_a_xyz);
+ ovb = affine_fn_plus (ovb, overlaps_b_xyz);
+ affine_fn_free (t0);
+ affine_fn_free (t2);
+ affine_fn_free (t4);
+ *last_conflicts = last_conflicts_xyz;
+ }
+ *overlaps_a = conflict_fn (2, ova1, ova2);
+ *overlaps_b = conflict_fn (1, ovb);
+ }
+ else
+ {
+ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *last_conflicts = integer_zero_node;
+ }
+
+ affine_fn_free (overlaps_a_xz);
+ affine_fn_free (overlaps_b_xz);
+ affine_fn_free (overlaps_a_yz);
+ affine_fn_free (overlaps_b_yz);
+ affine_fn_free (overlaps_a_xyz);
+ affine_fn_free (overlaps_b_xyz);
+}
+
+/* Determines the overlapping elements due to accesses CHREC_A and
+ CHREC_B, that are affine functions. This function cannot handle
+ symbolic evolution functions, ie. when initial conditions are
+ parameters, because it uses lambda matrices of integers. */
+
+static void
+analyze_subscript_affine_affine (tree chrec_a,
+ tree chrec_b,
+ conflict_function **overlaps_a,
+ conflict_function **overlaps_b,
+ tree *last_conflicts)
+{
+ unsigned nb_vars_a, nb_vars_b, dim;
+ int init_a, init_b, gamma, gcd_alpha_beta;
+ int tau1, tau2;
+ lambda_matrix A, U, S;
+
+ if (eq_evolutions_p (chrec_a, chrec_b))
+ {
+ /* The accessed index overlaps for each iteration in the
+ loop. */
+ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *last_conflicts = chrec_dont_know;
+ return;
+ }
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "(analyze_subscript_affine_affine \n");
+
+ /* For determining the initial intersection, we have to solve a
+ Diophantine equation. This is the most time consuming part.
+
+ For answering to the question: "Is there a dependence?" we have
+ to prove that there exists a solution to the Diophantine
+ equation, and that the solution is in the iteration domain,
+ i.e. the solution is positive or zero, and that the solution
+ happens before the upper bound loop.nb_iterations. Otherwise
+ there is no dependence. This function outputs a description of
+ the iterations that hold the intersections. */
+
+ nb_vars_a = nb_vars_in_chrec (chrec_a);
+ nb_vars_b = nb_vars_in_chrec (chrec_b);
+
+ dim = nb_vars_a + nb_vars_b;
+ U = lambda_matrix_new (dim, dim);
+ A = lambda_matrix_new (dim, 1);
+ S = lambda_matrix_new (dim, 1);
+
+ init_a = initialize_matrix_A (A, chrec_a, 0, 1);
+ init_b = initialize_matrix_A (A, chrec_b, nb_vars_a, -1);
+ gamma = init_b - init_a;
+
+ /* Don't do all the hard work of solving the Diophantine equation
+ when we already know the solution: for example,
+ | {3, +, 1}_1
+ | {3, +, 4}_2
+ | gamma = 3 - 3 = 0.
+ Then the first overlap occurs during the first iterations:
+ | {3, +, 1}_1 ({0, +, 4}_x) = {3, +, 4}_2 ({0, +, 1}_x)
+ */
+ if (gamma == 0)
+ {
+ if (nb_vars_a == 1 && nb_vars_b == 1)
+ {
+ int step_a, step_b;
+ HOST_WIDE_INT niter, niter_a, niter_b;
+ affine_fn ova, ovb;
+
+ niter_a = estimated_loop_iterations_int
+ (get_chrec_loop (chrec_a), true);
+ niter_b = estimated_loop_iterations_int
+ (get_chrec_loop (chrec_b), true);
+ if (niter_a < 0 || niter_b < 0)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: missing iteration counts.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ goto end_analyze_subs_aa;
+ }
+
+ niter = MIN (niter_a, niter_b);
+
+ step_a = int_cst_value (CHREC_RIGHT (chrec_a));
+ step_b = int_cst_value (CHREC_RIGHT (chrec_b));
+
+ compute_overlap_steps_for_affine_univar (niter, step_a, step_b,
+ &ova, &ovb,
+ last_conflicts, 1);
+ *overlaps_a = conflict_fn (1, ova);
+ *overlaps_b = conflict_fn (1, ovb);
+ }
+
+ else if (nb_vars_a == 2 && nb_vars_b == 1)
+ compute_overlap_steps_for_affine_1_2
+ (chrec_a, chrec_b, overlaps_a, overlaps_b, last_conflicts);
+
+ else if (nb_vars_a == 1 && nb_vars_b == 2)
+ compute_overlap_steps_for_affine_1_2
+ (chrec_b, chrec_a, overlaps_b, overlaps_a, last_conflicts);
+
+ else
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: too many variables.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ }
+ goto end_analyze_subs_aa;
+ }
+
+ /* U.A = S */
+ lambda_matrix_right_hermite (A, dim, 1, S, U);
+
+ if (S[0][0] < 0)
+ {
+ S[0][0] *= -1;
+ lambda_matrix_row_negate (U, dim, 0);
+ }
+ gcd_alpha_beta = S[0][0];
+
+ /* Something went wrong: for example in {1, +, 0}_5 vs. {0, +, 0}_5,
+ but that is a quite strange case. Instead of ICEing, answer
+ don't know. */
+ if (gcd_alpha_beta == 0)
+ {
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ goto end_analyze_subs_aa;
+ }
+
+ /* The classic "gcd-test". */
+ if (!int_divides_p (gcd_alpha_beta, gamma))
+ {
+ /* The "gcd-test" has determined that there is no integer
+ solution, i.e. there is no dependence. */
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ }
+
+ /* Both access functions are univariate. This includes SIV and MIV cases. */
+ else if (nb_vars_a == 1 && nb_vars_b == 1)
+ {
+ /* Both functions should have the same evolution sign. */
+ if (((A[0][0] > 0 && -A[1][0] > 0)
+ || (A[0][0] < 0 && -A[1][0] < 0)))
+ {
+ /* The solutions are given by:
+ |
+ | [GAMMA/GCD_ALPHA_BETA t].[u11 u12] = [x0]
+ | [u21 u22] [y0]
+
+ For a given integer t. Using the following variables,
+
+ | i0 = u11 * gamma / gcd_alpha_beta
+ | j0 = u12 * gamma / gcd_alpha_beta
+ | i1 = u21
+ | j1 = u22
+
+ the solutions are:
+
+ | x0 = i0 + i1 * t,
+ | y0 = j0 + j1 * t. */
+
+ int i0, j0, i1, j1;
+
+ /* X0 and Y0 are the first iterations for which there is a
+ dependence. X0, Y0 are two solutions of the Diophantine
+ equation: chrec_a (X0) = chrec_b (Y0). */
+ int x0, y0;
+ int niter, niter_a, niter_b;
+
+ niter_a = estimated_loop_iterations_int
+ (get_chrec_loop (chrec_a), true);
+ niter_b = estimated_loop_iterations_int
+ (get_chrec_loop (chrec_b), true);
+
+ if (niter_a < 0 || niter_b < 0)
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: missing iteration counts.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ goto end_analyze_subs_aa;
+ }
+
+ niter = MIN (niter_a, niter_b);
+
+ i0 = U[0][0] * gamma / gcd_alpha_beta;
+ j0 = U[0][1] * gamma / gcd_alpha_beta;
+ i1 = U[1][0];
+ j1 = U[1][1];
+
+ if ((i1 == 0 && i0 < 0)
+ || (j1 == 0 && j0 < 0))
+ {
+ /* There is no solution.
+ FIXME: The case "i0 > nb_iterations, j0 > nb_iterations"
+ falls in here, but for the moment we don't look at the
+ upper bound of the iteration domain. */
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ }
+
+ else
+ {
+ if (i1 > 0)
+ {
+ tau1 = CEIL (-i0, i1);
+ tau2 = FLOOR_DIV (niter - i0, i1);
+
+ if (j1 > 0)
+ {
+ int last_conflict, min_multiple;
+ tau1 = MAX (tau1, CEIL (-j0, j1));
+ tau2 = MIN (tau2, FLOOR_DIV (niter - j0, j1));
+
+ x0 = i1 * tau1 + i0;
+ y0 = j1 * tau1 + j0;
+
+ /* At this point (x0, y0) is one of the
+ solutions to the Diophantine equation. The
+ next step has to compute the smallest
+ positive solution: the first conflicts. */
+ min_multiple = MIN (x0 / i1, y0 / j1);
+ x0 -= i1 * min_multiple;
+ y0 -= j1 * min_multiple;
+
+ tau1 = (x0 - i0)/i1;
+ last_conflict = tau2 - tau1;
+
+ /* If the overlap occurs outside of the bounds of the
+ loop, there is no dependence. */
+ if (x0 > niter || y0 > niter)
+ {
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ }
+ else
+ {
+ *overlaps_a
+ = conflict_fn (1,
+ affine_fn_univar (build_int_cst (NULL_TREE, x0),
+ 1,
+ build_int_cst (NULL_TREE, i1)));
+ *overlaps_b
+ = conflict_fn (1,
+ affine_fn_univar (build_int_cst (NULL_TREE, y0),
+ 1,
+ build_int_cst (NULL_TREE, j1)));
+ *last_conflicts = build_int_cst (NULL_TREE, last_conflict);
+ }
+ }
+ else
+ {
+ /* FIXME: For the moment, the upper bound of the
+ iteration domain for j is not checked. */
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ }
+ }
+
+ else
+ {
+ /* FIXME: For the moment, the upper bound of the
+ iteration domain for i is not checked. */
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ }
+ }
+ }
+ else
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ }
+ }
+
+ else
+ {
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "affine-affine test failed: unimplemented.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ }
+
+end_analyze_subs_aa:
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, " (overlaps_a = ");
+ dump_conflict_function (dump_file, *overlaps_a);
+ fprintf (dump_file, ")\n (overlaps_b = ");
+ dump_conflict_function (dump_file, *overlaps_b);
+ fprintf (dump_file, ")\n");
+ fprintf (dump_file, ")\n");
+ }
+}
+
+/* Returns true when analyze_subscript_affine_affine can be used for
+ determining the dependence relation between chrec_a and chrec_b,
+ that contain symbols. This function modifies chrec_a and chrec_b
+ such that the analysis result is the same, and such that they don't
+ contain symbols, and then can safely be passed to the analyzer.
+
+ Example: The analysis of the following tuples of evolutions produce
+ the same results: {x+1, +, 1}_1 vs. {x+3, +, 1}_1, and {-2, +, 1}_1
+ vs. {0, +, 1}_1
+
+ {x+1, +, 1}_1 ({2, +, 1}_1) = {x+3, +, 1}_1 ({0, +, 1}_1)
+ {-2, +, 1}_1 ({2, +, 1}_1) = {0, +, 1}_1 ({0, +, 1}_1)
+*/
+
+static bool
+can_use_analyze_subscript_affine_affine (tree *chrec_a, tree *chrec_b)
+{
+ tree diff, type, left_a, left_b, right_b;
+
+ if (chrec_contains_symbols (CHREC_RIGHT (*chrec_a))
+ || chrec_contains_symbols (CHREC_RIGHT (*chrec_b)))
+ /* FIXME: For the moment not handled. Might be refined later. */
+ return false;
+
+ type = chrec_type (*chrec_a);
+ left_a = CHREC_LEFT (*chrec_a);
+ left_b = chrec_convert (type, CHREC_LEFT (*chrec_b), NULL_TREE);
+ diff = chrec_fold_minus (type, left_a, left_b);
+
+ if (!evolution_function_is_constant_p (diff))
+ return false;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "can_use_subscript_aff_aff_for_symbolic \n");
+
+ *chrec_a = build_polynomial_chrec (CHREC_VARIABLE (*chrec_a),
+ diff, CHREC_RIGHT (*chrec_a));
+ right_b = chrec_convert (type, CHREC_RIGHT (*chrec_b), NULL_TREE);
+ *chrec_b = build_polynomial_chrec (CHREC_VARIABLE (*chrec_b),
+ build_int_cst (type, 0),
+ right_b);
+ return true;
+}
+
+/* Analyze a SIV (Single Index Variable) subscript. *OVERLAPS_A and
+ *OVERLAPS_B are initialized to the functions that describe the
+ relation between the elements accessed twice by CHREC_A and
+ CHREC_B. For k >= 0, the following property is verified:
+
+ CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+
+static void
+analyze_siv_subscript (tree chrec_a,
+ tree chrec_b,
+ conflict_function **overlaps_a,
+ conflict_function **overlaps_b,
+ tree *last_conflicts)
+{
+ dependence_stats.num_siv++;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "(analyze_siv_subscript \n");
+
+ if (evolution_function_is_constant_p (chrec_a)
+ && evolution_function_is_affine_p (chrec_b))
+ analyze_siv_subscript_cst_affine (chrec_a, chrec_b,
+ overlaps_a, overlaps_b, last_conflicts);
+
+ else if (evolution_function_is_affine_p (chrec_a)
+ && evolution_function_is_constant_p (chrec_b))
+ analyze_siv_subscript_cst_affine (chrec_b, chrec_a,
+ overlaps_b, overlaps_a, last_conflicts);
+
+ else if (evolution_function_is_affine_p (chrec_a)
+ && evolution_function_is_affine_p (chrec_b))
+ {
+ if (!chrec_contains_symbols (chrec_a)
+ && !chrec_contains_symbols (chrec_b))
+ {
+ analyze_subscript_affine_affine (chrec_a, chrec_b,
+ overlaps_a, overlaps_b,
+ last_conflicts);
+
+ if (CF_NOT_KNOWN_P (*overlaps_a)
+ || CF_NOT_KNOWN_P (*overlaps_b))
+ dependence_stats.num_siv_unimplemented++;
+ else if (CF_NO_DEPENDENCE_P (*overlaps_a)
+ || CF_NO_DEPENDENCE_P (*overlaps_b))
+ dependence_stats.num_siv_independent++;
+ else
+ dependence_stats.num_siv_dependent++;
+ }
+ else if (can_use_analyze_subscript_affine_affine (&chrec_a,
+ &chrec_b))
+ {
+ analyze_subscript_affine_affine (chrec_a, chrec_b,
+ overlaps_a, overlaps_b,
+ last_conflicts);
+ /* FIXME: The number of iterations is a symbolic expression.
+ Compute it properly. */
+ *last_conflicts = chrec_dont_know;
+
+ if (CF_NOT_KNOWN_P (*overlaps_a)
+ || CF_NOT_KNOWN_P (*overlaps_b))
+ dependence_stats.num_siv_unimplemented++;
+ else if (CF_NO_DEPENDENCE_P (*overlaps_a)
+ || CF_NO_DEPENDENCE_P (*overlaps_b))
+ dependence_stats.num_siv_independent++;
+ else
+ dependence_stats.num_siv_dependent++;
+ }
+ else
+ goto siv_subscript_dontknow;
+ }
+
+ else
+ {
+ siv_subscript_dontknow:;
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "siv test failed: unimplemented.\n");
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ dependence_stats.num_siv_unimplemented++;
+ }
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, ")\n");
+}
+
+/* Returns false if we can prove that the greatest common divisor of the steps
+ of CHREC does not divide CST, false otherwise. */
+
+static bool
+gcd_of_steps_may_divide_p (tree chrec, tree cst)
+{
+ HOST_WIDE_INT cd = 0, val;
+ tree step;
+
+ if (!host_integerp (cst, 0))
+ return true;
+ val = tree_low_cst (cst, 0);
+
+ while (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
+ {
+ step = CHREC_RIGHT (chrec);
+ if (!host_integerp (step, 0))
+ return true;
+ cd = gcd (cd, tree_low_cst (step, 0));
+ chrec = CHREC_LEFT (chrec);
+ }
+
+ return val % cd == 0;
+}
+
+/* Analyze a MIV (Multiple Index Variable) subscript. *OVERLAPS_A and
+ *OVERLAPS_B are initialized to the functions that describe the
+ relation between the elements accessed twice by CHREC_A and
+ CHREC_B. For k >= 0, the following property is verified:
+
+ CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+
+static void
+analyze_miv_subscript (tree chrec_a,
+ tree chrec_b,
+ conflict_function **overlaps_a,
+ conflict_function **overlaps_b,
+ tree *last_conflicts)
+{
+ /* FIXME: This is a MIV subscript, not yet handled.
+ Example: (A[{1, +, 1}_1] vs. A[{1, +, 1}_2]) that comes from
+ (A[i] vs. A[j]).
+
+ In the SIV test we had to solve a Diophantine equation with two
+ variables. In the MIV case we have to solve a Diophantine
+ equation with 2*n variables (if the subscript uses n IVs).
+ */
+ tree difference;
+ dependence_stats.num_miv++;
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "(analyze_miv_subscript \n");
+
+ chrec_a = chrec_convert (integer_type_node, chrec_a, NULL_TREE);
+ chrec_b = chrec_convert (integer_type_node, chrec_b, NULL_TREE);
+ difference = chrec_fold_minus (integer_type_node, chrec_a, chrec_b);
+
+ if (eq_evolutions_p (chrec_a, chrec_b))
+ {
+ /* Access functions are the same: all the elements are accessed
+ in the same order. */
+ *overlaps_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *overlaps_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *last_conflicts = estimated_loop_iterations_tree
+ (get_chrec_loop (chrec_a), true);
+ dependence_stats.num_miv_dependent++;
+ }
+
+ else if (evolution_function_is_constant_p (difference)
+ /* For the moment, the following is verified:
+ evolution_function_is_affine_multivariate_p (chrec_a) */
+ && !gcd_of_steps_may_divide_p (chrec_a, difference))
+ {
+ /* testsuite/.../ssa-chrec-33.c
+ {{21, +, 2}_1, +, -2}_2 vs. {{20, +, 2}_1, +, -2}_2
+
+ The difference is 1, and all the evolution steps are multiples
+ of 2, consequently there are no overlapping elements. */
+ *overlaps_a = conflict_fn_no_dependence ();
+ *overlaps_b = conflict_fn_no_dependence ();
+ *last_conflicts = integer_zero_node;
+ dependence_stats.num_miv_independent++;
+ }
+
+ else if (evolution_function_is_affine_multivariate_p (chrec_a)
+ && !chrec_contains_symbols (chrec_a)
+ && evolution_function_is_affine_multivariate_p (chrec_b)
+ && !chrec_contains_symbols (chrec_b))
+ {
+ /* testsuite/.../ssa-chrec-35.c
+ {0, +, 1}_2 vs. {0, +, 1}_3
+ the overlapping elements are respectively located at iterations:
+ {0, +, 1}_x and {0, +, 1}_x,
+ in other words, we have the equality:
+ {0, +, 1}_2 ({0, +, 1}_x) = {0, +, 1}_3 ({0, +, 1}_x)
+
+ Other examples:
+ {{0, +, 1}_1, +, 2}_2 ({0, +, 1}_x, {0, +, 1}_y) =
+ {0, +, 1}_1 ({{0, +, 1}_x, +, 2}_y)
+
+ {{0, +, 2}_1, +, 3}_2 ({0, +, 1}_y, {0, +, 1}_x) =
+ {{0, +, 3}_1, +, 2}_2 ({0, +, 1}_x, {0, +, 1}_y)
+ */
+ analyze_subscript_affine_affine (chrec_a, chrec_b,
+ overlaps_a, overlaps_b, last_conflicts);
+
+ if (CF_NOT_KNOWN_P (*overlaps_a)
+ || CF_NOT_KNOWN_P (*overlaps_b))
+ dependence_stats.num_miv_unimplemented++;
+ else if (CF_NO_DEPENDENCE_P (*overlaps_a)
+ || CF_NO_DEPENDENCE_P (*overlaps_b))
+ dependence_stats.num_miv_independent++;
+ else
+ dependence_stats.num_miv_dependent++;
+ }
+
+ else
+ {
+ /* When the analysis is too difficult, answer "don't know". */
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "analyze_miv_subscript test failed: unimplemented.\n");
+
+ *overlaps_a = conflict_fn_not_known ();
+ *overlaps_b = conflict_fn_not_known ();
+ *last_conflicts = chrec_dont_know;
+ dependence_stats.num_miv_unimplemented++;
+ }
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, ")\n");
+}
+
+/* Determines the iterations for which CHREC_A is equal to CHREC_B.
+ OVERLAP_ITERATIONS_A and OVERLAP_ITERATIONS_B are initialized with
+ two functions that describe the iterations that contain conflicting
+ elements.
+
+ Remark: For an integer k >= 0, the following equality is true:
+
+ CHREC_A (OVERLAP_ITERATIONS_A (k)) == CHREC_B (OVERLAP_ITERATIONS_B (k)).
+*/
+
+static void
+analyze_overlapping_iterations (tree chrec_a,
+ tree chrec_b,
+ conflict_function **overlap_iterations_a,
+ conflict_function **overlap_iterations_b,
+ tree *last_conflicts)
+{
+ dependence_stats.num_subscript_tests++;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "(analyze_overlapping_iterations \n");
+ fprintf (dump_file, " (chrec_a = ");
+ print_generic_expr (dump_file, chrec_a, 0);
+ fprintf (dump_file, ")\n (chrec_b = ");
+ print_generic_expr (dump_file, chrec_b, 0);
+ fprintf (dump_file, ")\n");
+ }
+
+ if (chrec_a == NULL_TREE
+ || chrec_b == NULL_TREE
+ || chrec_contains_undetermined (chrec_a)
+ || chrec_contains_undetermined (chrec_b))
+ {
+ dependence_stats.num_subscript_undetermined++;
+
+ *overlap_iterations_a = conflict_fn_not_known ();
+ *overlap_iterations_b = conflict_fn_not_known ();
+ }
+
+ /* If they are the same chrec, and are affine, they overlap
+ on every iteration. */
+ else if (eq_evolutions_p (chrec_a, chrec_b)
+ && evolution_function_is_affine_multivariate_p (chrec_a))
+ {
+ dependence_stats.num_same_subscript_function++;
+ *overlap_iterations_a = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *overlap_iterations_b = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ *last_conflicts = chrec_dont_know;
+ }
+
+ /* If they aren't the same, and aren't affine, we can't do anything
+ yet. */
+ else if ((chrec_contains_symbols (chrec_a)
+ || chrec_contains_symbols (chrec_b))
+ && (!evolution_function_is_affine_multivariate_p (chrec_a)
+ || !evolution_function_is_affine_multivariate_p (chrec_b)))
+ {
+ dependence_stats.num_subscript_undetermined++;
+ *overlap_iterations_a = conflict_fn_not_known ();
+ *overlap_iterations_b = conflict_fn_not_known ();
+ }
+
+ else if (ziv_subscript_p (chrec_a, chrec_b))
+ analyze_ziv_subscript (chrec_a, chrec_b,
+ overlap_iterations_a, overlap_iterations_b,
+ last_conflicts);
+
+ else if (siv_subscript_p (chrec_a, chrec_b))
+ analyze_siv_subscript (chrec_a, chrec_b,
+ overlap_iterations_a, overlap_iterations_b,
+ last_conflicts);
+
+ else
+ analyze_miv_subscript (chrec_a, chrec_b,
+ overlap_iterations_a, overlap_iterations_b,
+ last_conflicts);
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, " (overlap_iterations_a = ");
+ dump_conflict_function (dump_file, *overlap_iterations_a);
+ fprintf (dump_file, ")\n (overlap_iterations_b = ");
+ dump_conflict_function (dump_file, *overlap_iterations_b);
+ fprintf (dump_file, ")\n");
+ fprintf (dump_file, ")\n");
+ }
+}
+
+/* Helper function for uniquely inserting distance vectors. */
+
+static void
+save_dist_v (struct data_dependence_relation *ddr, lambda_vector dist_v)
+{
+ unsigned i;
+ lambda_vector v;
+
+ for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, v); i++)
+ if (lambda_vector_equal (v, dist_v, DDR_NB_LOOPS (ddr)))
+ return;
+
+ VEC_safe_push (lambda_vector, heap, DDR_DIST_VECTS (ddr), dist_v);
+}
+
+/* Helper function for uniquely inserting direction vectors. */
+
+static void
+save_dir_v (struct data_dependence_relation *ddr, lambda_vector dir_v)
+{
+ unsigned i;
+ lambda_vector v;
+
+ for (i = 0; VEC_iterate (lambda_vector, DDR_DIR_VECTS (ddr), i, v); i++)
+ if (lambda_vector_equal (v, dir_v, DDR_NB_LOOPS (ddr)))
+ return;
+
+ VEC_safe_push (lambda_vector, heap, DDR_DIR_VECTS (ddr), dir_v);
+}
+
+/* Add a distance of 1 on all the loops outer than INDEX. If we
+ haven't yet determined a distance for this outer loop, push a new
+ distance vector composed of the previous distance, and a distance
+ of 1 for this outer loop. Example:
+
+ | loop_1
+ | loop_2
+ | A[10]
+ | endloop_2
+ | endloop_1
+
+ Saved vectors are of the form (dist_in_1, dist_in_2). First, we
+ save (0, 1), then we have to save (1, 0). */
+
+static void
+add_outer_distances (struct data_dependence_relation *ddr,
+ lambda_vector dist_v, int index)
+{
+ /* For each outer loop where init_v is not set, the accesses are
+ in dependence of distance 1 in the loop. */
+ while (--index >= 0)
+ {
+ lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+ lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr));
+ save_v[index] = 1;
+ save_dist_v (ddr, save_v);
+ }
+}
+
+/* Return false when fail to represent the data dependence as a
+ distance vector. INIT_B is set to true when a component has been
+ added to the distance vector DIST_V. INDEX_CARRY is then set to
+ the index in DIST_V that carries the dependence. */
+
+static bool
+build_classic_dist_vector_1 (struct data_dependence_relation *ddr,
+ struct data_reference *ddr_a,
+ struct data_reference *ddr_b,
+ lambda_vector dist_v, bool *init_b,
+ int *index_carry)
+{
+ unsigned i;
+ lambda_vector init_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+
+ for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
+ {
+ tree access_fn_a, access_fn_b;
+ struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
+
+ if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
+ {
+ non_affine_dependence_relation (ddr);
+ return false;
+ }
+
+ access_fn_a = DR_ACCESS_FN (ddr_a, i);
+ access_fn_b = DR_ACCESS_FN (ddr_b, i);
+
+ if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC
+ && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC)
+ {
+ int dist, index;
+ int index_a = index_in_loop_nest (CHREC_VARIABLE (access_fn_a),
+ DDR_LOOP_NEST (ddr));
+ int index_b = index_in_loop_nest (CHREC_VARIABLE (access_fn_b),
+ DDR_LOOP_NEST (ddr));
+
+ /* The dependence is carried by the outermost loop. Example:
+ | loop_1
+ | A[{4, +, 1}_1]
+ | loop_2
+ | A[{5, +, 1}_2]
+ | endloop_2
+ | endloop_1
+ In this case, the dependence is carried by loop_1. */
+ index = index_a < index_b ? index_a : index_b;
+ *index_carry = MIN (index, *index_carry);
+
+ if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
+ {
+ non_affine_dependence_relation (ddr);
+ return false;
+ }
+
+ dist = int_cst_value (SUB_DISTANCE (subscript));
+
+ /* This is the subscript coupling test. If we have already
+ recorded a distance for this loop (a distance coming from
+ another subscript), it should be the same. For example,
+ in the following code, there is no dependence:
+
+ | loop i = 0, N, 1
+ | T[i+1][i] = ...
+ | ... = T[i][i]
+ | endloop
+ */
+ if (init_v[index] != 0 && dist_v[index] != dist)
{
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- return;
+ finalize_ddr_dependent (ddr, chrec_known);
+ return false;
}
- else
+
+ dist_v[index] = dist;
+ init_v[index] = 1;
+ *init_b = true;
+ }
+ else
+ {
+ /* This can be for example an affine vs. constant dependence
+ (T[i] vs. T[3]) that is not an affine dependence and is
+ not representable as a distance vector. */
+ non_affine_dependence_relation (ddr);
+ return false;
+ }
+ }
+
+ return true;
+}
+
+/* Return true when the DDR contains two data references that have the
+ same access functions. */
+
+static bool
+same_access_functions (struct data_dependence_relation *ddr)
+{
+ unsigned i;
+
+ for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
+ if (!eq_evolutions_p (DR_ACCESS_FN (DDR_A (ddr), i),
+ DR_ACCESS_FN (DDR_B (ddr), i)))
+ return false;
+
+ return true;
+}
+
+/* Return true when the DDR contains only constant access functions. */
+
+static bool
+constant_access_functions (struct data_dependence_relation *ddr)
+{
+ unsigned i;
+
+ for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
+ if (!evolution_function_is_constant_p (DR_ACCESS_FN (DDR_A (ddr), i))
+ || !evolution_function_is_constant_p (DR_ACCESS_FN (DDR_B (ddr), i)))
+ return false;
+
+ return true;
+}
+
+
+/* Helper function for the case where DDR_A and DDR_B are the same
+ multivariate access function. */
+
+static void
+add_multivariate_self_dist (struct data_dependence_relation *ddr, tree c_2)
+{
+ int x_1, x_2;
+ tree c_1 = CHREC_LEFT (c_2);
+ tree c_0 = CHREC_LEFT (c_1);
+ lambda_vector dist_v;
+ int v1, v2, cd;
+
+ /* Polynomials with more than 2 variables are not handled yet. */
+ if (TREE_CODE (c_0) != INTEGER_CST)
+ {
+ DDR_ARE_DEPENDENT (ddr) = chrec_dont_know;
+ return;
+ }
+
+ x_2 = index_in_loop_nest (CHREC_VARIABLE (c_2), DDR_LOOP_NEST (ddr));
+ x_1 = index_in_loop_nest (CHREC_VARIABLE (c_1), DDR_LOOP_NEST (ddr));
+
+ /* For "{{0, +, 2}_1, +, 3}_2" the distance vector is (3, -2). */
+ dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+ v1 = int_cst_value (CHREC_RIGHT (c_1));
+ v2 = int_cst_value (CHREC_RIGHT (c_2));
+ cd = gcd (v1, v2);
+ v1 /= cd;
+ v2 /= cd;
+
+ if (v2 < 0)
+ {
+ v2 = -v2;
+ v1 = -v1;
+ }
+
+ dist_v[x_1] = v2;
+ dist_v[x_2] = -v1;
+ save_dist_v (ddr, dist_v);
+
+ add_outer_distances (ddr, dist_v, x_1);
+}
+
+/* Helper function for the case where DDR_A and DDR_B are the same
+ access functions. */
+
+static void
+add_other_self_distances (struct data_dependence_relation *ddr)
+{
+ lambda_vector dist_v;
+ unsigned i;
+ int index_carry = DDR_NB_LOOPS (ddr);
+
+ for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
+ {
+ tree access_fun = DR_ACCESS_FN (DDR_A (ddr), i);
+
+ if (TREE_CODE (access_fun) == POLYNOMIAL_CHREC)
+ {
+ if (!evolution_function_is_univariate_p (access_fun))
{
- if (value2 == false)
- {
- /* Example:
- chrec_a = 3
- chrec_b = {10, +, -1}
- */
- if (tree_fold_divides_p
- (integer_type_node, CHREC_RIGHT (chrec_b), difference))
- {
- *overlaps_a = integer_zero_node;
- *overlaps_b = fold
- (build (EXACT_DIV_EXPR, integer_type_node, difference,
- CHREC_RIGHT (chrec_b)));
- return;
- }
-
- /* When the step does not divides the difference, there
- are no overlaps. */
- else
- {
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
- return;
- }
- }
- else
+ if (DDR_NUM_SUBSCRIPTS (ddr) != 1)
{
- /* Example:
- chrec_a = 3
- chrec_b = {4, +, 1}
-
- In this case, chrec_a will not overlap with chrec_b. */
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
+ DDR_ARE_DEPENDENT (ddr) = chrec_dont_know;
return;
}
+
+ add_multivariate_self_dist (ddr, DR_ACCESS_FN (DDR_A (ddr), 0));
+ return;
}
+
+ index_carry = MIN (index_carry,
+ index_in_loop_nest (CHREC_VARIABLE (access_fun),
+ DDR_LOOP_NEST (ddr)));
}
}
+
+ dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+ add_outer_distances (ddr, dist_v, index_carry);
}
-/* Analyze a SIV (Single Index Variable) subscript where CHREC_A is an
- affine function, and CHREC_B is a constant. *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:
+static void
+insert_innermost_unit_dist_vector (struct data_dependence_relation *ddr)
+{
+ lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
- CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+ 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
-analyze_siv_subscript_affine_cst (tree chrec_a,
- tree chrec_b,
- tree *overlaps_a,
- tree *overlaps_b)
+add_distance_for_zero_overlaps (struct data_dependence_relation *ddr)
{
- analyze_siv_subscript_cst_affine (chrec_b, chrec_a, overlaps_b, overlaps_a);
+ 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;
+ }
+ }
}
-/* Determines the overlapping elements due to accesses CHREC_A and
- CHREC_B, that are affine functions. This is a part of the
- subscript analyzer. */
+/* 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 void
-analyze_subscript_affine_affine (tree chrec_a,
- tree chrec_b,
- tree *overlaps_a,
- tree *overlaps_b)
+static bool
+build_classic_dist_vector (struct data_dependence_relation *ddr)
{
- tree left_a, left_b, right_a, right_b;
-
- 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,
- ie. 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. */
+ bool init_b = false;
+ int index_carry = DDR_NB_LOOPS (ddr);
+ lambda_vector dist_v;
- left_a = CHREC_LEFT (chrec_a);
- left_b = CHREC_LEFT (chrec_b);
- right_a = CHREC_RIGHT (chrec_a);
- right_b = CHREC_RIGHT (chrec_b);
-
- if (chrec_zerop (chrec_fold_minus (integer_type_node, left_a, left_b)))
+ if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE)
+ return true;
+
+ if (same_access_functions (ddr))
{
- /* The first element accessed twice is on the first
- iteration. */
- *overlaps_a = build_polynomial_chrec
- (CHREC_VARIABLE (chrec_b), integer_zero_node, integer_one_node);
- *overlaps_b = build_polynomial_chrec
- (CHREC_VARIABLE (chrec_a), integer_zero_node, integer_one_node);
+ /* 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;
}
-
- else if (TREE_CODE (left_a) == INTEGER_CST
- && TREE_CODE (left_b) == INTEGER_CST
- && TREE_CODE (right_a) == INTEGER_CST
- && TREE_CODE (right_b) == INTEGER_CST
-
- /* Both functions should have the same evolution sign. */
- && ((tree_int_cst_sgn (right_a) > 0
- && tree_int_cst_sgn (right_b) > 0)
- || (tree_int_cst_sgn (right_a) < 0
- && tree_int_cst_sgn (right_b) < 0)))
- {
- /* Here we have to solve the Diophantine equation. Reference
- book: "Loop Transformations for Restructuring Compilers - The
- Foundations" by Utpal Banerjee, pages 59-80.
-
- ALPHA * X0 = BETA * Y0 + GAMMA.
-
- with:
- ALPHA = RIGHT_A
- BETA = RIGHT_B
- GAMMA = LEFT_B - LEFT_A
- CHREC_A = {LEFT_A, +, RIGHT_A}
- CHREC_B = {LEFT_B, +, RIGHT_B}
-
- The Diophantine equation has a solution if and only if gcd
- (ALPHA, BETA) divides GAMMA. This is commonly known under
- the name of the "gcd-test".
- */
- tree alpha, beta, gamma;
- tree la, lb;
- tree gcd_alpha_beta;
- tree u11, u12, u21, u22;
-
- /* Both alpha and beta have to be integer_type_node. The gcd
- function does not work correctly otherwise. */
- alpha = copy_node (right_a);
- beta = copy_node (right_b);
- la = copy_node (left_a);
- lb = copy_node (left_b);
- TREE_TYPE (alpha) = integer_type_node;
- TREE_TYPE (beta) = integer_type_node;
- TREE_TYPE (la) = integer_type_node;
- TREE_TYPE (lb) = integer_type_node;
-
- gamma = fold (build (MINUS_EXPR, integer_type_node, lb, la));
-
- /* FIXME: Use lambda_*_Hermite for implementing Bezout. */
- gcd_alpha_beta = tree_fold_bezout
- (alpha,
- fold (build (MULT_EXPR, integer_type_node, beta,
- integer_minus_one_node)),
- &u11, &u12,
- &u21, &u22);
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- {
- fprintf (dump_file, " (alpha = ");
- print_generic_expr (dump_file, alpha, 0);
- fprintf (dump_file, ")\n (beta = ");
- print_generic_expr (dump_file, beta, 0);
- fprintf (dump_file, ")\n (gamma = ");
- print_generic_expr (dump_file, gamma, 0);
- fprintf (dump_file, ")\n (gcd_alpha_beta = ");
- print_generic_expr (dump_file, gcd_alpha_beta, 0);
- fprintf (dump_file, ")\n");
- }
-
- /* The classic "gcd-test". */
- if (!tree_fold_divides_p (integer_type_node, gcd_alpha_beta, gamma))
+
+ 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)))
{
- /* The "gcd-test" has determined that there is no integer
- solution, ie. there is no dependence. */
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
+ lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+ subscript_dependence_tester_1 (ddr, DDR_B (ddr), DDR_A (ddr));
+ compute_subscript_distance (ddr);
+ build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr),
+ save_v, &init_b, &index_carry);
+ save_dist_v (ddr, save_v);
+
+ /* In this case there is a dependence forward for all the
+ outer loops:
+
+ | for (k = 1; k < 100; k++)
+ | for (i = 1; i < 100; i++)
+ | for (j = 1; j < 100; j++)
+ | {
+ | t = T[j+1][i-1]; // A
+ | T[j][i] = t + 2; // B
+ | }
+
+ the vectors are:
+ (0, 1, -1)
+ (1, 1, -1)
+ (1, -1, 1)
+ */
+ if (DDR_NB_LOOPS (ddr) > 1)
+ {
+ add_outer_distances (ddr, save_v, index_carry);
+ add_outer_distances (ddr, dist_v, index_carry);
+ }
}
-
else
{
- /* The solutions are given by:
- |
- | [GAMMA/GCD_ALPHA_BETA t].[u11 u12] = [X]
- | [u21 u22] [Y]
-
- 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:
-
- | x = i0 + i1 * t,
- | y = j0 + j1 * t. */
-
- tree i0, j0, i1, j1, t;
- tree gamma_gcd;
-
- /* X0 and Y0 are the first iterations for which there is a
- dependence. X0, Y0 are two solutions of the Diophantine
- equation: chrec_a (X0) = chrec_b (Y0). */
- tree x0, y0;
-
- /* Exact div because in this case gcd_alpha_beta divides
- gamma. */
- gamma_gcd = fold (build (EXACT_DIV_EXPR, integer_type_node, gamma,
- gcd_alpha_beta));
- i0 = fold (build (MULT_EXPR, integer_type_node, u11, gamma_gcd));
- j0 = fold (build (MULT_EXPR, integer_type_node, u12, gamma_gcd));
- i1 = u21;
- j1 = u22;
-
- if ((tree_int_cst_sgn (i1) == 0
- && tree_int_cst_sgn (i0) < 0)
- || (tree_int_cst_sgn (j1) == 0
- && tree_int_cst_sgn (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 = chrec_known;
- *overlaps_b = chrec_known;
- }
-
- else
+ lambda_vector save_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+ lambda_vector_copy (dist_v, save_v, DDR_NB_LOOPS (ddr));
+ save_dist_v (ddr, save_v);
+
+ if (DDR_NB_LOOPS (ddr) > 1)
{
- if (tree_int_cst_sgn (i1) > 0)
- {
- t = fold
- (build (CEIL_DIV_EXPR, integer_type_node,
- fold (build (MULT_EXPR, integer_type_node, i0,
- integer_minus_one_node)),
- i1));
-
- if (tree_int_cst_sgn (j1) > 0)
- {
- t = fold
- (build (MAX_EXPR, integer_type_node, t,
- fold (build (CEIL_DIV_EXPR, integer_type_node,
- fold (build
- (MULT_EXPR,
- integer_type_node, j0,
- integer_minus_one_node)),
- j1))));
-
- x0 = fold
- (build (PLUS_EXPR, integer_type_node, i0,
- fold (build
- (MULT_EXPR, integer_type_node, i1, t))));
- y0 = fold
- (build (PLUS_EXPR, integer_type_node, j0,
- fold (build
- (MULT_EXPR, integer_type_node, j1, t))));
-
- *overlaps_a = build_polynomial_chrec
- (CHREC_VARIABLE (chrec_b), x0, u21);
- *overlaps_b = build_polynomial_chrec
- (CHREC_VARIABLE (chrec_a), y0, u22);
- }
- else
- {
- /* FIXME: For the moment, the upper bound of the
- iteration domain for j is not checked. */
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- }
- }
-
- else
- {
- /* FIXME: For the moment, the upper bound of the
- iteration domain for i is not checked. */
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- }
+ lambda_vector opposite_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+
+ subscript_dependence_tester_1 (ddr, DDR_B (ddr), DDR_A (ddr));
+ compute_subscript_distance (ddr);
+ build_classic_dist_vector_1 (ddr, DDR_B (ddr), DDR_A (ddr),
+ opposite_v, &init_b, &index_carry);
+
+ add_outer_distances (ddr, dist_v, index_carry);
+ add_outer_distances (ddr, opposite_v, index_carry);
}
}
}
-
else
{
- /* For the moment, "don't know". */
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
+ /* 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))
{
- fprintf (dump_file, " (overlaps_a = ");
- print_generic_expr (dump_file, *overlaps_a, 0);
- fprintf (dump_file, ")\n (overlaps_b = ");
- print_generic_expr (dump_file, *overlaps_b, 0);
+ 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");
}
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, ")\n");
-}
-/* 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:
+ return true;
+}
+
+/* Return the direction for a given distance.
+ FIXME: Computing dir this way is suboptimal, since dir can catch
+ cases that dist is unable to represent. */
+
+static inline enum data_dependence_direction
+dir_from_dist (int dist)
+{
+ if (dist > 0)
+ return dir_positive;
+ else if (dist < 0)
+ return dir_negative;
+ else
+ return dir_equal;
+}
+
+/* Compute the classic per loop direction vector. DDR is the data
+ dependence relation to build a vector from. */
+
+static void
+build_classic_dir_vector (struct data_dependence_relation *ddr)
+{
+ unsigned i, j;
+ lambda_vector dist_v;
+
+ for (i = 0; VEC_iterate (lambda_vector, DDR_DIST_VECTS (ddr), i, dist_v); i++)
+ {
+ lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+
+ for (j = 0; j < DDR_NB_LOOPS (ddr); j++)
+ dir_v[j] = dir_from_dist (dist_v[j]);
+
+ save_dir_v (ddr, dir_v);
+ }
+}
+
+/* Helper function. Returns true when there is a dependence between
+ data references DRA and DRB. */
+
+static bool
+subscript_dependence_tester_1 (struct data_dependence_relation *ddr,
+ struct data_reference *dra,
+ struct data_reference *drb)
+{
+ unsigned int i;
+ tree last_conflicts;
+ struct subscript *subscript;
+
+ for (i = 0; VEC_iterate (subscript_p, DDR_SUBSCRIPTS (ddr), i, subscript);
+ i++)
+ {
+ conflict_function *overlaps_a, *overlaps_b;
+
+ analyze_overlapping_iterations (DR_ACCESS_FN (dra, i),
+ DR_ACCESS_FN (drb, i),
+ &overlaps_a, &overlaps_b,
+ &last_conflicts);
+
+ if (CF_NOT_KNOWN_P (overlaps_a)
+ || CF_NOT_KNOWN_P (overlaps_b))
+ {
+ finalize_ddr_dependent (ddr, chrec_dont_know);
+ dependence_stats.num_dependence_undetermined++;
+ free_conflict_function (overlaps_a);
+ free_conflict_function (overlaps_b);
+ return false;
+ }
+
+ else if (CF_NO_DEPENDENCE_P (overlaps_a)
+ || CF_NO_DEPENDENCE_P (overlaps_b))
+ {
+ finalize_ddr_dependent (ddr, chrec_known);
+ dependence_stats.num_dependence_independent++;
+ free_conflict_function (overlaps_a);
+ free_conflict_function (overlaps_b);
+ return false;
+ }
+
+ else
+ {
+ SUB_CONFLICTS_IN_A (subscript) = overlaps_a;
+ SUB_CONFLICTS_IN_B (subscript) = overlaps_b;
+ SUB_LAST_CONFLICT (subscript) = last_conflicts;
+ }
+ }
+
+ return true;
+}
- CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+/* Computes the conflicting iterations, and initialize DDR. */
static void
-analyze_siv_subscript (tree chrec_a,
- tree chrec_b,
- tree *overlaps_a,
- tree *overlaps_b)
+subscript_dependence_tester (struct data_dependence_relation *ddr)
{
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, "(analyze_siv_subscript \n");
-
- if (evolution_function_is_constant_p (chrec_a)
- && evolution_function_is_affine_p (chrec_b))
- analyze_siv_subscript_cst_affine (chrec_a, chrec_b,
- overlaps_a, overlaps_b);
-
- else if (evolution_function_is_affine_p (chrec_a)
- && evolution_function_is_constant_p (chrec_b))
- analyze_siv_subscript_affine_cst (chrec_a, chrec_b,
- overlaps_a, overlaps_b);
- else if (evolution_function_is_affine_p (chrec_a)
- && evolution_function_is_affine_p (chrec_b)
- && (CHREC_VARIABLE (chrec_a) == CHREC_VARIABLE (chrec_b)))
- analyze_subscript_affine_affine (chrec_a, chrec_b,
- overlaps_a, overlaps_b);
- else
- {
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
- }
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file, "(subscript_dependence_tester \n");
+ if (subscript_dependence_tester_1 (ddr, DDR_A (ddr), DDR_B (ddr)))
+ dependence_stats.num_dependence_dependent++;
+
+ compute_subscript_distance (ddr);
+ if (build_classic_dist_vector (ddr))
+ build_classic_dir_vector (ddr);
+
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, ")\n");
}
-/* Return true when the evolution steps of an affine CHREC divide the
- constant CST. */
+/* Returns true when all the access functions of A are affine or
+ constant. */
+
+static bool
+access_functions_are_affine_or_constant_p (struct data_reference *a)
+{
+ unsigned int i;
+ VEC(tree,heap) *fns = DR_ACCESS_FNS (a);
+ tree t;
+
+ for (i = 0; VEC_iterate (tree, fns, i, t); i++)
+ if (!evolution_function_is_constant_p (t)
+ && !evolution_function_is_affine_multivariate_p (t))
+ return false;
+
+ return true;
+}
+
+/* Initializes an equation for an OMEGA problem using the information
+ contained in the ACCESS_FUN. Returns true when the operation
+ succeeded.
+
+ PB is the omega constraint system.
+ EQ is the number of the equation to be initialized.
+ OFFSET is used for shifting the variables names in the constraints:
+ a constrain is composed of 2 * the number of variables surrounding
+ dependence accesses. OFFSET is set either to 0 for the first n variables,
+ then it is set to n.
+ ACCESS_FUN is expected to be an affine chrec. */
static bool
-chrec_steps_divide_constant_p (tree chrec,
- tree cst)
+init_omega_eq_with_af (omega_pb pb, unsigned eq,
+ unsigned int offset, tree access_fun,
+ struct data_dependence_relation *ddr)
{
- switch (TREE_CODE (chrec))
+ switch (TREE_CODE (access_fun))
{
case POLYNOMIAL_CHREC:
- return (tree_fold_divides_p (integer_type_node, CHREC_RIGHT (chrec), cst)
- && chrec_steps_divide_constant_p (CHREC_LEFT (chrec), cst));
-
- default:
- /* On the initial condition, return true. */
+ {
+ 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;
}
}
-/* Analyze a MIV (Multiple Index Variable) subscript. *OVERLAPS_A and
- *OVERLAPS_B are initialized to the functions that describe the
- relation between the elements accessed twice by CHREC_A and
- CHREC_B. For k >= 0, the following property is verified:
-
- CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)). */
+/* 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
-analyze_miv_subscript (tree chrec_a,
- tree chrec_b,
- tree *overlaps_a,
- tree *overlaps_b)
+omega_extract_distance_vectors (omega_pb pb,
+ struct data_dependence_relation *ddr)
{
- /* FIXME: This is a MIV subscript, not yet handled.
- Example: (A[{1, +, 1}_1] vs. A[{1, +, 1}_2]) that comes from
- (A[i] vs. A[j]).
-
- In the SIV test we had to solve a Diophantine equation with two
- variables. In the MIV case we have to solve a Diophantine
- equation with 2*n variables (if the subscript uses n IVs).
- */
- tree difference;
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, "(analyze_miv_subscript \n");
-
- difference = chrec_fold_minus (integer_type_node, chrec_a, chrec_b);
-
- if (chrec_zerop (difference))
+ int eq, geq;
+ unsigned i, j;
+ struct loop *loopi, *loopj;
+ enum omega_result res;
+
+ /* Set a new problem for each loop in the nest. The basis is the
+ problem that we have initialized until now. On top of this we
+ add new constraints. */
+ for (i = 0; i <= DDR_INNER_LOOP (ddr)
+ && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++)
{
- /* Access functions are the same: all the elements are accessed
- in the same order. */
- *overlaps_a = integer_zero_node;
- *overlaps_b = integer_zero_node;
+ int dist = 0;
+ omega_pb copy = omega_alloc_problem (2 * DDR_NB_LOOPS (ddr),
+ DDR_NB_LOOPS (ddr));
+
+ omega_copy_problem (copy, pb);
+
+ /* For all the outer loops "loop_j", add "dj = 0". */
+ for (j = 0;
+ j < i && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), j, loopj); j++)
+ {
+ eq = omega_add_zero_eq (copy, omega_black);
+ copy->eqs[eq].coef[j + 1] = 1;
+ }
+
+ /* For "loop_i", add "0 <= di". */
+ geq = omega_add_zero_geq (copy, omega_black);
+ copy->geqs[geq].coef[i + 1] = 1;
+
+ /* Reduce the constraint system, and test that the current
+ problem is feasible. */
+ res = omega_simplify_problem (copy);
+ if (res == omega_false
+ || res == omega_unknown
+ || copy->num_geqs > (int) DDR_NB_LOOPS (ddr))
+ goto next_problem;
+
+ for (eq = 0; eq < copy->num_subs; eq++)
+ if (copy->subs[eq].key == (int) i + 1)
+ {
+ dist = copy->subs[eq].coef[0];
+ goto found_dist;
+ }
+
+ if (dist == 0)
+ {
+ /* Reinitialize problem... */
+ omega_copy_problem (copy, pb);
+ for (j = 0;
+ j < i && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), j, loopj); j++)
+ {
+ eq = omega_add_zero_eq (copy, omega_black);
+ copy->eqs[eq].coef[j + 1] = 1;
+ }
+
+ /* ..., but this time "di = 1". */
+ eq = omega_add_zero_eq (copy, omega_black);
+ copy->eqs[eq].coef[i + 1] = 1;
+ copy->eqs[eq].coef[0] = -1;
+
+ res = omega_simplify_problem (copy);
+ if (res == omega_false
+ || res == omega_unknown
+ || copy->num_geqs > (int) DDR_NB_LOOPS (ddr))
+ goto next_problem;
+
+ for (eq = 0; eq < copy->num_subs; eq++)
+ if (copy->subs[eq].key == (int) i + 1)
+ {
+ dist = copy->subs[eq].coef[0];
+ goto found_dist;
+ }
+ }
+
+ found_dist:;
+ /* Save the lexicographically positive distance vector. */
+ if (dist >= 0)
+ {
+ lambda_vector dist_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+ lambda_vector dir_v = lambda_vector_new (DDR_NB_LOOPS (ddr));
+
+ dist_v[i] = dist;
+
+ for (eq = 0; eq < copy->num_subs; eq++)
+ if (copy->subs[eq].key > 0)
+ {
+ dist = copy->subs[eq].coef[0];
+ dist_v[copy->subs[eq].key - 1] = dist;
+ }
+
+ for (j = 0; j < DDR_NB_LOOPS (ddr); j++)
+ dir_v[j] = dir_from_dist (dist_v[j]);
+
+ save_dist_v (ddr, dist_v);
+ save_dir_v (ddr, dir_v);
+ }
+
+ next_problem:;
+ omega_free_problem (copy);
}
-
- else if (evolution_function_is_constant_p (difference)
- /* For the moment, the following is verified:
- evolution_function_is_affine_multivariate_p (chrec_a) */
- && !chrec_steps_divide_constant_p (chrec_a, difference))
+}
+
+/* This is called for each subscript of a tuple of data references:
+ insert an equality for representing the conflicts. */
+
+static bool
+omega_setup_subscript (tree access_fun_a, tree access_fun_b,
+ struct data_dependence_relation *ddr,
+ omega_pb pb, bool *maybe_dependent)
+{
+ int eq;
+ tree fun_a = chrec_convert (integer_type_node, access_fun_a, NULL_TREE);
+ tree fun_b = chrec_convert (integer_type_node, access_fun_b, NULL_TREE);
+ tree difference = chrec_fold_minus (integer_type_node, fun_a, fun_b);
+
+ /* When the fun_a - fun_b is not constant, the dependence is not
+ captured by the classic distance vector representation. */
+ if (TREE_CODE (difference) != INTEGER_CST)
+ return false;
+
+ /* ZIV test. */
+ if (ziv_subscript_p (fun_a, fun_b) && !integer_zerop (difference))
{
- /* testsuite/.../ssa-chrec-33.c
- {{21, +, 2}_1, +, -2}_2 vs. {{20, +, 2}_1, +, -2}_2
-
- The difference is 1, and the evolution steps are equal to 2,
- consequently there are no overlapping elements. */
- *overlaps_a = chrec_known;
- *overlaps_b = chrec_known;
+ /* There is no dependence. */
+ *maybe_dependent = false;
+ return true;
}
-
- else if (evolution_function_is_univariate_p (chrec_a)
- && evolution_function_is_univariate_p (chrec_b))
+
+ fun_b = chrec_fold_multiply (integer_type_node, fun_b,
+ integer_minus_one_node);
+
+ eq = omega_add_zero_eq (pb, omega_black);
+ if (!init_omega_eq_with_af (pb, eq, DDR_NB_LOOPS (ddr), fun_a, ddr)
+ || !init_omega_eq_with_af (pb, eq, 0, fun_b, ddr))
+ /* There is probably a dependence, but the system of
+ constraints cannot be built: answer "don't know". */
+ return false;
+
+ /* GCD test. */
+ if (DDR_NB_LOOPS (ddr) != 0 && pb->eqs[eq].coef[0]
+ && !int_divides_p (lambda_vector_gcd
+ ((lambda_vector) &(pb->eqs[eq].coef[1]),
+ 2 * DDR_NB_LOOPS (ddr)),
+ pb->eqs[eq].coef[0]))
{
- /* testsuite/.../ssa-chrec-35.c
- {0, +, 1}_2 vs. {0, +, 1}_3
- the overlapping elements are respectively located at iterations:
- {0, +, 1}_3 and {0, +, 1}_2.
- */
- if (evolution_function_is_affine_p (chrec_a)
- && evolution_function_is_affine_p (chrec_b))
- analyze_subscript_affine_affine (chrec_a, chrec_b,
- overlaps_a, overlaps_b);
- else
+ /* 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)
{
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
+ /* There is no dependence. */
+ DDR_ARE_DEPENDENT (ddr) = chrec_known;
+ return true;
}
}
-
- else
+
+ /* Insert inequalities: constraints corresponding to the iteration
+ domain, i.e. the loops surrounding the references "loop_x" and
+ the distance variables "dx". The layout of the OMEGA
+ representation is as follows:
+ - coef[0] is the constant
+ - coef[1..nb_loops] are the protected variables that will not be
+ removed by the solver: the "dx"
+ - coef[nb_loops + 1, 2*nb_loops] are the loop variables: "loop_x".
+ */
+ for (i = 0; i <= DDR_INNER_LOOP (ddr)
+ && VEC_iterate (loop_p, DDR_LOOP_NEST (ddr), i, loopi); i++)
{
- /* When the analysis is too difficult, answer "don't know". */
- *overlaps_a = chrec_dont_know;
- *overlaps_b = chrec_dont_know;
+ HOST_WIDE_INT nbi = estimated_loop_iterations_int (loopi, true);
+
+ /* 0 <= loop_x */
+ ineq = omega_add_zero_geq (pb, omega_black);
+ pb->geqs[ineq].coef[i + nb_loops + 1] = 1;
+
+ /* 0 <= loop_x + dx */
+ ineq = omega_add_zero_geq (pb, omega_black);
+ pb->geqs[ineq].coef[i + nb_loops + 1] = 1;
+ pb->geqs[ineq].coef[i + 1] = 1;
+
+ if (nbi != -1)
+ {
+ /* loop_x <= nb_iters */
+ ineq = omega_add_zero_geq (pb, omega_black);
+ pb->geqs[ineq].coef[i + nb_loops + 1] = -1;
+ pb->geqs[ineq].coef[0] = nbi;
+
+ /* loop_x + dx <= nb_iters */
+ ineq = omega_add_zero_geq (pb, omega_black);
+ pb->geqs[ineq].coef[i + nb_loops + 1] = -1;
+ pb->geqs[ineq].coef[i + 1] = -1;
+ pb->geqs[ineq].coef[0] = nbi;
+
+ /* A step "dx" bigger than nb_iters is not feasible, so
+ add "0 <= nb_iters + dx", */
+ ineq = omega_add_zero_geq (pb, omega_black);
+ pb->geqs[ineq].coef[i + 1] = 1;
+ pb->geqs[ineq].coef[0] = nbi;
+ /* and "dx <= nb_iters". */
+ ineq = omega_add_zero_geq (pb, omega_black);
+ pb->geqs[ineq].coef[i + 1] = -1;
+ pb->geqs[ineq].coef[0] = nbi;
+ }
}
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, ")\n");
+
+ omega_extract_distance_vectors (pb, ddr);
+
+ return true;
}
-/* Determines the iterations for which CHREC_A is equal to CHREC_B.
- OVERLAP_ITERATIONS_A and OVERLAP_ITERATIONS_B are initialized with
- two functions that describe the iterations that contain conflicting
- elements.
-
- Remark: For an integer k >= 0, the following equality is true:
+/* 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
- CHREC_A (OVERLAP_ITERATIONS_A (k)) == CHREC_B (OVERLAP_ITERATIONS_B (k)).
+ 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 void
-analyze_overlapping_iterations (tree chrec_a,
- tree chrec_b,
- tree *overlap_iterations_a,
- tree *overlap_iterations_b)
+static bool
+init_omega_for_ddr (struct data_dependence_relation *ddr,
+ bool *maybe_dependent)
{
- 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)
- || chrec_contains_symbols (chrec_a)
- || chrec_contains_symbols (chrec_b))
- {
- *overlap_iterations_a = chrec_dont_know;
- *overlap_iterations_b = chrec_dont_know;
- }
-
- else if (ziv_subscript_p (chrec_a, chrec_b))
- analyze_ziv_subscript (chrec_a, chrec_b,
- overlap_iterations_a, overlap_iterations_b);
-
- else if (siv_subscript_p (chrec_a, chrec_b))
- analyze_siv_subscript (chrec_a, chrec_b,
- overlap_iterations_a, overlap_iterations_b);
-
- else
- analyze_miv_subscript (chrec_a, chrec_b,
- overlap_iterations_a, overlap_iterations_b);
-
- if (dump_file && (dump_flags & TDF_DETAILS))
+ omega_pb pb;
+ bool res = false;
+
+ *maybe_dependent = true;
+
+ if (same_access_functions (ddr))
{
- fprintf (dump_file, " (overlap_iterations_a = ");
- print_generic_expr (dump_file, *overlap_iterations_a, 0);
- fprintf (dump_file, ")\n (overlap_iterations_b = ");
- print_generic_expr (dump_file, *overlap_iterations_b, 0);
- fprintf (dump_file, ")\n");
+ 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;
}
-}
-\f
+ /* 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);
-/* This section contains the affine functions dependences detector. */
+ return res;
+}
-/* Computes the conflicting iterations, and initialize DDR. */
+/* Return true when DDR contains the same information as that stored
+ in DIR_VECTS and in DIST_VECTS, return false otherwise. */
-static void
-subscript_dependence_tester (struct data_dependence_relation *ddr)
+static bool
+ddr_consistent_p (FILE *file,
+ struct data_dependence_relation *ddr,
+ VEC (lambda_vector, heap) *dist_vects,
+ VEC (lambda_vector, heap) *dir_vects)
{
- unsigned int i;
- struct data_reference *dra = DDR_A (ddr);
- struct data_reference *drb = DDR_B (ddr);
-
+ unsigned int i, j;
+
+ /* If dump_file is set, output there. */
if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, "(subscript_dependence_tester \n");
-
- for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
+ file = dump_file;
+
+ if (VEC_length (lambda_vector, dist_vects) != DDR_NUM_DIST_VECTS (ddr))
{
- tree overlaps_a, overlaps_b;
- struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
-
- analyze_overlapping_iterations (DR_ACCESS_FN (dra, i),
- DR_ACCESS_FN (drb, i),
- &overlaps_a, &overlaps_b);
-
- if (chrec_contains_undetermined (overlaps_a)
- || chrec_contains_undetermined (overlaps_b))
- {
- finalize_ddr_dependent (ddr, chrec_dont_know);
- break;
- }
-
- else if (overlaps_a == chrec_known
- || overlaps_b == chrec_known)
- {
- finalize_ddr_dependent (ddr, chrec_known);
- break;
- }
-
- else
- {
- SUB_CONFLICTS_IN_A (subscript) = overlaps_a;
- SUB_CONFLICTS_IN_B (subscript) = overlaps_b;
- }
- }
-
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file, ")\n");
-}
+ lambda_vector b_dist_v;
+ fprintf (file, "\n(Number of distance vectors differ: Banerjee has %d, Omega has %d.\n",
+ VEC_length (lambda_vector, dist_vects),
+ DDR_NUM_DIST_VECTS (ddr));
-/* Compute the classic per loop distance vector.
+ fprintf (file, "Banerjee dist vectors:\n");
+ for (i = 0; VEC_iterate (lambda_vector, dist_vects, i, b_dist_v); i++)
+ print_lambda_vector (file, b_dist_v, DDR_NB_LOOPS (ddr));
- RES is the data dependence relation to build a vector from.
- CLASSIC_DIST is the varray to place the vector in.
- NB_LOOPS is the total number of loops we are considering.
- FIRST_LOOP is the loop->num of the first loop. */
+ 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));
-static void
-build_classic_dist_vector (struct data_dependence_relation *res,
- varray_type *classic_dist,
- int nb_loops, unsigned int first_loop)
-{
- unsigned i;
- lambda_vector dist_v, init_v;
-
- dist_v = lambda_vector_new (nb_loops);
- init_v = lambda_vector_new (nb_loops);
- lambda_vector_clear (dist_v, nb_loops);
- lambda_vector_clear (init_v, nb_loops);
-
- if (DDR_ARE_DEPENDENT (res) != NULL_TREE)
- return;
-
- for (i = 0; i < DDR_NUM_SUBSCRIPTS (res); i++)
+ fprintf (file, "data dependence relation:\n");
+ dump_data_dependence_relation (file, ddr);
+
+ fprintf (file, ")\n");
+ return false;
+ }
+
+ if (VEC_length (lambda_vector, dir_vects) != DDR_NUM_DIR_VECTS (ddr))
{
- struct subscript *subscript = DDR_SUBSCRIPT (res, i);
+ fprintf (file, "\n(Number of direction vectors differ: Banerjee has %d, Omega has %d.)\n",
+ VEC_length (lambda_vector, dir_vects),
+ DDR_NUM_DIR_VECTS (ddr));
+ return false;
+ }
- if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
- return;
-
- if (TREE_CODE (SUB_CONFLICTS_IN_A (subscript)) == POLYNOMIAL_CHREC)
- {
- int dist;
- int loop_nb;
- loop_nb = CHREC_VARIABLE (SUB_CONFLICTS_IN_A (subscript));
- loop_nb -= first_loop;
- /* If the loop number is still greater than the number of
- loops we've been asked to analyze, or negative,
- something is borked. */
- if (loop_nb < 0 || loop_nb >= nb_loops)
- abort ();
- dist = int_cst_value (SUB_DISTANCE (subscript));
+ 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);
- /* This is the subscript coupling test.
- | loop i = 0, N, 1
- | T[i+1][i] = ...
- | ... = T[i][i]
- | endloop
- There is no dependence. */
- if (init_v[loop_nb] != 0
- && dist_v[loop_nb] != dist)
- {
- finalize_ddr_dependent (res, chrec_known);
- return;
- }
+ /* Distance vectors are not ordered in the same way in the DDR
+ and in the DIST_VECTS: search for a matching vector. */
+ for (j = 0; VEC_iterate (lambda_vector, dist_vects, j, a_dist_v); j++)
+ if (lambda_vector_equal (a_dist_v, b_dist_v, DDR_NB_LOOPS (ddr)))
+ break;
- dist_v[loop_nb] = dist;
- init_v[loop_nb] = 1;
+ if (j == VEC_length (lambda_vector, dist_vects))
+ {
+ fprintf (file, "\n(Dist vectors from the first dependence analyzer:\n");
+ print_dist_vectors (file, dist_vects, DDR_NB_LOOPS (ddr));
+ fprintf (file, "not found in Omega dist vectors:\n");
+ print_dist_vectors (file, DDR_DIST_VECTS (ddr), DDR_NB_LOOPS (ddr));
+ fprintf (file, "data dependence relation:\n");
+ dump_data_dependence_relation (file, ddr);
+ fprintf (file, ")\n");
}
}
-
- /* 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
- */
- {
- struct loop *lca, *loop_a, *loop_b;
- struct data_reference *a = DDR_A (res);
- struct data_reference *b = DDR_B (res);
- int lca_nb;
- loop_a = loop_containing_stmt (DR_STMT (a));
- loop_b = loop_containing_stmt (DR_STMT (b));
-
- /* Get the common ancestor loop. */
- lca = find_common_loop (loop_a, loop_b);
-
- lca_nb = lca->num;
- lca_nb -= first_loop;
- if (lca_nb < 0 || lca_nb >= nb_loops)
- abort ();
- /* For each outer loop where init_v is not set, the accesses are
- in dependence of distance 1 in the loop. */
- if (lca != loop_a
- && lca != loop_b
- && init_v[lca_nb] == 0)
- dist_v[lca_nb] = 1;
-
- lca = lca->outer;
-
- if (lca)
- {
- lca_nb = lca->num - first_loop;
- while (lca->depth != 0)
- {
- if (lca_nb < 0 || lca_nb >= nb_loops)
- abort ();
- if (init_v[lca_nb] == 0)
- dist_v[lca_nb] = 1;
- lca = lca->outer;
- lca_nb = lca->num - first_loop;
-
- }
- }
- }
-
- VARRAY_PUSH_GENERIC_PTR (*classic_dist, dist_v);
-}
-
-/* Compute the classic per loop direction vector.
-
- RES is the data dependence relation to build a vector from.
- CLASSIC_DIR is the varray to place the vector in.
- NB_LOOPS is the total number of loops we are considering.
- FIRST_LOOP is the loop->num of the first loop. */
-static void
-build_classic_dir_vector (struct data_dependence_relation *res,
- varray_type *classic_dir,
- int nb_loops, unsigned int first_loop)
-{
- unsigned i;
- lambda_vector dir_v, init_v;
-
- dir_v = lambda_vector_new (nb_loops);
- init_v = lambda_vector_new (nb_loops);
- lambda_vector_clear (dir_v, nb_loops);
- lambda_vector_clear (init_v, nb_loops);
-
- if (DDR_ARE_DEPENDENT (res) != NULL_TREE)
- return;
-
- for (i = 0; i < DDR_NUM_SUBSCRIPTS (res); i++)
+ for (i = 0; i < DDR_NUM_DIR_VECTS (ddr); i++)
{
- struct subscript *subscript = DDR_SUBSCRIPT (res, i);
+ lambda_vector a_dir_v;
+ lambda_vector b_dir_v = DDR_DIR_VECT (ddr, i);
+
+ /* Direction vectors are not ordered in the same way in the DDR
+ and in the DIR_VECTS: search for a matching vector. */
+ for (j = 0; VEC_iterate (lambda_vector, dir_vects, j, a_dir_v); j++)
+ if (lambda_vector_equal (a_dir_v, b_dir_v, DDR_NB_LOOPS (ddr)))
+ break;
- if (TREE_CODE (SUB_CONFLICTS_IN_A (subscript)) == POLYNOMIAL_CHREC
- && TREE_CODE (SUB_CONFLICTS_IN_B (subscript)) == POLYNOMIAL_CHREC)
+ if (j == VEC_length (lambda_vector, dist_vects))
{
- int loop_nb;
-
- enum data_dependence_direction dir = dir_star;
- loop_nb = CHREC_VARIABLE (SUB_CONFLICTS_IN_A (subscript));
- loop_nb -= first_loop;
-
- /* If the loop number is still greater than the number of
- loops we've been asked to analyze, or negative,
- something is borked. */
- if (loop_nb < 0 || loop_nb >= nb_loops)
- abort ();
- if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
- {
-
- }
- else
- {
- int dist = int_cst_value (SUB_DISTANCE (subscript));
-
- if (dist == 0)
- dir = dir_equal;
- else if (dist > 0)
- dir = dir_positive;
- else if (dist < 0)
- dir = dir_negative;
- }
-
- /* This is the subscript coupling test.
- | loop i = 0, N, 1
- | T[i+1][i] = ...
- | ... = T[i][i]
- | endloop
- There is no dependence. */
- if (init_v[loop_nb] != 0
- && dir != dir_star
- && (enum data_dependence_direction) dir_v[loop_nb] != dir
- && (enum data_dependence_direction) dir_v[loop_nb] != dir_star)
- {
- finalize_ddr_dependent (res, chrec_known);
- return;
- }
-
- dir_v[loop_nb] = dir;
- init_v[loop_nb] = 1;
+ 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");
}
}
-
- /* 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
- */
- {
- struct loop *lca, *loop_a, *loop_b;
- struct data_reference *a = DDR_A (res);
- struct data_reference *b = DDR_B (res);
- int lca_nb;
- loop_a = loop_containing_stmt (DR_STMT (a));
- loop_b = loop_containing_stmt (DR_STMT (b));
-
- /* Get the common ancestor loop. */
- lca = find_common_loop (loop_a, loop_b);
- lca_nb = lca->num - first_loop;
-
- if (lca_nb < 0 || lca_nb >= nb_loops)
- abort ();
- /* For each outer loop where init_v is not set, the accesses are
- in dependence of distance 1 in the loop. */
- if (lca != loop_a
- && lca != loop_b
- && init_v[lca_nb] == 0)
- dir_v[lca_nb] = dir_positive;
-
- lca = lca->outer;
- if (lca)
- {
- lca_nb = lca->num - first_loop;
- while (lca->depth != 0)
- {
- if (lca_nb < 0 || lca_nb >= nb_loops)
- abort ();
- if (init_v[lca_nb] == 0)
- dir_v[lca_nb] = dir_positive;
- lca = lca->outer;
- lca_nb = lca->num - first_loop;
-
- }
- }
- }
-
- VARRAY_PUSH_GENERIC_PTR (*classic_dir, dir_v);
-}
-
-/* Returns true when all the access functions of A are affine or
- constant. */
-static bool
-access_functions_are_affine_or_constant_p (struct data_reference *a)
-{
- unsigned int i;
- varray_type fns = DR_ACCESS_FNS (a);
-
- for (i = 0; i < VARRAY_ACTIVE_SIZE (fns); i++)
- if (!evolution_function_is_constant_p (VARRAY_TREE (fns, i))
- && !evolution_function_is_affine_multivariate_p (VARRAY_TREE (fns, i)))
- return false;
-
- return true;
+ return true;
}
/* This computes the affine dependence relation between A and B.
relation the first time we detect a CHREC_KNOWN element for a given
subscript. */
-void
+static void
compute_affine_dependence (struct data_dependence_relation *ddr)
{
struct data_reference *dra = DDR_A (ddr);
if (dump_file && (dump_flags & TDF_DETAILS))
{
- fprintf (dump_file, "(compute_affine_dependence (%d, %d)\n",
- DR_ID (dra), DR_ID (drb));
+ fprintf (dump_file, "(compute_affine_dependence\n");
fprintf (dump_file, " (stmt_a = \n");
print_generic_expr (dump_file, DR_STMT (dra), 0);
fprintf (dump_file, ")\n (stmt_b = \n");
print_generic_expr (dump_file, DR_STMT (drb), 0);
fprintf (dump_file, ")\n");
}
-
+
/* Analyze only when the dependence relation is not yet known. */
if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
{
+ dependence_stats.num_dependence_tests++;
+
if (access_functions_are_affine_or_constant_p (dra)
&& access_functions_are_affine_or_constant_p (drb))
- subscript_dependence_tester (ddr);
-
+ {
+ if (flag_check_data_deps)
+ {
+ /* Compute the dependences using the first algorithm. */
+ subscript_dependence_tester (ddr);
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "\n\nBanerjee Analyzer\n");
+ dump_data_dependence_relation (dump_file, ddr);
+ }
+
+ if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
+ {
+ bool maybe_dependent;
+ VEC (lambda_vector, heap) *dir_vects, *dist_vects;
+
+ /* Save the result of the first DD analyzer. */
+ dist_vects = DDR_DIST_VECTS (ddr);
+ dir_vects = DDR_DIR_VECTS (ddr);
+
+ /* Reset the information. */
+ DDR_DIST_VECTS (ddr) = NULL;
+ DDR_DIR_VECTS (ddr) = NULL;
+
+ /* Compute the same information using Omega. */
+ if (!init_omega_for_ddr (ddr, &maybe_dependent))
+ goto csys_dont_know;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "Omega Analyzer\n");
+ dump_data_dependence_relation (dump_file, ddr);
+ }
+
+ /* Check that we get the same information. */
+ if (maybe_dependent)
+ gcc_assert (ddr_consistent_p (stderr, ddr, dist_vects,
+ dir_vects));
+ }
+ }
+ else
+ subscript_dependence_tester (ddr);
+ }
+
/* As a last case, if the dependence cannot be determined, or if
the dependence is considered too difficult to determine, answer
"don't know". */
else
- finalize_ddr_dependent (ddr, chrec_dont_know);
+ {
+ csys_dont_know:;
+ dependence_stats.num_dependence_undetermined++;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "Data ref a:\n");
+ dump_data_reference (dump_file, dra);
+ fprintf (dump_file, "Data ref b:\n");
+ dump_data_reference (dump_file, drb);
+ fprintf (dump_file, "affine dependence test not usable: access function not affine or constant.\n");
+ }
+ finalize_ddr_dependent (ddr, chrec_dont_know);
+ }
}
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, ")\n");
}
-/* Compute a subset of the data dependence relation graph. Don't
- compute read-read relations, and avoid the computation of the
- opposite relation, ie. when AB has been computed, don't compute BA.
- DATAREFS contains a list of data references, and the result is set
- in DEPENDENCE_RELATIONS. */
+/* This computes the dependence relation for the same data
+ reference into DDR. */
+
+static void
+compute_self_dependence (struct data_dependence_relation *ddr)
+{
+ unsigned int i;
+ struct subscript *subscript;
+
+ for (i = 0; VEC_iterate (subscript_p, DDR_SUBSCRIPTS (ddr), i, subscript);
+ i++)
+ {
+ /* The accessed index overlaps for each iteration. */
+ SUB_CONFLICTS_IN_A (subscript)
+ = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ SUB_CONFLICTS_IN_B (subscript)
+ = conflict_fn (1, affine_fn_cst (integer_zero_node));
+ SUB_LAST_CONFLICT (subscript) = chrec_dont_know;
+ }
+
+ /* The distance vector is the zero vector. */
+ save_dist_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr)));
+ save_dir_v (ddr, lambda_vector_new (DDR_NB_LOOPS (ddr)));
+}
+
+/* Compute in DEPENDENCE_RELATIONS the data dependence graph for all
+ the data references in DATAREFS, in the LOOP_NEST. When
+ COMPUTE_SELF_AND_RR is FALSE, don't compute read-read and self
+ relations. */
static void
-compute_rw_wr_ww_dependences (varray_type datarefs,
- varray_type *dependence_relations)
+compute_all_dependences (VEC (data_reference_p, heap) *datarefs,
+ VEC (ddr_p, heap) **dependence_relations,
+ VEC (loop_p, heap) *loop_nest,
+ bool compute_self_and_rr)
{
- unsigned int i, j, N;
+ struct data_dependence_relation *ddr;
+ struct data_reference *a, *b;
+ unsigned int i, j;
- N = VARRAY_ACTIVE_SIZE (datarefs);
+ for (i = 0; VEC_iterate (data_reference_p, datarefs, i, a); i++)
+ for (j = i + 1; VEC_iterate (data_reference_p, datarefs, j, b); j++)
+ if (!DR_IS_READ (a) || !DR_IS_READ (b) || compute_self_and_rr)
+ {
+ ddr = initialize_data_dependence_relation (a, b, loop_nest);
+ VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
+ compute_affine_dependence (ddr);
+ }
- for (i = 0; i < N; i++)
- for (j = i; j < N; j++)
+ if (compute_self_and_rr)
+ for (i = 0; VEC_iterate (data_reference_p, datarefs, i, a); i++)
{
- struct data_reference *a, *b;
- struct data_dependence_relation *ddr;
+ ddr = initialize_data_dependence_relation (a, a, loop_nest);
+ VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
+ compute_self_dependence (ddr);
+ }
+}
+
+/* Stores the locations of memory references in STMT to REFERENCES. Returns
+ true if STMT clobbers memory, false otherwise. */
+
+bool
+get_references_in_stmt (tree stmt, VEC (data_ref_loc, heap) **references)
+{
+ bool clobbers_memory = false;
+ data_ref_loc *ref;
+ tree *op0, *op1, call;
+
+ *references = NULL;
+
+ /* ASM_EXPR and CALL_EXPR may embed arbitrary side effects.
+ Calls have side-effects, except those to const or pure
+ functions. */
+ call = get_call_expr_in (stmt);
+ if ((call
+ && !(call_expr_flags (call) & (ECF_CONST | ECF_PURE)))
+ || (TREE_CODE (stmt) == ASM_EXPR
+ && ASM_VOLATILE_P (stmt)))
+ clobbers_memory = true;
+
+ if (ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
+ return clobbers_memory;
+
+ if (TREE_CODE (stmt) == GIMPLE_MODIFY_STMT)
+ {
+ op0 = &GIMPLE_STMT_OPERAND (stmt, 0);
+ op1 = &GIMPLE_STMT_OPERAND (stmt, 1);
+
+ if (DECL_P (*op1)
+ || REFERENCE_CLASS_P (*op1))
+ {
+ ref = VEC_safe_push (data_ref_loc, heap, *references, NULL);
+ ref->pos = op1;
+ ref->is_read = true;
+ }
- a = VARRAY_GENERIC_PTR (datarefs, i);
- b = VARRAY_GENERIC_PTR (datarefs, j);
+ if (DECL_P (*op0)
+ || REFERENCE_CLASS_P (*op0))
+ {
+ ref = VEC_safe_push (data_ref_loc, heap, *references, NULL);
+ ref->pos = op0;
+ ref->is_read = false;
+ }
+ }
- /* Don't compute the "read-read" relations. */
- if (DR_IS_READ (a) && DR_IS_READ (b))
- continue;
+ if (call)
+ {
+ unsigned i, n = call_expr_nargs (call);
- ddr = initialize_data_dependence_relation (a, b);
+ for (i = 0; i < n; i++)
+ {
+ op0 = &CALL_EXPR_ARG (call, i);
- VARRAY_PUSH_GENERIC_PTR (*dependence_relations, ddr);
- compute_affine_dependence (ddr);
- compute_distance_vector (ddr);
- }
+ if (DECL_P (*op0)
+ || REFERENCE_CLASS_P (*op0))
+ {
+ ref = VEC_safe_push (data_ref_loc, heap, *references, NULL);
+ ref->pos = op0;
+ ref->is_read = true;
+ }
+ }
+ }
+
+ return clobbers_memory;
+}
+
+/* Stores the data references in STMT to DATAREFS. If there is an unanalyzable
+ reference, returns false, otherwise returns true. */
+
+static bool
+find_data_references_in_stmt (tree stmt,
+ VEC (data_reference_p, heap) **datarefs)
+{
+ unsigned i;
+ VEC (data_ref_loc, heap) *references;
+ data_ref_loc *ref;
+ bool ret = true;
+ data_reference_p dr;
+
+ if (get_references_in_stmt (stmt, &references))
+ {
+ VEC_free (data_ref_loc, heap, references);
+ return false;
+ }
+
+ for (i = 0; VEC_iterate (data_ref_loc, references, i, ref); i++)
+ {
+ dr = create_data_ref (*ref->pos, stmt, ref->is_read);
+ if (dr)
+ VEC_safe_push (data_reference_p, heap, *datarefs, dr);
+ else
+ {
+ ret = false;
+ break;
+ }
+ }
+ VEC_free (data_ref_loc, heap, references);
+ return ret;
}
/* Search the data references in LOOP, and record the information into
DATAREFS. Returns chrec_dont_know when failing to analyze a
difficult case, returns NULL_TREE otherwise.
- FIXME: This is a "dumb" walker over all the trees in the loop body.
- Find another technique that avoids this costly walk. This is
- acceptable for the moment, since this function is used only for
- debugging purposes. */
+ TODO: This function should be made smarter so that it can handle address
+ arithmetic as if they were array accesses, etc. */
-static tree
-find_data_references_in_loop (struct loop *loop, varray_type *datarefs)
+tree
+find_data_references_in_loop (struct loop *loop,
+ VEC (data_reference_p, heap) **datarefs)
{
- basic_block bb;
+ basic_block bb, *bbs;
+ unsigned int i;
block_stmt_iterator bsi;
-
- FOR_EACH_BB (bb)
- {
- if (!flow_bb_inside_loop_p (loop, bb))
- continue;
-
- for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
- {
- tree stmt = bsi_stmt (bsi);
- stmt_ann_t ann = stmt_ann (stmt);
- if (TREE_CODE (stmt) != MODIFY_EXPR)
- continue;
+ bbs = get_loop_body (loop);
- if (!VUSE_OPS (ann)
- && !V_MUST_DEF_OPS (ann)
- && !V_MAY_DEF_OPS (ann))
- continue;
-
- /* In the GIMPLE representation, a modify expression
- contains a single load or store to memory. */
- if (TREE_CODE (TREE_OPERAND (stmt, 0)) == ARRAY_REF)
- VARRAY_PUSH_GENERIC_PTR
- (*datarefs, analyze_array (stmt, TREE_OPERAND (stmt, 0),
- false));
+ for (i = 0; i < loop->num_nodes; i++)
+ {
+ bb = bbs[i];
- else if (TREE_CODE (TREE_OPERAND (stmt, 1)) == ARRAY_REF)
- VARRAY_PUSH_GENERIC_PTR
- (*datarefs, analyze_array (stmt, TREE_OPERAND (stmt, 1),
- true));
+ for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
+ {
+ tree stmt = bsi_stmt (bsi);
- else
- return chrec_dont_know;
+ if (!find_data_references_in_stmt (stmt, datarefs))
+ {
+ struct data_reference *res;
+ res = XNEW (struct data_reference);
+ DR_STMT (res) = NULL_TREE;
+ DR_REF (res) = NULL_TREE;
+ DR_BASE_OBJECT (res) = NULL;
+ DR_TYPE (res) = ARRAY_REF_TYPE;
+ DR_SET_ACCESS_FNS (res, NULL);
+ DR_BASE_OBJECT (res) = NULL;
+ DR_IS_READ (res) = false;
+ DR_BASE_ADDRESS (res) = NULL_TREE;
+ DR_OFFSET (res) = NULL_TREE;
+ DR_INIT (res) = NULL_TREE;
+ DR_STEP (res) = NULL_TREE;
+ DR_OFFSET_MISALIGNMENT (res) = NULL_TREE;
+ DR_MEMTAG (res) = NULL_TREE;
+ DR_PTR_INFO (res) = NULL;
+ VEC_safe_push (data_reference_p, heap, *datarefs, res);
+
+ free (bbs);
+ return chrec_dont_know;
+ }
}
}
+ free (bbs);
return NULL_TREE;
}
-\f
+/* Recursive helper function. */
+
+static bool
+find_loop_nest_1 (struct loop *loop, VEC (loop_p, heap) **loop_nest)
+{
+ /* Inner loops of the nest should not contain siblings. Example:
+ when there are two consecutive loops,
+
+ | loop_0
+ | loop_1
+ | A[{0, +, 1}_1]
+ | endloop_1
+ | loop_2
+ | A[{0, +, 1}_2]
+ | endloop_2
+ | endloop_0
+
+ the dependence relation cannot be captured by the distance
+ abstraction. */
+ if (loop->next)
+ return false;
+
+ VEC_safe_push (loop_p, heap, *loop_nest, loop);
+ if (loop->inner)
+ return find_loop_nest_1 (loop->inner, loop_nest);
+ return true;
+}
+
+/* Return false when the LOOP is not well nested. Otherwise return
+ true and insert in LOOP_NEST the loops of the nest. LOOP_NEST will
+ contain the loops from the outermost to the innermost, as they will
+ appear in the classic distance vector. */
-/* This section contains all the entry points. */
+static bool
+find_loop_nest (struct loop *loop, VEC (loop_p, heap) **loop_nest)
+{
+ VEC_safe_push (loop_p, heap, *loop_nest, loop);
+ if (loop->inner)
+ return find_loop_nest_1 (loop->inner, loop_nest);
+ return true;
+}
/* Given a loop nest LOOP, the following vectors are returned:
- *DATAREFS is initialized to all the array elements contained in this loop,
- *DEPENDENCE_RELATIONS contains the relations between the data references,
- *CLASSIC_DIST contains the set of distance vectors,
- *CLASSIC_DIR contains the set of direction vectors. */
+ DATAREFS is initialized to all the array elements contained in this loop,
+ DEPENDENCE_RELATIONS contains the relations between the data references.
+ Compute read-read and self relations if
+ COMPUTE_SELF_AND_READ_READ_DEPENDENCES is TRUE. */
void
-compute_data_dependences_for_loop (unsigned nb_loops,
- struct loop *loop,
- varray_type *datarefs,
- varray_type *dependence_relations,
- varray_type *classic_dist,
- varray_type *classic_dir)
+compute_data_dependences_for_loop (struct loop *loop,
+ bool compute_self_and_read_read_dependences,
+ VEC (data_reference_p, heap) **datarefs,
+ VEC (ddr_p, heap) **dependence_relations)
{
- unsigned int i;
+ struct loop *loop_nest = loop;
+ VEC (loop_p, heap) *vloops = VEC_alloc (loop_p, heap, 3);
+
+ memset (&dependence_stats, 0, sizeof (dependence_stats));
- /* If one of the data references is not computable, give up without
- spending time to compute other dependences. */
- if (find_data_references_in_loop (loop, datarefs) == chrec_dont_know)
+ /* If the loop nest is not well formed, or one of the data references
+ is not computable, give up without spending time to compute other
+ dependences. */
+ if (!loop_nest
+ || !find_loop_nest (loop_nest, &vloops)
+ || find_data_references_in_loop (loop, datarefs) == chrec_dont_know)
{
struct data_dependence_relation *ddr;
/* Insert a single relation into dependence_relations:
chrec_dont_know. */
- ddr = initialize_data_dependence_relation (NULL, NULL);
- VARRAY_PUSH_GENERIC_PTR (*dependence_relations, ddr);
- build_classic_dist_vector (ddr, classic_dist, nb_loops, loop->num);
- build_classic_dir_vector (ddr, classic_dir, nb_loops, loop->num);
- return;
+ ddr = initialize_data_dependence_relation (NULL, NULL, vloops);
+ VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
}
+ else
+ compute_all_dependences (*datarefs, dependence_relations, vloops,
+ compute_self_and_read_read_dependences);
- compute_rw_wr_ww_dependences (*datarefs, dependence_relations);
-
- for (i = 0; i < VARRAY_ACTIVE_SIZE (*dependence_relations); i++)
+ if (dump_file && (dump_flags & TDF_STATS))
{
- struct data_dependence_relation *ddr;
- ddr = VARRAY_GENERIC_PTR (*dependence_relations, i);
- build_classic_dist_vector (ddr, classic_dist, nb_loops, loop->num);
- build_classic_dir_vector (ddr, classic_dir, nb_loops, loop->num);
- }
+ fprintf (dump_file, "Dependence tester statistics:\n");
+
+ fprintf (dump_file, "Number of dependence tests: %d\n",
+ dependence_stats.num_dependence_tests);
+ fprintf (dump_file, "Number of dependence tests classified dependent: %d\n",
+ dependence_stats.num_dependence_dependent);
+ fprintf (dump_file, "Number of dependence tests classified independent: %d\n",
+ dependence_stats.num_dependence_independent);
+ fprintf (dump_file, "Number of undetermined dependence tests: %d\n",
+ dependence_stats.num_dependence_undetermined);
+
+ fprintf (dump_file, "Number of subscript tests: %d\n",
+ dependence_stats.num_subscript_tests);
+ fprintf (dump_file, "Number of undetermined subscript tests: %d\n",
+ dependence_stats.num_subscript_undetermined);
+ fprintf (dump_file, "Number of same subscript function: %d\n",
+ dependence_stats.num_same_subscript_function);
+
+ fprintf (dump_file, "Number of ziv tests: %d\n",
+ dependence_stats.num_ziv);
+ fprintf (dump_file, "Number of ziv tests returning dependent: %d\n",
+ dependence_stats.num_ziv_dependent);
+ fprintf (dump_file, "Number of ziv tests returning independent: %d\n",
+ dependence_stats.num_ziv_independent);
+ fprintf (dump_file, "Number of ziv tests unimplemented: %d\n",
+ dependence_stats.num_ziv_unimplemented);
+
+ fprintf (dump_file, "Number of siv tests: %d\n",
+ dependence_stats.num_siv);
+ fprintf (dump_file, "Number of siv tests returning dependent: %d\n",
+ dependence_stats.num_siv_dependent);
+ fprintf (dump_file, "Number of siv tests returning independent: %d\n",
+ dependence_stats.num_siv_independent);
+ fprintf (dump_file, "Number of siv tests unimplemented: %d\n",
+ dependence_stats.num_siv_unimplemented);
+
+ fprintf (dump_file, "Number of miv tests: %d\n",
+ dependence_stats.num_miv);
+ fprintf (dump_file, "Number of miv tests returning dependent: %d\n",
+ dependence_stats.num_miv_dependent);
+ fprintf (dump_file, "Number of miv tests returning independent: %d\n",
+ dependence_stats.num_miv_independent);
+ fprintf (dump_file, "Number of miv tests unimplemented: %d\n",
+ dependence_stats.num_miv_unimplemented);
+ }
}
/* Entry point (for testing only). Analyze all the data references
- and the dependence relations.
+ and the dependence relations in LOOP.
The data references are computed first.
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. */
-
-void
-analyze_all_data_dependences (struct loops *loops)
+static void
+analyze_all_data_dependences (struct loop *loop)
{
unsigned int i;
- varray_type datarefs;
- varray_type dependence_relations;
- varray_type classic_dist, classic_dir;
int nb_data_refs = 10;
-
- VARRAY_GENERIC_PTR_INIT (classic_dist, 10, "classic_dist");
- VARRAY_GENERIC_PTR_INIT (classic_dir, 10, "classic_dir");
- VARRAY_GENERIC_PTR_INIT (datarefs, nb_data_refs, "datarefs");
- VARRAY_GENERIC_PTR_INIT (dependence_relations,
- nb_data_refs * nb_data_refs,
- "dependence_relations");
+ VEC (data_reference_p, heap) *datarefs =
+ VEC_alloc (data_reference_p, heap, nb_data_refs);
+ VEC (ddr_p, heap) *dependence_relations =
+ VEC_alloc (ddr_p, heap, nb_data_refs * nb_data_refs);
/* Compute DDs on the whole function. */
- compute_data_dependences_for_loop (loops->num, loops->parray[0],
- &datarefs, &dependence_relations,
- &classic_dist, &classic_dir);
+ compute_data_dependences_for_loop (loop, false, &datarefs,
+ &dependence_relations);
if (dump_file)
{
dump_data_dependence_relations (dump_file, dependence_relations);
fprintf (dump_file, "\n\n");
- }
-
- /* Don't dump distances in order to avoid to update the
- testsuite. */
- if (dump_file && (dump_flags & TDF_DETAILS))
- {
- for (i = 0; i < VARRAY_ACTIVE_SIZE (classic_dist); i++)
- {
- fprintf (dump_file, "DISTANCE_V (");
- print_lambda_vector (dump_file,
- VARRAY_GENERIC_PTR (classic_dist, i),
- loops->num);
- fprintf (dump_file, ")\n");
- }
- for (i = 0; i < VARRAY_ACTIVE_SIZE (classic_dir); i++)
- {
- fprintf (dump_file, "DIRECTION_V (");
- print_lambda_vector (dump_file,
- VARRAY_GENERIC_PTR (classic_dir, i),
- loops->num);
- fprintf (dump_file, ")\n");
- }
- fprintf (dump_file, "\n\n");
- }
- if (dump_file && (dump_flags & TDF_STATS))
- {
- unsigned nb_top_relations = 0;
- unsigned nb_bot_relations = 0;
- unsigned nb_basename_differ = 0;
- unsigned nb_chrec_relations = 0;
+ if (dump_flags & TDF_DETAILS)
+ dump_dist_dir_vectors (dump_file, dependence_relations);
- for (i = 0; i < VARRAY_ACTIVE_SIZE (dependence_relations); i++)
+ if (dump_flags & TDF_STATS)
{
+ unsigned nb_top_relations = 0;
+ unsigned nb_bot_relations = 0;
+ unsigned nb_basename_differ = 0;
+ unsigned nb_chrec_relations = 0;
struct data_dependence_relation *ddr;
- ddr = VARRAY_GENERIC_PTR (dependence_relations, i);
-
- if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr)))
- nb_top_relations++;
-
- else if (DDR_ARE_DEPENDENT (ddr) == chrec_known)
+
+ for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++)
{
- struct data_reference *a = DDR_A (ddr);
- struct data_reference *b = DDR_B (ddr);
- bool differ_p;
+ if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr)))
+ nb_top_relations++;
+
+ else if (DDR_ARE_DEPENDENT (ddr) == chrec_known)
+ {
+ struct data_reference *a = DDR_A (ddr);
+ struct data_reference *b = DDR_B (ddr);
+ bool differ_p;
- if (DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b)
- || (array_base_name_differ_p (a, b, &differ_p) && differ_p))
- nb_basename_differ++;
- else
- nb_bot_relations++;
- }
+ if ((DR_BASE_OBJECT (a) && DR_BASE_OBJECT (b)
+ && DR_NUM_DIMENSIONS (a) != DR_NUM_DIMENSIONS (b))
+ || (base_object_differ_p (a, b, &differ_p)
+ && differ_p))
+ nb_basename_differ++;
+ else
+ nb_bot_relations++;
+ }
- else
- nb_chrec_relations++;
- }
-
- fprintf (dump_file, "\n(\n");
- fprintf (dump_file, "%d\tnb_top_relations\n", nb_top_relations);
- fprintf (dump_file, "%d\tnb_bot_relations\n", nb_bot_relations);
- fprintf (dump_file, "%d\tnb_basename_differ\n", nb_basename_differ);
- fprintf (dump_file, "%d\tnb_distance_relations\n", (int) VARRAY_ACTIVE_SIZE (classic_dist));
- fprintf (dump_file, "%d\tnb_chrec_relations\n", nb_chrec_relations);
- fprintf (dump_file, "\n)\n");
+ else
+ nb_chrec_relations++;
+ }
- gather_stats_on_scev_database ();
+ gather_stats_on_scev_database ();
+ }
}
-
- varray_clear (dependence_relations);
- varray_clear (datarefs);
- varray_clear (classic_dist);
- varray_clear (classic_dir);
+
+ free_dependence_relations (dependence_relations);
+ free_data_refs (datarefs);
}
+/* Computes all the data dependences and check that the results of
+ several analyzers are the same. */
+
+void
+tree_check_data_deps (void)
+{
+ loop_iterator li;
+ struct loop *loop_nest;
+
+ FOR_EACH_LOOP (li, loop_nest, 0)
+ analyze_all_data_dependences (loop_nest);
+}
+
+/* Free the memory used by a data dependence relation DDR. */
+
+void
+free_dependence_relation (struct data_dependence_relation *ddr)
+{
+ if (ddr == NULL)
+ return;
+
+ if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE && DDR_SUBSCRIPTS (ddr))
+ free_subscripts (DDR_SUBSCRIPTS (ddr));
+
+ free (ddr);
+}
+
+/* Free the memory used by the data dependence relations from
+ DEPENDENCE_RELATIONS. */
+
+void
+free_dependence_relations (VEC (ddr_p, heap) *dependence_relations)
+{
+ unsigned int i;
+ struct data_dependence_relation *ddr;
+ VEC (loop_p, heap) *loop_nest = NULL;
+
+ for (i = 0; VEC_iterate (ddr_p, dependence_relations, i, ddr); i++)
+ {
+ if (ddr == NULL)
+ continue;
+ if (loop_nest == NULL)
+ loop_nest = DDR_LOOP_NEST (ddr);
+ else
+ gcc_assert (DDR_LOOP_NEST (ddr) == NULL
+ || DDR_LOOP_NEST (ddr) == loop_nest);
+ free_dependence_relation (ddr);
+ }
+
+ if (loop_nest)
+ VEC_free (loop_p, heap, loop_nest);
+ VEC_free (ddr_p, heap, dependence_relations);
+}
+
+/* Free the memory used by the data references from DATAREFS. */
+
+void
+free_data_refs (VEC (data_reference_p, heap) *datarefs)
+{
+ unsigned int i;
+ struct data_reference *dr;
+
+ for (i = 0; VEC_iterate (data_reference_p, datarefs, i, dr); i++)
+ free_data_ref (dr);
+ VEC_free (data_reference_p, heap, datarefs);
+}
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