--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/gcc/tree-scalar-evolution.c	Fri Jul 17 14:47:48 2009 +0900
@@ -0,0 +1,3103 @@
+/* Scalar evolution detector.
+   Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009
+   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 3, or (at your option) any later
+version.
+
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with GCC; see the file COPYING3.  If not see
+<http://www.gnu.org/licenses/>.  */
+
+/* 
+   Description: 
+   
+   This pass analyzes the evolution of scalar variables in loop
+   structures.  The algorithm is based on the SSA representation,
+   and on the loop hierarchy tree.  This algorithm is not based on
+   the notion of versions of a variable, as it was the case for the
+   previous implementations of the scalar evolution algorithm, but
+   it assumes that each defined name is unique.
+
+   The notation used in this file is called "chains of recurrences",
+   and has been proposed by Eugene Zima, Robert Van Engelen, and
+   others for describing induction variables in programs.  For example
+   "b -> {0, +, 2}_1" means that the scalar variable "b" is equal to 0
+   when entering in the loop_1 and has a step 2 in this loop, in other
+   words "for (b = 0; b < N; b+=2);".  Note that the coefficients of
+   this chain of recurrence (or chrec [shrek]) can contain the name of
+   other variables, in which case they are called parametric chrecs.
+   For example, "b -> {a, +, 2}_1" means that the initial value of "b"
+   is the value of "a".  In most of the cases these parametric chrecs
+   are fully instantiated before their use because symbolic names can
+   hide some difficult cases such as self-references described later
+   (see the Fibonacci example).
+   
+   A short sketch of the algorithm is:
+     
+   Given a scalar variable to be analyzed, follow the SSA edge to
+   its definition:
+     
+   - When the definition is a GIMPLE_ASSIGN: if the right hand side
+   (RHS) of the definition cannot be statically analyzed, the answer
+   of the analyzer is: "don't know".  
+   Otherwise, for all the variables that are not yet analyzed in the
+   RHS, try to determine their evolution, and finally try to
+   evaluate the operation of the RHS that gives the evolution
+   function of the analyzed variable.
+
+   - When the definition is a condition-phi-node: determine the
+   evolution function for all the branches of the phi node, and
+   finally merge these evolutions (see chrec_merge).
+
+   - When the definition is a loop-phi-node: determine its initial
+   condition, that is the SSA edge defined in an outer loop, and
+   keep it symbolic.  Then determine the SSA edges that are defined
+   in the body of the loop.  Follow the inner edges until ending on
+   another loop-phi-node of the same analyzed loop.  If the reached
+   loop-phi-node is not the starting loop-phi-node, then we keep
+   this definition under a symbolic form.  If the reached
+   loop-phi-node is the same as the starting one, then we compute a
+   symbolic stride on the return path.  The result is then the
+   symbolic chrec {initial_condition, +, symbolic_stride}_loop.
+
+   Examples:
+   
+   Example 1: Illustration of the basic algorithm.
+   
+   | a = 3
+   | loop_1
+   |   b = phi (a, c)
+   |   c = b + 1
+   |   if (c > 10) exit_loop
+   | endloop
+   
+   Suppose that we want to know the number of iterations of the
+   loop_1.  The exit_loop is controlled by a COND_EXPR (c > 10).  We
+   ask the scalar evolution analyzer two questions: what's the
+   scalar evolution (scev) of "c", and what's the scev of "10".  For
+   "10" the answer is "10" since it is a scalar constant.  For the
+   scalar variable "c", it follows the SSA edge to its definition,
+   "c = b + 1", and then asks again what's the scev of "b".
+   Following the SSA edge, we end on a loop-phi-node "b = phi (a,
+   c)", where the initial condition is "a", and the inner loop edge
+   is "c".  The initial condition is kept under a symbolic form (it
+   may be the case that the copy constant propagation has done its
+   work and we end with the constant "3" as one of the edges of the
+   loop-phi-node).  The update edge is followed to the end of the
+   loop, and until reaching again the starting loop-phi-node: b -> c
+   -> b.  At this point we have drawn a path from "b" to "b" from
+   which we compute the stride in the loop: in this example it is
+   "+1".  The resulting scev for "b" is "b -> {a, +, 1}_1".  Now
+   that the scev for "b" is known, it is possible to compute the
+   scev for "c", that is "c -> {a + 1, +, 1}_1".  In order to
+   determine the number of iterations in the loop_1, we have to
+   instantiate_parameters (loop_1, {a + 1, +, 1}_1), that gives after some
+   more analysis the scev {4, +, 1}_1, or in other words, this is
+   the function "f (x) = x + 4", where x is the iteration count of
+   the loop_1.  Now we have to solve the inequality "x + 4 > 10",
+   and take the smallest iteration number for which the loop is
+   exited: x = 7.  This loop runs from x = 0 to x = 7, and in total
+   there are 8 iterations.  In terms of loop normalization, we have
+   created a variable that is implicitly defined, "x" or just "_1",
+   and all the other analyzed scalars of the loop are defined in
+   function of this variable:
+   
+   a -> 3
+   b -> {3, +, 1}_1
+   c -> {4, +, 1}_1
+     
+   or in terms of a C program: 
+     
+   | a = 3
+   | for (x = 0; x <= 7; x++)
+   |   {
+   |     b = x + 3
+   |     c = x + 4
+   |   }
+     
+   Example 2a: Illustration of the algorithm on nested loops.
+     
+   | loop_1
+   |   a = phi (1, b)
+   |   c = a + 2
+   |   loop_2  10 times
+   |     b = phi (c, d)
+   |     d = b + 3
+   |   endloop
+   | endloop
+     
+   For analyzing the scalar evolution of "a", the algorithm follows
+   the SSA edge into the loop's body: "a -> b".  "b" is an inner
+   loop-phi-node, and its analysis as in Example 1, gives: 
+     
+   b -> {c, +, 3}_2
+   d -> {c + 3, +, 3}_2
+     
+   Following the SSA edge for the initial condition, we end on "c = a
+   + 2", and then on the starting loop-phi-node "a".  From this point,
+   the loop stride is computed: back on "c = a + 2" we get a "+2" in
+   the loop_1, then on the loop-phi-node "b" we compute the overall
+   effect of the inner loop that is "b = c + 30", and we get a "+30"
+   in the loop_1.  That means that the overall stride in loop_1 is
+   equal to "+32", and the result is: 
+     
+   a -> {1, +, 32}_1
+   c -> {3, +, 32}_1
+
+   Example 2b: Multivariate chains of recurrences.
+
+   | loop_1
+   |   k = phi (0, k + 1)
+   |   loop_2  4 times
+   |     j = phi (0, j + 1)
+   |     loop_3 4 times
+   |       i = phi (0, i + 1)
+   |       A[j + k] = ...
+   |     endloop
+   |   endloop
+   | endloop
+
+   Analyzing the access function of array A with
+   instantiate_parameters (loop_1, "j + k"), we obtain the
+   instantiation and the analysis of the scalar variables "j" and "k"
+   in loop_1.  This leads to the scalar evolution {4, +, 1}_1: the end
+   value of loop_2 for "j" is 4, and the evolution of "k" in loop_1 is
+   {0, +, 1}_1.  To obtain the evolution function in loop_3 and
+   instantiate the scalar variables up to loop_1, one has to use:
+   instantiate_scev (block_before_loop (loop_1), loop_3, "j + k").
+   The result of this call is {{0, +, 1}_1, +, 1}_2.
+
+   Example 3: Higher degree polynomials.
+     
+   | loop_1
+   |   a = phi (2, b)
+   |   c = phi (5, d)
+   |   b = a + 1
+   |   d = c + a
+   | endloop
+     
+   a -> {2, +, 1}_1
+   b -> {3, +, 1}_1
+   c -> {5, +, a}_1
+   d -> {5 + a, +, a}_1
+     
+   instantiate_parameters (loop_1, {5, +, a}_1) -> {5, +, 2, +, 1}_1
+   instantiate_parameters (loop_1, {5 + a, +, a}_1) -> {7, +, 3, +, 1}_1
+     
+   Example 4: Lucas, Fibonacci, or mixers in general.
+     
+   | loop_1
+   |   a = phi (1, b)
+   |   c = phi (3, d)
+   |   b = c
+   |   d = c + a
+   | endloop
+     
+   a -> (1, c)_1
+   c -> {3, +, a}_1
+     
+   The syntax "(1, c)_1" stands for a PEELED_CHREC that has the
+   following semantics: during the first iteration of the loop_1, the
+   variable contains the value 1, and then it contains the value "c".
+   Note that this syntax is close to the syntax of the loop-phi-node:
+   "a -> (1, c)_1" vs. "a = phi (1, c)".
+     
+   The symbolic chrec representation contains all the semantics of the
+   original code.  What is more difficult is to use this information.
+     
+   Example 5: Flip-flops, or exchangers.
+     
+   | loop_1
+   |   a = phi (1, b)
+   |   c = phi (3, d)
+   |   b = c
+   |   d = a
+   | endloop
+     
+   a -> (1, c)_1
+   c -> (3, a)_1
+     
+   Based on these symbolic chrecs, it is possible to refine this
+   information into the more precise PERIODIC_CHRECs: 
+     
+   a -> |1, 3|_1
+   c -> |3, 1|_1
+     
+   This transformation is not yet implemented.
+     
+   Further readings:
+   
+   You can find a more detailed description of the algorithm in:
+   http://icps.u-strasbg.fr/~pop/DEA_03_Pop.pdf
+   http://icps.u-strasbg.fr/~pop/DEA_03_Pop.ps.gz.  But note that
+   this is a preliminary report and some of the details of the
+   algorithm have changed.  I'm working on a research report that
+   updates the description of the algorithms to reflect the design
+   choices used in this implementation.
+     
+   A set of slides show a high level overview of the algorithm and run
+   an example through the scalar evolution analyzer:
+   http://cri.ensmp.fr/~pop/gcc/mar04/slides.pdf
+
+   The slides that I have presented at the GCC Summit'04 are available
+   at: http://cri.ensmp.fr/~pop/gcc/20040604/gccsummit-lno-spop.pdf
+*/
+
+#include "config.h"
+#include "system.h"
+#include "coretypes.h"
+#include "tm.h"
+#include "ggc.h"
+#include "tree.h"
+#include "real.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-scalar-evolution.h"
+#include "tree-pass.h"
+#include "flags.h"
+#include "params.h"
+
+static tree analyze_scalar_evolution_1 (struct loop *, tree, tree);
+
+/* The cached information about an SSA name VAR, claiming that below
+   basic block INSTANTIATED_BELOW, the value of VAR can be expressed
+   as CHREC.  */
+
+struct scev_info_str GTY(())
+{
+  basic_block instantiated_below;
+  tree var;
+  tree chrec;
+};
+
+/* Counters for the scev database.  */
+static unsigned nb_set_scev = 0;
+static unsigned nb_get_scev = 0;
+
+/* 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;
+
+static GTY ((param_is (struct scev_info_str))) htab_t scalar_evolution_info;
+
+
+/* Constructs a new SCEV_INFO_STR structure for VAR and INSTANTIATED_BELOW.  */
+
+static inline struct scev_info_str *
+new_scev_info_str (basic_block instantiated_below, tree var)
+{
+  struct scev_info_str *res;
+  
+  res = GGC_NEW (struct scev_info_str);
+  res->var = var;
+  res->chrec = chrec_not_analyzed_yet;
+  res->instantiated_below = instantiated_below;
+
+  return res;
+}
+
+/* Computes a hash function for database element ELT.  */
+
+static hashval_t
+hash_scev_info (const void *elt)
+{
+  return SSA_NAME_VERSION (((const struct scev_info_str *) elt)->var);
+}
+
+/* Compares database elements E1 and E2.  */
+
+static int
+eq_scev_info (const void *e1, const void *e2)
+{
+  const struct scev_info_str *elt1 = (const struct scev_info_str *) e1;
+  const struct scev_info_str *elt2 = (const struct scev_info_str *) e2;
+
+  return (elt1->var == elt2->var
+	  && elt1->instantiated_below == elt2->instantiated_below);
+}
+
+/* Deletes database element E.  */
+
+static void
+del_scev_info (void *e)
+{
+  ggc_free (e);
+}
+
+/* Get the scalar evolution of VAR for INSTANTIATED_BELOW basic block.
+   A first query on VAR returns chrec_not_analyzed_yet.  */
+
+static tree *
+find_var_scev_info (basic_block instantiated_below, tree var)
+{
+  struct scev_info_str *res;
+  struct scev_info_str tmp;
+  PTR *slot;
+
+  tmp.var = var;
+  tmp.instantiated_below = instantiated_below;
+  slot = htab_find_slot (scalar_evolution_info, &tmp, INSERT);
+
+  if (!*slot)
+    *slot = new_scev_info_str (instantiated_below, var);
+  res = (struct scev_info_str *) *slot;
+
+  return &res->chrec;
+}
+
+/* Return true when CHREC contains symbolic names defined in
+   LOOP_NB.  */
+
+bool 
+chrec_contains_symbols_defined_in_loop (const_tree chrec, unsigned loop_nb)
+{
+  int i, n;
+
+  if (chrec == NULL_TREE)
+    return false;
+
+  if (is_gimple_min_invariant (chrec))
+    return false;
+
+  if (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;
+
+  if (TREE_CODE (chrec) == SSA_NAME)
+    {
+      gimple def = SSA_NAME_DEF_STMT (chrec);
+      struct loop *def_loop = loop_containing_stmt (def);
+      struct loop *loop = get_loop (loop_nb);
+
+      if (def_loop == NULL)
+	return false;
+
+      if (loop == def_loop || flow_loop_nested_p (loop, def_loop))
+	return true;
+
+      return false;
+    }
+
+  n = TREE_OPERAND_LENGTH (chrec);
+  for (i = 0; i < n; i++)
+    if (chrec_contains_symbols_defined_in_loop (TREE_OPERAND (chrec, i), 
+						loop_nb))
+      return true;
+  return false;
+}
+
+/* Return true when PHI is a loop-phi-node.  */
+
+static bool
+loop_phi_node_p (gimple phi)
+{
+  /* The implementation of this function is based on the following
+     property: "all the loop-phi-nodes of a loop are contained in the
+     loop's header basic block".  */
+
+  return loop_containing_stmt (phi)->header == gimple_bb (phi);
+}
+
+/* Compute the scalar evolution for EVOLUTION_FN after crossing LOOP.
+   In general, in the case of multivariate evolutions we want to get
+   the evolution in different loops.  LOOP specifies the level for
+   which to get the evolution.
+   
+   Example:
+   
+   | for (j = 0; j < 100; j++)
+   |   {
+   |     for (k = 0; k < 100; k++)
+   |       {
+   |         i = k + j;   - Here the value of i is a function of j, k. 
+   |       }
+   |      ... = i         - Here the value of i is a function of j. 
+   |   }
+   | ... = i              - Here the value of i is a scalar.  
+   
+   Example:  
+   
+   | i_0 = ...
+   | loop_1 10 times
+   |   i_1 = phi (i_0, i_2)
+   |   i_2 = i_1 + 2
+   | endloop
+    
+   This loop has the same effect as:
+   LOOP_1 has the same effect as:
+    
+   | i_1 = i_0 + 20
+   
+   The overall effect of the loop, "i_0 + 20" in the previous example, 
+   is obtained by passing in the parameters: LOOP = 1, 
+   EVOLUTION_FN = {i_0, +, 2}_1.
+*/
+ 
+static tree 
+compute_overall_effect_of_inner_loop (struct loop *loop, tree evolution_fn)
+{
+  bool val = false;
+
+  if (evolution_fn == chrec_dont_know)
+    return chrec_dont_know;
+
+  else if (TREE_CODE (evolution_fn) == POLYNOMIAL_CHREC)
+    {
+      struct loop *inner_loop = get_chrec_loop (evolution_fn);
+
+      if (inner_loop == loop
+	  || flow_loop_nested_p (loop, inner_loop))
+	{
+	  tree nb_iter = number_of_latch_executions (inner_loop);
+
+	  if (nb_iter == chrec_dont_know)
+	    return chrec_dont_know;
+	  else
+	    {
+	      tree res;
+
+	      /* evolution_fn is the evolution function in LOOP.  Get
+		 its value in the nb_iter-th iteration.  */
+	      res = chrec_apply (inner_loop->num, evolution_fn, nb_iter);
+	      
+	      /* Continue the computation until ending on a parent of LOOP.  */
+	      return compute_overall_effect_of_inner_loop (loop, res);
+	    }
+	}
+      else
+	return evolution_fn;
+     }
+  
+  /* If the evolution function is an invariant, there is nothing to do.  */
+  else if (no_evolution_in_loop_p (evolution_fn, loop->num, &val) && val)
+    return evolution_fn;
+  
+  else
+    return chrec_dont_know;
+}
+
+/* Determine whether the CHREC is always positive/negative.  If the expression
+   cannot be statically analyzed, return false, otherwise set the answer into
+   VALUE.  */
+
+bool
+chrec_is_positive (tree chrec, bool *value)
+{
+  bool value0, value1, value2;
+  tree end_value, nb_iter;
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      if (!chrec_is_positive (CHREC_LEFT (chrec), &value0)
+	  || !chrec_is_positive (CHREC_RIGHT (chrec), &value1))
+	return false;
+     
+      /* FIXME -- overflows.  */
+      if (value0 == value1)
+	{
+	  *value = value0;
+	  return true;
+	}
+
+      /* Otherwise the chrec is under the form: "{-197, +, 2}_1",
+	 and the proof consists in showing that the sign never
+	 changes during the execution of the loop, from 0 to
+	 loop->nb_iterations.  */
+      if (!evolution_function_is_affine_p (chrec))
+	return false;
+
+      nb_iter = number_of_latch_executions (get_chrec_loop (chrec));
+      if (chrec_contains_undetermined (nb_iter))
+	return false;
+
+#if 0
+      /* TODO -- If the test is after the exit, we may decrease the number of
+	 iterations by one.  */
+      if (after_exit)
+	nb_iter = chrec_fold_minus (type, nb_iter, build_int_cst (type, 1));
+#endif
+
+      end_value = chrec_apply (CHREC_VARIABLE (chrec), chrec, nb_iter);
+	      
+      if (!chrec_is_positive (end_value, &value2))
+	return false;
+	
+      *value = value0;
+      return value0 == value1;
+      
+    case INTEGER_CST:
+      *value = (tree_int_cst_sgn (chrec) == 1);
+      return true;
+      
+    default:
+      return false;
+    }
+}
+
+/* Associate CHREC to SCALAR.  */
+
+static void
+set_scalar_evolution (basic_block instantiated_below, tree scalar, tree chrec)
+{
+  tree *scalar_info;
+ 
+  if (TREE_CODE (scalar) != SSA_NAME)
+    return;
+
+  scalar_info = find_var_scev_info (instantiated_below, scalar);
+  
+  if (dump_file)
+    {
+      if (dump_flags & TDF_DETAILS)
+	{
+	  fprintf (dump_file, "(set_scalar_evolution \n");
+	  fprintf (dump_file, "  instantiated_below = %d \n",
+		   instantiated_below->index);
+	  fprintf (dump_file, "  (scalar = ");
+	  print_generic_expr (dump_file, scalar, 0);
+	  fprintf (dump_file, ")\n  (scalar_evolution = ");
+	  print_generic_expr (dump_file, chrec, 0);
+	  fprintf (dump_file, "))\n");
+	}
+      if (dump_flags & TDF_STATS)
+	nb_set_scev++;
+    }
+  
+  *scalar_info = chrec;
+}
+
+/* Retrieve the chrec associated to SCALAR instantiated below
+   INSTANTIATED_BELOW block.  */
+
+static tree
+get_scalar_evolution (basic_block instantiated_below, tree scalar)
+{
+  tree res;
+  
+  if (dump_file)
+    {
+      if (dump_flags & TDF_DETAILS)
+	{
+	  fprintf (dump_file, "(get_scalar_evolution \n");
+	  fprintf (dump_file, "  (scalar = ");
+	  print_generic_expr (dump_file, scalar, 0);
+	  fprintf (dump_file, ")\n");
+	}
+      if (dump_flags & TDF_STATS)
+	nb_get_scev++;
+    }
+  
+  switch (TREE_CODE (scalar))
+    {
+    case SSA_NAME:
+      res = *find_var_scev_info (instantiated_below, scalar);
+      break;
+
+    case REAL_CST:
+    case FIXED_CST:
+    case INTEGER_CST:
+      res = scalar;
+      break;
+
+    default:
+      res = chrec_not_analyzed_yet;
+      break;
+    }
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (scalar_evolution = ");
+      print_generic_expr (dump_file, res, 0);
+      fprintf (dump_file, "))\n");
+    }
+  
+  return res;
+}
+
+/* Helper function for add_to_evolution.  Returns the evolution
+   function for an assignment of the form "a = b + c", where "a" and
+   "b" are on the strongly connected component.  CHREC_BEFORE is the
+   information that we already have collected up to this point.
+   TO_ADD is the evolution of "c".  
+   
+   When CHREC_BEFORE has an evolution part in LOOP_NB, add to this
+   evolution the expression TO_ADD, otherwise construct an evolution
+   part for this loop.  */
+
+static tree
+add_to_evolution_1 (unsigned loop_nb, tree chrec_before, tree to_add,
+		    gimple at_stmt)
+{
+  tree type, left, right;
+  struct loop *loop = get_loop (loop_nb), *chloop;
+
+  switch (TREE_CODE (chrec_before))
+    {
+    case POLYNOMIAL_CHREC:
+      chloop = get_chrec_loop (chrec_before);
+      if (chloop == loop
+	  || flow_loop_nested_p (chloop, loop))
+	{
+	  unsigned var;
+
+	  type = chrec_type (chrec_before);
+	  
+	  /* When there is no evolution part in this loop, build it.  */
+	  if (chloop != loop)
+	    {
+	      var = loop_nb;
+	      left = chrec_before;
+	      right = SCALAR_FLOAT_TYPE_P (type)
+		? build_real (type, dconst0)
+		: build_int_cst (type, 0);
+	    }
+	  else
+	    {
+	      var = CHREC_VARIABLE (chrec_before);
+	      left = CHREC_LEFT (chrec_before);
+	      right = CHREC_RIGHT (chrec_before);
+	    }
+
+	  to_add = chrec_convert (type, to_add, at_stmt);
+	  right = chrec_convert_rhs (type, right, at_stmt);
+	  right = chrec_fold_plus (chrec_type (right), right, to_add);
+	  return build_polynomial_chrec (var, left, right);
+	}
+      else
+	{
+	  gcc_assert (flow_loop_nested_p (loop, chloop));
+
+	  /* Search the evolution in LOOP_NB.  */
+	  left = add_to_evolution_1 (loop_nb, CHREC_LEFT (chrec_before),
+				     to_add, at_stmt);
+	  right = CHREC_RIGHT (chrec_before);
+	  right = chrec_convert_rhs (chrec_type (left), right, at_stmt);
+	  return build_polynomial_chrec (CHREC_VARIABLE (chrec_before),
+					 left, right);
+	}
+      
+    default:
+      /* These nodes do not depend on a loop.  */
+      if (chrec_before == chrec_dont_know)
+	return chrec_dont_know;
+
+      left = chrec_before;
+      right = chrec_convert_rhs (chrec_type (left), to_add, at_stmt);
+      return build_polynomial_chrec (loop_nb, left, right);
+    }
+}
+
+/* Add TO_ADD to the evolution part of CHREC_BEFORE in the dimension
+   of LOOP_NB.  
+   
+   Description (provided for completeness, for those who read code in
+   a plane, and for my poor 62 bytes brain that would have forgotten
+   all this in the next two or three months):
+   
+   The algorithm of translation of programs from the SSA representation
+   into the chrecs syntax is based on a pattern matching.  After having
+   reconstructed the overall tree expression for a loop, there are only
+   two cases that can arise:
+   
+   1. a = loop-phi (init, a + expr)
+   2. a = loop-phi (init, expr)
+   
+   where EXPR is either a scalar constant with respect to the analyzed
+   loop (this is a degree 0 polynomial), or an expression containing
+   other loop-phi definitions (these are higher degree polynomials).
+   
+   Examples:
+   
+   1. 
+   | init = ...
+   | loop_1
+   |   a = phi (init, a + 5)
+   | endloop
+   
+   2. 
+   | inita = ...
+   | initb = ...
+   | loop_1
+   |   a = phi (inita, 2 * b + 3)
+   |   b = phi (initb, b + 1)
+   | endloop
+   
+   For the first case, the semantics of the SSA representation is: 
+   
+   | a (x) = init + \sum_{j = 0}^{x - 1} expr (j)
+   
+   that is, there is a loop index "x" that determines the scalar value
+   of the variable during the loop execution.  During the first
+   iteration, the value is that of the initial condition INIT, while
+   during the subsequent iterations, it is the sum of the initial
+   condition with the sum of all the values of EXPR from the initial
+   iteration to the before last considered iteration.  
+   
+   For the second case, the semantics of the SSA program is:
+   
+   | a (x) = init, if x = 0;
+   |         expr (x - 1), otherwise.
+   
+   The second case corresponds to the PEELED_CHREC, whose syntax is
+   close to the syntax of a loop-phi-node: 
+   
+   | phi (init, expr)  vs.  (init, expr)_x
+   
+   The proof of the translation algorithm for the first case is a
+   proof by structural induction based on the degree of EXPR.  
+   
+   Degree 0:
+   When EXPR is a constant with respect to the analyzed loop, or in
+   other words when EXPR is a polynomial of degree 0, the evolution of
+   the variable A in the loop is an affine function with an initial
+   condition INIT, and a step EXPR.  In order to show this, we start
+   from the semantics of the SSA representation:
+   
+   f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
+   
+   and since "expr (j)" is a constant with respect to "j",
+   
+   f (x) = init + x * expr 
+   
+   Finally, based on the semantics of the pure sum chrecs, by
+   identification we get the corresponding chrecs syntax:
+   
+   f (x) = init * \binom{x}{0} + expr * \binom{x}{1} 
+   f (x) -> {init, +, expr}_x
+   
+   Higher degree:
+   Suppose that EXPR is a polynomial of degree N with respect to the
+   analyzed loop_x for which we have already determined that it is
+   written under the chrecs syntax:
+   
+   | expr (x)  ->  {b_0, +, b_1, +, ..., +, b_{n-1}} (x)
+   
+   We start from the semantics of the SSA program:
+   
+   | f (x) = init + \sum_{j = 0}^{x - 1} expr (j)
+   |
+   | f (x) = init + \sum_{j = 0}^{x - 1} 
+   |                (b_0 * \binom{j}{0} + ... + b_{n-1} * \binom{j}{n-1})
+   |
+   | f (x) = init + \sum_{j = 0}^{x - 1} 
+   |                \sum_{k = 0}^{n - 1} (b_k * \binom{j}{k}) 
+   |
+   | f (x) = init + \sum_{k = 0}^{n - 1} 
+   |                (b_k * \sum_{j = 0}^{x - 1} \binom{j}{k}) 
+   |
+   | f (x) = init + \sum_{k = 0}^{n - 1} 
+   |                (b_k * \binom{x}{k + 1}) 
+   |
+   | f (x) = init + b_0 * \binom{x}{1} + ... 
+   |              + b_{n-1} * \binom{x}{n} 
+   |
+   | f (x) = init * \binom{x}{0} + b_0 * \binom{x}{1} + ... 
+   |                             + b_{n-1} * \binom{x}{n} 
+   |
+   
+   And finally from the definition of the chrecs syntax, we identify:
+   | f (x)  ->  {init, +, b_0, +, ..., +, b_{n-1}}_x 
+   
+   This shows the mechanism that stands behind the add_to_evolution
+   function.  An important point is that the use of symbolic
+   parameters avoids the need of an analysis schedule.
+   
+   Example:
+   
+   | inita = ...
+   | initb = ...
+   | loop_1 
+   |   a = phi (inita, a + 2 + b)
+   |   b = phi (initb, b + 1)
+   | endloop
+   
+   When analyzing "a", the algorithm keeps "b" symbolically:
+   
+   | a  ->  {inita, +, 2 + b}_1
+   
+   Then, after instantiation, the analyzer ends on the evolution:
+   
+   | a  ->  {inita, +, 2 + initb, +, 1}_1
+
+*/
+
+static tree 
+add_to_evolution (unsigned loop_nb, tree chrec_before, enum tree_code code,
+		  tree to_add, gimple at_stmt)
+{
+  tree type = chrec_type (to_add);
+  tree res = NULL_TREE;
+  
+  if (to_add == NULL_TREE)
+    return chrec_before;
+  
+  /* TO_ADD is either a scalar, or a parameter.  TO_ADD is not
+     instantiated at this point.  */
+  if (TREE_CODE (to_add) == POLYNOMIAL_CHREC)
+    /* This should not happen.  */
+    return chrec_dont_know;
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "(add_to_evolution \n");
+      fprintf (dump_file, "  (loop_nb = %d)\n", loop_nb);
+      fprintf (dump_file, "  (chrec_before = ");
+      print_generic_expr (dump_file, chrec_before, 0);
+      fprintf (dump_file, ")\n  (to_add = ");
+      print_generic_expr (dump_file, to_add, 0);
+      fprintf (dump_file, ")\n");
+    }
+
+  if (code == MINUS_EXPR)
+    to_add = chrec_fold_multiply (type, to_add, SCALAR_FLOAT_TYPE_P (type)
+				  ? build_real (type, dconstm1)
+				  : build_int_cst_type (type, -1));
+
+  res = add_to_evolution_1 (loop_nb, chrec_before, to_add, at_stmt);
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (res = ");
+      print_generic_expr (dump_file, res, 0);
+      fprintf (dump_file, "))\n");
+    }
+
+  return res;
+}
+
+/* Helper function.  */
+
+static inline tree
+set_nb_iterations_in_loop (struct loop *loop, 
+			   tree res)
+{
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (set_nb_iterations_in_loop = ");
+      print_generic_expr (dump_file, res, 0);
+      fprintf (dump_file, "))\n");
+    }
+  
+  loop->nb_iterations = res;
+  return res;
+}
+
+
+
+/* This section selects the loops that will be good candidates for the
+   scalar evolution analysis.  For the moment, greedily select all the
+   loop nests we could analyze.  */
+
+/* For a loop with a single exit edge, return the COND_EXPR that
+   guards the exit edge.  If the expression is too difficult to
+   analyze, then give up.  */
+
+gimple 
+get_loop_exit_condition (const struct loop *loop)
+{
+  gimple res = NULL;
+  edge exit_edge = single_exit (loop);
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, "(get_loop_exit_condition \n  ");
+  
+  if (exit_edge)
+    {
+      gimple stmt;
+      
+      stmt = last_stmt (exit_edge->src);
+      if (gimple_code (stmt) == GIMPLE_COND)
+	res = stmt;
+    }
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      print_gimple_stmt (dump_file, res, 0, 0);
+      fprintf (dump_file, ")\n");
+    }
+  
+  return res;
+}
+
+/* Recursively determine and enqueue the exit conditions for a loop.  */
+
+static void 
+get_exit_conditions_rec (struct loop *loop, 
+			 VEC(gimple,heap) **exit_conditions)
+{
+  if (!loop)
+    return;
+  
+  /* Recurse on the inner loops, then on the next (sibling) loops.  */
+  get_exit_conditions_rec (loop->inner, exit_conditions);
+  get_exit_conditions_rec (loop->next, exit_conditions);
+  
+  if (single_exit (loop))
+    {
+      gimple loop_condition = get_loop_exit_condition (loop);
+      
+      if (loop_condition)
+	VEC_safe_push (gimple, heap, *exit_conditions, loop_condition);
+    }
+}
+
+/* Select the candidate loop nests for the analysis.  This function
+   initializes the EXIT_CONDITIONS array.  */
+
+static void
+select_loops_exit_conditions (VEC(gimple,heap) **exit_conditions)
+{
+  struct loop *function_body = current_loops->tree_root;
+  
+  get_exit_conditions_rec (function_body->inner, exit_conditions);
+}
+
+
+/* Depth first search algorithm.  */
+
+typedef enum t_bool {
+  t_false,
+  t_true,
+  t_dont_know
+} t_bool;
+
+
+static t_bool follow_ssa_edge (struct loop *loop, gimple, gimple, tree *, int);
+
+/* Follow the ssa edge into the binary expression RHS0 CODE RHS1.
+   Return true if the strongly connected component has been found.  */
+
+static t_bool
+follow_ssa_edge_binary (struct loop *loop, gimple at_stmt,
+			tree type, tree rhs0, enum tree_code code, tree rhs1,
+			gimple halting_phi, tree *evolution_of_loop, int limit)
+{
+  t_bool res = t_false;
+  tree evol;
+
+  switch (code)
+    {
+    case POINTER_PLUS_EXPR:
+    case PLUS_EXPR:
+      if (TREE_CODE (rhs0) == SSA_NAME)
+	{
+	  if (TREE_CODE (rhs1) == SSA_NAME)
+	    {
+	      /* Match an assignment under the form: 
+		 "a = b + c".  */
+      
+	      /* We want only assignments of form "name + name" contribute to
+		 LIMIT, as the other cases do not necessarily contribute to
+		 the complexity of the expression.  */
+	      limit++;
+
+	      evol = *evolution_of_loop;
+	      res = follow_ssa_edge 
+		(loop, SSA_NAME_DEF_STMT (rhs0), halting_phi, &evol, limit);
+	      
+	      if (res == t_true)
+		*evolution_of_loop = add_to_evolution 
+		  (loop->num, 
+		   chrec_convert (type, evol, at_stmt), 
+		   code, rhs1, at_stmt);
+	      
+	      else if (res == t_false)
+		{
+		  res = follow_ssa_edge 
+		    (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi, 
+		     evolution_of_loop, limit);
+		  
+		  if (res == t_true)
+		    *evolution_of_loop = add_to_evolution 
+		      (loop->num, 
+		       chrec_convert (type, *evolution_of_loop, at_stmt), 
+		       code, rhs0, at_stmt);
+
+		  else if (res == t_dont_know)
+		    *evolution_of_loop = chrec_dont_know;
+		}
+
+	      else if (res == t_dont_know)
+		*evolution_of_loop = chrec_dont_know;
+	    }
+	  
+	  else
+	    {
+	      /* Match an assignment under the form: 
+		 "a = b + ...".  */
+	      res = follow_ssa_edge 
+		(loop, SSA_NAME_DEF_STMT (rhs0), halting_phi, 
+		 evolution_of_loop, limit);
+	      if (res == t_true)
+		*evolution_of_loop = add_to_evolution 
+		  (loop->num, chrec_convert (type, *evolution_of_loop,
+					     at_stmt),
+		   code, rhs1, at_stmt);
+
+	      else if (res == t_dont_know)
+		*evolution_of_loop = chrec_dont_know;
+	    }
+	}
+      
+      else if (TREE_CODE (rhs1) == SSA_NAME)
+	{
+	  /* Match an assignment under the form: 
+	     "a = ... + c".  */
+	  res = follow_ssa_edge 
+	    (loop, SSA_NAME_DEF_STMT (rhs1), halting_phi, 
+	     evolution_of_loop, limit);
+	  if (res == t_true)
+	    *evolution_of_loop = add_to_evolution 
+	      (loop->num, chrec_convert (type, *evolution_of_loop,
+					 at_stmt),
+	       code, rhs0, at_stmt);
+
+	  else if (res == t_dont_know)
+	    *evolution_of_loop = chrec_dont_know;
+	}
+
+      else
+	/* Otherwise, match an assignment under the form: 
+	   "a = ... + ...".  */
+	/* And there is nothing to do.  */
+	res = t_false;
+      break;
+      
+    case MINUS_EXPR:
+      /* This case is under the form "opnd0 = rhs0 - rhs1".  */
+      if (TREE_CODE (rhs0) == SSA_NAME)
+	{
+	  /* Match an assignment under the form: 
+	     "a = b - ...".  */
+
+	  /* We want only assignments of form "name - name" contribute to
+	     LIMIT, as the other cases do not necessarily contribute to
+	     the complexity of the expression.  */
+	  if (TREE_CODE (rhs1) == SSA_NAME)
+	    limit++;
+
+	  res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (rhs0), halting_phi, 
+				 evolution_of_loop, limit);
+	  if (res == t_true)
+	    *evolution_of_loop = add_to_evolution 
+	      (loop->num, chrec_convert (type, *evolution_of_loop, at_stmt),
+	       MINUS_EXPR, rhs1, at_stmt);
+
+	  else if (res == t_dont_know)
+	    *evolution_of_loop = chrec_dont_know;
+	}
+      else
+	/* Otherwise, match an assignment under the form: 
+	   "a = ... - ...".  */
+	/* And there is nothing to do.  */
+	res = t_false;
+      break;
+
+    default:
+      res = t_false;
+    }
+
+  return res;
+}
+    
+/* Follow the ssa edge into the expression EXPR.
+   Return true if the strongly connected component has been found.  */
+
+static t_bool
+follow_ssa_edge_expr (struct loop *loop, gimple at_stmt, tree expr, 
+		      gimple halting_phi, tree *evolution_of_loop, int limit)
+{
+  t_bool res = t_false;
+  tree rhs0, rhs1;
+  tree type = TREE_TYPE (expr);
+  enum tree_code code;
+  
+  /* The EXPR is one of the following cases:
+     - an SSA_NAME, 
+     - an INTEGER_CST,
+     - a PLUS_EXPR, 
+     - a POINTER_PLUS_EXPR, 
+     - a MINUS_EXPR,
+     - an ASSERT_EXPR,
+     - other cases are not yet handled.  */
+  code = TREE_CODE (expr);
+  switch (code)
+    {
+    case NOP_EXPR:
+      /* This assignment is under the form "a_1 = (cast) rhs.  */
+      res = follow_ssa_edge_expr (loop, at_stmt, TREE_OPERAND (expr, 0),
+				  halting_phi, evolution_of_loop, limit);
+      *evolution_of_loop = chrec_convert (type, *evolution_of_loop, at_stmt);
+      break;
+
+    case INTEGER_CST:
+      /* This assignment is under the form "a_1 = 7".  */
+      res = t_false;
+      break;
+      
+    case SSA_NAME:
+      /* This assignment is under the form: "a_1 = b_2".  */
+      res = follow_ssa_edge 
+	(loop, SSA_NAME_DEF_STMT (expr), halting_phi, evolution_of_loop, limit);
+      break;
+      
+    case POINTER_PLUS_EXPR:
+    case PLUS_EXPR:
+    case MINUS_EXPR:
+      /* This case is under the form "rhs0 +- rhs1".  */
+      rhs0 = TREE_OPERAND (expr, 0);
+      rhs1 = TREE_OPERAND (expr, 1);
+      STRIP_TYPE_NOPS (rhs0);
+      STRIP_TYPE_NOPS (rhs1);
+      return follow_ssa_edge_binary (loop, at_stmt, type, rhs0, code, rhs1,
+				     halting_phi, evolution_of_loop, limit);
+
+    case ASSERT_EXPR:
+      {
+	/* This assignment is of the form: "a_1 = ASSERT_EXPR <a_2, ...>"
+	   It must be handled as a copy assignment of the form a_1 = a_2.  */
+	tree op0 = ASSERT_EXPR_VAR (expr);
+	if (TREE_CODE (op0) == SSA_NAME)
+	  res = follow_ssa_edge (loop, SSA_NAME_DEF_STMT (op0),
+				 halting_phi, evolution_of_loop, limit);
+	else
+	  res = t_false;
+	break;
+      }
+
+
+    default:
+      res = t_false;
+      break;
+    }
+  
+  return res;
+}
+
+/* Follow the ssa edge into the right hand side of an assignment STMT.
+   Return true if the strongly connected component has been found.  */
+
+static t_bool
+follow_ssa_edge_in_rhs (struct loop *loop, gimple stmt,
+			gimple halting_phi, tree *evolution_of_loop, int limit)
+{
+  tree type = TREE_TYPE (gimple_assign_lhs (stmt));
+  enum tree_code code = gimple_assign_rhs_code (stmt);
+
+  switch (get_gimple_rhs_class (code))
+    {
+    case GIMPLE_BINARY_RHS:
+      return follow_ssa_edge_binary (loop, stmt, type,
+				     gimple_assign_rhs1 (stmt), code,
+				     gimple_assign_rhs2 (stmt),
+				     halting_phi, evolution_of_loop, limit);
+    case GIMPLE_SINGLE_RHS:
+      return follow_ssa_edge_expr (loop, stmt, gimple_assign_rhs1 (stmt),
+				   halting_phi, evolution_of_loop, limit);
+    case GIMPLE_UNARY_RHS:
+      if (code == NOP_EXPR)
+	{
+	  /* This assignment is under the form "a_1 = (cast) rhs.  */
+	  t_bool res
+	    = follow_ssa_edge_expr (loop, stmt, gimple_assign_rhs1 (stmt),
+				    halting_phi, evolution_of_loop, limit);
+	  *evolution_of_loop = chrec_convert (type, *evolution_of_loop, stmt);
+	  return res;
+	}
+      /* FALLTHRU */
+
+    default:
+      return t_false;
+    }
+}
+
+/* Checks whether the I-th argument of a PHI comes from a backedge.  */
+
+static bool
+backedge_phi_arg_p (gimple phi, int i)
+{
+  const_edge e = gimple_phi_arg_edge (phi, i);
+
+  /* We would in fact like to test EDGE_DFS_BACK here, but we do not care
+     about updating it anywhere, and this should work as well most of the
+     time.  */
+  if (e->flags & EDGE_IRREDUCIBLE_LOOP)
+    return true;
+
+  return false;
+}
+
+/* Helper function for one branch of the condition-phi-node.  Return
+   true if the strongly connected component has been found following
+   this path.  */
+
+static inline t_bool
+follow_ssa_edge_in_condition_phi_branch (int i,
+					 struct loop *loop, 
+					 gimple condition_phi, 
+					 gimple halting_phi,
+					 tree *evolution_of_branch,
+					 tree init_cond, int limit)
+{
+  tree branch = PHI_ARG_DEF (condition_phi, i);
+  *evolution_of_branch = chrec_dont_know;
+
+  /* Do not follow back edges (they must belong to an irreducible loop, which
+     we really do not want to worry about).  */
+  if (backedge_phi_arg_p (condition_phi, i))
+    return t_false;
+
+  if (TREE_CODE (branch) == SSA_NAME)
+    {
+      *evolution_of_branch = init_cond;
+      return follow_ssa_edge (loop, SSA_NAME_DEF_STMT (branch), halting_phi, 
+			      evolution_of_branch, limit);
+    }
+
+  /* This case occurs when one of the condition branches sets 
+     the variable to a constant: i.e. a phi-node like
+     "a_2 = PHI <a_7(5), 2(6)>;".  
+	 
+     FIXME:  This case have to be refined correctly: 
+     in some cases it is possible to say something better than
+     chrec_dont_know, for example using a wrap-around notation.  */
+  return t_false;
+}
+
+/* This function merges the branches of a condition-phi-node in a
+   loop.  */
+
+static t_bool
+follow_ssa_edge_in_condition_phi (struct loop *loop,
+				  gimple condition_phi, 
+				  gimple halting_phi, 
+				  tree *evolution_of_loop, int limit)
+{
+  int i, n;
+  tree init = *evolution_of_loop;
+  tree evolution_of_branch;
+  t_bool res = follow_ssa_edge_in_condition_phi_branch (0, loop, condition_phi,
+							halting_phi,
+							&evolution_of_branch,
+							init, limit);
+  if (res == t_false || res == t_dont_know)
+    return res;
+
+  *evolution_of_loop = evolution_of_branch;
+
+  /* If the phi node is just a copy, do not increase the limit.  */
+  n = gimple_phi_num_args (condition_phi);
+  if (n > 1)
+    limit++;
+
+  for (i = 1; i < n; i++)
+    {
+      /* Quickly give up when the evolution of one of the branches is
+	 not known.  */
+      if (*evolution_of_loop == chrec_dont_know)
+	return t_true;
+
+      res = follow_ssa_edge_in_condition_phi_branch (i, loop, condition_phi,
+						     halting_phi,
+						     &evolution_of_branch,
+						     init, limit);
+      if (res == t_false || res == t_dont_know)
+	return res;
+
+      *evolution_of_loop = chrec_merge (*evolution_of_loop,
+					evolution_of_branch);
+    }
+  
+  return t_true;
+}
+
+/* Follow an SSA edge in an inner loop.  It computes the overall
+   effect of the loop, and following the symbolic initial conditions,
+   it follows the edges in the parent loop.  The inner loop is
+   considered as a single statement.  */
+
+static t_bool
+follow_ssa_edge_inner_loop_phi (struct loop *outer_loop,
+				gimple loop_phi_node, 
+				gimple halting_phi,
+				tree *evolution_of_loop, int limit)
+{
+  struct loop *loop = loop_containing_stmt (loop_phi_node);
+  tree ev = analyze_scalar_evolution (loop, PHI_RESULT (loop_phi_node));
+
+  /* Sometimes, the inner loop is too difficult to analyze, and the
+     result of the analysis is a symbolic parameter.  */
+  if (ev == PHI_RESULT (loop_phi_node))
+    {
+      t_bool res = t_false;
+      int i, n = gimple_phi_num_args (loop_phi_node);
+
+      for (i = 0; i < n; i++)
+	{
+	  tree arg = PHI_ARG_DEF (loop_phi_node, i);
+	  basic_block bb;
+
+	  /* Follow the edges that exit the inner loop.  */
+	  bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
+	  if (!flow_bb_inside_loop_p (loop, bb))
+	    res = follow_ssa_edge_expr (outer_loop, loop_phi_node,
+					arg, halting_phi,
+					evolution_of_loop, limit);
+	  if (res == t_true)
+	    break;
+	}
+
+      /* If the path crosses this loop-phi, give up.  */
+      if (res == t_true)
+	*evolution_of_loop = chrec_dont_know;
+
+      return res;
+    }
+
+  /* Otherwise, compute the overall effect of the inner loop.  */
+  ev = compute_overall_effect_of_inner_loop (loop, ev);
+  return follow_ssa_edge_expr (outer_loop, loop_phi_node, ev, halting_phi,
+			       evolution_of_loop, limit);
+}
+
+/* Follow an SSA edge from a loop-phi-node to itself, constructing a
+   path that is analyzed on the return walk.  */
+
+static t_bool
+follow_ssa_edge (struct loop *loop, gimple def, gimple halting_phi,
+		 tree *evolution_of_loop, int limit)
+{
+  struct loop *def_loop;
+  
+  if (gimple_nop_p (def))
+    return t_false;
+  
+  /* Give up if the path is longer than the MAX that we allow.  */
+  if (limit > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
+    return t_dont_know;
+  
+  def_loop = loop_containing_stmt (def);
+  
+  switch (gimple_code (def))
+    {
+    case GIMPLE_PHI:
+      if (!loop_phi_node_p (def))
+	/* DEF is a condition-phi-node.  Follow the branches, and
+	   record their evolutions.  Finally, merge the collected
+	   information and set the approximation to the main
+	   variable.  */
+	return follow_ssa_edge_in_condition_phi 
+	  (loop, def, halting_phi, evolution_of_loop, limit);
+
+      /* When the analyzed phi is the halting_phi, the
+	 depth-first search is over: we have found a path from
+	 the halting_phi to itself in the loop.  */
+      if (def == halting_phi)
+	return t_true;
+	  
+      /* Otherwise, the evolution of the HALTING_PHI depends
+	 on the evolution of another loop-phi-node, i.e. the
+	 evolution function is a higher degree polynomial.  */
+      if (def_loop == loop)
+	return t_false;
+	  
+      /* Inner loop.  */
+      if (flow_loop_nested_p (loop, def_loop))
+	return follow_ssa_edge_inner_loop_phi 
+	  (loop, def, halting_phi, evolution_of_loop, limit + 1);
+
+      /* Outer loop.  */
+      return t_false;
+
+    case GIMPLE_ASSIGN:
+      return follow_ssa_edge_in_rhs (loop, def, halting_phi, 
+				     evolution_of_loop, limit);
+      
+    default:
+      /* At this level of abstraction, the program is just a set
+	 of GIMPLE_ASSIGNs and PHI_NODEs.  In principle there is no
+	 other node to be handled.  */
+      return t_false;
+    }
+}
+
+
+
+/* Given a LOOP_PHI_NODE, this function determines the evolution
+   function from LOOP_PHI_NODE to LOOP_PHI_NODE in the loop.  */
+
+static tree
+analyze_evolution_in_loop (gimple loop_phi_node, 
+			   tree init_cond)
+{
+  int i, n = gimple_phi_num_args (loop_phi_node);
+  tree evolution_function = chrec_not_analyzed_yet;
+  struct loop *loop = loop_containing_stmt (loop_phi_node);
+  basic_block bb;
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "(analyze_evolution_in_loop \n");
+      fprintf (dump_file, "  (loop_phi_node = ");
+      print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
+      fprintf (dump_file, ")\n");
+    }
+  
+  for (i = 0; i < n; i++)
+    {
+      tree arg = PHI_ARG_DEF (loop_phi_node, i);
+      gimple ssa_chain;
+      tree ev_fn;
+      t_bool res;
+
+      /* Select the edges that enter the loop body.  */
+      bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
+      if (!flow_bb_inside_loop_p (loop, bb))
+	continue;
+      
+      if (TREE_CODE (arg) == SSA_NAME)
+	{
+	  ssa_chain = SSA_NAME_DEF_STMT (arg);
+
+	  /* Pass in the initial condition to the follow edge function.  */
+	  ev_fn = init_cond;
+	  res = follow_ssa_edge (loop, ssa_chain, loop_phi_node, &ev_fn, 0);
+	}
+      else
+	res = t_false;
+	      
+      /* When it is impossible to go back on the same
+	 loop_phi_node by following the ssa edges, the
+	 evolution is represented by a peeled chrec, i.e. the
+	 first iteration, EV_FN has the value INIT_COND, then
+	 all the other iterations it has the value of ARG.  
+	 For the moment, PEELED_CHREC nodes are not built.  */
+      if (res != t_true)
+	ev_fn = chrec_dont_know;
+      
+      /* When there are multiple back edges of the loop (which in fact never
+	 happens currently, but nevertheless), merge their evolutions.  */
+      evolution_function = chrec_merge (evolution_function, ev_fn);
+    }
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (evolution_function = ");
+      print_generic_expr (dump_file, evolution_function, 0);
+      fprintf (dump_file, "))\n");
+    }
+  
+  return evolution_function;
+}
+
+/* Given a loop-phi-node, return the initial conditions of the
+   variable on entry of the loop.  When the CCP has propagated
+   constants into the loop-phi-node, the initial condition is
+   instantiated, otherwise the initial condition is kept symbolic.
+   This analyzer does not analyze the evolution outside the current
+   loop, and leaves this task to the on-demand tree reconstructor.  */
+
+static tree 
+analyze_initial_condition (gimple loop_phi_node)
+{
+  int i, n;
+  tree init_cond = chrec_not_analyzed_yet;
+  struct loop *loop = loop_containing_stmt (loop_phi_node);
+  
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "(analyze_initial_condition \n");
+      fprintf (dump_file, "  (loop_phi_node = \n");
+      print_gimple_stmt (dump_file, loop_phi_node, 0, 0);
+      fprintf (dump_file, ")\n");
+    }
+  
+  n = gimple_phi_num_args (loop_phi_node);
+  for (i = 0; i < n; i++)
+    {
+      tree branch = PHI_ARG_DEF (loop_phi_node, i);
+      basic_block bb = gimple_phi_arg_edge (loop_phi_node, i)->src;
+      
+      /* When the branch is oriented to the loop's body, it does
+     	 not contribute to the initial condition.  */
+      if (flow_bb_inside_loop_p (loop, bb))
+       	continue;
+
+      if (init_cond == chrec_not_analyzed_yet)
+	{
+	  init_cond = branch;
+	  continue;
+	}
+
+      if (TREE_CODE (branch) == SSA_NAME)
+	{
+	  init_cond = chrec_dont_know;
+      	  break;
+	}
+
+      init_cond = chrec_merge (init_cond, branch);
+    }
+
+  /* Ooops -- a loop without an entry???  */
+  if (init_cond == chrec_not_analyzed_yet)
+    init_cond = chrec_dont_know;
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (init_cond = ");
+      print_generic_expr (dump_file, init_cond, 0);
+      fprintf (dump_file, "))\n");
+    }
+  
+  return init_cond;
+}
+
+/* Analyze the scalar evolution for LOOP_PHI_NODE.  */
+
+static tree 
+interpret_loop_phi (struct loop *loop, gimple loop_phi_node)
+{
+  tree res;
+  struct loop *phi_loop = loop_containing_stmt (loop_phi_node);
+  tree init_cond;
+  
+  if (phi_loop != loop)
+    {
+      struct loop *subloop;
+      tree evolution_fn = analyze_scalar_evolution
+	(phi_loop, PHI_RESULT (loop_phi_node));
+
+      /* Dive one level deeper.  */
+      subloop = superloop_at_depth (phi_loop, loop_depth (loop) + 1);
+
+      /* Interpret the subloop.  */
+      res = compute_overall_effect_of_inner_loop (subloop, evolution_fn);
+      return res;
+    }
+
+  /* Otherwise really interpret the loop phi.  */
+  init_cond = analyze_initial_condition (loop_phi_node);
+  res = analyze_evolution_in_loop (loop_phi_node, init_cond);
+
+  return res;
+}
+
+/* This function merges the branches of a condition-phi-node,
+   contained in the outermost loop, and whose arguments are already
+   analyzed.  */
+
+static tree
+interpret_condition_phi (struct loop *loop, gimple condition_phi)
+{
+  int i, n = gimple_phi_num_args (condition_phi);
+  tree res = chrec_not_analyzed_yet;
+  
+  for (i = 0; i < n; i++)
+    {
+      tree branch_chrec;
+      
+      if (backedge_phi_arg_p (condition_phi, i))
+	{
+	  res = chrec_dont_know;
+	  break;
+	}
+
+      branch_chrec = analyze_scalar_evolution
+	(loop, PHI_ARG_DEF (condition_phi, i));
+      
+      res = chrec_merge (res, branch_chrec);
+    }
+
+  return res;
+}
+
+/* Interpret the operation RHS1 OP RHS2.  If we didn't
+   analyze this node before, follow the definitions until ending
+   either on an analyzed GIMPLE_ASSIGN, or on a loop-phi-node.  On the
+   return path, this function propagates evolutions (ala constant copy
+   propagation).  OPND1 is not a GIMPLE expression because we could
+   analyze the effect of an inner loop: see interpret_loop_phi.  */
+
+static tree
+interpret_rhs_expr (struct loop *loop, gimple at_stmt,
+		    tree type, tree rhs1, enum tree_code code, tree rhs2)
+{
+  tree res, chrec1, chrec2;
+
+  if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS)
+    {
+      if (is_gimple_min_invariant (rhs1))
+	return chrec_convert (type, rhs1, at_stmt);
+
+      if (code == SSA_NAME)
+	return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
+			      at_stmt);
+
+      if (code == ASSERT_EXPR)
+	{
+	  rhs1 = ASSERT_EXPR_VAR (rhs1);
+	  return chrec_convert (type, analyze_scalar_evolution (loop, rhs1),
+				at_stmt);
+	}
+
+      return chrec_dont_know;
+    }
+
+  switch (code)
+    {
+    case POINTER_PLUS_EXPR:
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      chrec2 = analyze_scalar_evolution (loop, rhs2);
+      chrec1 = chrec_convert (type, chrec1, at_stmt);
+      chrec2 = chrec_convert (sizetype, chrec2, at_stmt);
+      res = chrec_fold_plus (type, chrec1, chrec2);
+      break;
+
+    case PLUS_EXPR:
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      chrec2 = analyze_scalar_evolution (loop, rhs2);
+      chrec1 = chrec_convert (type, chrec1, at_stmt);
+      chrec2 = chrec_convert (type, chrec2, at_stmt);
+      res = chrec_fold_plus (type, chrec1, chrec2);
+      break;
+      
+    case MINUS_EXPR:
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      chrec2 = analyze_scalar_evolution (loop, rhs2);
+      chrec1 = chrec_convert (type, chrec1, at_stmt);
+      chrec2 = chrec_convert (type, chrec2, at_stmt);
+      res = chrec_fold_minus (type, chrec1, chrec2);
+      break;
+
+    case NEGATE_EXPR:
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      chrec1 = chrec_convert (type, chrec1, at_stmt);
+      /* TYPE may be integer, real or complex, so use fold_convert.  */
+      res = chrec_fold_multiply (type, chrec1,
+				 fold_convert (type, integer_minus_one_node));
+      break;
+
+    case BIT_NOT_EXPR:
+      /* Handle ~X as -1 - X.  */
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      chrec1 = chrec_convert (type, chrec1, at_stmt);
+      res = chrec_fold_minus (type,
+			      fold_convert (type, integer_minus_one_node),
+			      chrec1);
+      break;
+
+    case MULT_EXPR:
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      chrec2 = analyze_scalar_evolution (loop, rhs2);
+      chrec1 = chrec_convert (type, chrec1, at_stmt);
+      chrec2 = chrec_convert (type, chrec2, at_stmt);
+      res = chrec_fold_multiply (type, chrec1, chrec2);
+      break;
+      
+    CASE_CONVERT:
+      chrec1 = analyze_scalar_evolution (loop, rhs1);
+      res = chrec_convert (type, chrec1, at_stmt);
+      break;
+      
+    default:
+      res = chrec_dont_know;
+      break;
+    }
+  
+  return res;
+}
+
+/* Interpret the expression EXPR.  */
+
+static tree
+interpret_expr (struct loop *loop, gimple at_stmt, tree expr)
+{
+  enum tree_code code;
+  tree type = TREE_TYPE (expr), op0, op1;
+
+  if (automatically_generated_chrec_p (expr))
+    return expr;
+
+  if (TREE_CODE (expr) == POLYNOMIAL_CHREC)
+    return chrec_dont_know;
+
+  extract_ops_from_tree (expr, &code, &op0, &op1);
+
+  return interpret_rhs_expr (loop, at_stmt, type,
+			     op0, code, op1);
+}
+
+/* Interpret the rhs of the assignment STMT.  */
+
+static tree
+interpret_gimple_assign (struct loop *loop, gimple stmt)
+{
+  tree type = TREE_TYPE (gimple_assign_lhs (stmt));
+  enum tree_code code = gimple_assign_rhs_code (stmt);
+
+  return interpret_rhs_expr (loop, stmt, type,
+			     gimple_assign_rhs1 (stmt), code,
+			     gimple_assign_rhs2 (stmt));
+}
+
+
+
+/* This section contains all the entry points: 
+   - number_of_iterations_in_loop,
+   - analyze_scalar_evolution,
+   - instantiate_parameters.
+*/
+
+/* Compute and return the evolution function in WRTO_LOOP, the nearest
+   common ancestor of DEF_LOOP and USE_LOOP.  */
+
+static tree 
+compute_scalar_evolution_in_loop (struct loop *wrto_loop, 
+				  struct loop *def_loop, 
+				  tree ev)
+{
+  tree res;
+  if (def_loop == wrto_loop)
+    return ev;
+
+  def_loop = superloop_at_depth (def_loop, loop_depth (wrto_loop) + 1);
+  res = compute_overall_effect_of_inner_loop (def_loop, ev);
+
+  return analyze_scalar_evolution_1 (wrto_loop, res, chrec_not_analyzed_yet);
+}
+
+/* Helper recursive function.  */
+
+static tree
+analyze_scalar_evolution_1 (struct loop *loop, tree var, tree res)
+{
+  tree type = TREE_TYPE (var);
+  gimple def;
+  basic_block bb;
+  struct loop *def_loop;
+
+  if (loop == NULL || TREE_CODE (type) == VECTOR_TYPE)
+    return chrec_dont_know;
+
+  if (TREE_CODE (var) != SSA_NAME)
+    return interpret_expr (loop, NULL, var);
+
+  def = SSA_NAME_DEF_STMT (var);
+  bb = gimple_bb (def);
+  def_loop = bb ? bb->loop_father : NULL;
+
+  if (bb == NULL
+      || !flow_bb_inside_loop_p (loop, bb))
+    {
+      /* Keep the symbolic form.  */
+      res = var;
+      goto set_and_end;
+    }
+
+  if (res != chrec_not_analyzed_yet)
+    {
+      if (loop != bb->loop_father)
+	res = compute_scalar_evolution_in_loop 
+	    (find_common_loop (loop, bb->loop_father), bb->loop_father, res);
+
+      goto set_and_end;
+    }
+
+  if (loop != def_loop)
+    {
+      res = analyze_scalar_evolution_1 (def_loop, var, chrec_not_analyzed_yet);
+      res = compute_scalar_evolution_in_loop (loop, def_loop, res);
+
+      goto set_and_end;
+    }
+
+  switch (gimple_code (def))
+    {
+    case GIMPLE_ASSIGN:
+      res = interpret_gimple_assign (loop, def);
+      break;
+
+    case GIMPLE_PHI:
+      if (loop_phi_node_p (def))
+	res = interpret_loop_phi (loop, def);
+      else
+	res = interpret_condition_phi (loop, def);
+      break;
+
+    default:
+      res = chrec_dont_know;
+      break;
+    }
+
+ set_and_end:
+
+  /* Keep the symbolic form.  */
+  if (res == chrec_dont_know)
+    res = var;
+
+  if (loop == def_loop)
+    set_scalar_evolution (block_before_loop (loop), var, res);
+
+  return res;
+}
+
+/* Entry point for the scalar evolution analyzer.
+   Analyzes and returns the scalar evolution of the ssa_name VAR.
+   LOOP_NB is the identifier number of the loop in which the variable
+   is used.
+   
+   Example of use: having a pointer VAR to a SSA_NAME node, STMT a
+   pointer to the statement that uses this variable, in order to
+   determine the evolution function of the variable, use the following
+   calls:
+   
+   unsigned loop_nb = loop_containing_stmt (stmt)->num;
+   tree chrec_with_symbols = analyze_scalar_evolution (loop_nb, var);
+   tree chrec_instantiated = instantiate_parameters (loop, chrec_with_symbols);
+*/
+
+tree 
+analyze_scalar_evolution (struct loop *loop, tree var)
+{
+  tree res;
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "(analyze_scalar_evolution \n");
+      fprintf (dump_file, "  (loop_nb = %d)\n", loop->num);
+      fprintf (dump_file, "  (scalar = ");
+      print_generic_expr (dump_file, var, 0);
+      fprintf (dump_file, ")\n");
+    }
+
+  res = get_scalar_evolution (block_before_loop (loop), var);
+  res = analyze_scalar_evolution_1 (loop, var, res);
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, ")\n");
+
+  return res;
+}
+
+/* Analyze scalar evolution of use of VERSION in USE_LOOP with respect to
+   WRTO_LOOP (which should be a superloop of USE_LOOP)
+
+   FOLDED_CASTS is set to true if resolve_mixers used
+   chrec_convert_aggressive (TODO -- not really, we are way too conservative
+   at the moment in order to keep things simple). 
+   
+   To illustrate the meaning of USE_LOOP and WRTO_LOOP, consider the following
+   example:
+
+   for (i = 0; i < 100; i++)			-- loop 1
+     {
+       for (j = 0; j < 100; j++)		-- loop 2
+         {
+	   k1 = i;
+	   k2 = j;
+
+	   use2 (k1, k2);
+
+	   for (t = 0; t < 100; t++)		-- loop 3
+	     use3 (k1, k2);
+
+	 }
+       use1 (k1, k2);
+     }
+
+   Both k1 and k2 are invariants in loop3, thus
+     analyze_scalar_evolution_in_loop (loop3, loop3, k1) = k1
+     analyze_scalar_evolution_in_loop (loop3, loop3, k2) = k2
+
+   As they are invariant, it does not matter whether we consider their
+   usage in loop 3 or loop 2, hence
+     analyze_scalar_evolution_in_loop (loop2, loop3, k1) =
+       analyze_scalar_evolution_in_loop (loop2, loop2, k1) = i
+     analyze_scalar_evolution_in_loop (loop2, loop3, k2) =
+       analyze_scalar_evolution_in_loop (loop2, loop2, k2) = [0,+,1]_2
+
+   Similarly for their evolutions with respect to loop 1.  The values of K2
+   in the use in loop 2 vary independently on loop 1, thus we cannot express
+   the evolution with respect to loop 1:
+     analyze_scalar_evolution_in_loop (loop1, loop3, k1) =
+       analyze_scalar_evolution_in_loop (loop1, loop2, k1) = [0,+,1]_1
+     analyze_scalar_evolution_in_loop (loop1, loop3, k2) =
+       analyze_scalar_evolution_in_loop (loop1, loop2, k2) = dont_know
+
+   The value of k2 in the use in loop 1 is known, though:
+     analyze_scalar_evolution_in_loop (loop1, loop1, k1) = [0,+,1]_1
+     analyze_scalar_evolution_in_loop (loop1, loop1, k2) = 100
+   */
+
+static tree
+analyze_scalar_evolution_in_loop (struct loop *wrto_loop, struct loop *use_loop,
+				  tree version, bool *folded_casts)
+{
+  bool val = false;
+  tree ev = version, tmp;
+
+  /* We cannot just do 
+
+     tmp = analyze_scalar_evolution (use_loop, version);
+     ev = resolve_mixers (wrto_loop, tmp);
+
+     as resolve_mixers would query the scalar evolution with respect to
+     wrto_loop.  For example, in the situation described in the function
+     comment, suppose that wrto_loop = loop1, use_loop = loop3 and
+     version = k2.  Then
+
+     analyze_scalar_evolution (use_loop, version) = k2
+
+     and resolve_mixers (loop1, k2) finds that the value of k2 in loop 1
+     is 100, which is a wrong result, since we are interested in the
+     value in loop 3.
+
+     Instead, we need to proceed from use_loop to wrto_loop loop by loop,
+     each time checking that there is no evolution in the inner loop.  */
+
+  if (folded_casts)
+    *folded_casts = false;
+  while (1)
+    {
+      tmp = analyze_scalar_evolution (use_loop, ev);
+      ev = resolve_mixers (use_loop, tmp);
+
+      if (folded_casts && tmp != ev)
+	*folded_casts = true;
+
+      if (use_loop == wrto_loop)
+	return ev;
+
+      /* If the value of the use changes in the inner loop, we cannot express
+	 its value in the outer loop (we might try to return interval chrec,
+	 but we do not have a user for it anyway)  */
+      if (!no_evolution_in_loop_p (ev, use_loop->num, &val)
+	  || !val)
+	return chrec_dont_know;
+
+      use_loop = loop_outer (use_loop);
+    }
+}
+
+/* Returns from CACHE the value for VERSION instantiated below
+   INSTANTIATED_BELOW block.  */
+
+static tree
+get_instantiated_value (htab_t cache, basic_block instantiated_below,
+			tree version)
+{
+  struct scev_info_str *info, pattern;
+  
+  pattern.var = version;
+  pattern.instantiated_below = instantiated_below;
+  info = (struct scev_info_str *) htab_find (cache, &pattern);
+
+  if (info)
+    return info->chrec;
+  else
+    return NULL_TREE;
+}
+
+/* Sets in CACHE the value of VERSION instantiated below basic block
+   INSTANTIATED_BELOW to VAL.  */
+
+static void
+set_instantiated_value (htab_t cache, basic_block instantiated_below,
+			tree version, tree val)
+{
+  struct scev_info_str *info, pattern;
+  PTR *slot;
+  
+  pattern.var = version;
+  pattern.instantiated_below = instantiated_below;
+  slot = htab_find_slot (cache, &pattern, INSERT);
+
+  if (!*slot)
+    *slot = new_scev_info_str (instantiated_below, version);
+  info = (struct scev_info_str *) *slot;
+  info->chrec = val;
+}
+
+/* Return the closed_loop_phi node for VAR.  If there is none, return
+   NULL_TREE.  */
+
+static tree
+loop_closed_phi_def (tree var)
+{
+  struct loop *loop;
+  edge exit;
+  gimple phi;
+  gimple_stmt_iterator psi;
+
+  if (var == NULL_TREE
+      || TREE_CODE (var) != SSA_NAME)
+    return NULL_TREE;
+
+  loop = loop_containing_stmt (SSA_NAME_DEF_STMT (var));
+  exit = single_exit (loop);
+  if (!exit)
+    return NULL_TREE;
+
+  for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); gsi_next (&psi))
+    {
+      phi = gsi_stmt (psi);
+      if (PHI_ARG_DEF_FROM_EDGE (phi, exit) == var)
+	return PHI_RESULT (phi);
+    }
+
+  return NULL_TREE;
+}
+
+/* Analyze all the parameters of the chrec, between INSTANTIATE_BELOW
+   and EVOLUTION_LOOP, that were left under a symbolic form.  
+
+   CHREC is the scalar evolution to instantiate.
+
+   CACHE is the cache of already instantiated values.
+
+   FOLD_CONVERSIONS should be set to true when the conversions that
+   may wrap in signed/pointer type are folded, as long as the value of
+   the chrec is preserved.
+
+   SIZE_EXPR is used for computing the size of the expression to be
+   instantiated, and to stop if it exceeds some limit.  */
+  
+static tree
+instantiate_scev_1 (basic_block instantiate_below,
+		    struct loop *evolution_loop, tree chrec,
+		    bool fold_conversions, htab_t cache, int size_expr)
+{
+  tree res, op0, op1, op2;
+  basic_block def_bb;
+  struct loop *def_loop;
+  tree type = chrec_type (chrec);
+
+  /* Give up if the expression is larger than the MAX that we allow.  */
+  if (size_expr++ > PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
+    return chrec_dont_know;
+
+  if (automatically_generated_chrec_p (chrec)
+      || is_gimple_min_invariant (chrec))
+    return chrec;
+
+  switch (TREE_CODE (chrec))
+    {
+    case SSA_NAME:
+      def_bb = gimple_bb (SSA_NAME_DEF_STMT (chrec));
+
+      /* A parameter (or loop invariant and we do not want to include
+	 evolutions in outer loops), nothing to do.  */
+      if (!def_bb
+	  || loop_depth (def_bb->loop_father) == 0
+	  || dominated_by_p (CDI_DOMINATORS, instantiate_below, def_bb))
+	return chrec;
+
+      /* We cache the value of instantiated variable to avoid exponential
+	 time complexity due to reevaluations.  We also store the convenient
+	 value in the cache in order to prevent infinite recursion -- we do
+	 not want to instantiate the SSA_NAME if it is in a mixer
+	 structure.  This is used for avoiding the instantiation of
+	 recursively defined functions, such as: 
+
+	 | a_2 -> {0, +, 1, +, a_2}_1  */
+
+      res = get_instantiated_value (cache, instantiate_below, chrec);
+      if (res)
+	return res;
+
+      res = chrec_dont_know;
+      set_instantiated_value (cache, instantiate_below, chrec, res);
+
+      def_loop = find_common_loop (evolution_loop, def_bb->loop_father);
+
+      /* If the analysis yields a parametric chrec, instantiate the
+	 result again.  */
+      res = analyze_scalar_evolution (def_loop, chrec);
+
+      /* Don't instantiate loop-closed-ssa phi nodes.  */
+      if (TREE_CODE (res) == SSA_NAME
+	  && (loop_containing_stmt (SSA_NAME_DEF_STMT (res)) == NULL
+	      || (loop_depth (loop_containing_stmt (SSA_NAME_DEF_STMT (res)))
+		  > loop_depth (def_loop))))
+	{
+	  if (res == chrec)
+	    res = loop_closed_phi_def (chrec);
+	  else
+	    res = chrec;
+
+	  if (res == NULL_TREE)
+	    res = chrec_dont_know;
+	}
+
+      else if (res != chrec_dont_know)
+	res = instantiate_scev_1 (instantiate_below, evolution_loop, res,
+				  fold_conversions, cache, size_expr);
+
+      /* Store the correct value to the cache.  */
+      set_instantiated_value (cache, instantiate_below, chrec, res);
+      return res;
+
+    case POLYNOMIAL_CHREC:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				CHREC_LEFT (chrec), fold_conversions, cache,
+				size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				CHREC_RIGHT (chrec), fold_conversions, cache,
+				size_expr);
+      if (op1 == chrec_dont_know)
+	return chrec_dont_know;
+
+      if (CHREC_LEFT (chrec) != op0
+	  || CHREC_RIGHT (chrec) != op1)
+	{
+	  op1 = chrec_convert_rhs (chrec_type (op0), op1, NULL);
+	  chrec = build_polynomial_chrec (CHREC_VARIABLE (chrec), op0, op1);
+	}
+      return chrec;
+
+    case POINTER_PLUS_EXPR:
+    case PLUS_EXPR:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0), fold_conversions, cache,
+				size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 1), fold_conversions, cache,
+				size_expr);
+      if (op1 == chrec_dont_know)
+	return chrec_dont_know;
+
+      if (TREE_OPERAND (chrec, 0) != op0
+	  || TREE_OPERAND (chrec, 1) != op1)
+	{
+	  op0 = chrec_convert (type, op0, NULL);
+	  op1 = chrec_convert_rhs (type, op1, NULL);
+	  chrec = chrec_fold_plus (type, op0, op1);
+	}
+      return chrec;
+
+    case MINUS_EXPR:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0), fold_conversions, cache,
+				size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 1),
+				fold_conversions, cache, size_expr);
+      if (op1 == chrec_dont_know)
+	return chrec_dont_know;
+
+      if (TREE_OPERAND (chrec, 0) != op0
+	  || TREE_OPERAND (chrec, 1) != op1)
+	{
+	  op0 = chrec_convert (type, op0, NULL);
+	  op1 = chrec_convert (type, op1, NULL);
+	  chrec = chrec_fold_minus (type, op0, op1);
+	}
+      return chrec;
+
+    case MULT_EXPR:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0),
+				fold_conversions, cache, size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 1),
+				fold_conversions, cache, size_expr);
+      if (op1 == chrec_dont_know)
+	return chrec_dont_know;
+
+      if (TREE_OPERAND (chrec, 0) != op0
+	  || TREE_OPERAND (chrec, 1) != op1)
+	{
+	  op0 = chrec_convert (type, op0, NULL);
+	  op1 = chrec_convert (type, op1, NULL);
+	  chrec = chrec_fold_multiply (type, op0, op1);
+	}
+      return chrec;
+
+    CASE_CONVERT:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0),
+				fold_conversions, cache, size_expr);
+      if (op0 == chrec_dont_know)
+        return chrec_dont_know;
+
+      if (fold_conversions)
+	{
+	  tree tmp = chrec_convert_aggressive (TREE_TYPE (chrec), op0);
+	  if (tmp)
+	    return tmp;
+	}
+
+      if (op0 == TREE_OPERAND (chrec, 0))
+	return chrec;
+
+      /* If we used chrec_convert_aggressive, we can no longer assume that
+	 signed chrecs do not overflow, as chrec_convert does, so avoid
+         calling it in that case.  */
+      if (fold_conversions)
+	return fold_convert (TREE_TYPE (chrec), op0);
+
+      return chrec_convert (TREE_TYPE (chrec), op0, NULL);
+
+    case BIT_NOT_EXPR:
+      /* Handle ~X as -1 - X.  */
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0),
+				fold_conversions, cache, size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      if (TREE_OPERAND (chrec, 0) != op0)
+	{
+	  op0 = chrec_convert (type, op0, NULL);
+	  chrec = chrec_fold_minus (type,
+				    fold_convert (type,
+						  integer_minus_one_node),
+				    op0);
+	}
+      return chrec;
+
+    case SCEV_NOT_KNOWN:
+      return chrec_dont_know;
+
+    case SCEV_KNOWN:
+      return chrec_known;
+                                     
+    default:
+      break;
+    }
+
+  if (VL_EXP_CLASS_P (chrec))
+    return chrec_dont_know;
+
+  switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
+    {
+    case 3:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0),
+				fold_conversions, cache, size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 1),
+				fold_conversions, cache, size_expr);
+      if (op1 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op2 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 2),
+				fold_conversions, cache, size_expr);
+      if (op2 == chrec_dont_know)
+        return chrec_dont_know;
+
+      if (op0 == TREE_OPERAND (chrec, 0)
+	  && op1 == TREE_OPERAND (chrec, 1)
+	  && op2 == TREE_OPERAND (chrec, 2))
+	return chrec;
+
+      return fold_build3 (TREE_CODE (chrec),
+			  TREE_TYPE (chrec), op0, op1, op2);
+
+    case 2:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0),
+				fold_conversions, cache, size_expr);
+      if (op0 == chrec_dont_know)
+	return chrec_dont_know;
+
+      op1 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 1),
+				fold_conversions, cache, size_expr);
+      if (op1 == chrec_dont_know)
+        return chrec_dont_know;
+
+      if (op0 == TREE_OPERAND (chrec, 0)
+	  && op1 == TREE_OPERAND (chrec, 1))
+	return chrec;
+      return fold_build2 (TREE_CODE (chrec), TREE_TYPE (chrec), op0, op1);
+	    
+    case 1:
+      op0 = instantiate_scev_1 (instantiate_below, evolution_loop,
+				TREE_OPERAND (chrec, 0),
+				fold_conversions, cache, size_expr);
+      if (op0 == chrec_dont_know)
+        return chrec_dont_know;
+      if (op0 == TREE_OPERAND (chrec, 0))
+	return chrec;
+      return fold_build1 (TREE_CODE (chrec), TREE_TYPE (chrec), op0);
+
+    case 0:
+      return chrec;
+
+    default:
+      break;
+    }
+
+  /* Too complicated to handle.  */
+  return chrec_dont_know;
+}
+
+/* Analyze all the parameters of the chrec that were left under a
+   symbolic form.  INSTANTIATE_BELOW is the basic block that stops the
+   recursive instantiation of parameters: a parameter is a variable
+   that is defined in a basic block that dominates INSTANTIATE_BELOW or
+   a function parameter.  */
+
+tree
+instantiate_scev (basic_block instantiate_below, struct loop *evolution_loop,
+		  tree chrec)
+{
+  tree res;
+  htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "(instantiate_scev \n");
+      fprintf (dump_file, "  (instantiate_below = %d)\n", instantiate_below->index);
+      fprintf (dump_file, "  (evolution_loop = %d)\n", evolution_loop->num);
+      fprintf (dump_file, "  (chrec = ");
+      print_generic_expr (dump_file, chrec, 0);
+      fprintf (dump_file, ")\n");
+    }
+ 
+  res = instantiate_scev_1 (instantiate_below, evolution_loop, chrec, false,
+			    cache, 0);
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    {
+      fprintf (dump_file, "  (res = ");
+      print_generic_expr (dump_file, res, 0);
+      fprintf (dump_file, "))\n");
+    }
+
+  htab_delete (cache);
+  
+  return res;
+}
+
+/* Similar to instantiate_parameters, but does not introduce the
+   evolutions in outer loops for LOOP invariants in CHREC, and does not
+   care about causing overflows, as long as they do not affect value
+   of an expression.  */
+
+tree
+resolve_mixers (struct loop *loop, tree chrec)
+{
+  htab_t cache = htab_create (10, hash_scev_info, eq_scev_info, del_scev_info);
+  tree ret = instantiate_scev_1 (block_before_loop (loop), loop, chrec, true,
+				 cache, 0);
+  htab_delete (cache);
+  return ret;
+}
+
+/* Entry point for the analysis of the number of iterations pass.  
+   This function tries to safely approximate the number of iterations
+   the loop will run.  When this property is not decidable at compile
+   time, the result is chrec_dont_know.  Otherwise the result is
+   a scalar or a symbolic parameter.
+   
+   Example of analysis: suppose that the loop has an exit condition:
+   
+   "if (b > 49) goto end_loop;"
+   
+   and that in a previous analysis we have determined that the
+   variable 'b' has an evolution function:
+   
+   "EF = {23, +, 5}_2".  
+   
+   When we evaluate the function at the point 5, i.e. the value of the
+   variable 'b' after 5 iterations in the loop, we have EF (5) = 48,
+   and EF (6) = 53.  In this case the value of 'b' on exit is '53' and
+   the loop body has been executed 6 times.  */
+
+tree 
+number_of_latch_executions (struct loop *loop)
+{
+  tree res, type;
+  edge exit;
+  struct tree_niter_desc niter_desc;
+
+  /* Determine whether the number_of_iterations_in_loop has already
+     been computed.  */
+  res = loop->nb_iterations;
+  if (res)
+    return res;
+  res = chrec_dont_know;
+
+  if (dump_file && (dump_flags & TDF_DETAILS))
+    fprintf (dump_file, "(number_of_iterations_in_loop\n");
+  
+  exit = single_exit (loop);
+  if (!exit)
+    goto end;
+
+  if (!number_of_iterations_exit (loop, exit, &niter_desc, false))
+    goto end;
+
+  type = TREE_TYPE (niter_desc.niter);
+  if (integer_nonzerop (niter_desc.may_be_zero))
+    res = build_int_cst (type, 0);
+  else if (integer_zerop (niter_desc.may_be_zero))
+    res = niter_desc.niter;
+  else
+    res = chrec_dont_know;
+
+end:
+  return set_nb_iterations_in_loop (loop, res);
+}
+
+/* Returns the number of executions of the exit condition of LOOP,
+   i.e., the number by one higher than number_of_latch_executions.
+   Note that unlike number_of_latch_executions, this number does
+   not necessarily fit in the unsigned variant of the type of
+   the control variable -- if the number of iterations is a constant,
+   we return chrec_dont_know if adding one to number_of_latch_executions
+   overflows; however, in case the number of iterations is symbolic
+   expression, the caller is responsible for dealing with this
+   the possible overflow.  */
+
+tree 
+number_of_exit_cond_executions (struct loop *loop)
+{
+  tree ret = number_of_latch_executions (loop);
+  tree type = chrec_type (ret);
+
+  if (chrec_contains_undetermined (ret))
+    return ret;
+
+  ret = chrec_fold_plus (type, ret, build_int_cst (type, 1));
+  if (TREE_CODE (ret) == INTEGER_CST
+      && TREE_OVERFLOW (ret))
+    return chrec_dont_know;
+
+  return ret;
+}
+
+/* One of the drivers for testing the scalar evolutions analysis.
+   This function computes the number of iterations for all the loops
+   from the EXIT_CONDITIONS array.  */
+
+static void 
+number_of_iterations_for_all_loops (VEC(gimple,heap) **exit_conditions)
+{
+  unsigned int i;
+  unsigned nb_chrec_dont_know_loops = 0;
+  unsigned nb_static_loops = 0;
+  gimple cond;
+  
+  for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
+    {
+      tree res = number_of_latch_executions (loop_containing_stmt (cond));
+      if (chrec_contains_undetermined (res))
+	nb_chrec_dont_know_loops++;
+      else
+	nb_static_loops++;
+    }
+  
+  if (dump_file)
+    {
+      fprintf (dump_file, "\n(\n");
+      fprintf (dump_file, "-----------------------------------------\n");
+      fprintf (dump_file, "%d\tnb_chrec_dont_know_loops\n", nb_chrec_dont_know_loops);
+      fprintf (dump_file, "%d\tnb_static_loops\n", nb_static_loops);
+      fprintf (dump_file, "%d\tnb_total_loops\n", number_of_loops ());
+      fprintf (dump_file, "-----------------------------------------\n");
+      fprintf (dump_file, ")\n\n");
+      
+      print_loops (dump_file, 3);
+    }
+}
+
+
+
+/* Counters for the stats.  */
+
+struct chrec_stats 
+{
+  unsigned nb_chrecs;
+  unsigned nb_affine;
+  unsigned nb_affine_multivar;
+  unsigned nb_higher_poly;
+  unsigned nb_chrec_dont_know;
+  unsigned nb_undetermined;
+};
+
+/* Reset the counters.  */
+
+static inline void
+reset_chrecs_counters (struct chrec_stats *stats)
+{
+  stats->nb_chrecs = 0;
+  stats->nb_affine = 0;
+  stats->nb_affine_multivar = 0;
+  stats->nb_higher_poly = 0;
+  stats->nb_chrec_dont_know = 0;
+  stats->nb_undetermined = 0;
+}
+
+/* Dump the contents of a CHREC_STATS structure.  */
+
+static void
+dump_chrecs_stats (FILE *file, struct chrec_stats *stats)
+{
+  fprintf (file, "\n(\n");
+  fprintf (file, "-----------------------------------------\n");
+  fprintf (file, "%d\taffine univariate chrecs\n", stats->nb_affine);
+  fprintf (file, "%d\taffine multivariate chrecs\n", stats->nb_affine_multivar);
+  fprintf (file, "%d\tdegree greater than 2 polynomials\n", 
+	   stats->nb_higher_poly);
+  fprintf (file, "%d\tchrec_dont_know chrecs\n", stats->nb_chrec_dont_know);
+  fprintf (file, "-----------------------------------------\n");
+  fprintf (file, "%d\ttotal chrecs\n", stats->nb_chrecs);
+  fprintf (file, "%d\twith undetermined coefficients\n", 
+	   stats->nb_undetermined);
+  fprintf (file, "-----------------------------------------\n");
+  fprintf (file, "%d\tchrecs in the scev database\n", 
+	   (int) htab_elements (scalar_evolution_info));
+  fprintf (file, "%d\tsets in the scev database\n", nb_set_scev);
+  fprintf (file, "%d\tgets in the scev database\n", nb_get_scev);
+  fprintf (file, "-----------------------------------------\n");
+  fprintf (file, ")\n\n");
+}
+
+/* Gather statistics about CHREC.  */
+
+static void
+gather_chrec_stats (tree chrec, struct chrec_stats *stats)
+{
+  if (dump_file && (dump_flags & TDF_STATS))
+    {
+      fprintf (dump_file, "(classify_chrec ");
+      print_generic_expr (dump_file, chrec, 0);
+      fprintf (dump_file, "\n");
+    }
+  
+  stats->nb_chrecs++;
+  
+  if (chrec == NULL_TREE)
+    {
+      stats->nb_undetermined++;
+      return;
+    }
+  
+  switch (TREE_CODE (chrec))
+    {
+    case POLYNOMIAL_CHREC:
+      if (evolution_function_is_affine_p (chrec))
+	{
+	  if (dump_file && (dump_flags & TDF_STATS))
+	    fprintf (dump_file, "  affine_univariate\n");
+	  stats->nb_affine++;
+	}
+      else if (evolution_function_is_affine_multivariate_p (chrec, 0))
+	{
+	  if (dump_file && (dump_flags & TDF_STATS))
+	    fprintf (dump_file, "  affine_multivariate\n");
+	  stats->nb_affine_multivar++;
+	}
+      else
+	{
+	  if (dump_file && (dump_flags & TDF_STATS))
+	    fprintf (dump_file, "  higher_degree_polynomial\n");
+	  stats->nb_higher_poly++;
+	}
+      
+      break;
+
+    default:
+      break;
+    }
+  
+  if (chrec_contains_undetermined (chrec))
+    {
+      if (dump_file && (dump_flags & TDF_STATS))
+	fprintf (dump_file, "  undetermined\n");
+      stats->nb_undetermined++;
+    }
+  
+  if (dump_file && (dump_flags & TDF_STATS))
+    fprintf (dump_file, ")\n");
+}
+
+/* One of the drivers for testing the scalar evolutions analysis.
+   This function analyzes the scalar evolution of all the scalars
+   defined as loop phi nodes in one of the loops from the
+   EXIT_CONDITIONS array.  
+   
+   TODO Optimization: A loop is in canonical form if it contains only
+   a single scalar loop phi node.  All the other scalars that have an
+   evolution in the loop are rewritten in function of this single
+   index.  This allows the parallelization of the loop.  */
+
+static void 
+analyze_scalar_evolution_for_all_loop_phi_nodes (VEC(gimple,heap) **exit_conditions)
+{
+  unsigned int i;
+  struct chrec_stats stats;
+  gimple cond, phi;
+  gimple_stmt_iterator psi;
+  
+  reset_chrecs_counters (&stats);
+  
+  for (i = 0; VEC_iterate (gimple, *exit_conditions, i, cond); i++)
+    {
+      struct loop *loop;
+      basic_block bb;
+      tree chrec;
+      
+      loop = loop_containing_stmt (cond);
+      bb = loop->header;
+      
+      for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
+	{
+	  phi = gsi_stmt (psi);
+	  if (is_gimple_reg (PHI_RESULT (phi)))
+	    {
+	      chrec = instantiate_parameters 
+		        (loop, 
+			 analyze_scalar_evolution (loop, PHI_RESULT (phi)));
+	    
+	      if (dump_file && (dump_flags & TDF_STATS))
+		gather_chrec_stats (chrec, &stats);
+	    }
+	}
+    }
+  
+  if (dump_file && (dump_flags & TDF_STATS))
+    dump_chrecs_stats (dump_file, &stats);
+}
+
+/* Callback for htab_traverse, gathers information on chrecs in the
+   hashtable.  */
+
+static int
+gather_stats_on_scev_database_1 (void **slot, void *stats)
+{
+  struct scev_info_str *entry = (struct scev_info_str *) *slot;
+
+  gather_chrec_stats (entry->chrec, (struct chrec_stats *) stats);
+
+  return 1;
+}
+
+/* Classify the chrecs of the whole database.  */
+
+void 
+gather_stats_on_scev_database (void)
+{
+  struct chrec_stats stats;
+  
+  if (!dump_file)
+    return;
+  
+  reset_chrecs_counters (&stats);
+ 
+  htab_traverse (scalar_evolution_info, gather_stats_on_scev_database_1,
+		 &stats);
+
+  dump_chrecs_stats (dump_file, &stats);
+}
+
+
+
+/* Initializer.  */
+
+static 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) = void_type_node;
+      TREE_TYPE (chrec_known) = void_type_node;
+    }
+}
+
+/* Initialize the analysis of scalar evolutions for LOOPS.  */
+
+void
+scev_initialize (void)
+{
+  loop_iterator li;
+  struct loop *loop;
+
+  scalar_evolution_info = htab_create_alloc (100,
+					     hash_scev_info,
+					     eq_scev_info,
+					     del_scev_info,
+					     ggc_calloc,
+					     ggc_free);
+  
+  initialize_scalar_evolutions_analyzer ();
+
+  FOR_EACH_LOOP (li, loop, 0)
+    {
+      loop->nb_iterations = NULL_TREE;
+    }
+}
+
+/* Cleans up the information cached by the scalar evolutions analysis.  */
+
+void
+scev_reset (void)
+{
+  loop_iterator li;
+  struct loop *loop;
+
+  if (!scalar_evolution_info || !current_loops)
+    return;
+
+  htab_empty (scalar_evolution_info);
+  FOR_EACH_LOOP (li, loop, 0)
+    {
+      loop->nb_iterations = NULL_TREE;
+    }
+}
+
+/* Checks whether use of OP in USE_LOOP behaves as a simple affine iv with
+   respect to WRTO_LOOP and returns its base and step in IV if possible
+   (see analyze_scalar_evolution_in_loop for more details on USE_LOOP
+   and WRTO_LOOP).  If ALLOW_NONCONSTANT_STEP is true, we want step to be
+   invariant in LOOP.  Otherwise we require it to be an integer constant.
+   
+   IV->no_overflow is set to true if we are sure the iv cannot overflow (e.g.
+   because it is computed in signed arithmetics).  Consequently, adding an
+   induction variable
+   
+   for (i = IV->base; ; i += IV->step)
+
+   is only safe if IV->no_overflow is false, or TYPE_OVERFLOW_UNDEFINED is
+   false for the type of the induction variable, or you can prove that i does
+   not wrap by some other argument.  Otherwise, this might introduce undefined
+   behavior, and
+   
+   for (i = iv->base; ; i = (type) ((unsigned type) i + (unsigned type) iv->step))
+
+   must be used instead.  */
+
+bool
+simple_iv (struct loop *wrto_loop, struct loop *use_loop, tree op,
+	   affine_iv *iv, bool allow_nonconstant_step)
+{
+  tree type, ev;
+  bool folded_casts;
+
+  iv->base = NULL_TREE;
+  iv->step = NULL_TREE;
+  iv->no_overflow = false;
+
+  type = TREE_TYPE (op);
+  if (TREE_CODE (type) != INTEGER_TYPE
+      && TREE_CODE (type) != POINTER_TYPE)
+    return false;
+
+  ev = analyze_scalar_evolution_in_loop (wrto_loop, use_loop, op,
+					 &folded_casts);
+  if (chrec_contains_undetermined (ev)
+      || chrec_contains_symbols_defined_in_loop (ev, wrto_loop->num))
+    return false;
+
+  if (tree_does_not_contain_chrecs (ev))
+    {
+      iv->base = ev;
+      iv->step = build_int_cst (TREE_TYPE (ev), 0);
+      iv->no_overflow = true;
+      return true;
+    }
+
+  if (TREE_CODE (ev) != POLYNOMIAL_CHREC
+      || CHREC_VARIABLE (ev) != (unsigned) wrto_loop->num)
+    return false;
+
+  iv->step = CHREC_RIGHT (ev);
+  if ((!allow_nonconstant_step && TREE_CODE (iv->step) != INTEGER_CST)
+      || tree_contains_chrecs (iv->step, NULL))
+    return false;
+
+  iv->base = CHREC_LEFT (ev);
+  if (tree_contains_chrecs (iv->base, NULL))
+    return false;
+
+  iv->no_overflow = !folded_casts && TYPE_OVERFLOW_UNDEFINED (type);
+
+  return true;
+}
+
+/* Runs the analysis of scalar evolutions.  */
+
+void
+scev_analysis (void)
+{
+  VEC(gimple,heap) *exit_conditions;
+  
+  exit_conditions = VEC_alloc (gimple, heap, 37);
+  select_loops_exit_conditions (&exit_conditions);
+
+  if (dump_file && (dump_flags & TDF_STATS))
+    analyze_scalar_evolution_for_all_loop_phi_nodes (&exit_conditions);
+  
+  number_of_iterations_for_all_loops (&exit_conditions);
+  VEC_free (gimple, heap, exit_conditions);
+}
+
+/* Finalize the scalar evolution analysis.  */
+
+void
+scev_finalize (void)
+{
+  if (!scalar_evolution_info)
+    return;
+  htab_delete (scalar_evolution_info);
+  scalar_evolution_info = NULL;
+}
+
+/* Returns true if the expression EXPR is considered to be too expensive
+   for scev_const_prop.  */
+
+bool
+expression_expensive_p (tree expr)
+{
+  enum tree_code code;
+
+  if (is_gimple_val (expr))
+    return false;
+
+  code = TREE_CODE (expr);
+  if (code == TRUNC_DIV_EXPR
+      || code == CEIL_DIV_EXPR
+      || code == FLOOR_DIV_EXPR
+      || code == ROUND_DIV_EXPR
+      || code == TRUNC_MOD_EXPR
+      || code == CEIL_MOD_EXPR
+      || code == FLOOR_MOD_EXPR
+      || code == ROUND_MOD_EXPR
+      || code == EXACT_DIV_EXPR)
+    {
+      /* Division by power of two is usually cheap, so we allow it.
+	 Forbid anything else.  */
+      if (!integer_pow2p (TREE_OPERAND (expr, 1)))
+	return true;
+    }
+
+  switch (TREE_CODE_CLASS (code))
+    {
+    case tcc_binary:
+    case tcc_comparison:
+      if (expression_expensive_p (TREE_OPERAND (expr, 1)))
+	return true;
+
+      /* Fallthru.  */
+    case tcc_unary:
+      return expression_expensive_p (TREE_OPERAND (expr, 0));
+
+    default:
+      return true;
+    }
+}
+
+/* Replace ssa names for that scev can prove they are constant by the
+   appropriate constants.  Also perform final value replacement in loops,
+   in case the replacement expressions are cheap.
+   
+   We only consider SSA names defined by phi nodes; rest is left to the
+   ordinary constant propagation pass.  */
+
+unsigned int
+scev_const_prop (void)
+{
+  basic_block bb;
+  tree name, type, ev;
+  gimple phi, ass;
+  struct loop *loop, *ex_loop;
+  bitmap ssa_names_to_remove = NULL;
+  unsigned i;
+  loop_iterator li;
+  gimple_stmt_iterator psi;
+
+  if (number_of_loops () <= 1)
+    return 0;
+
+  FOR_EACH_BB (bb)
+    {
+      loop = bb->loop_father;
+
+      for (psi = gsi_start_phis (bb); !gsi_end_p (psi); gsi_next (&psi))
+	{
+	  phi = gsi_stmt (psi);
+	  name = PHI_RESULT (phi);
+
+	  if (!is_gimple_reg (name))
+	    continue;
+
+	  type = TREE_TYPE (name);
+
+	  if (!POINTER_TYPE_P (type)
+	      && !INTEGRAL_TYPE_P (type))
+	    continue;
+
+	  ev = resolve_mixers (loop, analyze_scalar_evolution (loop, name));
+	  if (!is_gimple_min_invariant (ev)
+	      || !may_propagate_copy (name, ev))
+	    continue;
+
+	  /* Replace the uses of the name.  */
+	  if (name != ev)
+	    replace_uses_by (name, ev);
+
+	  if (!ssa_names_to_remove)
+	    ssa_names_to_remove = BITMAP_ALLOC (NULL);
+	  bitmap_set_bit (ssa_names_to_remove, SSA_NAME_VERSION (name));
+	}
+    }
+
+  /* Remove the ssa names that were replaced by constants.  We do not
+     remove them directly in the previous cycle, since this
+     invalidates scev cache.  */
+  if (ssa_names_to_remove)
+    {
+      bitmap_iterator bi;
+
+      EXECUTE_IF_SET_IN_BITMAP (ssa_names_to_remove, 0, i, bi)
+	{
+	  gimple_stmt_iterator psi;
+	  name = ssa_name (i);
+	  phi = SSA_NAME_DEF_STMT (name);
+
+	  gcc_assert (gimple_code (phi) == GIMPLE_PHI);
+	  psi = gsi_for_stmt (phi);
+	  remove_phi_node (&psi, true);
+	}
+
+      BITMAP_FREE (ssa_names_to_remove);
+      scev_reset ();
+    }
+
+  /* Now the regular final value replacement.  */
+  FOR_EACH_LOOP (li, loop, LI_FROM_INNERMOST)
+    {
+      edge exit;
+      tree def, rslt, niter;
+      gimple_stmt_iterator bsi;
+
+      /* If we do not know exact number of iterations of the loop, we cannot
+	 replace the final value.  */
+      exit = single_exit (loop);
+      if (!exit)
+	continue;
+
+      niter = number_of_latch_executions (loop);
+      if (niter == chrec_dont_know)
+	continue;
+
+      /* Ensure that it is possible to insert new statements somewhere.  */
+      if (!single_pred_p (exit->dest))
+	split_loop_exit_edge (exit);
+      bsi = gsi_after_labels (exit->dest);
+
+      ex_loop = superloop_at_depth (loop,
+				    loop_depth (exit->dest->loop_father) + 1);
+
+      for (psi = gsi_start_phis (exit->dest); !gsi_end_p (psi); )
+	{
+	  phi = gsi_stmt (psi);
+	  rslt = PHI_RESULT (phi);
+	  def = PHI_ARG_DEF_FROM_EDGE (phi, exit);
+	  if (!is_gimple_reg (def))
+	    {
+	      gsi_next (&psi);
+	      continue;
+	    }
+
+	  if (!POINTER_TYPE_P (TREE_TYPE (def))
+	      && !INTEGRAL_TYPE_P (TREE_TYPE (def)))
+	    {
+	      gsi_next (&psi);
+	      continue;
+	    }
+
+	  def = analyze_scalar_evolution_in_loop (ex_loop, loop, def, NULL);
+	  def = compute_overall_effect_of_inner_loop (ex_loop, def);
+	  if (!tree_does_not_contain_chrecs (def)
+	      || chrec_contains_symbols_defined_in_loop (def, ex_loop->num)
+	      /* Moving the computation from the loop may prolong life range
+		 of some ssa names, which may cause problems if they appear
+		 on abnormal edges.  */
+	      || contains_abnormal_ssa_name_p (def)
+	      /* Do not emit expensive expressions.  The rationale is that
+		 when someone writes a code like
+
+		 while (n > 45) n -= 45;
+
+		 he probably knows that n is not large, and does not want it
+		 to be turned into n %= 45.  */
+	      || expression_expensive_p (def))
+	    {
+	      gsi_next (&psi);
+	      continue;
+	    }
+
+	  /* Eliminate the PHI node and replace it by a computation outside
+	     the loop.  */
+	  def = unshare_expr (def);
+	  remove_phi_node (&psi, false);
+
+	  def = force_gimple_operand_gsi (&bsi, def, false, NULL_TREE,
+      					  true, GSI_SAME_STMT);
+	  ass = gimple_build_assign (rslt, def);
+	  gsi_insert_before (&bsi, ass, GSI_SAME_STMT);
+	}
+    }
+  return 0;
+}
+
+#include "gt-tree-scalar-evolution.h"