tree-data-ref.c 113 KB
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/* Data references and dependences detectors.
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   Copyright (C) 2003, 2004, 2005 Free Software Foundation, Inc.
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   Contributed by Sebastian Pop <s.pop@laposte.net>

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Kelley Cook committed
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */
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/* This pass walks a given loop structure searching for array
   references.  The information about the array accesses is recorded
   in DATA_REFERENCE structures. 
   
   The basic test for determining the dependences is: 
   given two access functions chrec1 and chrec2 to a same array, and 
   x and y two vectors from the iteration domain, the same element of 
   the array is accessed twice at iterations x and y if and only if:
   |             chrec1 (x) == chrec2 (y).
   
   The goals of this analysis are:
   
   - to determine the independence: the relation between two
     independent accesses is qualified with the chrec_known (this
     information allows a loop parallelization),
     
   - when two data references access the same data, to qualify the
     dependence relation with classic dependence representations:
     
       - distance vectors
       - direction vectors
       - loop carried level dependence
       - polyhedron dependence
     or with the chains of recurrences based representation,
     
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   - to define a knowledge base for storing the data dependence 
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     information,
     
   - to define an interface to access this data.
   
   
   Definitions:
   
   - subscript: given two array accesses a subscript is the tuple
   composed of the access functions for a given dimension.  Example:
   Given A[f1][f2][f3] and B[g1][g2][g3], there are three subscripts:
   (f1, g1), (f2, g2), (f3, g3).

   - Diophantine equation: an equation whose coefficients and
   solutions are integer constants, for example the equation 
   |   3*x + 2*y = 1
   has an integer solution x = 1 and y = -1.
     
   References:
   
   - "Advanced Compilation for High Performance Computing" by Randy
   Allen and Ken Kennedy.
   http://citeseer.ist.psu.edu/goff91practical.html 
   
   - "Loop Transformations for Restructuring Compilers - The Foundations" 
   by Utpal Banerjee.

   
*/

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "ggc.h"
#include "tree.h"

/* These RTL headers are needed for basic-block.h.  */
#include "rtl.h"
#include "basic-block.h"
#include "diagnostic.h"
#include "tree-flow.h"
#include "tree-dump.h"
#include "timevar.h"
#include "cfgloop.h"
#include "tree-chrec.h"
#include "tree-data-ref.h"
#include "tree-scalar-evolution.h"
#include "tree-pass.h"

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static tree object_analysis (tree, tree, bool, struct data_reference **, 
			     tree *, tree *, tree *, tree *, tree *,
			     struct ptr_info_def **, subvar_t *);
static struct data_reference * init_data_ref (tree, tree, tree, tree, bool, 
					      tree, tree, tree, tree, tree, 
					      struct ptr_info_def *,
					      enum  data_ref_type);

/* Determine if PTR and DECL may alias, the result is put in ALIASED.
   Return FALSE if there is no type memory tag for PTR.
*/
static bool
ptr_decl_may_alias_p (tree ptr, tree decl, 
		      struct data_reference *ptr_dr, 
		      bool *aliased)
{
  tree tag;
   
  gcc_assert (TREE_CODE (ptr) == SSA_NAME && DECL_P (decl));

  tag = get_var_ann (SSA_NAME_VAR (ptr))->type_mem_tag;
  if (!tag)
    tag = DR_MEMTAG (ptr_dr);
  if (!tag)
    return false;
  
  *aliased = is_aliased_with (tag, decl);      
  return true;
}


/* Determine if two pointers may alias, the result is put in ALIASED.
   Return FALSE if there is no type 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, tag_b;

  tag_a = get_var_ann (SSA_NAME_VAR (ptr_a))->type_mem_tag;
  if (!tag_a)
    tag_a = DR_MEMTAG (dra);
  if (!tag_a)
    return false;
  tag_b = get_var_ann (SSA_NAME_VAR (ptr_b))->type_mem_tag;
  if (!tag_b)
    tag_b = DR_MEMTAG (drb);
  if (!tag_b)
    return false;
  *aliased = (tag_a == tag_b);
  return true;
}


/* Determine if BASE_A and BASE_B may alias, the result is put in ALIASED.
   Return FALSE if there is no type 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 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;
}


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/* This is the simplest data dependence test: determines whether the
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   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.  */
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static bool
base_object_differ_p (struct data_reference *a,
		      struct data_reference *b,
		      bool *differ_p)
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{
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  tree base_a = DR_BASE_OBJECT (a);
  tree base_b = DR_BASE_OBJECT (b);
  bool aliased;
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  if (!base_a || !base_b)
    return false;

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  /* Determine if same base.  Example: for the array accesses
     a[i], b[i] or pointer accesses *a, *b, bases are a, b.  */
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  if (base_a == base_b)
    {
      *differ_p = false;
      return true;
    }

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  /* For pointer based accesses, (*p)[i], (*q)[j], the bases are (*p)
     and (*q)  */
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  if (TREE_CODE (base_a) == INDIRECT_REF && TREE_CODE (base_b) == INDIRECT_REF
      && TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0))
    {
      *differ_p = false;
      return true;
    }

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  /* Record/union based accesses - s.a[i], t.b[j]. bases are s.a,t.b.  */ 
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  if (TREE_CODE (base_a) == COMPONENT_REF && TREE_CODE (base_b) == COMPONENT_REF
      && TREE_OPERAND (base_a, 0) == TREE_OPERAND (base_b, 0)
      && TREE_OPERAND (base_a, 1) == TREE_OPERAND (base_b, 1))
    {
      *differ_p = false;
      return true;
    }

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  /* Determine if different bases.  */
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  /* At this point we know that base_a != base_b.  However, pointer
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     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.  */
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  if (TREE_CODE (base_a) == VAR_DECL && TREE_CODE (base_b) == VAR_DECL)
    {
      *differ_p = true;
      return true;
    }

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  /* 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;
    }

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  /* Compare two record/union bases s.a and t.b: s != t or (a != b and
     s and t are not unions).  */
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  if (TREE_CODE (base_a) == COMPONENT_REF && TREE_CODE (base_b) == COMPONENT_REF
      && ((TREE_CODE (TREE_OPERAND (base_a, 0)) == VAR_DECL
           && TREE_CODE (TREE_OPERAND (base_b, 0)) == VAR_DECL
           && TREE_OPERAND (base_a, 0) != TREE_OPERAND (base_b, 0))
          || (TREE_CODE (TREE_TYPE (TREE_OPERAND (base_a, 0))) == RECORD_TYPE 
              && TREE_CODE (TREE_TYPE (TREE_OPERAND (base_b, 0))) == RECORD_TYPE
              && TREE_OPERAND (base_a, 1) != TREE_OPERAND (base_b, 1))))
    {
      *differ_p = true;
      return true;
    }

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  /* Compare a record/union access (b.c[i] or p->c[i]) and a pointer
     ((*q)[i]).  */
  if (record_ptr_differ_p (a, b) || record_ptr_differ_p (b, a))
    {
      *differ_p = true;
      return true;
    }

  /* Compare a record/union access (b.c[i] or p->c[i]) and an array access 
     (a[i]). In case of p->c[i] use alias analysis to verify that p is not
     pointing to a.  */
  if (record_array_differ_p (a, b) || record_array_differ_p (b, a))
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    {
      *differ_p = true;
      return true;
    }

  return false;
}
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/* Function base_addr_differ_p.

   This is the simplest data dependence test: determines whether the
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   data references DRA and DRB access the same array/region.  Returns
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   false when the property is not computable at compile time.
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   Otherwise return true, and DIFFER_P will record the result.

   The algorithm:   
   1. if (both DRA and DRB are represented as arrays)
          compare DRA.BASE_OBJECT and DRB.BASE_OBJECT
   2. else if (both DRA and DRB are represented as pointers)
          try to prove that DRA.FIRST_LOCATION == DRB.FIRST_LOCATION
   3. else if (DRA and DRB are represented differently or 2. fails)
          only try to prove that the bases are surely different
*/
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static bool
base_addr_differ_p (struct data_reference *dra,
		    struct data_reference *drb,
		    bool *differ_p)
{
  tree addr_a = DR_BASE_ADDRESS (dra);
  tree addr_b = DR_BASE_ADDRESS (drb);
  tree type_a, type_b;
  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));
  
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  /* 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)
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    return base_object_differ_p (dra, drb, differ_p);

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  /* 2. else if (both DRA and DRB are represented as pointers)
	    try to prove that DRA.FIRST_LOCATION == DRB.FIRST_LOCATION.  */
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  /* 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.  */
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  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))))
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    {
      /* Compare offsets.  */
      tree offset_a = DR_OFFSET (dra); 
      tree offset_b = DR_OFFSET (drb);
      
      STRIP_NOPS (offset_a);
      STRIP_NOPS (offset_b);

      /* FORNOW: we only compare offsets that are MULT_EXPR, i.e., we don't handle
	 PLUS_EXPR.  */
      if ((offset_a == offset_b)
	  || (TREE_CODE (offset_a) == MULT_EXPR 
	      && TREE_CODE (offset_b) == MULT_EXPR
	      && TREE_OPERAND (offset_a, 0) == TREE_OPERAND (offset_b, 0)
	      && TREE_OPERAND (offset_a, 1) == TREE_OPERAND (offset_b, 1)))
	{
	  *differ_p = false;
	  return true;
	}
    }

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  /*  3. else if (DRA and DRB are represented differently or 2. fails) 
              only try to prove that the bases are surely different.  */

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  /* Apply alias analysis.  */
  if (may_alias_p (addr_a, addr_b, dra, drb, &aliased) && !aliased)
    {
      *differ_p = true;
      return true;
    }
  
  /* An instruction writing through a restricted pointer is "independent" of any 
     instruction reading or writing through a different pointer, in the same 
     block/scope.  */
  else if ((TYPE_RESTRICT (type_a) && !DR_IS_READ (dra))
      || (TYPE_RESTRICT (type_b) && !DR_IS_READ (drb)))
    {
      *differ_p = true;
      return true;
    }
  return false;
}


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/* Returns true iff A divides B.  */

static inline bool 
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tree_fold_divides_p (tree a, 
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		     tree b)
{
  /* Determines whether (A == gcd (A, B)).  */
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  return tree_int_cst_equal (a, tree_fold_gcd (a, b));
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}

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/* Compute the greatest common denominator of two numbers using
   Euclid's algorithm.  */
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static int 
gcd (int a, int b)
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{
  
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  int x, y, z;
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  x = abs (a);
  y = abs (b);

  while (x>0)
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    {
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      z = y % x;
      y = x;
      x = z;
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    }
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  return (y);
}

/* Returns true iff A divides B.  */

static inline bool 
int_divides_p (int a, int b)
{
  return ((b % a) == 0);
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}



/* Dump into FILE all the data references from DATAREFS.  */ 

void 
dump_data_references (FILE *file, 
		      varray_type datarefs)
{
  unsigned int i;
  
  for (i = 0; i < VARRAY_ACTIVE_SIZE (datarefs); i++)
    dump_data_reference (file, VARRAY_GENERIC_PTR (datarefs, i));
}

/* Dump into FILE all the dependence relations from DDR.  */ 

void 
dump_data_dependence_relations (FILE *file, 
				varray_type ddr)
{
  unsigned int i;
  
  for (i = 0; i < VARRAY_ACTIVE_SIZE (ddr); i++)
    dump_data_dependence_relation (file, VARRAY_GENERIC_PTR (ddr, i));
}

/* Dump function for a DATA_REFERENCE structure.  */

void 
dump_data_reference (FILE *outf, 
		     struct data_reference *dr)
{
  unsigned int i;
  
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  fprintf (outf, "(Data Ref: \n  stmt: ");
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  print_generic_stmt (outf, DR_STMT (dr), 0);
  fprintf (outf, "  ref: ");
  print_generic_stmt (outf, DR_REF (dr), 0);
  fprintf (outf, "  base_name: ");
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  print_generic_stmt (outf, DR_BASE_OBJECT (dr), 0);
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  for (i = 0; i < DR_NUM_DIMENSIONS (dr); i++)
    {
      fprintf (outf, "  Access function %d: ", i);
      print_generic_stmt (outf, DR_ACCESS_FN (dr, i), 0);
    }
  fprintf (outf, ")\n");
}

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/* Dump function for a SUBSCRIPT structure.  */

void 
dump_subscript (FILE *outf, struct subscript *subscript)
{
  tree chrec = SUB_CONFLICTS_IN_A (subscript);

  fprintf (outf, "\n (subscript \n");
  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 (subscript);
      fprintf (outf, "  last_conflict: ");
      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 (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");
}

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/* Dump function for a DATA_DEPENDENCE_RELATION structure.  */

void 
dump_data_dependence_relation (FILE *outf, 
			       struct data_dependence_relation *ddr)
{
  struct data_reference *dra, *drb;
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  dra = DDR_A (ddr);
  drb = DDR_B (ddr);
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  fprintf (outf, "(Data Dep: \n");
  if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know)
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    fprintf (outf, "    (don't know)\n");
  
  else if (DDR_ARE_DEPENDENT (ddr) == chrec_known)
    fprintf (outf, "    (no dependence)\n");
  
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  else if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
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    {
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      unsigned int i;
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      for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
	{
	  fprintf (outf, "  access_fn_A: ");
	  print_generic_stmt (outf, DR_ACCESS_FN (dra, i), 0);
	  fprintf (outf, "  access_fn_B: ");
	  print_generic_stmt (outf, DR_ACCESS_FN (drb, i), 0);
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	  dump_subscript (outf, DDR_SUBSCRIPT (ddr, i));
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	}
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      if (DDR_DIST_VECT (ddr))
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	{
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	  fprintf (outf, "  distance_vect: ");
	  print_lambda_vector (outf, DDR_DIST_VECT (ddr), DDR_SIZE_VECT (ddr));
	}
      if (DDR_DIR_VECT (ddr))
	{
	  fprintf (outf, "  direction_vect: ");
	  print_lambda_vector (outf, DDR_DIR_VECT (ddr), DDR_SIZE_VECT (ddr));
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	}
    }

  fprintf (outf, ")\n");
}



/* Dump function for a DATA_DEPENDENCE_DIRECTION structure.  */

void
dump_data_dependence_direction (FILE *file, 
				enum data_dependence_direction dir)
{
  switch (dir)
    {
    case dir_positive: 
      fprintf (file, "+");
      break;
      
    case dir_negative:
      fprintf (file, "-");
      break;
      
    case dir_equal:
      fprintf (file, "=");
      break;
      
    case dir_positive_or_negative:
      fprintf (file, "+-");
      break;
      
    case dir_positive_or_equal: 
      fprintf (file, "+=");
      break;
      
    case dir_negative_or_equal: 
      fprintf (file, "-=");
      break;
      
    case dir_star: 
      fprintf (file, "*"); 
      break;
      
    default: 
      break;
    }
}

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/* 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, varray_type ddrs)
{
  unsigned int i;

  for (i = 0; i < VARRAY_ACTIVE_SIZE (ddrs); i++)
    {
      struct data_dependence_relation *ddr = 
	(struct data_dependence_relation *) 
	VARRAY_GENERIC_PTR (ddrs, i);
      if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE
	  && DDR_AFFINE_P (ddr))
	{
	  fprintf (file, "DISTANCE_V (");
	  print_lambda_vector (file, DDR_DIST_VECT (ddr), DDR_SIZE_VECT (ddr));
	  fprintf (file, ")\n");
	  fprintf (file, "DIRECTION_V (");
	  print_lambda_vector (file, DDR_DIR_VECT (ddr), DDR_SIZE_VECT (ddr));
	  fprintf (file, ")\n");
	}
    }
  fprintf (file, "\n\n");
}

/* Dumps the data dependence relations DDRS in FILE.  */

void 
dump_ddrs (FILE *file, varray_type ddrs)
{
  unsigned int i;

  for (i = 0; i < VARRAY_ACTIVE_SIZE (ddrs); i++)
    {
      struct data_dependence_relation *ddr = 
	(struct data_dependence_relation *) 
	VARRAY_GENERIC_PTR (ddrs, i);
      dump_data_dependence_relation (file, ddr);
    }
  fprintf (file, "\n\n");
}

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/* Estimate the number of iterations from the size of the data and the
   access functions.  */

static void
estimate_niter_from_size_of_data (struct loop *loop, 
				  tree opnd0, 
				  tree access_fn, 
				  tree stmt)
{
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  tree estimation = NULL_TREE;
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  tree array_size, data_size, element_size;
  tree init, step;

  init = initial_condition (access_fn);
  step = evolution_part_in_loop_num (access_fn, loop->num);

  array_size = TYPE_SIZE (TREE_TYPE (opnd0));
  element_size = TYPE_SIZE (TREE_TYPE (TREE_TYPE (opnd0)));
  if (array_size == NULL_TREE 
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      || TREE_CODE (array_size) != INTEGER_CST
      || TREE_CODE (element_size) != INTEGER_CST)
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    return;

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  data_size = fold_build2 (EXACT_DIV_EXPR, integer_type_node,
			   array_size, element_size);
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  if (init != NULL_TREE
      && step != NULL_TREE
      && TREE_CODE (init) == INTEGER_CST
      && TREE_CODE (step) == INTEGER_CST)
    {
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      tree i_plus_s = fold_build2 (PLUS_EXPR, integer_type_node, init, step);
      tree sign = fold_build2 (GT_EXPR, boolean_type_node, i_plus_s, init);

      if (sign == boolean_true_node)
	estimation = fold_build2 (CEIL_DIV_EXPR, integer_type_node,
				  fold_build2 (MINUS_EXPR, integer_type_node,
					       data_size, init), step);

      /* When the step is negative, as in PR23386: (init = 3, step =
	 0ffffffff, data_size = 100), we have to compute the
	 estimation as ceil_div (init, 0 - step) + 1.  */
      else if (sign == boolean_false_node)
	estimation = 
	  fold_build2 (PLUS_EXPR, integer_type_node,
		       fold_build2 (CEIL_DIV_EXPR, integer_type_node,
				    init,
				    fold_build2 (MINUS_EXPR, unsigned_type_node,
						 integer_zero_node, step)),
		       integer_one_node);

      if (estimation)
	record_estimate (loop, estimation, boolean_true_node, stmt);
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    }
}

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/* Given an ARRAY_REF node REF, records its access functions.
   Example: given A[i][3], record in ACCESS_FNS the opnd1 function,
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   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:
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   "A".  */

static tree
analyze_array_indexes (struct loop *loop,
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		       VEC(tree,heap) **access_fns, 
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		       tree ref, tree stmt)
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{
  tree opnd0, opnd1;
  tree access_fn;
  
  opnd0 = TREE_OPERAND (ref, 0);
  opnd1 = TREE_OPERAND (ref, 1);
  
  /* The detection of the evolution function for this data access is
     postponed until the dependence test.  This lazy strategy avoids
     the computation of access functions that are of no interest for
     the optimizers.  */
  access_fn = instantiate_parameters 
    (loop, analyze_scalar_evolution (loop, opnd1));
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  if (chrec_contains_undetermined (loop->estimated_nb_iterations))
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    estimate_niter_from_size_of_data (loop, opnd0, access_fn, stmt);
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  VEC_safe_push (tree, heap, *access_fns, access_fn);
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  /* Recursively record other array access functions.  */
  if (TREE_CODE (opnd0) == ARRAY_REF)
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    return analyze_array_indexes (loop, access_fns, opnd0, stmt);
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  /* Return the base name of the data access.  */
  else
    return opnd0;
}

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/* For a data reference REF contained in the statement STMT, initialize
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   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.  */

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struct data_reference *
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analyze_array (tree stmt, tree ref, bool is_read)
{
  struct data_reference *res;
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  VEC(tree,heap) *acc_fns;
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  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fprintf (dump_file, "(analyze_array \n");
      fprintf (dump_file, "  (ref = ");
      print_generic_stmt (dump_file, ref, 0);
      fprintf (dump_file, ")\n");
    }
  
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  res = xmalloc (sizeof (struct data_reference));
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  DR_STMT (res) = stmt;
  DR_REF (res) = ref;
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  acc_fns = VEC_alloc (tree, heap, 3);
  DR_BASE_OBJECT (res) = analyze_array_indexes 
    (loop_containing_stmt (stmt), &acc_fns, ref, stmt);
  DR_TYPE (res) = ARRAY_REF_TYPE;
  DR_SET_ACCESS_FNS (res, acc_fns);
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  DR_IS_READ (res) = is_read;
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  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;
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  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, ")\n");
  
  return res;
}

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/* Analyze an indirect memory reference, REF, that comes from STMT.
   IS_READ is true if this is an indirect load, and false if it is
   an indirect store.
   Return a new data reference structure representing the indirect_ref, or
   NULL if we cannot describe the access function.  */
  
static struct data_reference *
analyze_indirect_ref (tree stmt, tree ref, bool is_read) 
{
  struct loop *loop = loop_containing_stmt (stmt);
  tree ptr_ref = TREE_OPERAND (ref, 0);
  tree access_fn = analyze_scalar_evolution (loop, ptr_ref);
  tree init = initial_condition_in_loop_num (access_fn, loop->num);
  tree base_address = NULL_TREE, evolution, step = NULL_TREE;
  struct ptr_info_def *ptr_info = NULL;

  if (TREE_CODE (ptr_ref) == SSA_NAME)
    ptr_info = SSA_NAME_PTR_INFO (ptr_ref);

  STRIP_NOPS (init);   
  if (access_fn == chrec_dont_know || !init || init == chrec_dont_know)
    {
      if (dump_file && (dump_flags & TDF_DETAILS))
	{
	  fprintf (dump_file, "\nBad access function of ptr: ");
	  print_generic_expr (dump_file, ref, TDF_SLIM);
	  fprintf (dump_file, "\n");
	}
      return NULL;
    }

  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fprintf (dump_file, "\nAccess function of ptr: ");
      print_generic_expr (dump_file, access_fn, TDF_SLIM);
      fprintf (dump_file, "\n");
    }

  if (!expr_invariant_in_loop_p (loop, init))
    {
    if (dump_file && (dump_flags & TDF_DETAILS))
	fprintf (dump_file, "\ninitial condition is not loop invariant.\n");	
    }
  else
    {
      base_address = init;
      evolution = evolution_part_in_loop_num (access_fn, loop->num);
      if (evolution != chrec_dont_know)
	{       
	  if (!evolution)
	    step = ssize_int (0);
	  else  
	    {
	      if (TREE_CODE (evolution) == INTEGER_CST)
		step = fold_convert (ssizetype, evolution);
	      else
		if (dump_file && (dump_flags & TDF_DETAILS))
		  fprintf (dump_file, "\nnon constant step for ptr access.\n");	
	    }
	}
      else
	if (dump_file && (dump_flags & TDF_DETAILS))
	  fprintf (dump_file, "\nunknown evolution of ptr.\n");	
    }
  return init_data_ref (stmt, ref, NULL_TREE, access_fn, is_read, base_address, 
			NULL_TREE, step, NULL_TREE, NULL_TREE, 
			ptr_info, POINTER_REF_TYPE);
}

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/* For a data reference REF contained in the statement STMT, initialize
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   a DATA_REFERENCE structure, and return it.  */

struct data_reference *
init_data_ref (tree stmt, 
	       tree ref,
	       tree base,
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	       tree access_fn,
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	       bool is_read,
	       tree base_address,
	       tree init_offset,
	       tree step,
	       tree misalign,
	       tree memtag,
               struct ptr_info_def *ptr_info,
	       enum data_ref_type type)
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{
  struct data_reference *res;
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  VEC(tree,heap) *acc_fns;
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  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fprintf (dump_file, "(init_data_ref \n");
      fprintf (dump_file, "  (ref = ");
      print_generic_stmt (dump_file, ref, 0);
      fprintf (dump_file, ")\n");
    }
  
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  res = xmalloc (sizeof (struct data_reference));
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  DR_STMT (res) = stmt;
  DR_REF (res) = ref;
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  DR_BASE_OBJECT (res) = base;
  DR_TYPE (res) = type;
  acc_fns = VEC_alloc (tree, heap, 3);
  DR_SET_ACCESS_FNS (res, acc_fns);
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  VEC_quick_push (tree, DR_ACCESS_FNS (res), access_fn);
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  DR_IS_READ (res) = is_read;
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  DR_BASE_ADDRESS (res) = base_address;
  DR_OFFSET (res) = init_offset;
  DR_INIT (res) = NULL_TREE;
  DR_STEP (res) = step;
  DR_OFFSET_MISALIGNMENT (res) = misalign;
  DR_MEMTAG (res) = memtag;
  DR_PTR_INFO (res) = ptr_info;
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  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, ")\n");
  
  return res;
}



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/* Function strip_conversions

   Strip conversions that don't narrow the mode.  */

static tree 
strip_conversion (tree expr)
{
  tree to, ti, oprnd0;
  
  while (TREE_CODE (expr) == NOP_EXPR || TREE_CODE (expr) == CONVERT_EXPR)
    {
      to = TREE_TYPE (expr);
      oprnd0 = TREE_OPERAND (expr, 0);
      ti = TREE_TYPE (oprnd0);
 
      if (!INTEGRAL_TYPE_P (to) || !INTEGRAL_TYPE_P (ti))
	return NULL_TREE;
      if (GET_MODE_SIZE (TYPE_MODE (to)) < GET_MODE_SIZE (TYPE_MODE (ti)))
	return NULL_TREE;
      
      expr = oprnd0;
    }
  return expr; 
}


/* Function analyze_offset_expr

   Given an offset expression EXPR received from get_inner_reference, analyze
   it and create an expression for INITIAL_OFFSET by substituting the variables 
   of EXPR with initial_condition of the corresponding access_fn in the loop. 
   E.g., 
      for i
         for (j = 3; j < N; j++)
            a[j].b[i][j] = 0;
	 
   For a[j].b[i][j], EXPR will be 'i * C_i + j * C_j + C'. 'i' cannot be 
   substituted, since its access_fn in the inner loop is i. 'j' will be 
   substituted with 3. An INITIAL_OFFSET will be 'i * C_i + C`', where
   C` =  3 * C_j + C.

   Compute MISALIGN (the misalignment of the data reference initial access from
   its base). Misalignment can be calculated only if all the variables can be 
   substituted with constants, otherwise, we record maximum possible alignment
   in ALIGNED_TO. In the above example, since 'i' cannot be substituted, MISALIGN 
   will be NULL_TREE, and the biggest divider of C_i (a power of 2) will be 
   recorded in ALIGNED_TO.

   STEP is an evolution of the data reference in this loop in bytes.
   In the above example, STEP is C_j.

   Return FALSE, if the analysis fails, e.g., there is no access_fn for a 
   variable. In this case, all the outputs (INITIAL_OFFSET, MISALIGN, ALIGNED_TO
   and STEP) are NULL_TREEs. Otherwise, return TRUE.

*/

static bool
analyze_offset_expr (tree expr, 
		     struct loop *loop, 
		     tree *initial_offset,
		     tree *misalign,
		     tree *aligned_to,
		     tree *step)
{
  tree oprnd0;
  tree oprnd1;
  tree left_offset = ssize_int (0);
  tree right_offset = ssize_int (0);
  tree left_misalign = ssize_int (0);
  tree right_misalign = ssize_int (0);
  tree left_step = ssize_int (0);
  tree right_step = ssize_int (0);
  enum tree_code code;
  tree init, evolution;
  tree left_aligned_to = NULL_TREE, right_aligned_to = NULL_TREE;

  *step = NULL_TREE;
  *misalign = NULL_TREE;
  *aligned_to = NULL_TREE;  
  *initial_offset = NULL_TREE;

  /* Strip conversions that don't narrow the mode.  */
  expr = strip_conversion (expr);
  if (!expr)
    return false;

  /* Stop conditions:
     1. Constant.  */
  if (TREE_CODE (expr) == INTEGER_CST)
    {
      *initial_offset = fold_convert (ssizetype, expr);
      *misalign = fold_convert (ssizetype, expr);      
      *step = ssize_int (0);
      return true;
    }

  /* 2. Variable. Try to substitute with initial_condition of the corresponding
     access_fn in the current loop.  */
  if (SSA_VAR_P (expr))
    {
      tree access_fn = analyze_scalar_evolution (loop, expr);

      if (access_fn == chrec_dont_know)
	/* No access_fn.  */
	return false;

      init = initial_condition_in_loop_num (access_fn, loop->num);
      if (init == expr && !expr_invariant_in_loop_p (loop, init))
	/* Not enough information: may be not loop invariant.  
	   E.g., for a[b[i]], we get a[D], where D=b[i]. EXPR is D, its 
	   initial_condition is D, but it depends on i - loop's induction
	   variable.  */	  
	return false;

      evolution = evolution_part_in_loop_num (access_fn, loop->num);
      if (evolution && TREE_CODE (evolution) != INTEGER_CST)
	/* Evolution is not constant.  */
	return false;

      if (TREE_CODE (init) == INTEGER_CST)
	*misalign = fold_convert (ssizetype, init);
      else
	/* Not constant, misalignment cannot be calculated.  */
	*misalign = NULL_TREE;

      *initial_offset = fold_convert (ssizetype, init); 

      *step = evolution ? fold_convert (ssizetype, evolution) : ssize_int (0);
      return true;      
    }

  /* Recursive computation.  */
  if (!BINARY_CLASS_P (expr))
    {
      /* We expect to get binary expressions (PLUS/MINUS and MULT).  */
      if (dump_file && (dump_flags & TDF_DETAILS))
        {
	  fprintf (dump_file, "\nNot binary expression ");
          print_generic_expr (dump_file, expr, TDF_SLIM);
	  fprintf (dump_file, "\n");
	}
      return false;
    }
  oprnd0 = TREE_OPERAND (expr, 0);
  oprnd1 = TREE_OPERAND (expr, 1);

  if (!analyze_offset_expr (oprnd0, loop, &left_offset, &left_misalign, 
			    &left_aligned_to, &left_step)
      || !analyze_offset_expr (oprnd1, loop, &right_offset, &right_misalign, 
			       &right_aligned_to, &right_step))
    return false;

  /* The type of the operation: plus, minus or mult.  */
  code = TREE_CODE (expr);
  switch (code)
    {
    case MULT_EXPR:
      if (TREE_CODE (right_offset) != INTEGER_CST)
	/* RIGHT_OFFSET can be not constant. For example, for arrays of variable 
	   sized types. 
	   FORNOW: We don't support such cases.  */
	return false;

      /* Strip conversions that don't narrow the mode.  */
      left_offset = strip_conversion (left_offset);      
      if (!left_offset)
	return false;      
      /* Misalignment computation.  */
      if (SSA_VAR_P (left_offset))
	{
	  /* If the left side contains variables that can't be substituted with 
	     constants, the misalignment is unknown. However, if the right side 
	     is a multiple of some alignment, we know that the expression is
	     aligned to it. Therefore, we record such maximum possible value.
	   */
	  *misalign = NULL_TREE;
	  *aligned_to = ssize_int (highest_pow2_factor (right_offset));
	}
      else 
	{
	  /* The left operand was successfully substituted with constant.  */	  
	  if (left_misalign)
	    {
	      /* In case of EXPR '(i * C1 + j) * C2', LEFT_MISALIGN is 
		 NULL_TREE.  */
	      *misalign  = size_binop (code, left_misalign, right_misalign);
	      if (left_aligned_to && right_aligned_to)
		*aligned_to = size_binop (MIN_EXPR, left_aligned_to, 
					  right_aligned_to);
	      else 
		*aligned_to = left_aligned_to ? 
		  left_aligned_to : right_aligned_to;
	    }
	  else
	    *misalign = NULL_TREE; 
	}

      /* Step calculation.  */
      /* Multiply the step by the right operand.  */
      *step  = size_binop (MULT_EXPR, left_step, right_offset);
      break;
   
    case PLUS_EXPR:
    case MINUS_EXPR:
      /* Combine the recursive calculations for step and misalignment.  */
      *step = size_binop (code, left_step, right_step);

      /* Unknown alignment.  */
      if ((!left_misalign && !left_aligned_to)
	  || (!right_misalign && !right_aligned_to))
	{
	  *misalign = NULL_TREE;
	  *aligned_to = NULL_TREE;
	  break;
	}

      if (left_misalign && right_misalign)
	*misalign = size_binop (code, left_misalign, right_misalign);
      else
	*misalign = left_misalign ? left_misalign : right_misalign;

      if (left_aligned_to && right_aligned_to)
	*aligned_to = size_binop (MIN_EXPR, left_aligned_to, right_aligned_to);
      else 
	*aligned_to = left_aligned_to ? left_aligned_to : right_aligned_to;

      break;

    default:
      gcc_unreachable ();
    }

  /* Compute offset.  */
  *initial_offset = fold_convert (ssizetype, 
				  fold_build2 (code, TREE_TYPE (left_offset), 
					       left_offset, 
					       right_offset));
  return true;
}

/* Function address_analysis

   Return the BASE of the address expression EXPR.
   Also compute the OFFSET from BASE, MISALIGN and STEP.

   Input:
   EXPR - the address expression that is being analyzed
   STMT - the statement that contains EXPR or its original memory reference
   IS_READ - TRUE if STMT reads from EXPR, FALSE if writes to EXPR
   DR - data_reference struct for the original memory reference

   Output:
   BASE (returned value) - the base of the data reference EXPR.
   INITIAL_OFFSET - initial offset of EXPR from BASE (an expression)
   MISALIGN - offset of EXPR from BASE in bytes (a constant) or NULL_TREE if the
              computation is impossible 
   ALIGNED_TO - maximum alignment of EXPR or NULL_TREE if MISALIGN can be 
                calculated (doesn't depend on variables)
   STEP - evolution of EXPR in the loop
 
   If something unexpected is encountered (an unsupported form of data-ref),
   then NULL_TREE is returned.  
 */

static tree
address_analysis (tree expr, tree stmt, bool is_read, struct data_reference *dr, 
		  tree *offset, tree *misalign, tree *aligned_to, tree *step)
{
  tree oprnd0, oprnd1, base_address, offset_expr, base_addr0, base_addr1;
  tree address_offset = ssize_int (0), address_misalign = ssize_int (0);
  tree dummy, address_aligned_to = NULL_TREE;
  struct ptr_info_def *dummy1;
  subvar_t dummy2;

  switch (TREE_CODE (expr))
    {
    case PLUS_EXPR:
    case MINUS_EXPR:
      /* EXPR is of form {base +/- offset} (or {offset +/- base}).  */
      oprnd0 = TREE_OPERAND (expr, 0);
      oprnd1 = TREE_OPERAND (expr, 1);

      STRIP_NOPS (oprnd0);
      STRIP_NOPS (oprnd1);
      
      /* Recursively try to find the base of the address contained in EXPR.
	 For offset, the returned base will be NULL.  */
      base_addr0 = address_analysis (oprnd0, stmt, is_read, dr, &address_offset, 
				     &address_misalign, &address_aligned_to, 
				     step);

      base_addr1 = address_analysis (oprnd1, stmt, is_read,  dr, &address_offset, 
				     &address_misalign, &address_aligned_to, 
				     step);

      /* We support cases where only one of the operands contains an 
	 address.  */
      if ((base_addr0 && base_addr1) || (!base_addr0 && !base_addr1))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, 
		    "\neither more than one address or no addresses in expr ");
	      print_generic_expr (dump_file, expr, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }	
	  return NULL_TREE;
	}

      /* To revert STRIP_NOPS.  */
      oprnd0 = TREE_OPERAND (expr, 0);
      oprnd1 = TREE_OPERAND (expr, 1);
      
      offset_expr = base_addr0 ? 
	fold_convert (ssizetype, oprnd1) : fold_convert (ssizetype, oprnd0);

      /* EXPR is of form {base +/- offset} (or {offset +/- base}). If offset is 
	 a number, we can add it to the misalignment value calculated for base,
	 otherwise, misalignment is NULL.  */
      if (TREE_CODE (offset_expr) == INTEGER_CST && address_misalign)
	{
	  *misalign = size_binop (TREE_CODE (expr), address_misalign, 
				  offset_expr);
	  *aligned_to = address_aligned_to;
	}
      else
	{
	  *misalign = NULL_TREE;
	  *aligned_to = NULL_TREE;
	}

      /* Combine offset (from EXPR {base + offset}) with the offset calculated
	 for base.  */
      *offset = size_binop (TREE_CODE (expr), address_offset, offset_expr);
      return base_addr0 ? base_addr0 : base_addr1;

    case ADDR_EXPR:
      base_address = object_analysis (TREE_OPERAND (expr, 0), stmt, is_read, 
				      &dr, offset, misalign, aligned_to, step, 
				      &dummy, &dummy1, &dummy2);
      return base_address;

    case SSA_NAME:
      if (!POINTER_TYPE_P (TREE_TYPE (expr)))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nnot pointer SSA_NAME ");
	      print_generic_expr (dump_file, expr, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }	
	  return NULL_TREE;
	}
      *aligned_to = ssize_int (TYPE_ALIGN_UNIT (TREE_TYPE (TREE_TYPE (expr))));
      *misalign = ssize_int (0);
      *offset = ssize_int (0);
      *step = ssize_int (0);
      return expr;
      
    default:
      return NULL_TREE;
    }
}


/* Function object_analysis

   Create a data-reference structure DR for MEMREF.
   Return the BASE of the data reference MEMREF if the analysis is possible.
   Also compute the INITIAL_OFFSET from BASE, MISALIGN and STEP.
   E.g., for EXPR a.b[i] + 4B, BASE is a, and OFFSET is the overall offset  
   'a.b[i] + 4B' from a (can be an expression), MISALIGN is an OFFSET 
   instantiated with initial_conditions of access_functions of variables, 
   and STEP is the evolution of the DR_REF in this loop.
   
   Function get_inner_reference is used for the above in case of ARRAY_REF and
   COMPONENT_REF.

   The structure of the function is as follows:
   Part 1:
   Case 1. For handled_component_p refs 
          1.1 build data-reference structure for MEMREF
          1.2 call get_inner_reference
            1.2.1 analyze offset expr received from get_inner_reference
          (fall through with BASE)
   Case 2. For declarations 
          2.1 set MEMTAG
   Case 3. For INDIRECT_REFs 
          3.1 build data-reference structure for MEMREF
	  3.2 analyze evolution and initial condition of MEMREF
	  3.3 set data-reference structure for MEMREF
          3.4 call address_analysis to analyze INIT of the access function
	  3.5 extract memory tag

   Part 2:
   Combine the results of object and address analysis to calculate 
   INITIAL_OFFSET, STEP and misalignment info.   

   Input:
   MEMREF - the memory reference that is being analyzed
   STMT - the statement that contains MEMREF
   IS_READ - TRUE if STMT reads from MEMREF, FALSE if writes to MEMREF
   
   Output:
   BASE_ADDRESS (returned value) - the base address of the data reference MEMREF
                                   E.g, if MEMREF is a.b[k].c[i][j] the returned
			           base is &a.
   DR - data_reference struct for MEMREF
   INITIAL_OFFSET - initial offset of MEMREF from BASE (an expression)
   MISALIGN - offset of MEMREF from BASE in bytes (a constant) modulo alignment of 
              ALIGNMENT or NULL_TREE if the computation is impossible
   ALIGNED_TO - maximum alignment of EXPR or NULL_TREE if MISALIGN can be 
                calculated (doesn't depend on variables)
   STEP - evolution of the DR_REF in the loop
   MEMTAG - memory tag for aliasing purposes
   PTR_INFO - NULL or points-to aliasing info from a pointer SSA_NAME
   SUBVARS - Sub-variables of the variable

   If the analysis of MEMREF evolution in the loop fails, NULL_TREE is returned, 
   but DR can be created anyway.
   
*/
 
static tree
object_analysis (tree memref, tree stmt, bool is_read, 
		 struct data_reference **dr, tree *offset, tree *misalign, 
		 tree *aligned_to, tree *step, tree *memtag,
		 struct ptr_info_def **ptr_info, subvar_t *subvars)
{
  tree base = NULL_TREE, base_address = NULL_TREE;
  tree object_offset = ssize_int (0), object_misalign = ssize_int (0);
  tree object_step = ssize_int (0), address_step = ssize_int (0);
  tree address_offset = ssize_int (0), address_misalign = ssize_int (0);
  HOST_WIDE_INT pbitsize, pbitpos;
  tree poffset, bit_pos_in_bytes;
  enum machine_mode pmode;
  int punsignedp, pvolatilep;
  tree ptr_step = ssize_int (0), ptr_init = NULL_TREE;
  struct loop *loop = loop_containing_stmt (stmt);
  struct data_reference *ptr_dr = NULL;
  tree object_aligned_to = NULL_TREE, address_aligned_to = NULL_TREE;

 *ptr_info = NULL;

  /* Part 1:  */
  /* Case 1. handled_component_p refs.  */
  if (handled_component_p (memref))
    {
      /* 1.1 build data-reference structure for MEMREF.  */
      /* TODO: handle COMPONENT_REFs.  */
      if (!(*dr))
	{ 
	  if (TREE_CODE (memref) == ARRAY_REF)
	    *dr = analyze_array (stmt, memref, is_read);	  
	  else
	    {
	      /* FORNOW.  */
	      if (dump_file && (dump_flags & TDF_DETAILS))
		{
		  fprintf (dump_file, "\ndata-ref of unsupported type ");
		  print_generic_expr (dump_file, memref, TDF_SLIM);
		  fprintf (dump_file, "\n");
		}
	      return NULL_TREE;
	    }
	}

      /* 1.2 call get_inner_reference.  */
      /* Find the base and the offset from it.  */
      base = get_inner_reference (memref, &pbitsize, &pbitpos, &poffset,
				  &pmode, &punsignedp, &pvolatilep, false);
      if (!base)
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nfailed to get inner ref for ");
	      print_generic_expr (dump_file, memref, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }	  
	  return NULL_TREE;
	}

      /* 1.2.1 analyze offset expr received from get_inner_reference.  */
      if (poffset 
	  && !analyze_offset_expr (poffset, loop, &object_offset, 
				   &object_misalign, &object_aligned_to,
				   &object_step))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nfailed to compute offset or step for ");
	      print_generic_expr (dump_file, memref, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }
	  return NULL_TREE;
	}

      /* Add bit position to OFFSET and MISALIGN.  */

      bit_pos_in_bytes = ssize_int (pbitpos/BITS_PER_UNIT);
      /* Check that there is no remainder in bits.  */
      if (pbitpos%BITS_PER_UNIT)
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    fprintf (dump_file, "\nbit offset alignment.\n");
	  return NULL_TREE;
	}
      object_offset = size_binop (PLUS_EXPR, bit_pos_in_bytes, object_offset);     
      if (object_misalign) 
	object_misalign = size_binop (PLUS_EXPR, object_misalign, 
				      bit_pos_in_bytes); 
      
      memref = base; /* To continue analysis of BASE.  */
      /* fall through  */
    }
  
  /*  Part 1: Case 2. Declarations.  */ 
  if (DECL_P (memref))
    {
      /* We expect to get a decl only if we already have a DR.  */
      if (!(*dr))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nunhandled decl ");
	      print_generic_expr (dump_file, memref, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }
	  return NULL_TREE;
	}

      /* TODO: if during the analysis of INDIRECT_REF we get to an object, put 
	 the object in BASE_OBJECT field if we can prove that this is O.K., 
	 i.e., the data-ref access is bounded by the bounds of the BASE_OBJECT.
	 (e.g., if the object is an array base 'a', where 'a[N]', we must prove
	 that every access with 'p' (the original INDIRECT_REF based on '&a')
	 in the loop is within the array boundaries - from a[0] to a[N-1]).
	 Otherwise, our alias analysis can be incorrect.
	 Even if an access function based on BASE_OBJECT can't be build, update
	 BASE_OBJECT field to enable us to prove that two data-refs are 
	 different (without access function, distance analysis is impossible).
      */
     if (SSA_VAR_P (memref) && var_can_have_subvars (memref))	
	*subvars = get_subvars_for_var (memref);
      base_address = build_fold_addr_expr (memref);
      /* 2.1 set MEMTAG.  */
      *memtag = memref;
    }

  /* Part 1:  Case 3. INDIRECT_REFs.  */
  else if (TREE_CODE (memref) == INDIRECT_REF)
    {
      tree ptr_ref = TREE_OPERAND (memref, 0);
      if (TREE_CODE (ptr_ref) == SSA_NAME)
        *ptr_info = SSA_NAME_PTR_INFO (ptr_ref);

      /* 3.1 build data-reference structure for MEMREF.  */
      ptr_dr = analyze_indirect_ref (stmt, memref, is_read);
      if (!ptr_dr)
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nfailed to create dr for ");
	      print_generic_expr (dump_file, memref, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }	
	  return NULL_TREE;      
	}

      /* 3.2 analyze evolution and initial condition of MEMREF.  */
      ptr_step = DR_STEP (ptr_dr);
      ptr_init = DR_BASE_ADDRESS (ptr_dr);
      if (!ptr_init || !ptr_step || !POINTER_TYPE_P (TREE_TYPE (ptr_init)))
	{
	  *dr = (*dr) ? *dr : ptr_dr;
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nbad pointer access ");
	      print_generic_expr (dump_file, memref, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }
	  return NULL_TREE;
	}

      if (integer_zerop (ptr_step) && !(*dr))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS)) 
	    fprintf (dump_file, "\nptr is loop invariant.\n");	
	  *dr = ptr_dr;
	  return NULL_TREE;
	
	  /* If there exists DR for MEMREF, we are analyzing the base of
	     handled component (PTR_INIT), which not necessary has evolution in 
	     the loop.  */
	}
      object_step = size_binop (PLUS_EXPR, object_step, ptr_step);

      /* 3.3 set data-reference structure for MEMREF.  */
      if (!*dr)
        *dr = ptr_dr;

      /* 3.4 call address_analysis to analyze INIT of the access 
	 function.  */
      base_address = address_analysis (ptr_init, stmt, is_read, *dr, 
				       &address_offset, &address_misalign, 
				       &address_aligned_to, &address_step);
      if (!base_address)
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "\nfailed to analyze address ");
	      print_generic_expr (dump_file, ptr_init, TDF_SLIM);
	      fprintf (dump_file, "\n");
	    }
	  return NULL_TREE;
	}

      /* 3.5 extract memory tag.  */
      switch (TREE_CODE (base_address))
	{
	case SSA_NAME:
	  *memtag = get_var_ann (SSA_NAME_VAR (base_address))->type_mem_tag;
	  if (!(*memtag) && TREE_CODE (TREE_OPERAND (memref, 0)) == SSA_NAME)
	    *memtag = get_var_ann (
		      SSA_NAME_VAR (TREE_OPERAND (memref, 0)))->type_mem_tag;
	  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 (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 void 
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;
    }

  op0 = TREE_OPERAND (offset, 0);
  op1 = TREE_OPERAND (offset, 1);

  /* Recursive call with the operands.  */
  analyze_offset (op0, &invariant_0, &constant_0);
  analyze_offset (op1, &invariant_1, &constant_1);

  /* Combine the results.  */
  *constant = constant_0 ? constant_0 : constant_1;
  if (invariant_0 && invariant_1)
    *invariant = 
1724
      fold_build2 (code, TREE_TYPE (invariant_0), invariant_0, invariant_1);
1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805
  else
    *invariant = invariant_0 ? invariant_0 : invariant_1;
}


/* 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;

  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))));

  /* 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 access_fn;
      tree new_step;

      /* Extract CONSTANT and INVARIANT from OFFSET, and put them in DR_INIT and
	 DR_OFFSET fields of DR.  */
      analyze_offset (offset, &invariant, &constant); 
      if (constant)
	{
	  DR_INIT (dr) = fold_convert (ssizetype, constant);
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	  init_cond = fold_build2 (TRUNC_DIV_EXPR, TREE_TYPE (constant), 
				   constant, type_size);
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	}
      else
	DR_INIT (dr) = init_cond = ssize_int (0);;

      if (invariant)
	DR_OFFSET (dr) = invariant;
      else
	DR_OFFSET (dr) = ssize_int (0);

      /* Update access function.  */
      access_fn = DR_ACCESS_FN (dr, 0);
      new_step = size_binop (TRUNC_DIV_EXPR,  
			     fold_convert (ssizetype, step), type_size);

      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;  
}


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/* Returns true when all the functions of a tree_vec CHREC are the
   same.  */

static bool 
all_chrecs_equal_p (tree chrec)
{
  int j;

  for (j = 0; j < TREE_VEC_LENGTH (chrec) - 1; j++)
    {
      tree chrec_j = TREE_VEC_ELT (chrec, j);
      tree chrec_j_1 = TREE_VEC_ELT (chrec, j + 1);
      if (!integer_zerop 
	  (chrec_fold_minus 
	   (integer_type_node, chrec_j, chrec_j_1)))
	return false;
    }
  return true;
}

/* Determine for each subscript in the data dependence relation DDR
   the distance.  */
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void
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compute_subscript_distance (struct data_dependence_relation *ddr)
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{
  if (DDR_ARE_DEPENDENT (ddr) == NULL_TREE)
    {
      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);
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	  if (TREE_CODE (conflicts_a) == TREE_VEC)
	    {
	      if (!all_chrecs_equal_p (conflicts_a))
		{
		  SUB_DISTANCE (subscript) = chrec_dont_know;
		  return;
		}
	      else
		conflicts_a = TREE_VEC_ELT (conflicts_a, 0);
	    }

	  if (TREE_CODE (conflicts_b) == TREE_VEC)
	    {
	      if (!all_chrecs_equal_p (conflicts_b))
		{
		  SUB_DISTANCE (subscript) = chrec_dont_know;
		  return;
		}
	      else
		conflicts_b = TREE_VEC_ELT (conflicts_b, 0);
	    }

	  difference = chrec_fold_minus 
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	    (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;
 	}
    }
}

/* Initialize a ddr.  */

struct data_dependence_relation *
initialize_data_dependence_relation (struct data_reference *a, 
				     struct data_reference *b)
{
  struct data_dependence_relation *res;
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  bool differ_p;
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  unsigned int i;  
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  res = xmalloc (sizeof (struct data_dependence_relation));
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  DDR_A (res) = a;
  DDR_B (res) = b;

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  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;
    }
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    /* Compare the bases of the data-refs.  */
  if (!base_addr_differ_p (a, b, &differ_p))
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    {
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      /* 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_VECTOR_INIT (res, DR_NUM_DIMENSIONS (a));
  DDR_SIZE_VECT (res) = 0;
  DDR_DIST_VECT (res) = NULL;
  DDR_DIR_VECT (res) = NULL;
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  for (i = 0; i < DR_NUM_DIMENSIONS (a); i++)
    {
      struct subscript *subscript;
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      subscript = xmalloc (sizeof (struct subscript));
      SUB_CONFLICTS_IN_A (subscript) = chrec_dont_know;
      SUB_CONFLICTS_IN_B (subscript) = chrec_dont_know;
      SUB_LAST_CONFLICT (subscript) = chrec_dont_know;
      SUB_DISTANCE (subscript) = chrec_dont_know;
      VARRAY_PUSH_GENERIC_PTR (DDR_SUBSCRIPTS (res), subscript);
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    }
  
  return res;
}

/* 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)
{
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  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fprintf (dump_file, "(dependence classified: ");
      print_generic_expr (dump_file, chrec, 0);
      fprintf (dump_file, ")\n");
    }

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  DDR_ARE_DEPENDENT (ddr) = chrec;  
  varray_clear (DDR_SUBSCRIPTS (ddr));
}

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/* 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;
}

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/* 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;
}

/* 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, 
		       tree *overlaps_a,
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		       tree *overlaps_b, 
		       tree *last_conflicts)
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{
  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))
    {
    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 = integer_zero_node;
	  *overlaps_b = integer_zero_node;
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	  *last_conflicts = chrec_dont_know;
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	}
      else
	{
	  /* The accesses do not overlap.  */
	  *overlaps_a = chrec_known;
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	  *overlaps_b = chrec_known;
	  *last_conflicts = integer_zero_node;
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	}
      break;
      
    default:
      /* We're not sure whether the indexes overlap.  For the moment, 
	 conservatively answer "don't know".  */
      *overlaps_a = chrec_dont_know;
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      *overlaps_b = chrec_dont_know;
      *last_conflicts = chrec_dont_know;
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      break;
    }
  
  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)).  */

static void
analyze_siv_subscript_cst_affine (tree chrec_a, 
				  tree chrec_b,
				  tree *overlaps_a, 
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				  tree *overlaps_b, 
				  tree *last_conflicts)
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{
  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;
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      *last_conflicts = chrec_dont_know;
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      return;
    }
  else
    {
      if (value0 == false)
	{
	  if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value1))
	    {
	      *overlaps_a = chrec_dont_know;
	      *overlaps_b = chrec_dont_know;      
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	      *last_conflicts = chrec_dont_know;
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	      return;
	    }
	  else
	    {
	      if (value1 == true)
		{
		  /* Example:  
		     chrec_a = 12
		     chrec_b = {10, +, 1}
		  */
		  
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		  if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference))
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		    {
		      *overlaps_a = integer_zero_node;
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		      *overlaps_b = fold_build2 (EXACT_DIV_EXPR, integer_type_node,
						 fold_build1 (ABS_EXPR,
							      integer_type_node,
							      difference),
						 CHREC_RIGHT (chrec_b));
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		      *last_conflicts = integer_one_node;
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		      return;
		    }
		  
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		  /* When the step does not divide the difference, there are
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		     no overlaps.  */
		  else
		    {
		      *overlaps_a = chrec_known;
		      *overlaps_b = chrec_known;      
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		      *last_conflicts = integer_zero_node;
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		      return;
		    }
		}
	      
	      else
		{
		  /* Example:  
		     chrec_a = 12
		     chrec_b = {10, +, -1}
		     
		     In this case, chrec_a will not overlap with chrec_b.  */
		  *overlaps_a = chrec_known;
		  *overlaps_b = chrec_known;
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		  *last_conflicts = integer_zero_node;
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		  return;
		}
	    }
	}
      else 
	{
	  if (!chrec_is_positive (CHREC_RIGHT (chrec_b), &value2))
	    {
	      *overlaps_a = chrec_dont_know;
	      *overlaps_b = chrec_dont_know;      
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	      *last_conflicts = chrec_dont_know;
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	      return;
	    }
	  else
	    {
	      if (value2 == false)
		{
		  /* Example:  
		     chrec_a = 3
		     chrec_b = {10, +, -1}
		  */
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		  if (tree_fold_divides_p (CHREC_RIGHT (chrec_b), difference))
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		    {
		      *overlaps_a = integer_zero_node;
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		      *overlaps_b = fold_build2 (EXACT_DIV_EXPR,
				      		 integer_type_node, difference, 
						 CHREC_RIGHT (chrec_b));
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		      *last_conflicts = integer_one_node;
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		      return;
		    }
		  
2251
		  /* When the step does not divide the difference, there
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		     are no overlaps.  */
		  else
		    {
		      *overlaps_a = chrec_known;
		      *overlaps_b = chrec_known;      
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		      *last_conflicts = integer_zero_node;
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		      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;
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		  *last_conflicts = integer_zero_node;
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		  return;
		}
	    }
	}
    }
}

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/* Helper recursive function for initializing the matrix A.  Returns
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   the initial value of CHREC.  */
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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.  */
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static void
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compute_overlap_steps_for_affine_univar (int niter, int step_a, int step_b, 
					 tree *overlaps_a, tree *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 = build_polynomial_chrec
	(dim, integer_zero_node,
	 build_int_cst (NULL_TREE, step_overlaps_a));
      *overlaps_b = build_polynomial_chrec
	(dim, integer_zero_node,
	 build_int_cst (NULL_TREE, step_overlaps_b));
      *last_conflicts = build_int_cst (NULL_TREE, last_conflict);
    }

  else
    {
      *overlaps_a = integer_zero_node;
      *overlaps_b = 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

2351
   FORNOW: This is a specialized implementation for a case occurring in
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   a common benchmark.  Implement the general algorithm.  */

static void
compute_overlap_steps_for_affine_1_2 (tree chrec_a, tree chrec_b, 
				      tree *overlaps_a, tree *overlaps_b, 
				      tree *last_conflicts)
2358
{
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  bool xz_p, yz_p, xyz_p;
  int step_x, step_y, step_z;
  int niter_x, niter_y, niter_z, niter;
  tree numiter_x, numiter_y, numiter_z;
  tree overlaps_a_xz, overlaps_b_xz, last_conflicts_xz;
  tree overlaps_a_yz, overlaps_b_yz, last_conflicts_yz;
  tree overlaps_a_xyz, overlaps_b_xyz, 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));

  numiter_x = number_of_iterations_in_loop 
    (current_loops->parray[CHREC_VARIABLE (CHREC_LEFT (chrec_a))]);
  numiter_y = number_of_iterations_in_loop 
    (current_loops->parray[CHREC_VARIABLE (chrec_a)]);
  numiter_z = number_of_iterations_in_loop 
    (current_loops->parray[CHREC_VARIABLE (chrec_b)]);

  if (TREE_CODE (numiter_x) != INTEGER_CST)
    numiter_x = current_loops->parray[CHREC_VARIABLE (CHREC_LEFT (chrec_a))]
      ->estimated_nb_iterations;
  if (TREE_CODE (numiter_y) != INTEGER_CST)
    numiter_y = current_loops->parray[CHREC_VARIABLE (chrec_a)]
      ->estimated_nb_iterations;
  if (TREE_CODE (numiter_z) != INTEGER_CST)
    numiter_z = current_loops->parray[CHREC_VARIABLE (chrec_b)]
      ->estimated_nb_iterations;

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  if (chrec_contains_undetermined (numiter_x)
      || chrec_contains_undetermined (numiter_y)
      || chrec_contains_undetermined (numiter_z)
      || TREE_CODE (numiter_x) != INTEGER_CST
      || TREE_CODE (numiter_y) != INTEGER_CST
      || TREE_CODE (numiter_z) != INTEGER_CST)
2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468
    {
      *overlaps_a = chrec_dont_know;
      *overlaps_b = chrec_dont_know;
      *last_conflicts = chrec_dont_know;
      return;
    }

  niter_x = int_cst_value (numiter_x);
  niter_y = int_cst_value (numiter_y);
  niter_z = int_cst_value (numiter_z);

  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)
    {
      *overlaps_a = make_tree_vec (2);
      TREE_VEC_ELT (*overlaps_a, 0) = integer_zero_node;
      TREE_VEC_ELT (*overlaps_a, 1) = integer_zero_node;
      *overlaps_b = integer_zero_node;
      if (xz_p)
	{
	  TREE_VEC_ELT (*overlaps_a, 0) = 
	    chrec_fold_plus (integer_type_node, TREE_VEC_ELT (*overlaps_a, 0),
			     overlaps_a_xz);
	  *overlaps_b = 
	    chrec_fold_plus (integer_type_node, *overlaps_b, overlaps_b_xz);
	  *last_conflicts = last_conflicts_xz;
	}
      if (yz_p)
	{
	  TREE_VEC_ELT (*overlaps_a, 1) = 
	    chrec_fold_plus (integer_type_node, TREE_VEC_ELT (*overlaps_a, 1),
			     overlaps_a_yz);
	  *overlaps_b = 
	    chrec_fold_plus (integer_type_node, *overlaps_b, overlaps_b_yz);
	  *last_conflicts = last_conflicts_yz;
	}
      if (xyz_p)
	{
	  TREE_VEC_ELT (*overlaps_a, 0) = 
	    chrec_fold_plus (integer_type_node, TREE_VEC_ELT (*overlaps_a, 0),
			     overlaps_a_xyz);
	  TREE_VEC_ELT (*overlaps_a, 1) = 
	    chrec_fold_plus (integer_type_node, TREE_VEC_ELT (*overlaps_a, 1),
			     overlaps_a_xyz);
	  *overlaps_b = 
	    chrec_fold_plus (integer_type_node, *overlaps_b, overlaps_b_xyz);
	  *last_conflicts = last_conflicts_xyz;
	}
    }
  else
    {
      *overlaps_a = integer_zero_node;
      *overlaps_b = integer_zero_node;
      *last_conflicts = integer_zero_node;
    }
2469 2470 2471 2472 2473 2474 2475 2476 2477 2478
}

/* Determines the overlapping elements due to accesses CHREC_A and
   CHREC_B, that are affine functions.  This is a part of the
   subscript analyzer.  */

static void
analyze_subscript_affine_affine (tree chrec_a, 
				 tree chrec_b,
				 tree *overlaps_a, 
2479 2480
				 tree *overlaps_b, 
				 tree *last_conflicts)
2481
{
2482 2483 2484 2485 2486
  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;

2487 2488 2489 2490 2491 2492 2493 2494 2495
  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,
2496
     i.e. the solution is positive or zero, and that the solution
2497 2498 2499 2500 2501
     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.  */

  
2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522
  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)
2523
    {
2524
      if (nb_vars_a == 1 && nb_vars_b == 1)
2525
	{
2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540
	  int step_a, step_b;
	  int niter, niter_a, niter_b;
	  tree numiter_a, numiter_b;

	  numiter_a = number_of_iterations_in_loop 
	    (current_loops->parray[CHREC_VARIABLE (chrec_a)]);
	  numiter_b = number_of_iterations_in_loop 
	    (current_loops->parray[CHREC_VARIABLE (chrec_b)]);

	  if (TREE_CODE (numiter_a) != INTEGER_CST)
	    numiter_a = current_loops->parray[CHREC_VARIABLE (chrec_a)]
	      ->estimated_nb_iterations;
	  if (TREE_CODE (numiter_b) != INTEGER_CST)
	    numiter_b = current_loops->parray[CHREC_VARIABLE (chrec_b)]
	      ->estimated_nb_iterations;
2541 2542 2543 2544
	  if (chrec_contains_undetermined (numiter_a)
	      || chrec_contains_undetermined (numiter_b)
	      || TREE_CODE (numiter_a) != INTEGER_CST
	      || TREE_CODE (numiter_b) != INTEGER_CST)
2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561
	    {
	      *overlaps_a = chrec_dont_know;
	      *overlaps_b = chrec_dont_know;
	      *last_conflicts = chrec_dont_know;
	      return;
	    }

	  niter_a = int_cst_value (numiter_a);
	  niter_b = int_cst_value (numiter_b);
	  niter = MIN (niter_a, niter_b);

	  step_a = int_cst_value (CHREC_RIGHT (chrec_a));
	  step_b = int_cst_value (CHREC_RIGHT (chrec_b));

	  compute_overlap_steps_for_affine_univar (niter, step_a, step_b, 
						   overlaps_a, overlaps_b, 
						   last_conflicts, 1);
2562
	}
2563 2564 2565 2566 2567 2568 2569 2570 2571 2572

      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
2573
	{
2574 2575 2576
	  *overlaps_a = chrec_dont_know;
	  *overlaps_b = chrec_dont_know;
	  *last_conflicts = chrec_dont_know;
2577
	}
2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606
      return;
    }

  /* 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];

  /* 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 = chrec_known;
      *overlaps_b = chrec_known;
      *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)))
2607 2608 2609
	{
	  /* The solutions are given by:
	     | 
2610 2611 2612
	     | [GAMMA/GCD_ALPHA_BETA  t].[u11 u12]  = [x0]
	     |                           [u21 u22]    [y0]
	 
2613
	     For a given integer t.  Using the following variables,
2614
	 
2615 2616 2617 2618
	     | i0 = u11 * gamma / gcd_alpha_beta
	     | j0 = u12 * gamma / gcd_alpha_beta
	     | i1 = u21
	     | j1 = u22
2619
	 
2620
	     the solutions are:
2621 2622 2623 2624 2625 2626
	 
	     | x0 = i0 + i1 * t, 
	     | y0 = j0 + j1 * t.  */
      
	  int i0, j0, i1, j1;

2627 2628 2629
	  /* 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).  */
2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644
	  int x0, y0;
	  int niter, niter_a, niter_b;
	  tree numiter_a, numiter_b;

	  numiter_a = number_of_iterations_in_loop 
	    (current_loops->parray[CHREC_VARIABLE (chrec_a)]);
	  numiter_b = number_of_iterations_in_loop 
	    (current_loops->parray[CHREC_VARIABLE (chrec_b)]);

	  if (TREE_CODE (numiter_a) != INTEGER_CST)
	    numiter_a = current_loops->parray[CHREC_VARIABLE (chrec_a)]
	      ->estimated_nb_iterations;
	  if (TREE_CODE (numiter_b) != INTEGER_CST)
	    numiter_b = current_loops->parray[CHREC_VARIABLE (chrec_b)]
	      ->estimated_nb_iterations;
2645 2646 2647 2648
	  if (chrec_contains_undetermined (numiter_a)
	      || chrec_contains_undetermined (numiter_b)
	      || TREE_CODE (numiter_a) != INTEGER_CST
	      || TREE_CODE (numiter_b) != INTEGER_CST)
2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666
	    {
	      *overlaps_a = chrec_dont_know;
	      *overlaps_b = chrec_dont_know;
	      *last_conflicts = chrec_dont_know;
	      return;
	    }

	  niter_a = int_cst_value (numiter_a);
	  niter_b = int_cst_value (numiter_b);
	  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))
2667 2668 2669 2670 2671 2672 2673
	    {
	      /* 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;
2674 2675 2676
	      *last_conflicts = integer_zero_node;
	    }

2677 2678
	  else 
	    {
2679
	      if (i1 > 0)
2680
		{
2681 2682 2683 2684
		  tau1 = CEIL (-i0, i1);
		  tau2 = FLOOR_DIV (niter - i0, i1);

		  if (j1 > 0)
2685
		    {
2686
		      int last_conflict, min_multiple;
2687 2688 2689
		      tau1 = MAX (tau1, CEIL (-j0, j1));
		      tau2 = MIN (tau2, FLOOR_DIV (niter - j0, j1));

2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700
		      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;

2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712
		      tau1 = (x0 - i0)/i1;
		      last_conflict = tau2 - tau1;

		      *overlaps_a = build_polynomial_chrec
			(1,
			 build_int_cst (NULL_TREE, x0),
			 build_int_cst (NULL_TREE, i1));
		      *overlaps_b = build_polynomial_chrec
			(1,
			 build_int_cst (NULL_TREE, y0),
			 build_int_cst (NULL_TREE, j1));
		      *last_conflicts = build_int_cst (NULL_TREE, last_conflict);
2713 2714 2715 2716
		    }
		  else
		    {
		      /* FIXME: For the moment, the upper bound of the
2717
			 iteration domain for j is not checked.  */
2718 2719
		      *overlaps_a = chrec_dont_know;
		      *overlaps_b = chrec_dont_know;
2720
		      *last_conflicts = chrec_dont_know;
2721 2722
		    }
		}
2723
	  
2724 2725 2726
	      else
		{
		  /* FIXME: For the moment, the upper bound of the
2727
		     iteration domain for i is not checked.  */
2728 2729
		  *overlaps_a = chrec_dont_know;
		  *overlaps_b = chrec_dont_know;
2730
		  *last_conflicts = chrec_dont_know;
2731 2732 2733
		}
	    }
	}
2734 2735 2736 2737 2738 2739
      else
	{
	  *overlaps_a = chrec_dont_know;
	  *overlaps_b = chrec_dont_know;
	  *last_conflicts = chrec_dont_know;
	}
2740
    }
2741

2742 2743 2744 2745
  else
    {
      *overlaps_a = chrec_dont_know;
      *overlaps_b = chrec_dont_know;
2746
      *last_conflicts = chrec_dont_know;
2747
    }
2748 2749


2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773
  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);
      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:

   CHREC_A (*OVERLAPS_A (k)) = CHREC_B (*OVERLAPS_B (k)).  */

static void
analyze_siv_subscript (tree chrec_a, 
		       tree chrec_b,
		       tree *overlaps_a, 
2774 2775
		       tree *overlaps_b, 
		       tree *last_conflicts)
2776 2777 2778 2779 2780 2781 2782
{
  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, 
2783
				      overlaps_a, overlaps_b, last_conflicts);
2784 2785 2786
  
  else if (evolution_function_is_affine_p (chrec_a)
	   && evolution_function_is_constant_p (chrec_b))
2787 2788
    analyze_siv_subscript_cst_affine (chrec_b, chrec_a, 
				      overlaps_b, overlaps_a, last_conflicts);
2789 2790
  
  else if (evolution_function_is_affine_p (chrec_a)
2791
	   && evolution_function_is_affine_p (chrec_b))
2792
    analyze_subscript_affine_affine (chrec_a, chrec_b, 
2793
				     overlaps_a, overlaps_b, last_conflicts);
2794 2795 2796 2797
  else
    {
      *overlaps_a = chrec_dont_know;
      *overlaps_b = chrec_dont_know;
2798
      *last_conflicts = chrec_dont_know;
2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814
    }
  
  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.  */

static bool
chrec_steps_divide_constant_p (tree chrec, 
			       tree cst)
{
  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
2815
      return (tree_fold_divides_p (CHREC_RIGHT (chrec), cst)
2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834
	      && chrec_steps_divide_constant_p (CHREC_LEFT (chrec), cst));
      
    default:
      /* On the initial condition, return true.  */
      return true;
    }
}

/* 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, 
		       tree *overlaps_a, 
2835 2836
		       tree *overlaps_b, 
		       tree *last_conflicts)
2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858
{
  /* 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))
    {
      /* Access functions are the same: all the elements are accessed
	 in the same order.  */
      *overlaps_a = integer_zero_node;
      *overlaps_b = integer_zero_node;
2859 2860
      *last_conflicts = number_of_iterations_in_loop 
	(current_loops->parray[CHREC_VARIABLE (chrec_a)]);
2861 2862 2863 2864 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874
    }
  
  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))
    {
      /* 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;
2875
      *last_conflicts = integer_zero_node;
2876 2877
    }
  
2878 2879
  else if (evolution_function_is_affine_multivariate_p (chrec_a)
	   && evolution_function_is_affine_multivariate_p (chrec_b))
2880 2881 2882 2883
    {
      /* testsuite/.../ssa-chrec-35.c
	 {0, +, 1}_2  vs.  {0, +, 1}_3
	 the overlapping elements are respectively located at iterations:
2884 2885 2886 2887 2888 2889 2890 2891 2892 2893
	 {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)
2894
      */
2895 2896
      analyze_subscript_affine_affine (chrec_a, chrec_b, 
				       overlaps_a, overlaps_b, last_conflicts);
2897 2898 2899 2900 2901 2902 2903
    }
  
  else
    {
      /* When the analysis is too difficult, answer "don't know".  */
      *overlaps_a = chrec_dont_know;
      *overlaps_b = chrec_dont_know;
2904
      *last_conflicts = chrec_dont_know;
2905 2906 2907 2908 2909 2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924
    }
  
  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, 
				tree *overlap_iterations_a, 
2925 2926
				tree *overlap_iterations_b, 
				tree *last_conflicts)
2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950
{
  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, 
2951 2952
			   overlap_iterations_a, overlap_iterations_b,
			   last_conflicts);
2953 2954 2955
  
  else if (siv_subscript_p (chrec_a, chrec_b))
    analyze_siv_subscript (chrec_a, chrec_b, 
2956 2957
			   overlap_iterations_a, overlap_iterations_b, 
			   last_conflicts);
2958 2959 2960
  
  else
    analyze_miv_subscript (chrec_a, chrec_b, 
2961 2962
			   overlap_iterations_a, overlap_iterations_b,
			   last_conflicts);
2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 2977 2978 2979 2980 2981 2982 2983 2984 2985
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      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");
    }
}



/* This section contains the affine functions dependences detector.  */

/* Computes the conflicting iterations, and initialize DDR.  */

static void
subscript_dependence_tester (struct data_dependence_relation *ddr)
{
  unsigned int i;
  struct data_reference *dra = DDR_A (ddr);
  struct data_reference *drb = DDR_B (ddr);
2986
  tree last_conflicts;
2987 2988 2989 2990 2991 2992 2993 2994 2995 2996 2997
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, "(subscript_dependence_tester \n");
  
  for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
    {
      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),
2998 2999
				      &overlaps_a, &overlaps_b, 
				      &last_conflicts);
3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018
      
      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;
3019
	  SUB_LAST_CONFLICT (subscript) = last_conflicts;
3020 3021 3022 3023 3024 3025 3026 3027 3028
 	}
    }
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, ")\n");
}

/* Compute the classic per loop distance vector.

Daniel Berlin committed
3029
   DDR is the data dependence relation to build a vector from.
3030
   NB_LOOPS is the total number of loops we are considering.
3031
   FIRST_LOOP_DEPTH is the loop->depth of the first loop in the analyzed
3032
   loop nest.  
3033 3034
   Return FALSE when fail to represent the data dependence as a distance
   vector.
3035
   Return TRUE otherwise.  */
3036

3037
static bool
Daniel Berlin committed
3038
build_classic_dist_vector (struct data_dependence_relation *ddr, 
3039
			   int nb_loops, int first_loop_depth)
3040 3041 3042 3043 3044 3045 3046 3047 3048
{
  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);
  
Daniel Berlin committed
3049
  if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE)
3050
    return true;
3051
  
Daniel Berlin committed
3052
  for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
3053
    {
3054
      tree access_fn_a, access_fn_b;
Daniel Berlin committed
3055
      struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
3056 3057

      if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
3058 3059
	{
	  non_affine_dependence_relation (ddr);
3060
	  return true;
3061 3062 3063 3064
	}

      access_fn_a = DR_ACCESS_FN (DDR_A (ddr), i);
      access_fn_b = DR_ACCESS_FN (DDR_B (ddr), i);
3065

3066 3067
      if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC 
	  && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC)
3068
	{
3069
	  int dist, loop_nb, loop_depth;
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	  int loop_nb_a = CHREC_VARIABLE (access_fn_a);
	  int loop_nb_b = CHREC_VARIABLE (access_fn_b);
	  struct loop *loop_a = current_loops->parray[loop_nb_a];
	  struct loop *loop_b = current_loops->parray[loop_nb_b];
3074

3075 3076
	  /* If the loop for either variable is at a lower depth than 
	     the first_loop's depth, then we can't possibly have a
3077 3078
	     dependency at this level of the loop.  */
	     
3079 3080
	  if (loop_a->depth < first_loop_depth
	      || loop_b->depth < first_loop_depth)
3081
	    return false;
3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098

	  if (loop_nb_a != loop_nb_b
	      && !flow_loop_nested_p (loop_a, loop_b)
	      && !flow_loop_nested_p (loop_b, loop_a))
	    {
	      /* Example: when there are two consecutive loops,

		 | loop_1
		 |   A[{0, +, 1}_1]
		 | endloop_1
		 | loop_2
		 |   A[{0, +, 1}_2]
		 | endloop_2

		 the dependence relation cannot be captured by the
		 distance abstraction.  */
	      non_affine_dependence_relation (ddr);
3099
	      return true;
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	    }

	  /* 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.  */
	  loop_nb = loop_nb_a < loop_nb_b ? loop_nb_a : loop_nb_b;
3111
	  loop_depth = current_loops->parray[loop_nb]->depth - first_loop_depth;
3112

3113 3114 3115
	  /* If the loop number is still greater than the number of
	     loops we've been asked to analyze, or negative,
	     something is borked.  */
3116 3117
	  gcc_assert (loop_depth >= 0);
	  gcc_assert (loop_depth < nb_loops);
3118 3119 3120
	  if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
	    {
	      non_affine_dependence_relation (ddr);
3121
	      return true;
3122 3123
	    }
	  
3124 3125 3126 3127 3128 3129 3130 3131
	  dist = int_cst_value (SUB_DISTANCE (subscript));

	  /* This is the subscript coupling test.  
	     | loop i = 0, N, 1
	     |   T[i+1][i] = ...
	     |   ... = T[i][i]
	     | endloop
	     There is no dependence.  */
3132 3133
	  if (init_v[loop_depth] != 0
	      && dist_v[loop_depth] != dist)
3134
	    {
Daniel Berlin committed
3135
	      finalize_ddr_dependent (ddr, chrec_known);
3136
	      return true;
3137 3138
	    }

3139 3140
	  dist_v[loop_depth] = dist;
	  init_v[loop_depth] = 1;
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	}
    }
  
  /* 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;
Daniel Berlin committed
3153 3154
    struct data_reference *a = DDR_A (ddr);
    struct data_reference *b = DDR_B (ddr);
3155
    int lca_depth;
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    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); 
    
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    lca_depth = lca->depth;
    lca_depth -= first_loop_depth;
    gcc_assert (lca_depth >= 0);
    gcc_assert (lca_depth < nb_loops);
3166

3167 3168 3169 3170
    /* 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
3171 3172
	&& init_v[lca_depth] == 0)
      dist_v[lca_depth] = 1;
3173 3174 3175 3176 3177
    
    lca = lca->outer;
    
    if (lca)
      {
3178
	lca_depth = lca->depth - first_loop_depth;
3179 3180
	while (lca->depth != 0)
	  {
3181 3182
	    /* If we're considering just a sub-nest, then don't record
	       any information on the outer loops.  */
3183
	    if (lca_depth < 0)
3184 3185
	      break;

3186
	    gcc_assert (lca_depth < nb_loops);
3187

3188 3189
	    if (init_v[lca_depth] == 0)
	      dist_v[lca_depth] = 1;
3190
	    lca = lca->outer;
3191
	    lca_depth = lca->depth - first_loop_depth;
3192 3193 3194 3195 3196
	  
	  }
      }
  }
  
Daniel Berlin committed
3197
  DDR_DIST_VECT (ddr) = dist_v;
3198
  DDR_SIZE_VECT (ddr) = nb_loops;
3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215

  /* Verify a basic constraint: classic distance vectors should always
     be lexicographically positive.  */
  if (!lambda_vector_lexico_pos (DDR_DIST_VECT (ddr),
				 DDR_SIZE_VECT (ddr)))
    {
      if (DDR_SIZE_VECT (ddr) == 1)
	/* This one is simple to fix, and can be fixed.
	   Multidimensional arrays cannot be fixed that simply.  */
	lambda_vector_negate (DDR_DIST_VECT (ddr), DDR_DIST_VECT (ddr),
			      DDR_SIZE_VECT (ddr));
      else
	/* This is not valid: we need the delta test for properly
	   fixing all this.  */
	return false;
    }

3216
  return true;
3217 3218 3219 3220
}

/* Compute the classic per loop direction vector.  

Daniel Berlin committed
3221
   DDR is the data dependence relation to build a vector from.
3222
   NB_LOOPS is the total number of loops we are considering.
3223
   FIRST_LOOP_DEPTH is the loop->depth of the first loop in the analyzed 
3224 3225
   loop nest.
   Return FALSE if the dependence relation is outside of the loop nest
3226
   at FIRST_LOOP_DEPTH. 
3227
   Return TRUE otherwise.  */
3228

3229
static bool
Daniel Berlin committed
3230
build_classic_dir_vector (struct data_dependence_relation *ddr, 
3231
			  int nb_loops, int first_loop_depth)
3232 3233 3234 3235 3236 3237 3238 3239 3240
{
  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);
  
Daniel Berlin committed
3241
  if (DDR_ARE_DEPENDENT (ddr) != NULL_TREE)
3242
    return true;
3243
  
Daniel Berlin committed
3244
  for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
3245
    {
3246
      tree access_fn_a, access_fn_b;
Daniel Berlin committed
3247
      struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
3248

3249
      if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
3250
	{
3251
	  non_affine_dependence_relation (ddr);
3252
	  return true;
3253 3254 3255 3256 3257 3258 3259
	}

      access_fn_a = DR_ACCESS_FN (DDR_A (ddr), i);
      access_fn_b = DR_ACCESS_FN (DDR_B (ddr), i);
      if (TREE_CODE (access_fn_a) == POLYNOMIAL_CHREC
	  && TREE_CODE (access_fn_b) == POLYNOMIAL_CHREC)
	{
3260
	  int dist, loop_nb, loop_depth;
3261
	  enum data_dependence_direction dir = dir_star;
3262 3263 3264 3265
	  int loop_nb_a = CHREC_VARIABLE (access_fn_a);
	  int loop_nb_b = CHREC_VARIABLE (access_fn_b);
	  struct loop *loop_a = current_loops->parray[loop_nb_a];
	  struct loop *loop_b = current_loops->parray[loop_nb_b];
3266
 
3267 3268 3269
	  /* If the loop for either variable is at a lower depth than 
	     the first_loop's depth, then we can't possibly have a
	     dependency at this level of the loop.  */
3270
	     
3271 3272
	  if (loop_a->depth < first_loop_depth
	      || loop_b->depth < first_loop_depth)
3273
	    return false;
3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290

	  if (loop_nb_a != loop_nb_b
	      && !flow_loop_nested_p (loop_a, loop_b)
	      && !flow_loop_nested_p (loop_b, loop_a))
	    {
	      /* Example: when there are two consecutive loops,

		 | loop_1
		 |   A[{0, +, 1}_1]
		 | endloop_1
		 | loop_2
		 |   A[{0, +, 1}_2]
		 | endloop_2

		 the dependence relation cannot be captured by the
		 distance abstraction.  */
	      non_affine_dependence_relation (ddr);
3291
	      return true;
3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302
	    }

	  /* 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.  */
	  loop_nb = loop_nb_a < loop_nb_b ? loop_nb_a : loop_nb_b;
3303
	  loop_depth = current_loops->parray[loop_nb]->depth - first_loop_depth;
3304 3305 3306 3307

	  /* If the loop number is still greater than the number of
	     loops we've been asked to analyze, or negative,
	     something is borked.  */
3308 3309
	  gcc_assert (loop_depth >= 0);
	  gcc_assert (loop_depth < nb_loops);
3310 3311

	  if (chrec_contains_undetermined (SUB_DISTANCE (subscript)))
3312
	    {
3313
	      non_affine_dependence_relation (ddr);
3314
	      return true;
3315
	    }
3316 3317 3318 3319 3320 3321 3322 3323 3324

	  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;
3325 3326 3327 3328 3329 3330 3331
	  
	  /* This is the subscript coupling test.  
	     | loop i = 0, N, 1
	     |   T[i+1][i] = ...
	     |   ... = T[i][i]
	     | endloop
	     There is no dependence.  */
3332
	  if (init_v[loop_depth] != 0
3333
	      && dir != dir_star
3334 3335
	      && (enum data_dependence_direction) dir_v[loop_depth] != dir
	      && (enum data_dependence_direction) dir_v[loop_depth] != dir_star)
3336
	    {
Daniel Berlin committed
3337
	      finalize_ddr_dependent (ddr, chrec_known);
3338
	      return true;
3339 3340
	    }
	  
3341 3342
	  dir_v[loop_depth] = dir;
	  init_v[loop_depth] = 1;
3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354
	}
    }
  
  /* 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;
Daniel Berlin committed
3355 3356
    struct data_reference *a = DDR_A (ddr);
    struct data_reference *b = DDR_B (ddr);
3357
    int lca_depth;
3358 3359 3360 3361 3362
    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); 
3363
    lca_depth = lca->depth - first_loop_depth;
3364

3365 3366
    gcc_assert (lca_depth >= 0);
    gcc_assert (lca_depth < nb_loops);
3367

3368 3369 3370 3371
    /* 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
3372 3373
	&& init_v[lca_depth] == 0)
      dir_v[lca_depth] = dir_positive;
3374 3375 3376 3377
    
    lca = lca->outer;
    if (lca)
      {
3378
	lca_depth = lca->depth - first_loop_depth;
3379 3380
	while (lca->depth != 0)
	  {
3381 3382
	    /* If we're considering just a sub-nest, then don't record
	       any information on the outer loops.  */
3383
	    if (lca_depth < 0)
3384 3385
	      break;

3386
	    gcc_assert (lca_depth < nb_loops);
3387

3388 3389
	    if (init_v[lca_depth] == 0)
	      dir_v[lca_depth] = dir_positive;
3390
	    lca = lca->outer;
3391
	    lca_depth = lca->depth - first_loop_depth;
3392 3393 3394 3395 3396
	   
	  }
      }
  }
  
Daniel Berlin committed
3397
  DDR_DIR_VECT (ddr) = dir_v;
3398
  DDR_SIZE_VECT (ddr) = nb_loops;
3399
  return true;
3400 3401 3402 3403 3404 3405 3406 3407 3408
}

/* 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;
3409
  VEC(tree,heap) **fns = DR_ACCESS_FNS_ADDR (a);
3410
  tree t;
3411
  
3412 3413 3414
  for (i = 0; VEC_iterate (tree, *fns, i, t); i++)
    if (!evolution_function_is_constant_p (t)
	&& !evolution_function_is_affine_multivariate_p (t))
3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436
      return false;
  
  return true;
}

/* This computes the affine dependence relation between A and B.
   CHREC_KNOWN is used for representing the independence between two
   accesses, while CHREC_DONT_KNOW is used for representing the unknown
   relation.
   
   Note that it is possible to stop the computation of the dependence
   relation the first time we detect a CHREC_KNOWN element for a given
   subscript.  */

void
compute_affine_dependence (struct data_dependence_relation *ddr)
{
  struct data_reference *dra = DDR_A (ddr);
  struct data_reference *drb = DDR_B (ddr);
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    {
Daniel Berlin committed
3437
      fprintf (dump_file, "(compute_affine_dependence\n");
3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462
      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)
    {
      if (access_functions_are_affine_or_constant_p (dra)
	  && access_functions_are_affine_or_constant_p (drb))
	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);
    }
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, ")\n");
}

3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481
/* 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;

  for (i = 0; i < DDR_NUM_SUBSCRIPTS (ddr); i++)
    {
      struct subscript *subscript = DDR_SUBSCRIPT (ddr, i);
      
      /* The accessed index overlaps for each iteration.  */
      SUB_CONFLICTS_IN_A (subscript) = integer_zero_node;
      SUB_CONFLICTS_IN_B (subscript) = integer_zero_node;
      SUB_LAST_CONFLICT (subscript) = chrec_dont_know;
    }
}

3482 3483 3484 3485 3486

typedef struct data_dependence_relation *ddr_p;
DEF_VEC_P(ddr_p);
DEF_VEC_ALLOC_P(ddr_p,heap);

3487
/* Compute a subset of the data dependence relation graph.  Don't
3488 3489 3490
   compute read-read and self relations if 
   COMPUTE_SELF_AND_READ_READ_DEPENDENCES is FALSE, and avoid the computation 
   of the opposite relation, i.e. when AB has been computed, don't compute BA.
3491 3492 3493 3494
   DATAREFS contains a list of data references, and the result is set
   in DEPENDENCE_RELATIONS.  */

static void 
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3495
compute_all_dependences (varray_type datarefs, 
3496
			 bool compute_self_and_read_read_dependences,
3497
			 VEC(ddr_p,heap) **dependence_relations)
3498 3499 3500 3501 3502
{
  unsigned int i, j, N;

  N = VARRAY_ACTIVE_SIZE (datarefs);

3503 3504 3505
  /* Note that we specifically skip i == j because it's a self dependence, and
     use compute_self_dependence below.  */

3506
  for (i = 0; i < N; i++)
3507
    for (j = i + 1; j < N; j++)
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      {
	struct data_reference *a, *b;
	struct data_dependence_relation *ddr;

	a = VARRAY_GENERIC_PTR (datarefs, i);
	b = VARRAY_GENERIC_PTR (datarefs, j);
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	if (DR_IS_READ (a) && DR_IS_READ (b)
            && !compute_self_and_read_read_dependences)
	  continue;
3517 3518
	ddr = initialize_data_dependence_relation (a, b);

3519
	VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
3520
	compute_affine_dependence (ddr);
3521
	compute_subscript_distance (ddr);
3522
      }
3523 3524
  if (!compute_self_and_read_read_dependences)
    return;
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  /* Compute self dependence relation of each dataref to itself.  */

  for (i = 0; i < N; i++)
    {
      struct data_reference *a, *b;
      struct data_dependence_relation *ddr;

      a = VARRAY_GENERIC_PTR (datarefs, i);
      b = VARRAY_GENERIC_PTR (datarefs, i);
      ddr = initialize_data_dependence_relation (a, b);

      VEC_safe_push (ddr_p, heap, *dependence_relations, ddr);
      compute_self_dependence (ddr);
      compute_subscript_distance (ddr);
    }
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}

/* 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.
   
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   TODO: This function should be made smarter so that it can handle address
   arithmetic as if they were array accesses, etc.  */
3549

3550
tree 
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find_data_references_in_loop (struct loop *loop, varray_type *datarefs)
{
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  basic_block bb, *bbs;
  unsigned int i;
3555
  block_stmt_iterator bsi;
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  struct data_reference *dr;
3557

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  bbs = get_loop_body (loop);

  for (i = 0; i < loop->num_nodes; i++)
3561
    {
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      bb = bbs[i];

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      for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
        {
	  tree stmt = bsi_stmt (bsi);

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	  /* ASM_EXPR and CALL_EXPR may embed arbitrary side effects.
	     Calls have side-effects, except those to const or pure
	     functions.  */
	  if ((TREE_CODE (stmt) == CALL_EXPR
	       && !(call_expr_flags (stmt) & (ECF_CONST | ECF_PURE)))
	      || (TREE_CODE (stmt) == ASM_EXPR
		  && ASM_VOLATILE_P (stmt)))
	    goto insert_dont_know_node;
3576

3577
	  if (ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
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	    continue;
3579 3580

	  switch (TREE_CODE (stmt))
3581
	    {
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	    case MODIFY_EXPR:
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	      {
		bool one_inserted = false;
		tree opnd0 = TREE_OPERAND (stmt, 0);
		tree opnd1 = TREE_OPERAND (stmt, 1);
		
		if (TREE_CODE (opnd0) == ARRAY_REF 
		    || TREE_CODE (opnd0) == INDIRECT_REF)
		  {
		    dr = create_data_ref (opnd0, stmt, false);
		    if (dr) 
		      {
			VARRAY_PUSH_GENERIC_PTR (*datarefs, dr);
			one_inserted = true;
		      }
		  }

		if (TREE_CODE (opnd1) == ARRAY_REF 
		    || TREE_CODE (opnd1) == INDIRECT_REF)
		  {
		    dr = create_data_ref (opnd1, stmt, true);
		    if (dr) 
		      {
			VARRAY_PUSH_GENERIC_PTR (*datarefs, dr);
			one_inserted = true;
		      }
		  }
3609

3610 3611
		if (!one_inserted)
		  goto insert_dont_know_node;
3612

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		break;
	      }
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	    case CALL_EXPR:
	      {
		tree args;
		bool one_inserted = false;

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		for (args = TREE_OPERAND (stmt, 1); args; 
		     args = TREE_CHAIN (args))
		  if (TREE_CODE (TREE_VALUE (args)) == ARRAY_REF
		      || TREE_CODE (TREE_VALUE (args)) == INDIRECT_REF)
3625
		    {
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		      dr = create_data_ref (TREE_VALUE (args), stmt, true);
		      if (dr)
			{
			  VARRAY_PUSH_GENERIC_PTR (*datarefs, dr);
			  one_inserted = true;
			}
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		    }

		if (!one_inserted)
		  goto insert_dont_know_node;

		break;
	      }

	    default:
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		{
		  struct data_reference *res;
3643 3644

		insert_dont_know_node:;
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		  res = xmalloc (sizeof (struct data_reference));
		  DR_STMT (res) = NULL_TREE;
		  DR_REF (res) = NULL_TREE;
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		  DR_BASE_OBJECT (res) = NULL;
		  DR_TYPE (res) = ARRAY_REF_TYPE;
		  DR_SET_ACCESS_FNS (res, NULL);
		  DR_BASE_OBJECT (res) = NULL;
3652
		  DR_IS_READ (res) = false;
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		  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;
3660
		  VARRAY_PUSH_GENERIC_PTR (*datarefs, res);
3661 3662 3663

		  free (bbs);
		  return chrec_dont_know;
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		}
	    }

	  /* When there are no defs in the loop, the loop is parallel.  */
3668
	  if (!ZERO_SSA_OPERANDS (stmt, SSA_OP_VIRTUAL_DEFS))
3669
	    loop->parallel_p = false;
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	}
    }

3673 3674
  free (bbs);

3675
  return NULL_TREE;
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}



/* This section contains all the entry points.  */

/* Given a loop nest LOOP, the following vectors are returned:
   *DATAREFS is initialized to all the array elements contained in this loop, 
3684 3685 3686
   *DEPENDENCE_RELATIONS contains the relations between the data references.  
   Compute read-read and self relations if 
   COMPUTE_SELF_AND_READ_READ_DEPENDENCES is TRUE.  */
3687 3688

void
3689 3690
compute_data_dependences_for_loop (struct loop *loop, 
				   bool compute_self_and_read_read_dependences,
3691
				   varray_type *datarefs,
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				   varray_type *dependence_relations)
3693
{
3694
  unsigned int i, nb_loops;
3695 3696
  VEC(ddr_p,heap) *allrelations;
  struct data_dependence_relation *ddr;
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  struct loop *loop_nest = loop;

  while (loop_nest && loop_nest->outer && loop_nest->outer->outer)
    loop_nest = loop_nest->outer;

  nb_loops = loop_nest->level;
3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713

  /* 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)
    {
      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);
3714 3715
      build_classic_dist_vector (ddr, nb_loops, loop->depth);
      build_classic_dir_vector (ddr, nb_loops, loop->depth);
3716 3717 3718
      return;
    }

3719
  allrelations = NULL;
3720 3721
  compute_all_dependences (*datarefs, compute_self_and_read_read_dependences,
			   &allrelations);
3722

3723
  for (i = 0; VEC_iterate (ddr_p, allrelations, i, ddr); i++)
3724
    {
3725
      if (build_classic_dist_vector (ddr, nb_loops, loop_nest->depth))
3726 3727
	{
	  VARRAY_PUSH_GENERIC_PTR (*dependence_relations, ddr);
3728
	  build_classic_dir_vector (ddr, nb_loops, loop_nest->depth);
3729
	}
3730 3731 3732 3733 3734 3735 3736 3737 3738 3739 3740 3741 3742 3743 3744 3745 3746 3747 3748 3749 3750 3751 3752 3753 3754 3755 3756 3757 3758 3759 3760 3761 3762 3763 3764 3765 3766 3767 3768
    }
}

/* Entry point (for testing only).  Analyze all the data references
   and the dependence relations.

   The data references are computed first.  
   
   A relation on these nodes is represented by a complete graph.  Some
   of the relations could be of no interest, thus the relations can be
   computed on demand.
   
   In the following function we compute all the relations.  This is
   just a first implementation that is here for:
   - for showing how to ask for the dependence relations, 
   - for the debugging the whole dependence graph,
   - for the dejagnu testcases and maintenance.
   
   It is possible to ask only for a part of the graph, avoiding to
   compute the whole dependence graph.  The computed dependences are
   stored in a knowledge base (KB) such that later queries don't
   recompute the same information.  The implementation of this KB is
   transparent to the optimizer, and thus the KB can be changed with a
   more efficient implementation, or the KB could be disabled.  */

void 
analyze_all_data_dependences (struct loops *loops)
{
  unsigned int i;
  varray_type datarefs;
  varray_type dependence_relations;
  int nb_data_refs = 10;

  VARRAY_GENERIC_PTR_INIT (datarefs, nb_data_refs, "datarefs");
  VARRAY_GENERIC_PTR_INIT (dependence_relations, 
			   nb_data_refs * nb_data_refs,
			   "dependence_relations");

  /* Compute DDs on the whole function.  */
3769
  compute_data_dependences_for_loop (loops->parray[0], false,
Daniel Berlin committed
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				     &datarefs, &dependence_relations);
3771 3772 3773 3774 3775 3776

  if (dump_file)
    {
      dump_data_dependence_relations (dump_file, dependence_relations);
      fprintf (dump_file, "\n\n");

3777 3778
      if (dump_flags & TDF_DETAILS)
	dump_dist_dir_vectors (dump_file, dependence_relations);
3779

3780
      if (dump_flags & TDF_STATS)
3781
	{
3782 3783 3784 3785 3786 3787 3788 3789 3790
	  unsigned nb_top_relations = 0;
	  unsigned nb_bot_relations = 0;
	  unsigned nb_basename_differ = 0;
	  unsigned nb_chrec_relations = 0;

	  for (i = 0; i < VARRAY_ACTIVE_SIZE (dependence_relations); i++)
	    {
	      struct data_dependence_relation *ddr;
	      ddr = VARRAY_GENERIC_PTR (dependence_relations, i);
3791
	  
3792 3793
	      if (chrec_contains_undetermined (DDR_ARE_DEPENDENT (ddr)))
		nb_top_relations++;
3794
	  
3795 3796 3797 3798 3799
	      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;	
3800
	      
3801 3802 3803 3804
		  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))
3805 3806 3807 3808
		    nb_basename_differ++;
		  else
		    nb_bot_relations++;
		}
3809
	  
3810 3811 3812
	      else 
		nb_chrec_relations++;
	    }
3813
      
3814 3815
	  gather_stats_on_scev_database ();
	}
3816
    }
Daniel Berlin committed
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  free_dependence_relations (dependence_relations);
  free_data_refs (datarefs);
}

/* 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))
    varray_clear (DDR_SUBSCRIPTS (ddr));
  free (ddr);
}

/* Free the memory used by the data dependence relations from
   DEPENDENCE_RELATIONS.  */

void 
free_dependence_relations (varray_type dependence_relations)
{
  unsigned int i;
  if (dependence_relations == NULL)
    return;

  for (i = 0; i < VARRAY_ACTIVE_SIZE (dependence_relations); i++)
    free_dependence_relation (VARRAY_GENERIC_PTR (dependence_relations, i));
3847 3848 3849
  varray_clear (dependence_relations);
}

Daniel Berlin committed
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/* Free the memory used by the data references from DATAREFS.  */

void
free_data_refs (varray_type datarefs)
{
  unsigned int i;
  
  if (datarefs == NULL)
    return;
3859

Daniel Berlin committed
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  for (i = 0; i < VARRAY_ACTIVE_SIZE (datarefs); i++)
    {
      struct data_reference *dr = (struct data_reference *) 
	VARRAY_GENERIC_PTR (datarefs, i);
3864 3865
      if (dr)
	{
3866
	  DR_FREE_ACCESS_FNS (dr);
3867 3868
	  free (dr);
	}
Daniel Berlin committed
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    }
  varray_clear (datarefs);
}
3872