tree-chrec.c

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/* Chains of recurrences.
   Copyright (C) 2003, 2004, 2005, 2006 Free Software Foundation, Inc.
   Contributed by Sebastian Pop <pop@cri.ensmp.fr>

This file is part of GCC.

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

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

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */

/* This file implements operations on chains of recurrences.  Chains
   of recurrences are used for modeling evolution functions of scalar
   variables.
*/

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "ggc.h"
#include "tree.h"
#include "real.h"
#include "diagnostic.h"
#include "cfgloop.h"
#include "tree-flow.h"
#include "tree-chrec.h"
#include "tree-pass.h"
#include "params.h"
#include "tree-scalar-evolution.h"



/* Extended folder for chrecs.  */

/* Determines whether CST is not a constant evolution.  */

static inline bool
is_not_constant_evolution (tree cst)
{
  return (TREE_CODE (cst) == POLYNOMIAL_CHREC);
}

/* Fold CODE for a polynomial function and a constant.  */

static inline tree 
chrec_fold_poly_cst (enum tree_code code, 
                     tree type, 
                     tree poly, 
                     tree cst)
{
  gcc_assert (poly);
  gcc_assert (cst);
  gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC);
  gcc_assert (!is_not_constant_evolution (cst));
  gcc_assert (type == chrec_type (poly));

  switch (code)
    {
    case PLUS_EXPR:
      return build_polynomial_chrec 
        (CHREC_VARIABLE (poly), 
         chrec_fold_plus (type, CHREC_LEFT (poly), cst),
         CHREC_RIGHT (poly));
      
    case MINUS_EXPR:
      return build_polynomial_chrec 
        (CHREC_VARIABLE (poly), 
         chrec_fold_minus (type, CHREC_LEFT (poly), cst),
         CHREC_RIGHT (poly));
      
    case MULT_EXPR:
      return build_polynomial_chrec 
        (CHREC_VARIABLE (poly), 
         chrec_fold_multiply (type, CHREC_LEFT (poly), cst),
         chrec_fold_multiply (type, CHREC_RIGHT (poly), cst));
      
    default:
      return chrec_dont_know;
    }
}

/* Fold the addition of two polynomial functions.  */

static inline tree 
chrec_fold_plus_poly_poly (enum tree_code code, 
                           tree type, 
                           tree poly0, 
                           tree poly1)
{
  tree left, right;

  gcc_assert (poly0);
  gcc_assert (poly1);
  gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
  gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
  gcc_assert (chrec_type (poly0) == chrec_type (poly1));
  gcc_assert (type == chrec_type (poly0));
  
  /*
    {a, +, b}_1 + {c, +, d}_2  ->  {{a, +, b}_1 + c, +, d}_2,
    {a, +, b}_2 + {c, +, d}_1  ->  {{c, +, d}_1 + a, +, b}_2,
    {a, +, b}_x + {c, +, d}_x  ->  {a+c, +, b+d}_x.  */
  if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1))
    {
      if (code == PLUS_EXPR)
        return build_polynomial_chrec 
          (CHREC_VARIABLE (poly1), 
           chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)),
           CHREC_RIGHT (poly1));
      else
        return build_polynomial_chrec 
          (CHREC_VARIABLE (poly1), 
           chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)),
           chrec_fold_multiply (type, CHREC_RIGHT (poly1), 
                                SCALAR_FLOAT_TYPE_P (type)
                                ? build_real (type, dconstm1)
                                : build_int_cst_type (type, -1)));
    }
  
  if (CHREC_VARIABLE (poly0) > CHREC_VARIABLE (poly1))
    {
      if (code == PLUS_EXPR)
        return build_polynomial_chrec 
          (CHREC_VARIABLE (poly0), 
           chrec_fold_plus (type, CHREC_LEFT (poly0), poly1),
           CHREC_RIGHT (poly0));
      else
        return build_polynomial_chrec 
          (CHREC_VARIABLE (poly0), 
           chrec_fold_minus (type, CHREC_LEFT (poly0), poly1),
           CHREC_RIGHT (poly0));
    }
  
  if (code == PLUS_EXPR)
    {
      left = chrec_fold_plus 
        (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
      right = chrec_fold_plus 
        (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
    }
  else
    {
      left = chrec_fold_minus 
        (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
      right = chrec_fold_minus 
        (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
    }

  if (chrec_zerop (right))
    return left;
  else
    return build_polynomial_chrec 
      (CHREC_VARIABLE (poly0), left, right); 
}



/* Fold the multiplication of two polynomial functions.  */

static inline tree 
chrec_fold_multiply_poly_poly (tree type, 
                               tree poly0, 
                               tree poly1)
{
  tree t0, t1, t2;
  int var;

  gcc_assert (poly0);
  gcc_assert (poly1);
  gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
  gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
  gcc_assert (chrec_type (poly0) == chrec_type (poly1));
  gcc_assert (type == chrec_type (poly0));
  
  /* {a, +, b}_1 * {c, +, d}_2  ->  {c*{a, +, b}_1, +, d}_2,
     {a, +, b}_2 * {c, +, d}_1  ->  {a*{c, +, d}_1, +, b}_2,
     {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
  if (CHREC_VARIABLE (poly0) < CHREC_VARIABLE (poly1))
    /* poly0 is a constant wrt. poly1.  */
    return build_polynomial_chrec 
      (CHREC_VARIABLE (poly1), 
       chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0),
       CHREC_RIGHT (poly1));
  
  if (CHREC_VARIABLE (poly1) < CHREC_VARIABLE (poly0))
    /* poly1 is a constant wrt. poly0.  */
    return build_polynomial_chrec 
      (CHREC_VARIABLE (poly0), 
       chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
       CHREC_RIGHT (poly0));
  
  /* poly0 and poly1 are two polynomials in the same variable,
     {a, +, b}_x * {c, +, d}_x  ->  {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x.  */
      
  /* "a*c".  */
  t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));

  /* "a*d + b*c + b*d".  */
  t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1));
  t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
                                                       CHREC_RIGHT (poly0),
                                                       CHREC_LEFT (poly1)));
  t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type,
                                                       CHREC_RIGHT (poly0),
                                                       CHREC_RIGHT (poly1)));
  /* "2*b*d".  */
  t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
  t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type)
                            ? build_real (type, dconst2)
                            : build_int_cst (type, 2), t2);

  var = CHREC_VARIABLE (poly0);
  return build_polynomial_chrec (var, t0,
                                 build_polynomial_chrec (var, t1, t2));
}

/* When the operands are automatically_generated_chrec_p, the fold has
   to respect the semantics of the operands.  */

static inline tree 
chrec_fold_automatically_generated_operands (tree op0, 
                                             tree op1)
{
  if (op0 == chrec_dont_know
      || op1 == chrec_dont_know)
    return chrec_dont_know;
  
  if (op0 == chrec_known
      || op1 == chrec_known)
    return chrec_known;
  
  if (op0 == chrec_not_analyzed_yet
      || op1 == chrec_not_analyzed_yet)
    return chrec_not_analyzed_yet;
  
  /* The default case produces a safe result.  */
  return chrec_dont_know;
}

/* Fold the addition of two chrecs.  */

static tree
chrec_fold_plus_1 (enum tree_code code, tree type, 
                   tree op0, tree op1)
{
  if (automatically_generated_chrec_p (op0)
      || automatically_generated_chrec_p (op1))
    return chrec_fold_automatically_generated_operands (op0, op1);
  
  switch (TREE_CODE (op0))
    {
    case POLYNOMIAL_CHREC:
      switch (TREE_CODE (op1))
        {
        case POLYNOMIAL_CHREC:
          return chrec_fold_plus_poly_poly (code, type, op0, op1);

        default:
          if (code == PLUS_EXPR)
            return build_polynomial_chrec 
              (CHREC_VARIABLE (op0), 
               chrec_fold_plus (type, CHREC_LEFT (op0), op1),
               CHREC_RIGHT (op0));
          else
            return build_polynomial_chrec 
              (CHREC_VARIABLE (op0), 
               chrec_fold_minus (type, CHREC_LEFT (op0), op1),
               CHREC_RIGHT (op0));
        }

    default:
      switch (TREE_CODE (op1))
        {
        case POLYNOMIAL_CHREC:
          if (code == PLUS_EXPR)
            return build_polynomial_chrec 
              (CHREC_VARIABLE (op1), 
               chrec_fold_plus (type, op0, CHREC_LEFT (op1)),
               CHREC_RIGHT (op1));
          else
            return build_polynomial_chrec 
              (CHREC_VARIABLE (op1), 
               chrec_fold_minus (type, op0, CHREC_LEFT (op1)),
               chrec_fold_multiply (type, CHREC_RIGHT (op1), 
                                    SCALAR_FLOAT_TYPE_P (type)
                                    ? build_real (type, dconstm1)
                                    : build_int_cst_type (type, -1)));

        default:
          {
            int size = 0;
            if ((tree_contains_chrecs (op0, &size)
                 || tree_contains_chrecs (op1, &size))
                && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
              return build2 (code, type, op0, op1);
            else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE))
              return fold_build2 (code, type,
                                  fold_convert (type, op0),
                                  fold_convert (type, op1));
            else
              return chrec_dont_know;
          }
        }
    }
}

/* Fold the addition of two chrecs.  */

tree
chrec_fold_plus (tree type, 
                 tree op0,
                 tree op1)
{
  if (automatically_generated_chrec_p (op0)
      || automatically_generated_chrec_p (op1))
    return chrec_fold_automatically_generated_operands (op0, op1);

  if (integer_zerop (op0))
    return op1;
  if (integer_zerop (op1))
    return op0;
  
  return chrec_fold_plus_1 (PLUS_EXPR, type, op0, op1);
}

/* Fold the subtraction of two chrecs.  */

tree 
chrec_fold_minus (tree type, 
                  tree op0, 
                  tree op1)
{
  if (automatically_generated_chrec_p (op0)
      || automatically_generated_chrec_p (op1))
    return chrec_fold_automatically_generated_operands (op0, op1);

  if (integer_zerop (op1))
    return op0;
  
  return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1);
}

/* Fold the multiplication of two chrecs.  */

tree
chrec_fold_multiply (tree type, 
                     tree op0,
                     tree op1)
{
  if (automatically_generated_chrec_p (op0)
      || automatically_generated_chrec_p (op1))
    return chrec_fold_automatically_generated_operands (op0, op1);
  
  switch (TREE_CODE (op0))
    {
    case POLYNOMIAL_CHREC:
      switch (TREE_CODE (op1))
        {
        case POLYNOMIAL_CHREC:
          return chrec_fold_multiply_poly_poly (type, op0, op1);
          
        default:
          if (integer_onep (op1))
            return op0;
          if (integer_zerop (op1))
            return build_int_cst (type, 0);
          
          return build_polynomial_chrec 
            (CHREC_VARIABLE (op0), 
             chrec_fold_multiply (type, CHREC_LEFT (op0), op1),
             chrec_fold_multiply (type, CHREC_RIGHT (op0), op1));
        }
      
    default:
      if (integer_onep (op0))
        return op1;
      
      if (integer_zerop (op0))
        return build_int_cst (type, 0);
      
      switch (TREE_CODE (op1))
        {
        case POLYNOMIAL_CHREC:
          return build_polynomial_chrec 
            (CHREC_VARIABLE (op1), 
             chrec_fold_multiply (type, CHREC_LEFT (op1), op0),
             chrec_fold_multiply (type, CHREC_RIGHT (op1), op0));
          
        default:
          if (integer_onep (op1))
            return op0;
          if (integer_zerop (op1))
            return build_int_cst (type, 0);
          return fold_build2 (MULT_EXPR, type, op0, op1);
        }
    }
}



/* Operations.  */

/* Evaluate the binomial coefficient.  Return NULL_TREE if the intermediate
   calculation overflows, otherwise return C(n,k) with type TYPE.  */

static tree 
tree_fold_binomial (tree type, tree n, unsigned int k)
{
  unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum;
  HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum;
  unsigned int i;
  tree res;

  /* Handle the most frequent cases.  */
  if (k == 0)
    return build_int_cst (type, 1);
  if (k == 1)
    return fold_convert (type, n);

  /* Check that k <= n.  */
  if (TREE_INT_CST_HIGH (n) == 0
      && TREE_INT_CST_LOW (n) < k)
    return NULL_TREE;

  /* Numerator = n.  */
  lnum = TREE_INT_CST_LOW (n);
  hnum = TREE_INT_CST_HIGH (n);

  /* Denominator = 2.  */
  ldenom = 2;
  hdenom = 0;

  /* Index = Numerator-1.  */
  if (lnum == 0)
    {
      hidx = hnum - 1;
      lidx = ~ (unsigned HOST_WIDE_INT) 0;
    }
  else
    {
      hidx = hnum;
      lidx = lnum - 1;
    }

  /* Numerator = Numerator*Index = n*(n-1).  */
  if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
    return NULL_TREE;

  for (i = 3; i <= k; i++)
    {
      /* Index--.  */
      if (lidx == 0)
        {
          hidx--;
          lidx = ~ (unsigned HOST_WIDE_INT) 0;
        }
      else
        lidx--;

      /* Numerator *= Index.  */
      if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum))
        return NULL_TREE;

      /* Denominator *= i.  */
      mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom);
    }

  /* Result = Numerator / Denominator.  */
  div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom,
                        &lres, &hres, &ldum, &hdum);

  res = build_int_cst_wide (type, lres, hres);
  return int_fits_type_p (res, type) ? res : NULL_TREE;
}

/* Helper function.  Use the Newton's interpolating formula for
   evaluating the value of the evolution function.  */

static tree 
chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
{
  tree arg0, arg1, binomial_n_k;
  tree type = TREE_TYPE (chrec);

  while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
         && CHREC_VARIABLE (chrec) > var)
    chrec = CHREC_LEFT (chrec);

  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
      && CHREC_VARIABLE (chrec) == var)
    {
      arg0 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1);
      if (arg0 == chrec_dont_know)
        return chrec_dont_know;
      binomial_n_k = tree_fold_binomial (type, n, k);
      if (!binomial_n_k)
        return chrec_dont_know;
      arg1 = fold_build2 (MULT_EXPR, type,
                          CHREC_LEFT (chrec), binomial_n_k);
      return chrec_fold_plus (type, arg0, arg1);
    }

  binomial_n_k = tree_fold_binomial (type, n, k);
  if (!binomial_n_k)
    return chrec_dont_know;
  
  return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k);
}

/* Evaluates "CHREC (X)" when the varying variable is VAR.  
   Example:  Given the following parameters, 
   
   var = 1
   chrec = {3, +, 4}_1
   x = 10
   
   The result is given by the Newton's interpolating formula: 
   3 * \binom{10}{0} + 4 * \binom{10}{1}.
*/

tree 
chrec_apply (unsigned var,
             tree chrec, 
             tree x)
{
  tree type = chrec_type (chrec);
  tree res = chrec_dont_know;

  if (automatically_generated_chrec_p (chrec)
      || automatically_generated_chrec_p (x)

      /* When the symbols are defined in an outer loop, it is possible
         to symbolically compute the apply, since the symbols are
         constants with respect to the varying loop.  */
      || chrec_contains_symbols_defined_in_loop (chrec, var))
    return chrec_dont_know;
 
  if (dump_file && (dump_flags & TDF_DETAILS))
    fprintf (dump_file, "(chrec_apply \n");

  if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type))
    x = build_real_from_int_cst (type, x);

  if (evolution_function_is_affine_p (chrec))
    {
      /* "{a, +, b} (x)"  ->  "a + b*x".  */
      x = chrec_convert (type, x, NULL_TREE);
      res = chrec_fold_multiply (type, CHREC_RIGHT (chrec), x);
      if (!integer_zerop (CHREC_LEFT (chrec)))
        res = chrec_fold_plus (type, CHREC_LEFT (chrec), res);
    }
  
  else if (TREE_CODE (chrec) != POLYNOMIAL_CHREC)
    res = chrec;
  
  else if (TREE_CODE (x) == INTEGER_CST
           && tree_int_cst_sgn (x) == 1)
    /* testsuite/.../ssa-chrec-38.c.  */
    res = chrec_evaluate (var, chrec, x, 0);
  else
    res = chrec_dont_know;
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fprintf (dump_file, "  (varying_loop = %d\n", var);
      fprintf (dump_file, ")\n  (chrec = ");
      print_generic_expr (dump_file, chrec, 0);
      fprintf (dump_file, ")\n  (x = ");
      print_generic_expr (dump_file, x, 0);
      fprintf (dump_file, ")\n  (res = ");
      print_generic_expr (dump_file, res, 0);
      fprintf (dump_file, "))\n");
    }
  
  return res;
}

/* Replaces the initial condition in CHREC with INIT_COND.  */

tree 
chrec_replace_initial_condition (tree chrec, 
                                 tree init_cond)
{
  if (automatically_generated_chrec_p (chrec))
    return chrec;

  gcc_assert (chrec_type (chrec) == chrec_type (init_cond));

  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      return build_polynomial_chrec 
        (CHREC_VARIABLE (chrec),
         chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond),
         CHREC_RIGHT (chrec));
      
    default:
      return init_cond;
    }
}

/* Returns the initial condition of a given CHREC.  */

tree 
initial_condition (tree chrec)
{
  if (automatically_generated_chrec_p (chrec))
    return chrec;
  
  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
    return initial_condition (CHREC_LEFT (chrec));
  else
    return chrec;
}

/* Returns a univariate function that represents the evolution in
   LOOP_NUM.  Mask the evolution of any other loop.  */

tree 
hide_evolution_in_other_loops_than_loop (tree chrec, 
                                         unsigned loop_num)
{
  if (automatically_generated_chrec_p (chrec))
    return chrec;
  
  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      if (CHREC_VARIABLE (chrec) == loop_num)
        return build_polynomial_chrec 
          (loop_num, 
           hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), 
                                                    loop_num), 
           CHREC_RIGHT (chrec));
      
      else if (CHREC_VARIABLE (chrec) < loop_num)
        /* There is no evolution in this loop.  */
        return initial_condition (chrec);
      
      else
        return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), 
                                                        loop_num);
      
    default:
      return chrec;
    }
}

/* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
   true, otherwise returns the initial condition in LOOP_NUM.  */

static tree 
chrec_component_in_loop_num (tree chrec, 
                             unsigned loop_num,
                             bool right)
{
  tree component;

  if (automatically_generated_chrec_p (chrec))
    return chrec;
  
  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      if (CHREC_VARIABLE (chrec) == loop_num)
        {
          if (right)
            component = CHREC_RIGHT (chrec);
          else
            component = CHREC_LEFT (chrec);

          if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
              || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec))
            return component;
          
          else
            return build_polynomial_chrec
              (loop_num, 
               chrec_component_in_loop_num (CHREC_LEFT (chrec), 
                                            loop_num, 
                                            right), 
               component);
        }
      
      else if (CHREC_VARIABLE (chrec) < loop_num)
        /* There is no evolution part in this loop.  */
        return NULL_TREE;
      
      else
        return chrec_component_in_loop_num (CHREC_LEFT (chrec), 
                                            loop_num, 
                                            right);
      
     default:
      if (right)
        return NULL_TREE;
      else
        return chrec;
    }
}

/* Returns the evolution part in LOOP_NUM.  Example: the call
   evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns 
   {1, +, 2}_1  */

tree 
evolution_part_in_loop_num (tree chrec, 
                            unsigned loop_num)
{
  return chrec_component_in_loop_num (chrec, loop_num, true);
}

/* Returns the initial condition in LOOP_NUM.  Example: the call
   initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns 
   {0, +, 1}_1  */

tree 
initial_condition_in_loop_num (tree chrec, 
                               unsigned loop_num)
{
  return chrec_component_in_loop_num (chrec, loop_num, false);
}

/* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
   This function is essentially used for setting the evolution to
   chrec_dont_know, for example after having determined that it is
   impossible to say how many times a loop will execute.  */

tree 
reset_evolution_in_loop (unsigned loop_num,
                         tree chrec, 
                         tree new_evol)
{
  gcc_assert (chrec_type (chrec) == chrec_type (new_evol));

  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
      && CHREC_VARIABLE (chrec) > loop_num)
    {
      tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec),
                                           new_evol);
      tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec),
                                            new_evol);
      return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left),
                     build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)),
                     left, right);
    }

  while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
         && CHREC_VARIABLE (chrec) == loop_num)
    chrec = CHREC_LEFT (chrec);
  
  return build_polynomial_chrec (loop_num, chrec, new_evol);
}

/* Merges two evolution functions that were found by following two
   alternate paths of a conditional expression.  */

tree
chrec_merge (tree chrec1, 
             tree chrec2)
{
  if (chrec1 == chrec_dont_know
      || chrec2 == chrec_dont_know)
    return chrec_dont_know;

  if (chrec1 == chrec_known 
      || chrec2 == chrec_known)
    return chrec_known;

  if (chrec1 == chrec_not_analyzed_yet)
    return chrec2;
  if (chrec2 == chrec_not_analyzed_yet)
    return chrec1;

  if (eq_evolutions_p (chrec1, chrec2))
    return chrec1;

  return chrec_dont_know;
}



/* Observers.  */

/* Helper function for is_multivariate_chrec.  */

static bool 
is_multivariate_chrec_rec (tree chrec, unsigned int rec_var)
{
  if (chrec == NULL_TREE)
    return false;
  
  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
    {
      if (CHREC_VARIABLE (chrec) != rec_var)
        return true;
      else
        return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) 
                || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var));
    }
  else
    return false;
}

/* Determine whether the given chrec is multivariate or not.  */

bool 
is_multivariate_chrec (tree chrec)
{
  if (chrec == NULL_TREE)
    return false;
  
  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
    return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), 
                                       CHREC_VARIABLE (chrec))
            || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), 
                                          CHREC_VARIABLE (chrec)));
  else
    return false;
}

/* Determines whether the chrec contains symbolic names or not.  */

bool 
chrec_contains_symbols (tree chrec)
{
  if (chrec == NULL_TREE)
    return false;
  
  if (TREE_CODE (chrec) == SSA_NAME
      || TREE_CODE (chrec) == VAR_DECL
      || TREE_CODE (chrec) == PARM_DECL
      || TREE_CODE (chrec) == FUNCTION_DECL
      || TREE_CODE (chrec) == LABEL_DECL
      || TREE_CODE (chrec) == RESULT_DECL
      || TREE_CODE (chrec) == FIELD_DECL)
    return true;
  
  switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
    {
    case 3:
      if (chrec_contains_symbols (TREE_OPERAND (chrec, 2)))
        return true;
      
    case 2:
      if (chrec_contains_symbols (TREE_OPERAND (chrec, 1)))
        return true;
      
    case 1:
      if (chrec_contains_symbols (TREE_OPERAND (chrec, 0)))
        return true;
      
    default:
      return false;
    }
}

/* Determines whether the chrec contains undetermined coefficients.  */

bool 
chrec_contains_undetermined (tree chrec)
{
  if (chrec == chrec_dont_know
      || chrec == chrec_not_analyzed_yet
      || chrec == NULL_TREE)
    return true;
  
  switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
    {
    case 3:
      if (chrec_contains_undetermined (TREE_OPERAND (chrec, 2)))
        return true;
      
    case 2:
      if (chrec_contains_undetermined (TREE_OPERAND (chrec, 1)))
        return true;
      
    case 1:
      if (chrec_contains_undetermined (TREE_OPERAND (chrec, 0)))
        return true;
      
    default:
      return false;
    }
}

/* Determines whether the tree EXPR contains chrecs, and increment
   SIZE if it is not a NULL pointer by an estimation of the depth of
   the tree.  */

bool
tree_contains_chrecs (tree expr, int *size)
{
  if (expr == NULL_TREE)
    return false;

  if (size)
    (*size)++;
  
  if (tree_is_chrec (expr))
    return true;

  switch (TREE_CODE_LENGTH (TREE_CODE (expr)))
    {
    case 3:
      if (tree_contains_chrecs (TREE_OPERAND (expr, 2), size))
        return true;
      
    case 2:
      if (tree_contains_chrecs (TREE_OPERAND (expr, 1), size))
        return true;
      
    case 1:
      if (tree_contains_chrecs (TREE_OPERAND (expr, 0), size))
        return true;
      
    default:
      return false;
    }
}

/* Recursive helper function.  */

static bool
evolution_function_is_invariant_rec_p (tree chrec, int loopnum)
{
  if (evolution_function_is_constant_p (chrec))
    return true;

  if (TREE_CODE (chrec) == SSA_NAME 
      && expr_invariant_in_loop_p (current_loops->parray[loopnum],
                                   chrec))
    return true;

  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
    {
      if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
          || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec),
                                                     loopnum)
          || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec),
                                                     loopnum))
        return false;
      return true;
    }

  switch (TREE_CODE_LENGTH (TREE_CODE (chrec)))
    {
    case 2:
      if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
                                                  loopnum))
        return false;
      
    case 1:
      if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
                                                  loopnum))
        return false;
      return true;

    default:
      return false;
    }

  return false;
}

/* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */

bool
evolution_function_is_invariant_p (tree chrec, int loopnum)
{
  if (evolution_function_is_constant_p (chrec))
    return true;
  
  if (current_loops != NULL)
    return evolution_function_is_invariant_rec_p (chrec, loopnum);

  return false;
}

/* Determine whether the given tree is an affine multivariate
   evolution.  */

bool 
evolution_function_is_affine_multivariate_p (tree chrec)
{
  if (chrec == NULL_TREE)
    return false;
  
  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      if (evolution_function_is_constant_p (CHREC_LEFT (chrec)))
        {
          if (evolution_function_is_constant_p (CHREC_RIGHT (chrec)))
            return true;
          else
            {
              if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC
                  && CHREC_VARIABLE (CHREC_RIGHT (chrec)) 
                     != CHREC_VARIABLE (chrec)
                  && evolution_function_is_affine_multivariate_p 
                  (CHREC_RIGHT (chrec)))
                return true;
              else
                return false;
            }
        }
      else
        {
          if (evolution_function_is_constant_p (CHREC_RIGHT (chrec))
              && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
              && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
              && evolution_function_is_affine_multivariate_p 
              (CHREC_LEFT (chrec)))
            return true;
          else
            return false;
        }
      
    default:
      return false;
    }
}

/* Determine whether the given tree is a function in zero or one 
   variables.  */

bool
evolution_function_is_univariate_p (tree chrec)
{
  if (chrec == NULL_TREE)
    return true;
  
  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      switch (TREE_CODE (CHREC_LEFT (chrec)))
        {
        case POLYNOMIAL_CHREC:
          if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec)))
            return false;
          if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec)))
            return false;
          break;
          
        default:
          break;
        }
      
      switch (TREE_CODE (CHREC_RIGHT (chrec)))
        {
        case POLYNOMIAL_CHREC:
          if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec)))
            return false;
          if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec)))
            return false;
          break;
          
        default:
          break;          
        }
      
    default:
      return true;
    }
}

/* Returns the number of variables of CHREC.  Example: the call
   nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2.  */

unsigned 
nb_vars_in_chrec (tree chrec)
{
  if (chrec == NULL_TREE)
    return 0;

  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      return 1 + nb_vars_in_chrec 
        (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec)));

    default:
      return 0;
    }
}

/* Returns true if TYPE is a type in that we cannot directly perform
   arithmetics, even though it is a scalar type.  */

static bool
avoid_arithmetics_in_type_p (tree type)
{
  /* Ada frontend uses subtypes -- an arithmetic cannot be directly performed
     in the subtype, but a base type must be used, and the result then can
     be casted to the subtype.  */
  if (TREE_CODE (type) == INTEGER_TYPE && TREE_TYPE (type) != NULL_TREE)
    return true;

  return false;
}

static tree chrec_convert_1 (tree, tree, tree, bool);

/* Converts BASE and STEP of affine scev to TYPE.  LOOP is the loop whose iv
   the scev corresponds to.  AT_STMT is the statement at that the scev is
   evaluated.  USE_OVERFLOW_SEMANTICS is true if this function should assume that
   the rules for overflow of the given language apply (e.g., that signed
   arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
   tests, but also to enforce that the result follows them.  Returns true if the
   conversion succeeded, false otherwise.  */

bool
convert_affine_scev (struct loop *loop, tree type,
                     tree *base, tree *step, tree at_stmt,
                     bool use_overflow_semantics)
{
  tree ct = TREE_TYPE (*step);
  bool enforce_overflow_semantics;
  bool must_check_src_overflow, must_check_rslt_overflow;
  tree new_base, new_step;

  /* If we cannot perform arithmetic in TYPE, avoid creating an scev.  */
  if (avoid_arithmetics_in_type_p (type))
    return false;

  /* In general,
     (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
     but we must check some assumptions.
     
     1) If [BASE, +, STEP] wraps, the equation is not valid when precision
        of CT is smaller than the precision of TYPE.  For example, when we
        cast unsigned char [254, +, 1] to unsigned, the values on left side
        are 254, 255, 0, 1, ..., but those on the right side are
        254, 255, 256, 257, ...
     2) In case that we must also preserve the fact that signed ivs do not
        overflow, we must additionally check that the new iv does not wrap.
        For example, unsigned char [125, +, 1] casted to signed char could
        become a wrapping variable with values 125, 126, 127, -128, -127, ...,
        which would confuse optimizers that assume that this does not
        happen.  */
  must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type);

  enforce_overflow_semantics = (use_overflow_semantics
                                && nowrap_type_p (type));
  if (enforce_overflow_semantics)
    {
      /* We can avoid checking whether the result overflows in the following
         cases:

         -- must_check_src_overflow is true, and the range of TYPE is superset
            of the range of CT -- i.e., in all cases except if CT signed and
            TYPE unsigned.
         -- both CT and TYPE have the same precision and signedness, and we
            verify instead that the source does not overflow (this may be
            easier than verifying it for the result, as we may use the
            information about the semantics of overflow in CT).  */
      if (must_check_src_overflow)
        {
          if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct))
            must_check_rslt_overflow = true;
          else
            must_check_rslt_overflow = false;
        }
      else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type)
               && TYPE_PRECISION (ct) == TYPE_PRECISION (type))
        {
          must_check_rslt_overflow = false;
          must_check_src_overflow = true;
        }
      else
        must_check_rslt_overflow = true;
    }
  else
    must_check_rslt_overflow = false;

  if (must_check_src_overflow
      && scev_probably_wraps_p (*base, *step, at_stmt, loop,
                                use_overflow_semantics))
    return false;

  new_base = chrec_convert_1 (type, *base, at_stmt,
                              use_overflow_semantics);
  /* The step must be sign extended, regardless of the signedness
     of