gcc/tree-chrec.cc

/* Chains of recurrences.
   Copyright (C) 2003-2024 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 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/>.  */

/* 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 "backend.h"
#include "tree.h"
#include "gimple-expr.h"
#include "tree-pretty-print.h"
#include "fold-const.h"
#include "cfgloop.h"
#include "tree-ssa-loop-ivopts.h"
#include "tree-ssa-loop-niter.h"
#include "tree-chrec.h"
#include "gimple.h"
#include "tree-ssa-loop.h"
#include "dumpfile.h"
#include "tree-scalar-evolution.h"

/* Extended folder for chrecs.  */

/* 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;
  class loop *loop0 = get_chrec_loop (poly0);
  class loop *loop1 = get_chrec_loop (poly1);
  tree rtype = code == POINTER_PLUS_EXPR ? chrec_type (poly1) : type;

  gcc_assert (poly0);
  gcc_assert (poly1);
  gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
  gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
  if (POINTER_TYPE_P (chrec_type (poly0)))
    gcc_checking_assert (ptrofftype_p (chrec_type (poly1))
			 && useless_type_conversion_p (type, chrec_type (poly0)));
  else
    gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
			 && useless_type_conversion_p (type, chrec_type (poly1)));

  /*
    {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 (flow_loop_nested_p (loop0, loop1))
    {
      if (code == PLUS_EXPR || code == POINTER_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 (flow_loop_nested_p (loop1, loop0))
    {
      if (code == PLUS_EXPR || code == POINTER_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));
    }

  /* This function should never be called for chrecs of loops that
     do not belong to the same loop nest.  */
  if (loop0 != loop1)
    {
      /* It still can happen if we are not in loop-closed SSA form.  */
      gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
      return chrec_dont_know;
    }

  if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR)
    {
      left = chrec_fold_plus
	(type, CHREC_LEFT (poly0), CHREC_LEFT (poly1));
      right = chrec_fold_plus
	(rtype, 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;
  class loop *loop0 = get_chrec_loop (poly0);
  class loop *loop1 = get_chrec_loop (poly1);

  gcc_assert (poly0);
  gcc_assert (poly1);
  gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC);
  gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC);
  gcc_checking_assert (useless_type_conversion_p (type, chrec_type (poly0))
		       && useless_type_conversion_p (type, chrec_type (poly1)));

  /* {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 (flow_loop_nested_p (loop0, loop1))
    /* 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 (flow_loop_nested_p (loop1, loop0))
    /* poly1 is a constant wrt. poly0.  */
    return build_polynomial_chrec
      (CHREC_VARIABLE (poly0),
       chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1),
       CHREC_RIGHT (poly0));

  if (loop0 != loop1)
    {
      /* It still can happen if we are not in loop-closed SSA form.  */
      gcc_assert (! loops_state_satisfies_p (LOOP_CLOSED_SSA));
      return chrec_dont_know;
    }

  /* 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".  */
  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)));
  /* "b*d".  */
  t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1));
  /* "a*d + b*c + b*d".  */
  t1 = chrec_fold_plus (type, t1, t2);
  /* "2*b*d".  */
  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:
      gcc_checking_assert
	(!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
      switch (TREE_CODE (op1))
	{
	case POLYNOMIAL_CHREC:
	  gcc_checking_assert
	    (!chrec_contains_symbols_defined_in_loop (op1,
						      CHREC_VARIABLE (op1)));
	  return chrec_fold_plus_poly_poly (code, type, op0, op1);

	CASE_CONVERT:
	  if (tree_contains_chrecs (op1, NULL))
	    {
	      /* We can strip sign-conversions to signed by performing the
		 operation in unsigned.  */
	      tree optype = TREE_TYPE (TREE_OPERAND (op1, 0));
	      if (INTEGRAL_TYPE_P (type)
		  && INTEGRAL_TYPE_P (optype)
		  && tree_nop_conversion_p (type, optype)
		  && TYPE_UNSIGNED (optype))
		{
		  tree tem = chrec_convert (optype, op0, NULL);
		  if (TREE_CODE (tem) == POLYNOMIAL_CHREC)
		    return chrec_convert (type,
					  chrec_fold_plus_1 (code, optype,
							     tem,
							     TREE_OPERAND
							       (op1, 0)),
					  NULL);
		}
	      return chrec_dont_know;
	    }
	  /* FALLTHRU */

	default:
	  if (code == PLUS_EXPR || code == POINTER_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));
	}

    CASE_CONVERT:
      if (tree_contains_chrecs (op0, NULL))
	{
	  /* We can strip sign-conversions to signed by performing the
	     operation in unsigned.  */
	  tree optype = TREE_TYPE (TREE_OPERAND (op0, 0));
	  if (INTEGRAL_TYPE_P (type)
	      && INTEGRAL_TYPE_P (optype)
	      && tree_nop_conversion_p (type, optype)
	      && TYPE_UNSIGNED (optype))
	    return chrec_convert (type,
				  chrec_fold_plus_1 (code, optype,
						     TREE_OPERAND (op0, 0),
						     chrec_convert (optype,
								    op1, NULL)),
				  NULL);
	  return chrec_dont_know;
	}
      /* FALLTHRU */

    default:
      gcc_checking_assert (!tree_contains_chrecs (op0, NULL));
      switch (TREE_CODE (op1))
	{
	case POLYNOMIAL_CHREC:
	  gcc_checking_assert
	    (!chrec_contains_symbols_defined_in_loop (op1,
						      CHREC_VARIABLE (op1)));
	  if (code == PLUS_EXPR || code == POINTER_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)));

	CASE_CONVERT:
	  if (tree_contains_chrecs (op1, NULL))
	    {
	      /* We can strip sign-conversions to signed by performing the
		 operation in unsigned.  */
	      tree optype = TREE_TYPE (TREE_OPERAND (op1, 0));
	      if (INTEGRAL_TYPE_P (type)
		  && INTEGRAL_TYPE_P (optype)
		  && tree_nop_conversion_p (type, optype)
		  && TYPE_UNSIGNED (optype))
		return chrec_convert (type,
				      chrec_fold_plus_1 (code, optype,
							 chrec_convert (optype,
									op0,
									NULL),
							 TREE_OPERAND (op1, 0)),
				      NULL);
	      return chrec_dont_know;
	    }
	  /* FALLTHRU */

	default:
	  {
	    int size = 0;
	    if ((tree_contains_chrecs (op0, &size)
		 || tree_contains_chrecs (op1, &size))
		&& size < param_scev_max_expr_size)
	      return build2 (code, type, op0, op1);
	    else if (size < param_scev_max_expr_size)
	      {
		if (code == POINTER_PLUS_EXPR)
		  return fold_build_pointer_plus (fold_convert (type, op0),
						  op1);
		else
		  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)
{
  enum tree_code code;
  if (automatically_generated_chrec_p (op0)
      || automatically_generated_chrec_p (op1))
    return chrec_fold_automatically_generated_operands (op0, op1);

  if (integer_zerop (op0))
    return chrec_convert (type, op1, NULL);
  if (integer_zerop (op1))
    return chrec_convert (type, op0, NULL);

  if (POINTER_TYPE_P (type))
    code = POINTER_PLUS_EXPR;
  else
    code = PLUS_EXPR;

  return chrec_fold_plus_1 (code, 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);

  if (TREE_CODE (op0) != POLYNOMIAL_CHREC
      && TREE_CODE (op1) == POLYNOMIAL_CHREC)
    std::swap (op0, op1);

  switch (TREE_CODE (op0))
    {
    case POLYNOMIAL_CHREC:
      gcc_checking_assert
	(!chrec_contains_symbols_defined_in_loop (op0, CHREC_VARIABLE (op0)));
      switch (TREE_CODE (op1))
	{
	case POLYNOMIAL_CHREC:
	  gcc_checking_assert
	    (!chrec_contains_symbols_defined_in_loop (op1,
						      CHREC_VARIABLE (op1)));
	  return chrec_fold_multiply_poly_poly (type, op0, op1);

	CASE_CONVERT:
	  if (tree_contains_chrecs (op1, NULL))
	    {
	      /* We can strip sign-conversions to signed by performing the
		 operation in unsigned.  */
	      tree optype = TREE_TYPE (TREE_OPERAND (op1, 0));
	      if (INTEGRAL_TYPE_P (type)
		  && INTEGRAL_TYPE_P (optype)
		  && tree_nop_conversion_p (type, optype)
		  && TYPE_UNSIGNED (optype))
		{
		  tree tem = chrec_convert (optype, op0, NULL);
		  if (TREE_CODE (tem) == POLYNOMIAL_CHREC)
		    return chrec_convert (type,
					  chrec_fold_multiply (optype, tem,
							       TREE_OPERAND
								 (op1, 0)),
					  NULL);
		}
	      return chrec_dont_know;
	    }
	  /* FALLTHRU */

	default:
	  if (integer_onep (op1))
	    return op0;
	  if (integer_zerop (op1))
	    return build_int_cst (type, 0);

	  /* When overflow is undefined and CHREC_LEFT/RIGHT do not have the
	     same sign or CHREC_LEFT is zero then folding the multiply into
	     the addition does not have the same behavior on overflow.
	     Using unsigned arithmetic in that case causes too many performance
	     regressions, but catch the constant case where the multiplication
	     of the step overflows.  */
	  if (INTEGRAL_TYPE_P (type)
	      && TYPE_OVERFLOW_UNDEFINED (type)
	      && !integer_zerop (CHREC_LEFT (op0))
	      && TREE_CODE (op1) == INTEGER_CST
	      && TREE_CODE (CHREC_RIGHT (op0)) == INTEGER_CST)
	    {
	      wi::overflow_type ovf = wi::OVF_NONE;
	      wide_int res
		= wi::mul (wi::to_wide (CHREC_RIGHT (op0)),
			   wi::to_wide (op1), TYPE_SIGN (type), &ovf);
	      if (ovf != wi::OVF_NONE)
		{
		  tree utype = unsigned_type_for (type);
		  tree uop1 = chrec_convert_rhs (utype, op1);
		  tree uleft0 = chrec_convert_rhs (utype, CHREC_LEFT (op0));
		  tree uright0 = chrec_convert_rhs (utype, CHREC_RIGHT (op0));
		  tree left = chrec_fold_multiply (utype, uleft0, uop1);
		  tree right = chrec_fold_multiply (utype, uright0, uop1);
		  tree tem = build_polynomial_chrec (CHREC_VARIABLE (op0),
						     left, right);
		  return chrec_convert_rhs (type, tem);
		}
	    }
	  tree left = chrec_fold_multiply (type, CHREC_LEFT (op0), op1);
	  tree right = chrec_fold_multiply (type, CHREC_RIGHT (op0), op1);
	  return build_polynomial_chrec (CHREC_VARIABLE (op0), left, right);
	}

    CASE_CONVERT:
      if (tree_contains_chrecs (op0, NULL))
	{
	  /* We can strip sign-conversions to signed by performing the
	     operation in unsigned.  */
	  tree optype = TREE_TYPE (TREE_OPERAND (op0, 0));
	  if (INTEGRAL_TYPE_P (type)
	      && INTEGRAL_TYPE_P (optype)
	      && tree_nop_conversion_p (type, optype)
	      && TYPE_UNSIGNED (optype))
	    return chrec_convert (type,
				  chrec_fold_multiply (optype,
						       TREE_OPERAND (op0, 0),
						       chrec_convert (optype,
								      op1,
								      NULL)),
				  NULL);
	  return chrec_dont_know;
	}
      /* FALLTHRU */

    default:
      gcc_checking_assert (!tree_contains_chrecs (op0, NULL));
      if (integer_onep (op0))
	return op1;

      if (integer_zerop (op0))
    	return build_int_cst (type, 0);

      switch (TREE_CODE (op1))
	{
	case POLYNOMIAL_CHREC:
	  gcc_unreachable ();

	CASE_CONVERT:
	  if (tree_contains_chrecs (op1, NULL))
	    return chrec_fold_multiply (type, op1, op0);
	  /* FALLTHRU */

	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)
{
  wi::overflow_type overflow;
  unsigned int i;

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

  widest_int num = wi::to_widest (n);

  /* Check that k <= n.  */
  if (wi::ltu_p (num, k))
    return NULL_TREE;

  /* Denominator = 2.  */
  widest_int denom = 2;

  /* Index = Numerator-1.  */
  widest_int idx = num - 1;

  /* Numerator = Numerator*Index = n*(n-1).  */
  num = wi::smul (num, idx, &overflow);
  if (overflow)
    return NULL_TREE;

  for (i = 3; i <= k; i++)
    {
      /* Index--.  */
      --idx;

      /* Numerator *= Index.  */
      num = wi::smul (num, idx, &overflow);
      if (overflow)
	return NULL_TREE;

      /* Denominator *= i.  */
      denom *= i;
    }

  /* Result = Numerator / Denominator.  */
  num = wi::udiv_trunc (num, denom);
  if (! wi::fits_to_tree_p (num, type))
    return NULL_TREE;
  return wide_int_to_tree (type, num);
}

/* Helper function.  Use the Newton's interpolating formula for
   evaluating the value of the evolution function.
   The result may be in an unsigned type of CHREC.  */

static tree
chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k)
{
  tree arg0, arg1, binomial_n_k;
  tree type = TREE_TYPE (chrec);
  class loop *var_loop = get_loop (cfun, var);

  while (TREE_CODE (chrec) == POLYNOMIAL_CHREC
	 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec)))
    chrec = CHREC_LEFT (chrec);

  /* The formula associates the expression and thus we have to make
     sure to not introduce undefined overflow.  */
  tree ctype = type;
  if (INTEGRAL_TYPE_P (type)
      && ! TYPE_OVERFLOW_WRAPS (type))
    ctype = unsigned_type_for (type);

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

  binomial_n_k = tree_fold_binomial (ctype, n, k);
  if (!binomial_n_k)
    return chrec_dont_know;

  return fold_build2 (MULT_EXPR, ctype,
		      chrec_convert (ctype, chrec, NULL), 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_SCEV))
    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);

  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      if (evolution_function_is_affine_p (chrec))
	{
	  tree chrecr = CHREC_RIGHT (chrec);
	  tree chrecl = CHREC_LEFT (chrec);
	  if (CHREC_VARIABLE (chrec) != var)
	    res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
					  chrec_apply (var, chrecl, x),
					  chrec_apply (var, chrecr, x));

	  /* "{a, +, a}" (x-1) -> "a*x".  */
	  else if (operand_equal_p (chrecl, chrecr)
		   && TREE_CODE (x) == PLUS_EXPR
		   && integer_all_onesp (TREE_OPERAND (x, 1))
		   && !POINTER_TYPE_P (type)
		   && TYPE_PRECISION (TREE_TYPE (x))
		      >= TYPE_PRECISION (type))
	    {
	      /* We know the number of iterations can't be negative.  */
	      res = build_int_cst (TREE_TYPE (x), 1);
	      res = chrec_fold_plus (TREE_TYPE (x), x, res);
	      res = chrec_convert_rhs (type, res, NULL);
	      res = chrec_fold_multiply (type, chrecr, res);
	    }
	  /* "{a, +, b} (x)"  ->  "a + b*x".  */
	  else
	    {
	      /* The overall increment might not fit in a signed type so
		 use an unsigned computation to get at the final value
		 and avoid undefined signed overflow.  */
	      tree utype = TREE_TYPE (chrecr);
	      if (INTEGRAL_TYPE_P (utype) && !TYPE_OVERFLOW_WRAPS (utype))
		utype = unsigned_type_for (TREE_TYPE (chrecr));
	      res = chrec_convert_rhs (utype, x, NULL);
	      res = chrec_fold_multiply (utype,
					 chrec_convert (utype, chrecr, NULL),
					 res);
	      /* When the resulting increment fits the original type
		 do the increment in it.  */
	      if (TREE_CODE (res) == INTEGER_CST
		  && int_fits_type_p (res, TREE_TYPE (chrecr)))
		{
		  res = chrec_convert (TREE_TYPE (chrecr), res, NULL);
		  res = chrec_fold_plus (type, chrecl, res);
		}
	      else
		{
		  res = chrec_fold_plus (utype,
					 chrec_convert (utype, chrecl, NULL),
					 res);
		  res = chrec_convert (type, res, NULL);
		}
	    }
	}
      else if (TREE_CODE (x) == INTEGER_CST
	       && tree_int_cst_sgn (x) == 1)
	/* testsuite/.../ssa-chrec-38.c.  */
	res = chrec_convert (type, chrec_evaluate (var, chrec, x, 0), NULL);
      else
	res = chrec_dont_know;
      break;

    CASE_CONVERT:
      res = chrec_convert (TREE_TYPE (chrec),
			   chrec_apply (var, TREE_OPERAND (chrec, 0), x),
			   NULL);
      break;

    default:
      res = chrec;
      break;
    }

  if (dump_file && (dump_flags & TDF_SCEV))
    {
      fprintf (dump_file, "  (varying_loop = %d", var);
      fprintf (dump_file, ")\n  (chrec = ");
      print_generic_expr (dump_file, chrec);
      fprintf (dump_file, ")\n  (x = ");
      print_generic_expr (dump_file, x);
      fprintf (dump_file, ")\n  (res = ");
      print_generic_expr (dump_file, res);
      fprintf (dump_file, "))\n");
    }

  return res;
}

/* For a given CHREC and an induction variable map IV_MAP that maps
   (loop->num, expr) for every loop number of the current_loops an
   expression, calls chrec_apply when the expression is not NULL.  */

tree
chrec_apply_map (tree chrec, vec<tree> iv_map)
{
  int i;
  tree expr;

  FOR_EACH_VEC_ELT (iv_map, i, expr)
    if (expr)
      chrec = chrec_apply (i, chrec, expr);

  return chrec;
}

/* 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)
{
  class loop *loop = get_loop (cfun, loop_num), *chloop;
  if (automatically_generated_chrec_p (chrec))
    return chrec;

  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      chloop = get_chrec_loop (chrec);

      if (chloop == loop)
	return build_polynomial_chrec
	  (loop_num,
	   hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
						    loop_num),
	   CHREC_RIGHT (chrec));

      else if (flow_loop_nested_p (chloop, loop))
	/* There is no evolution in this loop.  */
	return initial_condition (chrec);

      else if (flow_loop_nested_p (loop, chloop))
	return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec),
							loop_num);

      else
	return chrec_dont_know;

    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;
  class loop *loop = get_loop (cfun, loop_num), *chloop;

  if (automatically_generated_chrec_p (chrec))
    return chrec;

  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      chloop = get_chrec_loop (chrec);

      if (chloop == loop)
	{
	  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 (flow_loop_nested_p (chloop, loop))
	/* There is no evolution part in this loop.  */
	return NULL_TREE;

      else
	{
	  gcc_assert (flow_loop_nested_p (loop, chloop));
	  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)
{
  class loop *loop = get_loop (cfun, loop_num);

  if (POINTER_TYPE_P (chrec_type (chrec)))
    gcc_assert (ptrofftype_p (chrec_type (new_evol)));
  else
    gcc_assert (chrec_type (chrec) == chrec_type (new_evol));

  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC
      && flow_loop_nested_p (loop, get_chrec_loop (chrec)))
    {
      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 build_polynomial_chrec (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 (const_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 (const_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.  If LOOP isn't
   NULL, we also consider chrec wrto outer loops of LOOP as symbol.  */

static bool
chrec_contains_symbols (const_tree chrec, hash_set<const_tree> &visited,
			class loop *loop)
{
  int i, n;

  if (chrec == NULL_TREE)
    return false;

  if (TREE_CODE (chrec) == SSA_NAME
      || VAR_P (chrec)
      || TREE_CODE (chrec) == POLY_INT_CST
      || 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 (loop != NULL
      && TREE_CODE (chrec) == POLYNOMIAL_CHREC
      && flow_loop_nested_p (get_chrec_loop (chrec), loop))
    return true;

  if (visited.add (chrec))
    return false;

  n = TREE_OPERAND_LENGTH (chrec);
  for (i = 0; i < n; i++)
    if (chrec_contains_symbols (TREE_OPERAND (chrec, i), visited, loop))
      return true;
  return false;
}

/* Return true if CHREC contains any symbols.  If LOOP is not NULL, check if
   CHREC contains any chrec which is invariant wrto the loop (nest), in other
   words, chrec defined by outer loops of loop, so from LOOP's point of view,
   the chrec is considered as a SYMBOL.  */

bool
chrec_contains_symbols (const_tree chrec, class loop* loop)
{
  hash_set<const_tree> visited;
  return chrec_contains_symbols (chrec, visited, loop);
}

/* Return true when CHREC contains symbolic names defined in
   LOOP_NB.  */

static bool
chrec_contains_symbols_defined_in_loop (const_tree chrec, unsigned loop_nb,
					hash_set<const_tree> &visited)
{
  int i, n;

  if (chrec == NULL_TREE)
    return false;

  if (is_gimple_min_invariant (chrec))
    return false;

  if (TREE_CODE (chrec) == SSA_NAME)
    {
      gimple *def;
      loop_p def_loop, loop;

      if (SSA_NAME_IS_DEFAULT_DEF (chrec))
	return false;

      def = SSA_NAME_DEF_STMT (chrec);
      def_loop = loop_containing_stmt (def);
      loop = get_loop (cfun, loop_nb);

      if (def_loop == NULL)
	return false;

      if (loop == def_loop || flow_loop_nested_p (loop, def_loop))
	return true;

      return false;
    }

  if (visited.add (chrec))
    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, visited))
      return true;
  return false;
}

/* Return true when CHREC contains symbolic names defined in
   LOOP_NB.  */

bool
chrec_contains_symbols_defined_in_loop (const_tree chrec, unsigned loop_nb)
{
  hash_set<const_tree> visited;
  return chrec_contains_symbols_defined_in_loop (chrec, loop_nb, visited);
}

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

static bool
chrec_contains_undetermined (const_tree chrec, hash_set<const_tree> &visited)
{
  int i, n;

  if (chrec == chrec_dont_know)
    return true;

  if (chrec == NULL_TREE)
    return false;

  if (visited.add (chrec))
    return false;

  n = TREE_OPERAND_LENGTH (chrec);
  for (i = 0; i < n; i++)
    if (chrec_contains_undetermined (TREE_OPERAND (chrec, i), visited))
      return true;
  return false;
}

bool
chrec_contains_undetermined (const_tree chrec)
{
  hash_set<const_tree> visited;
  return chrec_contains_undetermined (chrec, visited);
}

/* 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.  */

static bool
tree_contains_chrecs (const_tree expr, int *size, hash_set<const_tree> &visited)
{
  int i, n;

  if (expr == NULL_TREE)
    return false;

  if (size)
    (*size)++;

  if (tree_is_chrec (expr))
    return true;

  if (visited.add (expr))
    return false;

  n = TREE_OPERAND_LENGTH (expr);
  for (i = 0; i < n; i++)
    if (tree_contains_chrecs (TREE_OPERAND (expr, i), size, visited))
      return true;
  return false;
}

bool
tree_contains_chrecs (const_tree expr, int *size)
{
  hash_set<const_tree> visited;
  return tree_contains_chrecs (expr, size, visited);
}


/* 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
      && (loopnum == 0
	  || expr_invariant_in_loop_p (get_loop (cfun, loopnum), chrec)))
    return true;

  if (TREE_CODE (chrec) == POLYNOMIAL_CHREC)
    {
      if (CHREC_VARIABLE (chrec) == (unsigned) loopnum
	  || flow_loop_nested_p (get_loop (cfun, loopnum),
				 get_chrec_loop (chrec))
	  || !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_OPERAND_LENGTH (chrec))
    {
    case 2:
      if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1),
						  loopnum))
	return false;
      /* FALLTHRU */

    case 1:
      if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0),
						  loopnum))
	return false;
      return true;

    default:
      return false;
    }
}

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

bool
evolution_function_is_invariant_p (tree chrec, int loopnum)
{
  return evolution_function_is_invariant_rec_p (chrec, loopnum);
}

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

bool
evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum)
{
  if (chrec == NULL_TREE)
    return false;

  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum))
	{
	  if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum))
	    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), loopnum))
		return true;
	      else
		return false;
	    }
	}
      else
	{
	  if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)
	      && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC
	      && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)
	      && evolution_function_is_affine_multivariate_p
	      (CHREC_LEFT (chrec), loopnum))
	    return true;
	  else
	    return false;
	}

    default:
      return false;
    }
}

/* Determine whether the given tree is a function in zero or one
   variables with respect to loop specified by LOOPNUM.  Note only positive
   LOOPNUM stands for a real loop.  */

bool
evolution_function_is_univariate_p (const_tree chrec, int loopnum)
{
  if (chrec == NULL_TREE)
    return true;

  tree sub_chrec;
  switch (TREE_CODE (chrec))
    {
    case POLYNOMIAL_CHREC:
      switch (TREE_CODE (CHREC_LEFT (chrec)))
	{
	case POLYNOMIAL_CHREC:
	  sub_chrec = CHREC_LEFT (chrec);
	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (sub_chrec)
	      && (loopnum <= 0
		  || CHREC_VARIABLE (sub_chrec) == (unsigned) loopnum
		  || flow_loop_nested_p (get_loop (cfun, loopnum),
					 get_chrec_loop (sub_chrec))))
	    return false;
	  if (!evolution_function_is_univariate_p (sub_chrec, loopnum))
	    return false;
	  break;

	default:
	  if (tree_contains_chrecs (CHREC_LEFT (chrec), NULL))
	    return false;
	  break;
	}

      switch (TREE_CODE (CHREC_RIGHT (chrec)))
	{
	case POLYNOMIAL_CHREC:
	  sub_chrec = CHREC_RIGHT (chrec);
	  if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (sub_chrec)
	      && (loopnum <= 0
		  || CHREC_VARIABLE (sub_chrec) == (unsigned) loopnum
		  || flow_loop_nested_p (get_loop (cfun, loopnum),
					 get_chrec_loop (sub_chrec))))
	    return false;
	  if (!evolution_function_is_univariate_p (sub_chrec, loopnum))
	    return false;
	  break;

	default:
	  if (tree_contains_chrecs (CHREC_RIGHT (chrec), NULL))
	    return false;
	  break;
	}
      return true;

    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;
    }
}

/* 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.
   FROM is the source variable converted if it's not NULL.  Returns true if
   the conversion succeeded, false otherwise.  */

bool
convert_affine_scev (class loop *loop, tree type,
		     tree *base, tree *step, gimple *at_stmt,
		     bool use_overflow_semantics, tree from)
{
  tree ct = TREE_TYPE (*step);
  bool enforce_overflow_semantics;
  bool must_check_src_overflow, must_check_rslt_overflow;
  tree new_base, new_step;
  tree step_type = POINTER_TYPE_P (type) ? sizetype : type;

  /* 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 (from, *base, *step, at_stmt, loop,
				use_overflow_semantics))
    return false;

  new_base = chrec_convert (type, *base, at_stmt, use_overflow_semantics);
  /* The step must be sign extended, regardless of the signedness
     of CT and TYPE.  This only needs to be handled specially when
     CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
     (with values 100, 99, 98, ...) from becoming signed or unsigned
     [100, +, 255] with values 100, 355, ...; the sign-extension is
     performed by default when CT is signed.  */
  new_step = *step;
  if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct))
    {
      tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0);
      new_step = chrec_convert (signed_ct, new_step, at_stmt,
                                use_overflow_semantics);
    }
  new_step = chrec_convert (step_type, new_step, at_stmt,
			    use_overflow_semantics);

  if (automatically_generated_chrec_p (new_base)
      || automatically_generated_chrec_p (new_step))
    return false;

  if (must_check_rslt_overflow
      /* Note that in this case we cannot use the fact that signed variables
	 do not overflow, as this is what we are verifying for the new iv.  */
      && scev_probably_wraps_p (NULL_TREE, new_base, new_step,
				at_stmt, loop, false))
    return false;

  *base = new_base;
  *step = new_step;
  return true;
}


/* Convert CHREC for the right hand side of a CHREC.
   The increment for a pointer type is always sizetype.  */

tree
chrec_convert_rhs (tree type, tree chrec, gimple *at_stmt)
{
  if (POINTER_TYPE_P (type))
    type = sizetype;

  return chrec_convert (type, chrec, at_stmt);
}

/* Convert CHREC to TYPE.  When the analyzer knows the context in
   which the CHREC is built, it sets AT_STMT to the statement that
   contains the definition of the analyzed variable, otherwise the
   conversion is less accurate: the information is used for
   determining a more accurate estimation of the number of iterations.
   By default AT_STMT could be safely set to NULL_TREE.

   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.

   FROM is the source variable converted if it's not NULL.  */

static tree
chrec_convert_1 (tree type, tree chrec, gimple *at_stmt,
		 bool use_overflow_semantics, tree from)
{
  tree ct, res;
  tree base, step;
  class loop *loop;

  if (automatically_generated_chrec_p (chrec))
    return chrec;

  ct = chrec_type (chrec);
  if (useless_type_conversion_p (type, ct))
    return chrec;

  if (!evolution_function_is_affine_p (chrec))
    goto keep_cast;

  loop = get_chrec_loop (chrec);
  base = CHREC_LEFT (chrec);
  step = CHREC_RIGHT (chrec);

  if (convert_affine_scev (loop, type, &base, &step, at_stmt,
			   use_overflow_semantics, from))
    return build_polynomial_chrec (loop->num, base, step);

  /* If we cannot propagate the cast inside the chrec, just keep the cast.  */
keep_cast:
  /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that
     may be more expensive.  We do want to perform this optimization here
     though for canonicalization reasons.  */
  if (use_overflow_semantics
      && (TREE_CODE (chrec) == PLUS_EXPR
	  || TREE_CODE (chrec) == MINUS_EXPR)
      && TREE_CODE (type) == INTEGER_TYPE
      && TREE_CODE (ct) == INTEGER_TYPE
      && TYPE_PRECISION (type) > TYPE_PRECISION (ct)
      && TYPE_OVERFLOW_UNDEFINED (ct))
    res = fold_build2 (TREE_CODE (chrec), type,
		       fold_convert (type, TREE_OPERAND (chrec, 0)),
		       fold_convert (type, TREE_OPERAND (chrec, 1)));
  /* Similar perform the trick that (signed char)((int)x + 2) can be
     narrowed to (signed char)((unsigned char)x + 2).  */
  else if (use_overflow_semantics
	   && TREE_CODE (chrec) == POLYNOMIAL_CHREC
	   && TREE_CODE (ct) == INTEGER_TYPE
	   && TREE_CODE (type) == INTEGER_TYPE
	   && TYPE_OVERFLOW_UNDEFINED (type)
	   && TYPE_PRECISION (type) < TYPE_PRECISION (ct))
    {
      tree utype = unsigned_type_for (type);
      res = build_polynomial_chrec (CHREC_VARIABLE (chrec),
				    fold_convert (utype,
						  CHREC_LEFT (chrec)),
				    fold_convert (utype,
						  CHREC_RIGHT (chrec)));
      res = chrec_convert_1 (type, res, at_stmt, use_overflow_semantics, from);
    }
  else
    res = fold_convert (type, chrec);

  /* Don't propagate overflows.  */
  if (CONSTANT_CLASS_P (res))
    TREE_OVERFLOW (res) = 0;

  /* But reject constants that don't fit in their type after conversion.
     This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
     natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
     and can cause problems later when computing niters of loops.  Note
     that we don't do the check before converting because we don't want
     to reject conversions of negative chrecs to unsigned types.  */
  if (TREE_CODE (res) == INTEGER_CST
      && TREE_CODE (type) == INTEGER_TYPE
      && !int_fits_type_p (res, type))
    res = chrec_dont_know;

  return res;
}

/* Convert CHREC to TYPE.  When the analyzer knows the context in
   which the CHREC is built, it sets AT_STMT to the statement that
   contains the definition of the analyzed variable, otherwise the
   conversion is less accurate: the information is used for
   determining a more accurate estimation of the number of iterations.
   By default AT_STMT could be safely set to NULL_TREE.

   The following rule is always true: TREE_TYPE (chrec) ==
   TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
   An example of what could happen when adding two chrecs and the type
   of the CHREC_RIGHT is different than CHREC_LEFT is:

   {(uint) 0, +, (uchar) 10} +
   {(uint) 0, +, (uchar) 250}

   that would produce a wrong result if CHREC_RIGHT is not (uint):

   {(uint) 0, +, (uchar) 4}

   instead of

   {(uint) 0, +, (uint) 260}

   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.

   FROM is the source variable converted if it's not NULL.  */

tree
chrec_convert (tree type, tree chrec, gimple *at_stmt,
	       bool use_overflow_semantics, tree from)
{
  return chrec_convert_1 (type, chrec, at_stmt, use_overflow_semantics, from);
}

/* Convert CHREC to TYPE, without regard to signed overflows.  Returns the new
   chrec if something else than what chrec_convert would do happens, NULL_TREE
   otherwise.  This function set TRUE to variable pointed by FOLD_CONVERSIONS
   if the result chrec may overflow.  */

tree
chrec_convert_aggressive (tree type, tree chrec, bool *fold_conversions)
{
  tree inner_type, left, right, lc, rc, rtype;

  gcc_assert (fold_conversions != NULL);

  if (automatically_generated_chrec_p (chrec)
      || TREE_CODE (chrec) != POLYNOMIAL_CHREC)
    return NULL_TREE;

  inner_type = TREE_TYPE (chrec);
  if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type))
    return NULL_TREE;

  if (useless_type_conversion_p (type, inner_type))
    return NULL_TREE;

  if (!*fold_conversions && evolution_function_is_affine_p (chrec))
    {
      tree base, step;
      class loop *loop;

      loop = get_chrec_loop (chrec);
      base = CHREC_LEFT (chrec);
      step = CHREC_RIGHT (chrec);
      if (convert_affine_scev (loop, type, &base, &step, NULL, true))
	return build_polynomial_chrec (loop->num, base, step);
    }
  rtype = POINTER_TYPE_P (type) ? sizetype : type;

  left = CHREC_LEFT (chrec);
  right = CHREC_RIGHT (chrec);
  lc = chrec_convert_aggressive (type, left, fold_conversions);
  if (!lc)
    lc = chrec_convert (type, left, NULL);
  rc = chrec_convert_aggressive (rtype, right, fold_conversions);
  if (!rc)
    rc = chrec_convert (rtype, right, NULL);

  *fold_conversions = true;

  return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc);
}

/* Returns true when CHREC0 == CHREC1.  */

bool
eq_evolutions_p (const_tree chrec0, const_tree chrec1)
{
  if (chrec0 == NULL_TREE
      || chrec1 == NULL_TREE
      || TREE_CODE (chrec0) != TREE_CODE (chrec1))
    return false;

  if (chrec0 == chrec1)
    return true;

  if (! types_compatible_p (TREE_TYPE (chrec0), TREE_TYPE (chrec1)))
    return false;

  switch (TREE_CODE (chrec0))
    {
    case POLYNOMIAL_CHREC:
      return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1)
	      && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1))
	      && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1)));

    case PLUS_EXPR:
    case MULT_EXPR:
    case MINUS_EXPR:
    case POINTER_PLUS_EXPR:
      return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
			      TREE_OPERAND (chrec1, 0))
	  && eq_evolutions_p (TREE_OPERAND (chrec0, 1),
			      TREE_OPERAND (chrec1, 1));

    CASE_CONVERT:
      return eq_evolutions_p (TREE_OPERAND (chrec0, 0),
			      TREE_OPERAND (chrec1, 0));

    default:
      return operand_equal_p (chrec0, chrec1, 0);
    }
}

/* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
   EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
   which of these cases happens.  */

enum ev_direction
scev_direction (const_tree chrec)
{
  const_tree step;

  if (!evolution_function_is_affine_p (chrec))
    return EV_DIR_UNKNOWN;

  step = CHREC_RIGHT (chrec);
  if (TREE_CODE (step) != INTEGER_CST)
    return EV_DIR_UNKNOWN;

  if (tree_int_cst_sign_bit (step))
    return EV_DIR_DECREASES;
  else
    return EV_DIR_GROWS;
}

/* Iterates over all the components of SCEV, and calls CBCK.  */

void
for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data)
{
  switch (TREE_CODE_LENGTH (TREE_CODE (*scev)))
    {
    case 3:
      for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data);
      /* FALLTHRU */

    case 2:
      for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data);
      /* FALLTHRU */

    case 1:
      for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data);
      /* FALLTHRU */

    default:
      cbck (scev, data);
      break;
    }
}

/* Returns true when the operation can be part of a linear
   expression.  */

static inline bool
operator_is_linear (tree scev)
{
  switch (TREE_CODE (scev))
    {
    case INTEGER_CST:
    case POLYNOMIAL_CHREC:
    case PLUS_EXPR:
    case POINTER_PLUS_EXPR:
    case MULT_EXPR:
    case MINUS_EXPR:
    case NEGATE_EXPR:
    case SSA_NAME:
    case NON_LVALUE_EXPR:
    case BIT_NOT_EXPR:
    CASE_CONVERT:
      return true;

    default:
      return false;
    }
}

/* Return true when SCEV is a linear expression.  Linear expressions
   can contain additions, substractions and multiplications.
   Multiplications are restricted to constant scaling: "cst * x".  */

bool
scev_is_linear_expression (tree scev)
{
  if (evolution_function_is_constant_p (scev))
    return true;

  if (scev == NULL
      || !operator_is_linear (scev))
    return false;

  if (TREE_CODE (scev) == MULT_EXPR)
    return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL)
	     && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL));

  if (TREE_CODE (scev) == POLYNOMIAL_CHREC
      && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev)))
    return false;

  switch (TREE_CODE_LENGTH (TREE_CODE (scev)))
    {
    case 3:
      return scev_is_linear_expression (TREE_OPERAND (scev, 0))
	&& scev_is_linear_expression (TREE_OPERAND (scev, 1))
	&& scev_is_linear_expression (TREE_OPERAND (scev, 2));

    case 2:
      return scev_is_linear_expression (TREE_OPERAND (scev, 0))
	&& scev_is_linear_expression (TREE_OPERAND (scev, 1));

    case 1:
      return scev_is_linear_expression (TREE_OPERAND (scev, 0));

    case 0:
      return true;

    default:
      return false;
    }
}

/* Determines whether the expression CHREC contains only interger consts
   in the right parts.  */

bool
evolution_function_right_is_integer_cst (const_tree chrec)
{
  if (chrec == NULL_TREE)
    return false;

  switch (TREE_CODE (chrec))
    {
    case INTEGER_CST:
      return true;

    case POLYNOMIAL_CHREC:
      return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST
	&& (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC
	    || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec)));

    CASE_CONVERT:
      return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0));

    default:
      return false;
    }
}