* Makefile.in (OBJS-common): Add tree-chrec.o.

	(tree-chrec.o): New rule.
	(GTFILES): Add tree-chrec.h.
	* gengtype.c (open_base_files): Add tree-chrec.h.
	* tree-chrec.c: New file.
	* tree-chrec.h: New file.
	* tree.def (SCEV_KNOWN, SCEV_NOT_KNOWN, POLYNOMIAL_CHREC): New nodes.


git-svn-id: svn+ssh://gcc.gnu.org/svn/gcc/trunk@83909 138bc75d-0d04-0410-961f-82ee72b054a4

1 files changed, 1019 insertions, 0 deletions

diff --git a/gcc/tree-chrec.c b/gcc/tree-chrec.c
new file mode 100644
index 00000000000..9146ec36b36
--- /dev/null
+++ b/gcc/tree-chrec.c
@@ -0,0 +1,1019 @@
+/* Chains of recurrences.
+   Copyright (C) 2003, 2004 Free Software Foundation, Inc.
+   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
+Software Foundation, 59 Temple Place - Suite 330, Boston, MA
+02111-1307, USA.  */
+
+/* This file implements operations on chains of recurrences.  Chains
+   of recurrences are used for modeling evolution functions of scalar
+   variables.
+*/
+
+#include "config.h"
+#include "system.h"
+#include "coretypes.h"
+#include "tm.h"
+#include "errors.h"
+#include "ggc.h"
+#include "tree.h"
+#include "diagnostic.h"
+#include "varray.h"
+#include "tree-chrec.h"
+#include "tree-pass.h"
+
+
+/* This part will be removed once the merging is finished.  */
+
+
+
+/* The following trees are unique elements.  Thus the comparison of
+   another element to these elements should be done on the pointer to
+   these trees, and not on their value.  */
+
+/* The SSA_NAMEs that are not yet analyzed are qualified with NULL_TREE.  */
+tree chrec_not_analyzed_yet;
+
+/* Reserved to the cases where the analyzer has detected an
+   undecidable property at compile time.  */
+tree chrec_dont_know;
+
+/* When the analyzer has detected that a property will never
+   happen, then it qualifies it with chrec_known.  */
+tree chrec_known;
+
+/* Empty hook.  Will be replaced by the main function from
+   tree-scalar-evolution.c.  */
+
+tree
+count_ev_in_wider_type (tree foo ATTRIBUTE_UNUSED, 
+			tree bar ATTRIBUTE_UNUSED)
+{
+  return NULL_TREE;
+}
+
+/* Empty hook.  Will be replaced by the main function from
+   tree-scalar-evolution.c.  */
+
+bool 
+chrec_contains_symbols_defined_in_loop (tree chrec ATTRIBUTE_UNUSED, 
+					unsigned loop_nb ATTRIBUTE_UNUSED)
+{
+  return true;
+}
+
+
+
+
+/* Extended folder for chrecs.  */
+
+/* Determines whether CST is not a constant evolution.  */
+
+static inline bool
+is_not_constant_evolution (tree cst)
+{
+  return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
+}
+
+/* Fold CODE for a polynomial function and a constant.  */
+
+static inline tree 
+chrec_fold_poly_cst (enum tree_code code, 
+		     tree type, 
+		     tree poly, 
+		     tree cst)
+{
+#if defined ENABLE_CHECKING
+  if (poly == NULL_TREE
+      || cst == NULL_TREE
+      || TREE_CODE (poly) != POLYNOMIAL_CHREC
+      || is_not_constant_evolution (cst))
+    abort ();
+#endif
+  
+  switch (code)
+    {
+    case PLUS_EXPR:
+      return build_polynomial_chrec 
+	(CHREC_VARIABLE (poly), 
+	 chrec_fold_plus (type, CHREC_LEFT (poly), cst),
+	 CHREC_RIGHT (poly));
+      
+    case MINUS_EXPR:
+      return build_polynomial_chrec 
+	(CHREC_VARIABLE (poly), 
+	 chrec_fold_minus (type, CHREC_LEFT (poly), cst),
+	 CHREC_RIGHT (poly));
+      
+    case MULT_EXPR:
+      return build_polynomial_chrec 
+	(CHREC_VARIABLE (poly), 
+	 chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
+	 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
+      
+    default:
+      return chrec_dont_know;
+    }
+}
+
+/* Fold the addition of two polynomial functions.  */
+
+static inline tree 
+chrec_fold_plus_poly_poly (enum tree_code code, 
+			   tree type, 
+			   tree poly0, 
+			   tree poly1)
+{
+  tree left, right;
+  
+#if defined ENABLE_CHECKING
+  if (poly0 == NULL_TREE
+      || poly1 == NULL_TREE
+      || TREE_CODE (poly0) != POLYNOMIAL_CHREC
+      || TREE_CODE (poly1) != POLYNOMIAL_CHREC)
+    abort ();
+#endif
+  
+  /*
+    {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
+    {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
+    {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
+  if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1))
+    {
+      if (code == PLUS_EXPR)
+	return build_polynomial_chrec 
+	  (CHREC_VARIABLE (poly1), 
+	   chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
+	   CHREC_RIGHT (poly1));
+      else
+	return build_polynomial_chrec 
+	  (CHREC_VARIABLE (poly1), 
+	   chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
+	   chrec_fold_multiply (type, CHREC_RIGHT (poly1), 
+				convert (type, integer_minus_one_node)));
+    }
+  
+  if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1))
+    {
+      if (code == PLUS_EXPR)
+	return build_polynomial_chrec 
+	  (CHREC_VARIABLE (poly0), 
+	   chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
+	   CHREC_RIGHT (poly0));
+      else
+	return build_polynomial_chrec 
+	  (CHREC_VARIABLE (poly0), 
+	   chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
+	   CHREC_RIGHT (poly0));
+    }
+  
+  if (code == PLUS_EXPR)
+    {
+      left = chrec_fold_plus 
+	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
+      right = chrec_fold_plus 
+	(type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
+    }
+  else
+    {
+      left = chrec_fold_minus 
+	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
+      right = chrec_fold_minus 
+	(type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
+    }
+
+  if (chrec_zerop (right))
+    return left;
+  else
+    return build_polynomial_chrec 
+      (CHREC_VARIABLE (poly0), left, right); 
+}
+
+
+
+/* Fold the multiplication of two polynomial functions.  */
+
+static inline tree 
+chrec_fold_multiply_poly_poly (tree type, 
+			       tree poly0, 
+			       tree poly1)
+{
+#if defined ENABLE_CHECKING
+  if (poly0 == NULL_TREE
+      || poly1 == NULL_TREE
+      || TREE_CODE (poly0) != POLYNOMIAL_CHREC
+      || TREE_CODE (poly1) != POLYNOMIAL_CHREC)
+    abort ();
+#endif
+  
+  /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
+     {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
+     {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
+  if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1))
+    /* poly0 is a constant wrt. poly1.  */
+    return build_polynomial_chrec 
+      (CHREC_VARIABLE (poly1), 
+       chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
+       CHREC_RIGHT (poly1));
+  
+  if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0))
+    /* poly1 is a constant wrt. poly0.  */
+    return build_polynomial_chrec 
+      (CHREC_VARIABLE (poly0), 
+       chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
+       CHREC_RIGHT (poly0));
+  
+  /* poly0 and poly1 are two polynomials in the same variable,
+     {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
+  return 
+    build_polynomial_chrec 
+    (CHREC_VARIABLE (poly0), 
+     build_polynomial_chrec 
+     (CHREC_VARIABLE (poly0), 
+      
+      /* "a*c".  */
+      chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)),
+      
+      /* "a*d + b*c + b*d".  */
+      chrec_fold_plus 
+      (type, chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)),
+       
+       chrec_fold_plus 
+       (type, 
+	chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_LEFT (poly1)),
+	chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1))))),
+     
+     /* "2*b*d".  */
+     chrec_fold_multiply
+     (type, build_int_2 (2, 0),
+      chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1))));
+}
+
+/* When the operands are automatically_generated_chrec_p, the fold has
+   to respect the semantics of the operands.  */
+
+static inline tree 
+chrec_fold_automatically_generated_operands (tree op0, 
+					     tree op1)
+{
+  if (op0 == chrec_dont_know
+      || op1 == chrec_dont_know)
+    return chrec_dont_know;
+  
+  if (op0 == chrec_known
+      || op1 == chrec_known)
+    return chrec_known;
+  
+  if (op0 == chrec_not_analyzed_yet
+      || op1 == chrec_not_analyzed_yet)
+    return chrec_not_analyzed_yet;
+  
+  /* The default case produces a safe result. */
+  return chrec_dont_know;
+}
+
+/* Fold the addition of two chrecs.  */
+
+static tree
+chrec_fold_plus_1 (enum tree_code code, 
+		   tree type, 
+		   tree op0,
+		   tree op1)
+{
+  if (automatically_generated_chrec_p (op0)
+      || automatically_generated_chrec_p (op1))
+    return chrec_fold_automatically_generated_operands (op0, op1);
+  
+  switch (TREE_CODE (op0))
+    {
+    case POLYNOMIAL_CHREC:
+      switch (TREE_CODE (op1))
+	{
+	case POLYNOMIAL_CHREC:
+	  return chrec_fold_plus_poly_poly (code, type, op0, op1);
+
+	default:
+	  if (code == PLUS_EXPR)
+	    return build_polynomial_chrec 
+	      (CHREC_VARIABLE (op0), 
+	       chrec_fold_plus (type, CHREC_LEFT (op0), op1),
+	       CHREC_RIGHT (op0));
+	  else
+	    return build_polynomial_chrec 
+	      (CHREC_VARIABLE (op0), 
+	       chrec_fold_minus (type, CHREC_LEFT (op0), op1),
+	       CHREC_RIGHT (op0));
+	}
+
+    default:
+      switch (TREE_CODE (op1))
+	{
+	case POLYNOMIAL_CHREC:
+	  if (code == PLUS_EXPR)
+	    return build_polynomial_chrec 
+	      (CHREC_VARIABLE (op1), 
+	       chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
+	       CHREC_RIGHT (op1));
+	  else
+	    return build_polynomial_chrec 
+	      (CHREC_VARIABLE (op1), 
+	       chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
+	       chrec_fold_multiply (type, CHREC_RIGHT (op1), 
+				    convert (type,
+					     integer_minus_one_node)));
+
+	default:
+	  if (tree_contains_chrecs (op0)
+	      || tree_contains_chrecs (op1))
+	    return build (code, type, op0, op1);
+	  else
+	    return fold (build (code, type, op0, op1));
+	}
+    }
+}
+
+/* Fold the addition of two chrecs.  */
+
+tree
+chrec_fold_plus (tree type, 
+		 tree op0,
+		 tree op1)
+{
+  if (integer_zerop (op0))
+    return op1;
+  if (integer_zerop (op1))
+    return op0;
+  
+  return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1);
+}
+
+/* Fold the subtraction of two chrecs.  */
+
+tree 
+chrec_fold_minus (tree type, 
+		  tree op0, 
+		  tree op1)
+{
+  if (integer_zerop (op1))
+    return op0;
+  
+  return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
+}
+
+/* Fold the multiplication of two chrecs.  */
+
+tree
+chrec_fold_multiply (tree type, 
+		     tree op0,
+		     tree op1)
+{
+  if (automatically_generated_chrec_p (op0)
+      || automatically_generated_chrec_p (op1))
+    return chrec_fold_automatically_generated_operands (op0, op1);
+  
+  switch (TREE_CODE (op0))
+    {
+    case POLYNOMIAL_CHREC:
+      switch (TREE_CODE (op1))
+	{
+	case POLYNOMIAL_CHREC:
+	  return chrec_fold_multiply_poly_poly (type, op0, op1);
+	  
+	default:
+	  if (integer_onep (op1))
+	    return op0;
+	  if (integer_zerop (op1))
+	    return convert (type, integer_zero_node);
+	  
+	  return build_polynomial_chrec 
+	    (CHREC_VARIABLE (op0), 
+	     chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
+	     chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
+	}
+      
+    default:
+      if (integer_onep (op0))
+	return op1;
+      
+      if (integer_zerop (op0))
+	return convert (type, integer_zero_node);
+      
+      switch (TREE_CODE (op1))
+	{
+	case POLYNOMIAL_CHREC:
+	  return build_polynomial_chrec 
+	    (CHREC_VARIABLE (op1), 
+	     chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
+	     chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
+	  
+	default:
+	  if (integer_onep (op1))
+	    return op0;
+	  if (integer_zerop (op1))
+	    return convert (type, integer_zero_node);
+	  return fold (build (MULT_EXPR, type, op0, op1));
+	}
+    }
+}
+
+
+
+/* Operations.  */
+
+/* The factorial.  */
+ 
+static tree 
+tree_fold_factorial (tree f)
+{
+  if (tree_int_cst_sgn (f) <= 0)
+    return integer_one_node;
+  else
+    return fold 
+      (build (MULT_EXPR, integer_type_node, f, 
+	      tree_fold_factorial (fold (build (MINUS_EXPR, integer_type_node, 
+						f, integer_one_node)))));
+}
+
+/* The binomial coefficient.  */
+
+static tree 
+tree_fold_binomial (tree n,
+		    tree k)
+{
+  return fold 
+    (build (EXACT_DIV_EXPR, integer_type_node, tree_fold_factorial (n), 
+	    fold (build (MULT_EXPR, integer_type_node, 
+			 tree_fold_factorial (k),
+			 tree_fold_factorial 
+			 (fold (build (MINUS_EXPR, integer_type_node, 
+				       n, k)))))));
+}
+
+/* Helper function.  Use the Newton's interpolating formula for
+   evaluating the value of the evolution function.  */
+
+static tree 
+chrec_evaluate (unsigned var,
+		tree chrec,
+		tree n,
+		tree k)
+{
+  tree type = chrec_type (chrec);
+  tree binomial_n_k = tree_fold_binomial (n, k);
+  
+  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
+    {
+      if (CHREC_VARIABLE (chrec) > var)
+	return chrec_evaluate (var, CHREC_LEFT (chrec), n, k);
+      
+      if (CHREC_VARIABLE (chrec) == var)
+	return chrec_fold_plus 
+	  (type, 
+	   fold (build (MULT_EXPR, type, binomial_n_k, CHREC_LEFT (chrec))),
+	   chrec_evaluate (var, CHREC_RIGHT (chrec), n, 
+			   fold (build (PLUS_EXPR, type, k, integer_one_node))));
+      
+      return fold (build (MULT_EXPR, type, binomial_n_k, chrec));
+    }
+  else
+    return fold (build (MULT_EXPR, type, binomial_n_k, chrec));
+}
+
+/* Evaluates "CHREC (X)" when the varying variable is VAR.  
+   Example:  Given the following parameters, 
+   
+   var = 1
+   chrec = {3, +, 4}_1
+   x = 10
+   
+   The result is given by the Newton's interpolating formula: 
+   3 * \binom{10}{0} + 4 * \binom{10}{1}.
+*/
+
+tree 
+chrec_apply (unsigned var,
+	     tree chrec, 
+	     tree x)
+{
+  tree type = chrec_type (chrec);
+  tree res = chrec_dont_know;
+
+  if (automatically_generated_chrec_p (chrec)
+      || automatically_generated_chrec_p (x)
+
+      /* When the symbols are defined in an outer loop, it is possible
+	 to symbolically compute the apply, since the symbols are
+	 constants with respect to the varying loop.  */
+      || chrec_contains_symbols_defined_in_loop (chrec, var)
+      || chrec_contains_symbols (x))
+    return chrec_dont_know;
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, "(chrec_apply \n");
+
+  if (evolution_function_is_affine_p (chrec))
+    {
+      /* "{a, +, b} (x)"  ->  "a + b*x".  */
+      if (TREE_CODE (CHREC_LEFT (chrec)) == INTEGER_CST
+	  && integer_zerop (CHREC_LEFT (chrec)))
+	res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x);
+      
+      else
+	res = chrec_fold_plus (type, CHREC_LEFT (chrec), 
+			       chrec_fold_multiply (type, 
+						    CHREC_RIGHT (chrec), x));
+    }
+  
+  else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC)
+    res = chrec;
+  
+  else if (TREE_CODE (x) == INTEGER_CST
+	   && tree_int_cst_sgn (x) == 1)
+    /* testsuite/.../ssa-chrec-38.c.  */
+    res = chrec_evaluate (var, chrec, x, integer_zero_node);
+
+  else
+    res = chrec_dont_know;
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (varying_loop = %d\n", var);
+      fprintf (dump_file, ")\n  (chrec = ");
+      print_generic_expr (dump_file, chrec, 0);
+      fprintf (dump_file, ")\n  (x = ");
+      print_generic_expr (dump_file, x, 0);
+      fprintf (dump_file, ")\n  (res = ");
+      print_generic_expr (dump_file, res, 0);
+      fprintf (dump_file, "))\n");
+    }
+  
+  return res;
+}
+
+/* Replaces the initial condition in CHREC with INIT_COND.  */
+
+tree 
+chrec_replace_initial_condition (tree chrec, 
+				 tree init_cond)
+{
+  if (automatically_generated_chrec_p (chrec))
+    return chrec;
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      return build_polynomial_chrec 
+	(CHREC_VARIABLE (chrec),
+	 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
+	 CHREC_RIGHT (chrec));
+      
+    default:
+      return init_cond;
+    }
+}
+
+/* Returns the initial condition of a given CHREC.  */
+
+tree 
+initial_condition (tree chrec)
+{
+  if (automatically_generated_chrec_p (chrec))
+    return chrec;
+  
+  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
+    return initial_condition (CHREC_LEFT (chrec));
+  else
+    return chrec;
+}
+
+/* Returns a univariate function that represents the evolution in
+   LOOP_NUM.  Mask the evolution of any other loop.  */
+
+tree 
+hide_evolution_in_other_loops_than_loop (tree chrec, 
+					 unsigned loop_num)
+{
+  if (automatically_generated_chrec_p (chrec))
+    return chrec;
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      if (CHREC_VARIABLE (chrec) == loop_num)
+	return build_polynomial_chrec 
+	  (loop_num, 
+	   hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), 
+						    loop_num), 
+	   CHREC_RIGHT (chrec));
+      
+      else if (CHREC_VARIABLE (chrec) < loop_num)
+	/* There is no evolution in this loop.  */
+	return initial_condition (chrec);
+      
+      else
+	return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), 
+							loop_num);
+      
+    default:
+      return chrec;
+    }
+}
+
+/* Returns the evolution part in LOOP_NUM.  Example: the call
+   get_evolution_in_loop (1, {{0, +, 1}_1, +, 2}_1) returns 
+   {1, +, 2}_1  */
+
+tree 
+evolution_part_in_loop_num (tree chrec, 
+			    unsigned loop_num)
+{
+  if (automatically_generated_chrec_p (chrec))
+    return chrec;
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      if (CHREC_VARIABLE (chrec) == loop_num)
+	{
+	  if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
+	      || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
+	    return CHREC_RIGHT (chrec);
+	  
+	  else
+	    return build_polynomial_chrec
+	      (loop_num, 
+	       evolution_part_in_loop_num (CHREC_LEFT (chrec), loop_num), 
+	       CHREC_RIGHT (chrec));
+	}
+      
+      else if (CHREC_VARIABLE (chrec) < loop_num)
+	/* There is no evolution part in this loop.  */
+	return NULL_TREE;
+      
+      else
+	return evolution_part_in_loop_num (CHREC_LEFT (chrec), loop_num);
+      
+    default:
+      return NULL_TREE;
+    }
+}
+
+/* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
+   This function is essentially used for setting the evolution to
+   chrec_dont_know, for example after having determined that it is
+   impossible to say how many times a loop will execute.  */
+
+tree 
+reset_evolution_in_loop (unsigned loop_num,
+			 tree chrec, 
+			 tree new_evol)
+{
+  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
+      && CHREC_VARIABLE (chrec) > loop_num)
+    return build 
+      (TREE_CODE (chrec), 
+       build_int_2 (CHREC_VARIABLE (chrec), 0), 
+       reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), new_evol), 
+       reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), new_evol));
+  
+  while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
+	 && CHREC_VARIABLE (chrec) == loop_num)
+    chrec = CHREC_LEFT (chrec);
+  
+  return build_polynomial_chrec (loop_num, chrec, new_evol);
+}
+
+/* Merges two evolution functions that were found by following two
+   alternate paths of a conditional expression.  */
+
+tree
+chrec_merge (tree chrec1, 
+	     tree chrec2)
+{
+  if (chrec1 == chrec_dont_know
+      || chrec2 == chrec_dont_know)
+    return chrec_dont_know;
+
+  if (chrec1 == chrec_known 
+      || chrec2 == chrec_known)
+    return chrec_known;
+
+  if (chrec1 == chrec_not_analyzed_yet)
+    return chrec2;
+  if (chrec2 == chrec_not_analyzed_yet)
+    return chrec1;
+
+  if (operand_equal_p (chrec1, chrec2, 0))
+    return chrec1;
+
+  return chrec_dont_know;
+}
+
+
+
+/* Observers.  */
+
+/* Helper function for is_multivariate_chrec.  */
+
+static bool 
+is_multivariate_chrec_rec (tree chrec, unsigned int rec_var)
+{
+  if (chrec == NULL_TREE)
+    return false;
+  
+  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
+    {
+      if (CHREC_VARIABLE (chrec) != rec_var)
+	return true;
+      else
+	return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) 
+		|| is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
+    }
+  else
+    return false;
+}
+
+/* Determine whether the given chrec is multivariate or not.  */
+
+bool 
+is_multivariate_chrec (tree chrec)
+{
+  if (chrec == NULL_TREE)
+    return false;
+  
+  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
+    return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), 
+				       CHREC_VARIABLE (chrec))
+	    || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), 
+					  CHREC_VARIABLE (chrec)));
+  else
+    return false;
+}
+
+/* Determines whether the chrec contains symbolic names or not.  */
+
+bool 
+chrec_contains_symbols (tree chrec)
+{
+  if (chrec == NULL_TREE)
+    return false;
+  
+  if (TREE_CODE (chrec) == SSA_NAME
+      || TREE_CODE (chrec) == VAR_DECL
+      || TREE_CODE (chrec) == PARM_DECL
+      || TREE_CODE (chrec) == FUNCTION_DECL
+      || TREE_CODE (chrec) == LABEL_DECL
+      || TREE_CODE (chrec) == RESULT_DECL
+      || TREE_CODE (chrec) == FIELD_DECL)
+    return true;
+  
+  switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
+    {
+    case 3:
+      if (chrec_contains_symbols (TREE_OPERAND (chrec, 2)))
+	return true;
+      
+    case 2:
+      if (chrec_contains_symbols (TREE_OPERAND (chrec, 1)))
+	return true;
+      
+    case 1:
+      if (chrec_contains_symbols (TREE_OPERAND (chrec, 0)))
+	return true;
+      
+    default:
+      return false;
+    }
+}
+
+/* Determines whether the chrec contains undetermined coefficients.  */
+
+bool 
+chrec_contains_undetermined (tree chrec)
+{
+  if (chrec == chrec_dont_know
+      || chrec == chrec_not_analyzed_yet
+      || chrec == NULL_TREE)
+    return true;
+  
+  switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
+    {
+    case 3:
+      if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2)))
+	return true;
+      
+    case 2:
+      if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1)))
+	return true;
+      
+    case 1:
+      if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0)))
+	return true;
+      
+    default:
+      return false;
+    }
+}
+
+/* Determines whether the tree EXPR contains chrecs.  */
+
+bool
+tree_contains_chrecs (tree expr)
+{
+  if (expr == NULL_TREE)
+    return false;
+  
+  if (tree_is_chrec (expr))
+    return true;
+  
+  switch (TREE_CODE_LENGTH (TREE_CODE (expr)))
+    {
+    case 3:
+      if (tree_contains_chrecs (TREE_OPERAND (expr, 2)))
+	return true;
+      
+    case 2:
+      if (tree_contains_chrecs (TREE_OPERAND (expr, 1)))
+	return true;
+      
+    case 1:
+      if (tree_contains_chrecs (TREE_OPERAND (expr, 0)))
+	return true;
+      
+    default:
+      return false;
+    }
+}
+
+/* Determine whether the given tree is an affine multivariate
+   evolution.  */
+
+bool 
+evolution_function_is_affine_multivariate_p (tree chrec)
+{
+  if (chrec == NULL_TREE)
+    return false;
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      if (evolution_function_is_constant_p (CHREC_LEFT (chrec)))
+	{
+	  if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)))
+	    return true;
+	  else
+	    {
+	      if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
+		  && CHREC_VARIABLE (CHREC_RIGHT (chrec)) 
+		     != CHREC_VARIABLE (chrec)
+		  && evolution_function_is_affine_multivariate_p 
+		  (CHREC_RIGHT (chrec)))
+		return true;
+	      else
+		return false;
+	    }
+	}
+      else
+	{
+	  if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))
+	      && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
+	      && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
+	      && evolution_function_is_affine_multivariate_p 
+	      (CHREC_LEFT (chrec)))
+	    return true;
+	  else
+	    return false;
+	}
+      
+    default:
+      return false;
+    }
+}
+
+/* Determine whether the given tree is a function in zero or one 
+   variables.  */
+
+bool
+evolution_function_is_univariate_p (tree chrec)
+{
+  if (chrec == NULL_TREE)
+    return true;
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      switch (TREE_CODE (CHREC_LEFT (chrec)))
+	{
+	case POLYNOMIAL_CHREC:
+	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
+	    return false;
+	  if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
+	    return false;
+	  break;
+	  
+	default:
+	  break;
+	}
+      
+      switch (TREE_CODE (CHREC_RIGHT (chrec)))
+	{
+	case POLYNOMIAL_CHREC:
+	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
+	    return false;
+	  if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
+	    return false;
+	  break;
+	  
+	default:
+	  break;	  
+	}
+      
+    default:
+      return true;
+    }
+}
+
+
+
+/* Convert the initial condition of chrec to type.  */
+
+tree 
+chrec_convert (tree type, 
+	       tree chrec)
+{
+  tree ct;
+  
+  if (automatically_generated_chrec_p (chrec))
+    return chrec;
+  
+  ct = chrec_type (chrec);
+  if (ct == type)
+    return chrec;
+
+  if (TYPE_PRECISION (ct) < TYPE_PRECISION (type))
+    return count_ev_in_wider_type (type, chrec);
+
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      return build_polynomial_chrec (CHREC_VARIABLE (chrec),
+				     chrec_convert (type,
+						    CHREC_LEFT (chrec)),
+				     chrec_convert (type,
+						    CHREC_RIGHT (chrec)));
+
+    default:
+      {
+	tree res = convert (type, chrec);
+
+	/* Don't propagate overflows.  */
+	TREE_OVERFLOW (res) = 0;
+	if (TREE_CODE_CLASS (TREE_CODE (res)) == 'c')
+	  TREE_CONSTANT_OVERFLOW (res) = 0;
+	return res;
+      }
+    }
+}
+
+/* Returns the type of the chrec.  */
+
+tree 
+chrec_type (tree chrec)
+{
+  if (automatically_generated_chrec_p (chrec))
+    return NULL_TREE;
+  
+  return TREE_TYPE (chrec);
+}
+
+extern void initialize_scalar_evolutions_analyzer (void);
+
+/* Initializer.  */
+
+void
+initialize_scalar_evolutions_analyzer (void)
+{
+  /* The elements below are unique.  */
+  if (chrec_dont_know == NULL_TREE)
+    {
+      chrec_not_analyzed_yet = NULL_TREE;
+      chrec_dont_know = make_node (SCEV_NOT_KNOWN);
+      chrec_known = make_node (SCEV_KNOWN);
+      TREE_TYPE (chrec_dont_know) = NULL_TREE;
+      TREE_TYPE (chrec_known) = NULL_TREE;
+    }
+}