/* Support routines for Value Range Propagation (VRP).
   Copyright (C) 2005-2021 Free Software Foundation, Inc.
   Contributed by Diego Novillo <dnovillo@redhat.com>.

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/>.  */

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "basic-block.h"
#include "bitmap.h"
#include "sbitmap.h"
#include "options.h"
#include "dominance.h"
#include "function.h"
#include "cfg.h"
#include "tree.h"
#include "gimple.h"
#include "tree-pass.h"
#include "ssa.h"
#include "gimple-pretty-print.h"
#include "fold-const.h"
#include "cfganal.h"
#include "gimple-iterator.h"
#include "tree-cfg.h"
#include "tree-ssa-loop-manip.h"
#include "tree-ssa-loop-niter.h"
#include "tree-into-ssa.h"
#include "cfgloop.h"
#include "tree-scalar-evolution.h"
#include "tree-ssa-propagate.h"
#include "tree-ssa-threadedge.h"
#include "domwalk.h"
#include "vr-values.h"
#include "gimple-array-bounds.h"
#include "gimple-range.h"
#include "gimple-range-path.h"

/* Set of SSA names found live during the RPO traversal of the function
   for still active basic-blocks.  */
class live_names
{
public:
  live_names ();
  ~live_names ();
  void set (tree, basic_block);
  void clear (tree, basic_block);
  void merge (basic_block dest, basic_block src);
  bool live_on_block_p (tree, basic_block);
  bool live_on_edge_p (tree, edge);
  bool block_has_live_names_p (basic_block);
  void clear_block (basic_block);

private:
  sbitmap *live;
  unsigned num_blocks;
  void init_bitmap_if_needed (basic_block);
};

void
live_names::init_bitmap_if_needed (basic_block bb)
{
  unsigned i = bb->index;
  if (!live[i])
    {
      live[i] = sbitmap_alloc (num_ssa_names);
      bitmap_clear (live[i]);
    }
}

bool
live_names::block_has_live_names_p (basic_block bb)
{
  unsigned i = bb->index;
  return live[i] && bitmap_empty_p (live[i]);
}

void
live_names::clear_block (basic_block bb)
{
  unsigned i = bb->index;
  if (live[i])
    {
      sbitmap_free (live[i]);
      live[i] = NULL;
    }
}

void
live_names::merge (basic_block dest, basic_block src)
{
  init_bitmap_if_needed (dest);
  init_bitmap_if_needed (src);
  bitmap_ior (live[dest->index], live[dest->index], live[src->index]);
}

void
live_names::set (tree name, basic_block bb)
{
  init_bitmap_if_needed (bb);
  bitmap_set_bit (live[bb->index], SSA_NAME_VERSION (name));
}

void
live_names::clear (tree name, basic_block bb)
{
  unsigned i = bb->index;
  if (live[i])
    bitmap_clear_bit (live[i], SSA_NAME_VERSION (name));
}

live_names::live_names ()
{
  num_blocks = last_basic_block_for_fn (cfun);
  live = XCNEWVEC (sbitmap, num_blocks);
}

live_names::~live_names ()
{
  for (unsigned i = 0; i < num_blocks; ++i)
    if (live[i])
      sbitmap_free (live[i]);
  XDELETEVEC (live);
}

bool
live_names::live_on_block_p (tree name, basic_block bb)
{
  return (live[bb->index]
	  && bitmap_bit_p (live[bb->index], SSA_NAME_VERSION (name)));
}

/* Return true if the SSA name NAME is live on the edge E.  */

bool
live_names::live_on_edge_p (tree name, edge e)
{
  return live_on_block_p (name, e->dest);
}


/* VR_TYPE describes a range with mininum value *MIN and maximum
   value *MAX.  Restrict the range to the set of values that have
   no bits set outside NONZERO_BITS.  Update *MIN and *MAX and
   return the new range type.

   SGN gives the sign of the values described by the range.  */

enum value_range_kind
intersect_range_with_nonzero_bits (enum value_range_kind vr_type,
				   wide_int *min, wide_int *max,
				   const wide_int &nonzero_bits,
				   signop sgn)
{
  if (vr_type == VR_ANTI_RANGE)
    {
      /* The VR_ANTI_RANGE is equivalent to the union of the ranges
	 A: [-INF, *MIN) and B: (*MAX, +INF].  First use NONZERO_BITS
	 to create an inclusive upper bound for A and an inclusive lower
	 bound for B.  */
      wide_int a_max = wi::round_down_for_mask (*min - 1, nonzero_bits);
      wide_int b_min = wi::round_up_for_mask (*max + 1, nonzero_bits);

      /* If the calculation of A_MAX wrapped, A is effectively empty
	 and A_MAX is the highest value that satisfies NONZERO_BITS.
	 Likewise if the calculation of B_MIN wrapped, B is effectively
	 empty and B_MIN is the lowest value that satisfies NONZERO_BITS.  */
      bool a_empty = wi::ge_p (a_max, *min, sgn);
      bool b_empty = wi::le_p (b_min, *max, sgn);

      /* If both A and B are empty, there are no valid values.  */
      if (a_empty && b_empty)
	return VR_UNDEFINED;

      /* If exactly one of A or B is empty, return a VR_RANGE for the
	 other one.  */
      if (a_empty || b_empty)
	{
	  *min = b_min;
	  *max = a_max;
	  gcc_checking_assert (wi::le_p (*min, *max, sgn));
	  return VR_RANGE;
	}

      /* Update the VR_ANTI_RANGE bounds.  */
      *min = a_max + 1;
      *max = b_min - 1;
      gcc_checking_assert (wi::le_p (*min, *max, sgn));

      /* Now check whether the excluded range includes any values that
	 satisfy NONZERO_BITS.  If not, switch to a full VR_RANGE.  */
      if (wi::round_up_for_mask (*min, nonzero_bits) == b_min)
	{
	  unsigned int precision = min->get_precision ();
	  *min = wi::min_value (precision, sgn);
	  *max = wi::max_value (precision, sgn);
	  vr_type = VR_RANGE;
	}
    }
  if (vr_type == VR_RANGE || vr_type == VR_VARYING)
    {
      *max = wi::round_down_for_mask (*max, nonzero_bits);

      /* Check that the range contains at least one valid value.  */
      if (wi::gt_p (*min, *max, sgn))
	return VR_UNDEFINED;

      *min = wi::round_up_for_mask (*min, nonzero_bits);
      gcc_checking_assert (wi::le_p (*min, *max, sgn));
    }
  return vr_type;
}

/* Return true if max and min of VR are INTEGER_CST.  It's not necessary
   a singleton.  */

bool
range_int_cst_p (const value_range *vr)
{
  return (vr->kind () == VR_RANGE && range_has_numeric_bounds_p (vr));
}

/* Return the single symbol (an SSA_NAME) contained in T if any, or NULL_TREE
   otherwise.  We only handle additive operations and set NEG to true if the
   symbol is negated and INV to the invariant part, if any.  */

tree
get_single_symbol (tree t, bool *neg, tree *inv)
{
  bool neg_;
  tree inv_;

  *inv = NULL_TREE;
  *neg = false;

  if (TREE_CODE (t) == PLUS_EXPR
      || TREE_CODE (t) == POINTER_PLUS_EXPR
      || TREE_CODE (t) == MINUS_EXPR)
    {
      if (is_gimple_min_invariant (TREE_OPERAND (t, 0)))
	{
	  neg_ = (TREE_CODE (t) == MINUS_EXPR);
	  inv_ = TREE_OPERAND (t, 0);
	  t = TREE_OPERAND (t, 1);
	}
      else if (is_gimple_min_invariant (TREE_OPERAND (t, 1)))
	{
	  neg_ = false;
	  inv_ = TREE_OPERAND (t, 1);
	  t = TREE_OPERAND (t, 0);
	}
      else
        return NULL_TREE;
    }
  else
    {
      neg_ = false;
      inv_ = NULL_TREE;
    }

  if (TREE_CODE (t) == NEGATE_EXPR)
    {
      t = TREE_OPERAND (t, 0);
      neg_ = !neg_;
    }

  if (TREE_CODE (t) != SSA_NAME)
    return NULL_TREE;

  if (inv_ && TREE_OVERFLOW_P (inv_))
    inv_ = drop_tree_overflow (inv_);

  *neg = neg_;
  *inv = inv_;
  return t;
}

/* The reverse operation: build a symbolic expression with TYPE
   from symbol SYM, negated according to NEG, and invariant INV.  */

static tree
build_symbolic_expr (tree type, tree sym, bool neg, tree inv)
{
  const bool pointer_p = POINTER_TYPE_P (type);
  tree t = sym;

  if (neg)
    t = build1 (NEGATE_EXPR, type, t);

  if (integer_zerop (inv))
    return t;

  return build2 (pointer_p ? POINTER_PLUS_EXPR : PLUS_EXPR, type, t, inv);
}

/* Return
   1 if VAL < VAL2
   0 if !(VAL < VAL2)
   -2 if those are incomparable.  */
int
operand_less_p (tree val, tree val2)
{
  /* LT is folded faster than GE and others.  Inline the common case.  */
  if (TREE_CODE (val) == INTEGER_CST && TREE_CODE (val2) == INTEGER_CST)
    return tree_int_cst_lt (val, val2);
  else if (TREE_CODE (val) == SSA_NAME && TREE_CODE (val2) == SSA_NAME)
    return val == val2 ? 0 : -2;
  else
    {
      int cmp = compare_values (val, val2);
      if (cmp == -1)
	return 1;
      else if (cmp == 0 || cmp == 1)
	return 0;
      else
	return -2;
    }

  return 0;
}

/* Compare two values VAL1 and VAL2.  Return

   	-2 if VAL1 and VAL2 cannot be compared at compile-time,
   	-1 if VAL1 < VAL2,
   	 0 if VAL1 == VAL2,
	+1 if VAL1 > VAL2, and
	+2 if VAL1 != VAL2

   This is similar to tree_int_cst_compare but supports pointer values
   and values that cannot be compared at compile time.

   If STRICT_OVERFLOW_P is not NULL, then set *STRICT_OVERFLOW_P to
   true if the return value is only valid if we assume that signed
   overflow is undefined.  */

int
compare_values_warnv (tree val1, tree val2, bool *strict_overflow_p)
{
  if (val1 == val2)
    return 0;

  /* Below we rely on the fact that VAL1 and VAL2 are both pointers or
     both integers.  */
  gcc_assert (POINTER_TYPE_P (TREE_TYPE (val1))
	      == POINTER_TYPE_P (TREE_TYPE (val2)));

  /* Convert the two values into the same type.  This is needed because
     sizetype causes sign extension even for unsigned types.  */
  if (!useless_type_conversion_p (TREE_TYPE (val1), TREE_TYPE (val2)))
    val2 = fold_convert (TREE_TYPE (val1), val2);

  const bool overflow_undefined
    = INTEGRAL_TYPE_P (TREE_TYPE (val1))
      && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (val1));
  tree inv1, inv2;
  bool neg1, neg2;
  tree sym1 = get_single_symbol (val1, &neg1, &inv1);
  tree sym2 = get_single_symbol (val2, &neg2, &inv2);

  /* If VAL1 and VAL2 are of the form '[-]NAME [+ CST]', return -1 or +1
     accordingly.  If VAL1 and VAL2 don't use the same name, return -2.  */
  if (sym1 && sym2)
    {
      /* Both values must use the same name with the same sign.  */
      if (sym1 != sym2 || neg1 != neg2)
	return -2;

      /* [-]NAME + CST == [-]NAME + CST.  */
      if (inv1 == inv2)
	return 0;

      /* If overflow is defined we cannot simplify more.  */
      if (!overflow_undefined)
	return -2;

      if (strict_overflow_p != NULL
	  /* Symbolic range building sets the no-warning bit to declare
	     that overflow doesn't happen.  */
	  && (!inv1 || !warning_suppressed_p (val1, OPT_Woverflow))
	  && (!inv2 || !warning_suppressed_p (val2, OPT_Woverflow)))
	*strict_overflow_p = true;

      if (!inv1)
	inv1 = build_int_cst (TREE_TYPE (val1), 0);
      if (!inv2)
	inv2 = build_int_cst (TREE_TYPE (val2), 0);

      return wi::cmp (wi::to_wide (inv1), wi::to_wide (inv2),
		      TYPE_SIGN (TREE_TYPE (val1)));
    }

  const bool cst1 = is_gimple_min_invariant (val1);
  const bool cst2 = is_gimple_min_invariant (val2);

  /* If one is of the form '[-]NAME + CST' and the other is constant, then
     it might be possible to say something depending on the constants.  */
  if ((sym1 && inv1 && cst2) || (sym2 && inv2 && cst1))
    {
      if (!overflow_undefined)
	return -2;

      if (strict_overflow_p != NULL
	  /* Symbolic range building sets the no-warning bit to declare
	     that overflow doesn't happen.  */
	  && (!sym1 || !warning_suppressed_p (val1, OPT_Woverflow))
	  && (!sym2 || !warning_suppressed_p (val2, OPT_Woverflow)))
	*strict_overflow_p = true;

      const signop sgn = TYPE_SIGN (TREE_TYPE (val1));
      tree cst = cst1 ? val1 : val2;
      tree inv = cst1 ? inv2 : inv1;

      /* Compute the difference between the constants.  If it overflows or
	 underflows, this means that we can trivially compare the NAME with
	 it and, consequently, the two values with each other.  */
      wide_int diff = wi::to_wide (cst) - wi::to_wide (inv);
      if (wi::cmp (0, wi::to_wide (inv), sgn)
	  != wi::cmp (diff, wi::to_wide (cst), sgn))
	{
	  const int res = wi::cmp (wi::to_wide (cst), wi::to_wide (inv), sgn);
	  return cst1 ? res : -res;
	}

      return -2;
    }

  /* We cannot say anything more for non-constants.  */
  if (!cst1 || !cst2)
    return -2;

  if (!POINTER_TYPE_P (TREE_TYPE (val1)))
    {
      /* We cannot compare overflowed values.  */
      if (TREE_OVERFLOW (val1) || TREE_OVERFLOW (val2))
	return -2;

      if (TREE_CODE (val1) == INTEGER_CST
	  && TREE_CODE (val2) == INTEGER_CST)
	return tree_int_cst_compare (val1, val2);

      if (poly_int_tree_p (val1) && poly_int_tree_p (val2))
	{
	  if (known_eq (wi::to_poly_widest (val1),
			wi::to_poly_widest (val2)))
	    return 0;
	  if (known_lt (wi::to_poly_widest (val1),
			wi::to_poly_widest (val2)))
	    return -1;
	  if (known_gt (wi::to_poly_widest (val1),
			wi::to_poly_widest (val2)))
	    return 1;
	}

      return -2;
    }
  else
    {
      if (TREE_CODE (val1) == INTEGER_CST && TREE_CODE (val2) == INTEGER_CST)
	{
	  /* We cannot compare overflowed values.  */
	  if (TREE_OVERFLOW (val1) || TREE_OVERFLOW (val2))
	    return -2;

	  return tree_int_cst_compare (val1, val2);
	}

      /* First see if VAL1 and VAL2 are not the same.  */
      if (operand_equal_p (val1, val2, 0))
	return 0;

      fold_defer_overflow_warnings ();

      /* If VAL1 is a lower address than VAL2, return -1.  */
      tree t = fold_binary_to_constant (LT_EXPR, boolean_type_node, val1, val2);
      if (t && integer_onep (t))
	{
	  fold_undefer_and_ignore_overflow_warnings ();
	  return -1;
	}

      /* If VAL1 is a higher address than VAL2, return +1.  */
      t = fold_binary_to_constant (LT_EXPR, boolean_type_node, val2, val1);
      if (t && integer_onep (t))
	{
	  fold_undefer_and_ignore_overflow_warnings ();
	  return 1;
	}

      /* If VAL1 is different than VAL2, return +2.  */
      t = fold_binary_to_constant (NE_EXPR, boolean_type_node, val1, val2);
      fold_undefer_and_ignore_overflow_warnings ();
      if (t && integer_onep (t))
	return 2;

      return -2;
    }
}

/* Compare values like compare_values_warnv.  */

int
compare_values (tree val1, tree val2)
{
  bool sop;
  return compare_values_warnv (val1, val2, &sop);
}

/* If BOUND will include a symbolic bound, adjust it accordingly,
   otherwise leave it as is.

   CODE is the original operation that combined the bounds (PLUS_EXPR
   or MINUS_EXPR).

   TYPE is the type of the original operation.

   SYM_OPn is the symbolic for OPn if it has a symbolic.

   NEG_OPn is TRUE if the OPn was negated.  */

static void
adjust_symbolic_bound (tree &bound, enum tree_code code, tree type,
		       tree sym_op0, tree sym_op1,
		       bool neg_op0, bool neg_op1)
{
  bool minus_p = (code == MINUS_EXPR);
  /* If the result bound is constant, we're done; otherwise, build the
     symbolic lower bound.  */
  if (sym_op0 == sym_op1)
    ;
  else if (sym_op0)
    bound = build_symbolic_expr (type, sym_op0,
				 neg_op0, bound);
  else if (sym_op1)
    {
      /* We may not negate if that might introduce
	 undefined overflow.  */
      if (!minus_p
	  || neg_op1
	  || TYPE_OVERFLOW_WRAPS (type))
	bound = build_symbolic_expr (type, sym_op1,
				     neg_op1 ^ minus_p, bound);
      else
	bound = NULL_TREE;
    }
}

/* Combine OP1 and OP1, which are two parts of a bound, into one wide
   int bound according to CODE.  CODE is the operation combining the
   bound (either a PLUS_EXPR or a MINUS_EXPR).

   TYPE is the type of the combine operation.

   WI is the wide int to store the result.

   OVF is -1 if an underflow occurred, +1 if an overflow occurred or 0
   if over/underflow occurred.  */

static void
combine_bound (enum tree_code code, wide_int &wi, wi::overflow_type &ovf,
	       tree type, tree op0, tree op1)
{
  bool minus_p = (code == MINUS_EXPR);
  const signop sgn = TYPE_SIGN (type);
  const unsigned int prec = TYPE_PRECISION (type);

  /* Combine the bounds, if any.  */
  if (op0 && op1)
    {
      if (minus_p)
	wi = wi::sub (wi::to_wide (op0), wi::to_wide (op1), sgn, &ovf);
      else
	wi = wi::add (wi::to_wide (op0), wi::to_wide (op1), sgn, &ovf);
    }
  else if (op0)
    wi = wi::to_wide (op0);
  else if (op1)
    {
      if (minus_p)
	wi = wi::neg (wi::to_wide (op1), &ovf);
      else
	wi = wi::to_wide (op1);
    }
  else
    wi = wi::shwi (0, prec);
}

/* Given a range in [WMIN, WMAX], adjust it for possible overflow and
   put the result in VR.

   TYPE is the type of the range.

   MIN_OVF and MAX_OVF indicate what type of overflow, if any,
   occurred while originally calculating WMIN or WMAX.  -1 indicates
   underflow.  +1 indicates overflow.  0 indicates neither.  */

static void
set_value_range_with_overflow (value_range_kind &kind, tree &min, tree &max,
			       tree type,
			       const wide_int &wmin, const wide_int &wmax,
			       wi::overflow_type min_ovf,
			       wi::overflow_type max_ovf)
{
  const signop sgn = TYPE_SIGN (type);
  const unsigned int prec = TYPE_PRECISION (type);

  /* For one bit precision if max < min, then the swapped
     range covers all values.  */
  if (prec == 1 && wi::lt_p (wmax, wmin, sgn))
    {
      kind = VR_VARYING;
      return;
    }

  if (TYPE_OVERFLOW_WRAPS (type))
    {
      /* If overflow wraps, truncate the values and adjust the
	 range kind and bounds appropriately.  */
      wide_int tmin = wide_int::from (wmin, prec, sgn);
      wide_int tmax = wide_int::from (wmax, prec, sgn);
      if ((min_ovf != wi::OVF_NONE) == (max_ovf != wi::OVF_NONE))
	{
	  /* If the limits are swapped, we wrapped around and cover
	     the entire range.  */
	  if (wi::gt_p (tmin, tmax, sgn))
	    kind = VR_VARYING;
	  else
	    {
	      kind = VR_RANGE;
	      /* No overflow or both overflow or underflow.  The
		 range kind stays VR_RANGE.  */
	      min = wide_int_to_tree (type, tmin);
	      max = wide_int_to_tree (type, tmax);
	    }
	  return;
	}
      else if ((min_ovf == wi::OVF_UNDERFLOW && max_ovf == wi::OVF_NONE)
	       || (max_ovf == wi::OVF_OVERFLOW && min_ovf == wi::OVF_NONE))
	{
	  /* Min underflow or max overflow.  The range kind
	     changes to VR_ANTI_RANGE.  */
	  bool covers = false;
	  wide_int tem = tmin;
	  tmin = tmax + 1;
	  if (wi::cmp (tmin, tmax, sgn) < 0)
	    covers = true;
	  tmax = tem - 1;
	  if (wi::cmp (tmax, tem, sgn) > 0)
	    covers = true;
	  /* If the anti-range would cover nothing, drop to varying.
	     Likewise if the anti-range bounds are outside of the
	     types values.  */
	  if (covers || wi::cmp (tmin, tmax, sgn) > 0)
	    {
	      kind = VR_VARYING;
	      return;
	    }
	  kind = VR_ANTI_RANGE;
	  min = wide_int_to_tree (type, tmin);
	  max = wide_int_to_tree (type, tmax);
	  return;
	}
      else
	{
	  /* Other underflow and/or overflow, drop to VR_VARYING.  */
	  kind = VR_VARYING;
	  return;
	}
    }
  else
    {
      /* If overflow does not wrap, saturate to the types min/max
	 value.  */
      wide_int type_min = wi::min_value (prec, sgn);
      wide_int type_max = wi::max_value (prec, sgn);
      kind = VR_RANGE;
      if (min_ovf == wi::OVF_UNDERFLOW)
	min = wide_int_to_tree (type, type_min);
      else if (min_ovf == wi::OVF_OVERFLOW)
	min = wide_int_to_tree (type, type_max);
      else
	min = wide_int_to_tree (type, wmin);

      if (max_ovf == wi::OVF_UNDERFLOW)
	max = wide_int_to_tree (type, type_min);
      else if (max_ovf == wi::OVF_OVERFLOW)
	max = wide_int_to_tree (type, type_max);
      else
	max = wide_int_to_tree (type, wmax);
    }
}

/* Fold two value range's of a POINTER_PLUS_EXPR into VR.  */

static void
extract_range_from_pointer_plus_expr (value_range *vr,
				      enum tree_code code,
				      tree expr_type,
				      const value_range *vr0,
				      const value_range *vr1)
{
  gcc_checking_assert (POINTER_TYPE_P (expr_type)
		       && code == POINTER_PLUS_EXPR);
  /* For pointer types, we are really only interested in asserting
     whether the expression evaluates to non-NULL.
     With -fno-delete-null-pointer-checks we need to be more
     conservative.  As some object might reside at address 0,
     then some offset could be added to it and the same offset
     subtracted again and the result would be NULL.
     E.g.
     static int a[12]; where &a[0] is NULL and
     ptr = &a[6];
     ptr -= 6;
     ptr will be NULL here, even when there is POINTER_PLUS_EXPR
     where the first range doesn't include zero and the second one
     doesn't either.  As the second operand is sizetype (unsigned),
     consider all ranges where the MSB could be set as possible
     subtractions where the result might be NULL.  */
  if ((!range_includes_zero_p (vr0)
       || !range_includes_zero_p (vr1))
      && !TYPE_OVERFLOW_WRAPS (expr_type)
      && (flag_delete_null_pointer_checks
	  || (range_int_cst_p (vr1)
	      && !tree_int_cst_sign_bit (vr1->max ()))))
    vr->set_nonzero (expr_type);
  else if (vr0->zero_p () && vr1->zero_p ())
    vr->set_zero (expr_type);
  else
    vr->set_varying (expr_type);
}

/* Extract range information from a PLUS/MINUS_EXPR and store the
   result in *VR.  */

static void
extract_range_from_plus_minus_expr (value_range *vr,
				    enum tree_code code,
				    tree expr_type,
				    const value_range *vr0_,
				    const value_range *vr1_)
{
  gcc_checking_assert (code == PLUS_EXPR || code == MINUS_EXPR);

  value_range vr0 = *vr0_, vr1 = *vr1_;
  value_range vrtem0, vrtem1;

  /* Now canonicalize anti-ranges to ranges when they are not symbolic
     and express ~[] op X as ([]' op X) U ([]'' op X).  */
  if (vr0.kind () == VR_ANTI_RANGE
      && ranges_from_anti_range (&vr0, &vrtem0, &vrtem1))
    {
      extract_range_from_plus_minus_expr (vr, code, expr_type, &vrtem0, vr1_);
      if (!vrtem1.undefined_p ())
	{
	  value_range vrres;
	  extract_range_from_plus_minus_expr (&vrres, code, expr_type,
					      &vrtem1, vr1_);
	  vr->union_ (&vrres);
	}
      return;
    }
  /* Likewise for X op ~[].  */
  if (vr1.kind () == VR_ANTI_RANGE
      && ranges_from_anti_range (&vr1, &vrtem0, &vrtem1))
    {
      extract_range_from_plus_minus_expr (vr, code, expr_type, vr0_, &vrtem0);
      if (!vrtem1.undefined_p ())
	{
	  value_range vrres;
	  extract_range_from_plus_minus_expr (&vrres, code, expr_type,
					      vr0_, &vrtem1);
	  vr->union_ (&vrres);
	}
      return;
    }

  value_range_kind kind;
  value_range_kind vr0_kind = vr0.kind (), vr1_kind = vr1.kind ();
  tree vr0_min = vr0.min (), vr0_max = vr0.max ();
  tree vr1_min = vr1.min (), vr1_max = vr1.max ();
  tree min = NULL_TREE, max = NULL_TREE;

  /* This will normalize things such that calculating
     [0,0] - VR_VARYING is not dropped to varying, but is
     calculated as [MIN+1, MAX].  */
  if (vr0.varying_p ())
    {
      vr0_kind = VR_RANGE;
      vr0_min = vrp_val_min (expr_type);
      vr0_max = vrp_val_max (expr_type);
    }
  if (vr1.varying_p ())
    {
      vr1_kind = VR_RANGE;
      vr1_min = vrp_val_min (expr_type);
      vr1_max = vrp_val_max (expr_type);
    }

  const bool minus_p = (code == MINUS_EXPR);
  tree min_op0 = vr0_min;
  tree min_op1 = minus_p ? vr1_max : vr1_min;
  tree max_op0 = vr0_max;
  tree max_op1 = minus_p ? vr1_min : vr1_max;
  tree sym_min_op0 = NULL_TREE;
  tree sym_min_op1 = NULL_TREE;
  tree sym_max_op0 = NULL_TREE;
  tree sym_max_op1 = NULL_TREE;
  bool neg_min_op0, neg_min_op1, neg_max_op0, neg_max_op1;

  neg_min_op0 = neg_min_op1 = neg_max_op0 = neg_max_op1 = false;

  /* If we have a PLUS or MINUS with two VR_RANGEs, either constant or
     single-symbolic ranges, try to compute the precise resulting range,
     but only if we know that this resulting range will also be constant
     or single-symbolic.  */
  if (vr0_kind == VR_RANGE && vr1_kind == VR_RANGE
      && (TREE_CODE (min_op0) == INTEGER_CST
	  || (sym_min_op0
	      = get_single_symbol (min_op0, &neg_min_op0, &min_op0)))
      && (TREE_CODE (min_op1) == INTEGER_CST
	  || (sym_min_op1
	      = get_single_symbol (min_op1, &neg_min_op1, &min_op1)))
      && (!(sym_min_op0 && sym_min_op1)
	  || (sym_min_op0 == sym_min_op1
	      && neg_min_op0 == (minus_p ? neg_min_op1 : !neg_min_op1)))
      && (TREE_CODE (max_op0) == INTEGER_CST
	  || (sym_max_op0
	      = get_single_symbol (max_op0, &neg_max_op0, &max_op0)))
      && (TREE_CODE (max_op1) == INTEGER_CST
	  || (sym_max_op1
	      = get_single_symbol (max_op1, &neg_max_op1, &max_op1)))
      && (!(sym_max_op0 && sym_max_op1)
	  || (sym_max_op0 == sym_max_op1
	      && neg_max_op0 == (minus_p ? neg_max_op1 : !neg_max_op1))))
    {
      wide_int wmin, wmax;
      wi::overflow_type min_ovf = wi::OVF_NONE;
      wi::overflow_type max_ovf = wi::OVF_NONE;

      /* Build the bounds.  */
      combine_bound (code, wmin, min_ovf, expr_type, min_op0, min_op1);
      combine_bound (code, wmax, max_ovf, expr_type, max_op0, max_op1);

      /* If the resulting range will be symbolic, we need to eliminate any
	 explicit or implicit overflow introduced in the above computation
	 because compare_values could make an incorrect use of it.  That's
	 why we require one of the ranges to be a singleton.  */
      if ((sym_min_op0 != sym_min_op1 || sym_max_op0 != sym_max_op1)
	  && ((bool)min_ovf || (bool)max_ovf
	      || (min_op0 != max_op0 && min_op1 != max_op1)))
	{
	  vr->set_varying (expr_type);
	  return;
	}

      /* Adjust the range for possible overflow.  */
      set_value_range_with_overflow (kind, min, max, expr_type,
				     wmin, wmax, min_ovf, max_ovf);
      if (kind == VR_VARYING)
	{
	  vr->set_varying (expr_type);
	  return;
	}

      /* Build the symbolic bounds if needed.  */
      adjust_symbolic_bound (min, code, expr_type,
			     sym_min_op0, sym_min_op1,
			     neg_min_op0, neg_min_op1);
      adjust_symbolic_bound (max, code, expr_type,
			     sym_max_op0, sym_max_op1,
			     neg_max_op0, neg_max_op1);
    }
  else
    {
      /* For other cases, for example if we have a PLUS_EXPR with two
	 VR_ANTI_RANGEs, drop to VR_VARYING.  It would take more effort
	 to compute a precise range for such a case.
	 ???  General even mixed range kind operations can be expressed
	 by for example transforming ~[3, 5] + [1, 2] to range-only
	 operations and a union primitive:
	 [-INF, 2] + [1, 2]  U  [5, +INF] + [1, 2]
	 [-INF+1, 4]     U    [6, +INF(OVF)]
	 though usually the union is not exactly representable with
	 a single range or anti-range as the above is
	 [-INF+1, +INF(OVF)] intersected with ~[5, 5]
	 but one could use a scheme similar to equivalences for this. */
      vr->set_varying (expr_type);
      return;
    }

  /* If either MIN or MAX overflowed, then set the resulting range to
     VARYING.  */
  if (min == NULL_TREE
      || TREE_OVERFLOW_P (min)
      || max == NULL_TREE
      || TREE_OVERFLOW_P (max))
    {
      vr->set_varying (expr_type);
      return;
    }

  int cmp = compare_values (min, max);
  if (cmp == -2 || cmp == 1)
    {
      /* If the new range has its limits swapped around (MIN > MAX),
	 then the operation caused one of them to wrap around, mark
	 the new range VARYING.  */
      vr->set_varying (expr_type);
    }
  else
    vr->set (min, max, kind);
}

/* Return the range-ops handler for CODE and EXPR_TYPE.  If no
   suitable operator is found, return NULL and set VR to VARYING.  */

static const range_operator *
get_range_op_handler (value_range *vr,
		      enum tree_code code,
		      tree expr_type)
{
  const range_operator *op = range_op_handler (code, expr_type);
  if (!op)
    vr->set_varying (expr_type);
  return op;
}

/* If the types passed are supported, return TRUE, otherwise set VR to
   VARYING and return FALSE.  */

static bool
supported_types_p (value_range *vr,
		   tree type0,
		   tree type1 = NULL)
{
  if (!value_range::supports_type_p (type0)
      || (type1 && !value_range::supports_type_p (type1)))
    {
      vr->set_varying (type0);
      return false;
    }
  return true;
}

/* If any of the ranges passed are defined, return TRUE, otherwise set
   VR to UNDEFINED and return FALSE.  */

static bool
defined_ranges_p (value_range *vr,
		  const value_range *vr0, const value_range *vr1 = NULL)
{
  if (vr0->undefined_p () && (!vr1 || vr1->undefined_p ()))
    {
      vr->set_undefined ();
      return false;
    }
  return true;
}

static value_range
drop_undefines_to_varying (const value_range *vr, tree expr_type)
{
  if (vr->undefined_p ())
    return value_range (expr_type);
  else
    return *vr;
}

/* If any operand is symbolic, perform a binary operation on them and
   return TRUE, otherwise return FALSE.  */

static bool
range_fold_binary_symbolics_p (value_range *vr,
			       tree_code code,
			       tree expr_type,
			       const value_range *vr0_,
			       const value_range *vr1_)
{
  if (vr0_->symbolic_p () || vr1_->symbolic_p ())
    {
      value_range vr0 = drop_undefines_to_varying (vr0_, expr_type);
      value_range vr1 = drop_undefines_to_varying (vr1_, expr_type);
      if ((code == PLUS_EXPR || code == MINUS_EXPR))
	{
	  extract_range_from_plus_minus_expr (vr, code, expr_type,
					      &vr0, &vr1);
	  return true;
	}
      if (POINTER_TYPE_P (expr_type) && code == POINTER_PLUS_EXPR)
	{
	  extract_range_from_pointer_plus_expr (vr, code, expr_type,
						&vr0, &vr1);
	  return true;
	}
      const range_operator *op = get_range_op_handler (vr, code, expr_type);
      vr0.normalize_symbolics ();
      vr1.normalize_symbolics ();
      return op->fold_range (*vr, expr_type, vr0, vr1);
    }
  return false;
}

/* If operand is symbolic, perform a unary operation on it and return
   TRUE, otherwise return FALSE.  */

static bool
range_fold_unary_symbolics_p (value_range *vr,
			      tree_code code,
			      tree expr_type,
			      const value_range *vr0)
{
  if (vr0->symbolic_p ())
    {
      if (code == NEGATE_EXPR)
	{
	  /* -X is simply 0 - X.  */
	  value_range zero;
	  zero.set_zero (vr0->type ());
	  range_fold_binary_expr (vr, MINUS_EXPR, expr_type, &zero, vr0);
	  return true;
	}
      if (code == BIT_NOT_EXPR)
	{
	  /* ~X is simply -1 - X.  */
	  value_range minusone;
	  minusone.set (build_int_cst (vr0->type (), -1));
	  range_fold_binary_expr (vr, MINUS_EXPR, expr_type, &minusone, vr0);
	  return true;
	}
      const range_operator *op = get_range_op_handler (vr, code, expr_type);
      value_range vr0_cst (*vr0);
      vr0_cst.normalize_symbolics ();
      return op->fold_range (*vr, expr_type, vr0_cst, value_range (expr_type));
    }
  return false;
}

/* Perform a binary operation on a pair of ranges.  */

void
range_fold_binary_expr (value_range *vr,
			enum tree_code code,
			tree expr_type,
			const value_range *vr0_,
			const value_range *vr1_)
{
  if (!supported_types_p (vr, expr_type)
      || !defined_ranges_p (vr, vr0_, vr1_))
    return;
  const range_operator *op = get_range_op_handler (vr, code, expr_type);
  if (!op)
    return;

  if (range_fold_binary_symbolics_p (vr, code, expr_type, vr0_, vr1_))
    return;

  value_range vr0 (*vr0_);
  value_range vr1 (*vr1_);
  if (vr0.undefined_p ())
    vr0.set_varying (expr_type);
  if (vr1.undefined_p ())
    vr1.set_varying (expr_type);
  vr0.normalize_addresses ();
  vr1.normalize_addresses ();
  op->fold_range (*vr, expr_type, vr0, vr1);
}

/* Perform a unary operation on a range.  */

void
range_fold_unary_expr (value_range *vr,
		       enum tree_code code, tree expr_type,
		       const value_range *vr0,
		       tree vr0_type)
{
  if (!supported_types_p (vr, expr_type, vr0_type)
      || !defined_ranges_p (vr, vr0))
    return;
  const range_operator *op = get_range_op_handler (vr, code, expr_type);
  if (!op)
    return;

  if (range_fold_unary_symbolics_p (vr, code, expr_type, vr0))
    return;

  value_range vr0_cst (*vr0);
  vr0_cst.normalize_addresses ();
  op->fold_range (*vr, expr_type, vr0_cst, value_range (expr_type));
}

/* If the range of values taken by OP can be inferred after STMT executes,
   return the comparison code (COMP_CODE_P) and value (VAL_P) that
   describes the inferred range.  Return true if a range could be
   inferred.  */

bool
infer_value_range (gimple *stmt, tree op, tree_code *comp_code_p, tree *val_p)
{
  *val_p = NULL_TREE;
  *comp_code_p = ERROR_MARK;

  /* Do not attempt to infer anything in names that flow through
     abnormal edges.  */
  if (SSA_NAME_OCCURS_IN_ABNORMAL_PHI (op))
    return false;

  /* If STMT is the last statement of a basic block with no normal
     successors, there is no point inferring anything about any of its
     operands.  We would not be able to find a proper insertion point
     for the assertion, anyway.  */
  if (stmt_ends_bb_p (stmt))
    {
      edge_iterator ei;
      edge e;

      FOR_EACH_EDGE (e, ei, gimple_bb (stmt)->succs)
	if (!(e->flags & (EDGE_ABNORMAL|EDGE_EH)))
	  break;
      if (e == NULL)
	return false;
    }

  if (infer_nonnull_range (stmt, op))
    {
      *val_p = build_int_cst (TREE_TYPE (op), 0);
      *comp_code_p = NE_EXPR;
      return true;
    }

  return false;
}

/* Dump assert_info structure.  */

void
dump_assert_info (FILE *file, const assert_info &assert)
{
  fprintf (file, "Assert for: ");
  print_generic_expr (file, assert.name);
  fprintf (file, "\n\tPREDICATE: expr=[");
  print_generic_expr (file, assert.expr);
  fprintf (file, "] %s ", get_tree_code_name (assert.comp_code));
  fprintf (file, "val=[");
  print_generic_expr (file, assert.val);
  fprintf (file, "]\n\n");
}

DEBUG_FUNCTION void
debug (const assert_info &assert)
{
  dump_assert_info (stderr, assert);
}

/* Dump a vector of assert_info's.  */

void
dump_asserts_info (FILE *file, const vec<assert_info> &asserts)
{
  for (unsigned i = 0; i < asserts.length (); ++i)
    {
      dump_assert_info (file, asserts[i]);
      fprintf (file, "\n");
    }
}

DEBUG_FUNCTION void
debug (const vec<assert_info> &asserts)
{
  dump_asserts_info (stderr, asserts);
}

/* Push the assert info for NAME, EXPR, COMP_CODE and VAL to ASSERTS.  */

static void
add_assert_info (vec<assert_info> &asserts,
		 tree name, tree expr, enum tree_code comp_code, tree val)
{
  assert_info info;
  info.comp_code = comp_code;
  info.name = name;
  if (TREE_OVERFLOW_P (val))
    val = drop_tree_overflow (val);
  info.val = val;
  info.expr = expr;
  asserts.safe_push (info);
  if (dump_enabled_p ())
    dump_printf (MSG_NOTE | MSG_PRIORITY_INTERNALS,
		 "Adding assert for %T from %T %s %T\n",
		 name, expr, op_symbol_code (comp_code), val);
}

/* (COND_OP0 COND_CODE COND_OP1) is a predicate which uses NAME.
   Extract a suitable test code and value and store them into *CODE_P and
   *VAL_P so the predicate is normalized to NAME *CODE_P *VAL_P.

   If no extraction was possible, return FALSE, otherwise return TRUE.

   If INVERT is true, then we invert the result stored into *CODE_P.  */

static bool
extract_code_and_val_from_cond_with_ops (tree name, enum tree_code cond_code,
					 tree cond_op0, tree cond_op1,
					 bool invert, enum tree_code *code_p,
					 tree *val_p)
{
  enum tree_code comp_code;
  tree val;

  /* Otherwise, we have a comparison of the form NAME COMP VAL
     or VAL COMP NAME.  */
  if (name == cond_op1)
    {
      /* If the predicate is of the form VAL COMP NAME, flip
	 COMP around because we need to register NAME as the
	 first operand in the predicate.  */
      comp_code = swap_tree_comparison (cond_code);
      val = cond_op0;
    }
  else if (name == cond_op0)
    {
      /* The comparison is of the form NAME COMP VAL, so the
	 comparison code remains unchanged.  */
      comp_code = cond_code;
      val = cond_op1;
    }
  else
    gcc_unreachable ();

  /* Invert the comparison code as necessary.  */
  if (invert)
    comp_code = invert_tree_comparison (comp_code, 0);

  /* VRP only handles integral and pointer types.  */
  if (! INTEGRAL_TYPE_P (TREE_TYPE (val))
      && ! POINTER_TYPE_P (TREE_TYPE (val)))
    return false;

  /* Do not register always-false predicates.
     FIXME:  this works around a limitation in fold() when dealing with
     enumerations.  Given 'enum { N1, N2 } x;', fold will not
     fold 'if (x > N2)' to 'if (0)'.  */
  if ((comp_code == GT_EXPR || comp_code == LT_EXPR)
      && INTEGRAL_TYPE_P (TREE_TYPE (val)))
    {
      tree min = TYPE_MIN_VALUE (TREE_TYPE (val));
      tree max = TYPE_MAX_VALUE (TREE_TYPE (val));

      if (comp_code == GT_EXPR
	  && (!max
	      || compare_values (val, max) == 0))
	return false;

      if (comp_code == LT_EXPR
	  && (!min
	      || compare_values (val, min) == 0))
	return false;
    }
  *code_p = comp_code;
  *val_p = val;
  return true;
}

/* Find out smallest RES where RES > VAL && (RES & MASK) == RES, if any
   (otherwise return VAL).  VAL and MASK must be zero-extended for
   precision PREC.  If SGNBIT is non-zero, first xor VAL with SGNBIT
   (to transform signed values into unsigned) and at the end xor
   SGNBIT back.  */

wide_int
masked_increment (const wide_int &val_in, const wide_int &mask,
		  const wide_int &sgnbit, unsigned int prec)
{
  wide_int bit = wi::one (prec), res;
  unsigned int i;

  wide_int val = val_in ^ sgnbit;
  for (i = 0; i < prec; i++, bit += bit)
    {
      res = mask;
      if ((res & bit) == 0)
	continue;
      res = bit - 1;
      res = wi::bit_and_not (val + bit, res);
      res &= mask;
      if (wi::gtu_p (res, val))
	return res ^ sgnbit;
    }
  return val ^ sgnbit;
}

/* Helper for overflow_comparison_p

   OP0 CODE OP1 is a comparison.  Examine the comparison and potentially
   OP1's defining statement to see if it ultimately has the form
   OP0 CODE (OP0 PLUS INTEGER_CST)

   If so, return TRUE indicating this is an overflow test and store into
   *NEW_CST an updated constant that can be used in a narrowed range test.

   REVERSED indicates if the comparison was originally:

   OP1 CODE' OP0.

   This affects how we build the updated constant.  */

static bool
overflow_comparison_p_1 (enum tree_code code, tree op0, tree op1,
		         bool follow_assert_exprs, bool reversed, tree *new_cst)
{
  /* See if this is a relational operation between two SSA_NAMES with
     unsigned, overflow wrapping values.  If so, check it more deeply.  */
  if ((code == LT_EXPR || code == LE_EXPR
       || code == GE_EXPR || code == GT_EXPR)
      && TREE_CODE (op0) == SSA_NAME
      && TREE_CODE (op1) == SSA_NAME
      && INTEGRAL_TYPE_P (TREE_TYPE (op0))
      && TYPE_UNSIGNED (TREE_TYPE (op0))
      && TYPE_OVERFLOW_WRAPS (TREE_TYPE (op0)))
    {
      gimple *op1_def = SSA_NAME_DEF_STMT (op1);

      /* If requested, follow any ASSERT_EXPRs backwards for OP1.  */
      if (follow_assert_exprs)
	{
	  while (gimple_assign_single_p (op1_def)
		 && TREE_CODE (gimple_assign_rhs1 (op1_def)) == ASSERT_EXPR)
	    {
	      op1 = TREE_OPERAND (gimple_assign_rhs1 (op1_def), 0);
	      if (TREE_CODE (op1) != SSA_NAME)
		break;
	      op1_def = SSA_NAME_DEF_STMT (op1);
	    }
	}

      /* Now look at the defining statement of OP1 to see if it adds
	 or subtracts a nonzero constant from another operand.  */
      if (op1_def
	  && is_gimple_assign (op1_def)
	  && gimple_assign_rhs_code (op1_def) == PLUS_EXPR
	  && TREE_CODE (gimple_assign_rhs2 (op1_def)) == INTEGER_CST
	  && !integer_zerop (gimple_assign_rhs2 (op1_def)))
	{
	  tree target = gimple_assign_rhs1 (op1_def);

	  /* If requested, follow ASSERT_EXPRs backwards for op0 looking
	     for one where TARGET appears on the RHS.  */
	  if (follow_assert_exprs)
	    {
	      /* Now see if that "other operand" is op0, following the chain
		 of ASSERT_EXPRs if necessary.  */
	      gimple *op0_def = SSA_NAME_DEF_STMT (op0);
	      while (op0 != target
		     && gimple_assign_single_p (op0_def)
		     && TREE_CODE (gimple_assign_rhs1 (op0_def)) == ASSERT_EXPR)
		{
		  op0 = TREE_OPERAND (gimple_assign_rhs1 (op0_def), 0);
		  if (TREE_CODE (op0) != SSA_NAME)
		    break;
		  op0_def = SSA_NAME_DEF_STMT (op0);
		}
	    }

	  /* If we did not find our target SSA_NAME, then this is not
	     an overflow test.  */
	  if (op0 != target)
	    return false;

	  tree type = TREE_TYPE (op0);
	  wide_int max = wi::max_value (TYPE_PRECISION (type), UNSIGNED);
	  tree inc = gimple_assign_rhs2 (op1_def);
	  if (reversed)
	    *new_cst = wide_int_to_tree (type, max + wi::to_wide (inc));
	  else
	    *new_cst = wide_int_to_tree (type, max - wi::to_wide (inc));
	  return true;
	}
    }
  return false;
}

/* OP0 CODE OP1 is a comparison.  Examine the comparison and potentially
   OP1's defining statement to see if it ultimately has the form
   OP0 CODE (OP0 PLUS INTEGER_CST)

   If so, return TRUE indicating this is an overflow test and store into
   *NEW_CST an updated constant that can be used in a narrowed range test.

   These statements are left as-is in the IL to facilitate discovery of
   {ADD,SUB}_OVERFLOW sequences later in the optimizer pipeline.  But
   the alternate range representation is often useful within VRP.  */

bool
overflow_comparison_p (tree_code code, tree name, tree val,
		       bool use_equiv_p, tree *new_cst)
{
  if (overflow_comparison_p_1 (code, name, val, use_equiv_p, false, new_cst))
    return true;
  return overflow_comparison_p_1 (swap_tree_comparison (code), val, name,
				  use_equiv_p, true, new_cst);
}


/* Try to register an edge assertion for SSA name NAME on edge E for
   the condition COND contributing to the conditional jump pointed to by BSI.
   Invert the condition COND if INVERT is true.  */

static void
register_edge_assert_for_2 (tree name, edge e,
			    enum tree_code cond_code,
			    tree cond_op0, tree cond_op1, bool invert,
			    vec<assert_info> &asserts)
{
  tree val;
  enum tree_code comp_code;

  if (!extract_code_and_val_from_cond_with_ops (name, cond_code,
						cond_op0,
						cond_op1,
						invert, &comp_code, &val))
    return;

  /* Queue the assert.  */
  tree x;
  if (overflow_comparison_p (comp_code, name, val, false, &x))
    {
      enum tree_code new_code = ((comp_code == GT_EXPR || comp_code == GE_EXPR)
				 ? GT_EXPR : LE_EXPR);
      add_assert_info (asserts, name, name, new_code, x);
    }
  add_assert_info (asserts, name, name, comp_code, val);

  /* In the case of NAME <= CST and NAME being defined as
     NAME = (unsigned) NAME2 + CST2 we can assert NAME2 >= -CST2
     and NAME2 <= CST - CST2.  We can do the same for NAME > CST.
     This catches range and anti-range tests.  */
  if ((comp_code == LE_EXPR
       || comp_code == GT_EXPR)
      && TREE_CODE (val) == INTEGER_CST
      && TYPE_UNSIGNED (TREE_TYPE (val)))
    {
      gimple *def_stmt = SSA_NAME_DEF_STMT (name);
      tree cst2 = NULL_TREE, name2 = NULL_TREE, name3 = NULL_TREE;

      /* Extract CST2 from the (optional) addition.  */
      if (is_gimple_assign (def_stmt)
	  && gimple_assign_rhs_code (def_stmt) == PLUS_EXPR)
	{
	  name2 = gimple_assign_rhs1 (def_stmt);
	  cst2 = gimple_assign_rhs2 (def_stmt);
	  if (TREE_CODE (name2) == SSA_NAME
	      && TREE_CODE (cst2) == INTEGER_CST)
	    def_stmt = SSA_NAME_DEF_STMT (name2);
	}

      /* Extract NAME2 from the (optional) sign-changing cast.  */
      if (gassign *ass = dyn_cast <gassign *> (def_stmt))
	{
	  if (CONVERT_EXPR_CODE_P (gimple_assign_rhs_code (ass))
	      && ! TYPE_UNSIGNED (TREE_TYPE (gimple_assign_rhs1 (ass)))
	      && (TYPE_PRECISION (TREE_TYPE (gimple_assign_lhs (ass)))
		  == TYPE_PRECISION (TREE_TYPE (gimple_assign_rhs1 (ass)))))
	    name3 = gimple_assign_rhs1 (ass);
	}

      /* If name3 is used later, create an ASSERT_EXPR for it.  */
      if (name3 != NULL_TREE
      	  && TREE_CODE (name3) == SSA_NAME
	  && (cst2 == NULL_TREE
	      || TREE_CODE (cst2) == INTEGER_CST)
	  && INTEGRAL_TYPE_P (TREE_TYPE (name3)))
	{
	  tree tmp;

	  /* Build an expression for the range test.  */
	  tmp = build1 (NOP_EXPR, TREE_TYPE (name), name3);
	  if (cst2 != NULL_TREE)
	    tmp = build2 (PLUS_EXPR, TREE_TYPE (name), tmp, cst2);
	  add_assert_info (asserts, name3, tmp, comp_code, val);
	}

      /* If name2 is used later, create an ASSERT_EXPR for it.  */
      if (name2 != NULL_TREE
      	  && TREE_CODE (name2) == SSA_NAME
	  && TREE_CODE (cst2) == INTEGER_CST
	  && INTEGRAL_TYPE_P (TREE_TYPE (name2)))
	{
	  tree tmp;

	  /* Build an expression for the range test.  */
	  tmp = name2;
	  if (TREE_TYPE (name) != TREE_TYPE (name2))
	    tmp = build1 (NOP_EXPR, TREE_TYPE (name), tmp);
	  if (cst2 != NULL_TREE)
	    tmp = build2 (PLUS_EXPR, TREE_TYPE (name), tmp, cst2);
	  add_assert_info (asserts, name2, tmp, comp_code, val);
	}
    }

  /* In the case of post-in/decrement tests like if (i++) ... and uses
     of the in/decremented value on the edge the extra name we want to
     assert for is not on the def chain of the name compared.  Instead
     it is in the set of use stmts.
     Similar cases happen for conversions that were simplified through
     fold_{sign_changed,widened}_comparison.  */
  if ((comp_code == NE_EXPR
       || comp_code == EQ_EXPR)
      && TREE_CODE (val) == INTEGER_CST)
    {
      imm_use_iterator ui;
      gimple *use_stmt;
      FOR_EACH_IMM_USE_STMT (use_stmt, ui, name)
	{
	  if (!is_gimple_assign (use_stmt))
	    continue;

	  /* Cut off to use-stmts that are dominating the predecessor.  */
	  if (!dominated_by_p (CDI_DOMINATORS, e->src, gimple_bb (use_stmt)))
	    continue;

	  tree name2 = gimple_assign_lhs (use_stmt);
	  if (TREE_CODE (name2) != SSA_NAME)
	    continue;

	  enum tree_code code = gimple_assign_rhs_code (use_stmt);
	  tree cst;
	  if (code == PLUS_EXPR
	      || code == MINUS_EXPR)
	    {
	      cst = gimple_assign_rhs2 (use_stmt);
	      if (TREE_CODE (cst) != INTEGER_CST)
		continue;
	      cst = int_const_binop (code, val, cst);
	    }
	  else if (CONVERT_EXPR_CODE_P (code))
	    {
	      /* For truncating conversions we cannot record
		 an inequality.  */
	      if (comp_code == NE_EXPR
		  && (TYPE_PRECISION (TREE_TYPE (name2))
		      < TYPE_PRECISION (TREE_TYPE (name))))
		continue;
	      cst = fold_convert (TREE_TYPE (name2), val);
	    }
	  else
	    continue;

	  if (TREE_OVERFLOW_P (cst))
	    cst = drop_tree_overflow (cst);
	  add_assert_info (asserts, name2, name2, comp_code, cst);
	}
    }
 
  if (TREE_CODE_CLASS (comp_code) == tcc_comparison
      && TREE_CODE (val) == INTEGER_CST)
    {
      gimple *def_stmt = SSA_NAME_DEF_STMT (name);
      tree name2 = NULL_TREE, names[2], cst2 = NULL_TREE;
      tree val2 = NULL_TREE;
      unsigned int prec = TYPE_PRECISION (TREE_TYPE (val));
      wide_int mask = wi::zero (prec);
      unsigned int nprec = prec;
      enum tree_code rhs_code = ERROR_MARK;

      if (is_gimple_assign (def_stmt))
	rhs_code = gimple_assign_rhs_code (def_stmt);

      /* In the case of NAME != CST1 where NAME = A +- CST2 we can
         assert that A != CST1 -+ CST2.  */
      if ((comp_code == EQ_EXPR || comp_code == NE_EXPR)
	  && (rhs_code == PLUS_EXPR || rhs_code == MINUS_EXPR))
	{
	  tree op0 = gimple_assign_rhs1 (def_stmt);
	  tree op1 = gimple_assign_rhs2 (def_stmt);
	  if (TREE_CODE (op0) == SSA_NAME
	      && TREE_CODE (op1) == INTEGER_CST)
	    {
	      enum tree_code reverse_op = (rhs_code == PLUS_EXPR
					   ? MINUS_EXPR : PLUS_EXPR);
	      op1 = int_const_binop (reverse_op, val, op1);
	      if (TREE_OVERFLOW (op1))
		op1 = drop_tree_overflow (op1);
	      add_assert_info (asserts, op0, op0, comp_code, op1);
	    }
	}

      /* Add asserts for NAME cmp CST and NAME being defined
	 as NAME = (int) NAME2.  */
      if (!TYPE_UNSIGNED (TREE_TYPE (val))
	  && (comp_code == LE_EXPR || comp_code == LT_EXPR
	      || comp_code == GT_EXPR || comp_code == GE_EXPR)
	  && gimple_assign_cast_p (def_stmt))
	{
	  name2 = gimple_assign_rhs1 (def_stmt);
	  if (CONVERT_EXPR_CODE_P (rhs_code)
	      && TREE_CODE (name2) == SSA_NAME
	      && INTEGRAL_TYPE_P (TREE_TYPE (name2))
	      && TYPE_UNSIGNED (TREE_TYPE (name2))
	      && prec == TYPE_PRECISION (TREE_TYPE (name2))
	      && (comp_code == LE_EXPR || comp_code == GT_EXPR
		  || !tree_int_cst_equal (val,
					  TYPE_MIN_VALUE (TREE_TYPE (val)))))
	    {
	      tree tmp, cst;
	      enum tree_code new_comp_code = comp_code;

	      cst = fold_convert (TREE_TYPE (name2),
				  TYPE_MIN_VALUE (TREE_TYPE (val)));
	      /* Build an expression for the range test.  */
	      tmp = build2 (PLUS_EXPR, TREE_TYPE (name2), name2, cst);
	      cst = fold_build2 (PLUS_EXPR, TREE_TYPE (name2), cst,
				 fold_convert (TREE_TYPE (name2), val));
	      if (comp_code == LT_EXPR || comp_code == GE_EXPR)
		{
		  new_comp_code = comp_code == LT_EXPR ? LE_EXPR : GT_EXPR;
		  cst = fold_build2 (MINUS_EXPR, TREE_TYPE (name2), cst,
				     build_int_cst (TREE_TYPE (name2), 1));
		}
	      add_assert_info (asserts, name2, tmp, new_comp_code, cst);
	    }
	}

      /* Add asserts for NAME cmp CST and NAME being defined as
	 NAME = NAME2 >> CST2.

	 Extract CST2 from the right shift.  */
      if (rhs_code == RSHIFT_EXPR)
	{
	  name2 = gimple_assign_rhs1 (def_stmt);
	  cst2 = gimple_assign_rhs2 (def_stmt);
	  if (TREE_CODE (name2) == SSA_NAME
	      && tree_fits_uhwi_p (cst2)
	      && INTEGRAL_TYPE_P (TREE_TYPE (name2))
	      && IN_RANGE (tree_to_uhwi (cst2), 1, prec - 1)
	      && type_has_mode_precision_p (TREE_TYPE (val)))
	    {
	      mask = wi::mask (tree_to_uhwi (cst2), false, prec);
	      val2 = fold_binary (LSHIFT_EXPR, TREE_TYPE (val), val, cst2);
	    }
	}
      if (val2 != NULL_TREE
	  && TREE_CODE (val2) == INTEGER_CST
	  && simple_cst_equal (fold_build2 (RSHIFT_EXPR,
					    TREE_TYPE (val),
					    val2, cst2), val))
	{
	  enum tree_code new_comp_code = comp_code;
	  tree tmp, new_val;

	  tmp = name2;
	  if (comp_code == EQ_EXPR || comp_code == NE_EXPR)
	    {
	      if (!TYPE_UNSIGNED (TREE_TYPE (val)))
		{
		  tree type = build_nonstandard_integer_type (prec, 1);
		  tmp = build1 (NOP_EXPR, type, name2);
		  val2 = fold_convert (type, val2);
		}
	      tmp = fold_build2 (MINUS_EXPR, TREE_TYPE (tmp), tmp, val2);
	      new_val = wide_int_to_tree (TREE_TYPE (tmp), mask);
	      new_comp_code = comp_code == EQ_EXPR ? LE_EXPR : GT_EXPR;
	    }
	  else if (comp_code == LT_EXPR || comp_code == GE_EXPR)
	    {
	      wide_int minval
		= wi::min_value (prec, TYPE_SIGN (TREE_TYPE (val)));
	      new_val = val2;
	      if (minval == wi::to_wide (new_val))
		new_val = NULL_TREE;
	    }
	  else
	    {
	      wide_int maxval
		= wi::max_value (prec, TYPE_SIGN (TREE_TYPE (val)));
	      mask |= wi::to_wide (val2);
	      if (wi::eq_p (mask, maxval))
		new_val = NULL_TREE;
	      else
		new_val = wide_int_to_tree (TREE_TYPE (val2), mask);
	    }

	  if (new_val)
	    add_assert_info (asserts, name2, tmp, new_comp_code, new_val);
	}

      /* If we have a conversion that doesn't change the value of the source
         simply register the same assert for it.  */
      if (CONVERT_EXPR_CODE_P (rhs_code))
	{
	  value_range vr;
	  tree rhs1 = gimple_assign_rhs1 (def_stmt);
	  if (INTEGRAL_TYPE_P (TREE_TYPE (rhs1))
	      && TREE_CODE (rhs1) == SSA_NAME
	      /* Make sure the relation preserves the upper/lower boundary of
	         the range conservatively.  */
	      && (comp_code == NE_EXPR
		  || comp_code == EQ_EXPR
		  || (TYPE_SIGN (TREE_TYPE (name))
		      == TYPE_SIGN (TREE_TYPE (rhs1)))
		  || ((comp_code == LE_EXPR
		       || comp_code == LT_EXPR)
		      && !TYPE_UNSIGNED (TREE_TYPE (rhs1)))
		  || ((comp_code == GE_EXPR
		       || comp_code == GT_EXPR)
		      && TYPE_UNSIGNED (TREE_TYPE (rhs1))))
	      /* And the conversion does not alter the value we compare
	         against and all values in rhs1 can be represented in
		 the converted to type.  */
	      && int_fits_type_p (val, TREE_TYPE (rhs1))
	      && ((TYPE_PRECISION (TREE_TYPE (name))
		   > TYPE_PRECISION (TREE_TYPE (rhs1)))
		  || ((get_range_query (cfun)->range_of_expr (vr, rhs1)
		       && vr.kind () == VR_RANGE)
		      && wi::fits_to_tree_p
			   (widest_int::from (vr.lower_bound (),
					      TYPE_SIGN (TREE_TYPE (rhs1))),
			    TREE_TYPE (name))
		      && wi::fits_to_tree_p
			   (widest_int::from (vr.upper_bound (),
					      TYPE_SIGN (TREE_TYPE (rhs1))),
			    TREE_TYPE (name)))))
	    add_assert_info (asserts, rhs1, rhs1,
		 	     comp_code, fold_convert (TREE_TYPE (rhs1), val));
	}

      /* Add asserts for NAME cmp CST and NAME being defined as
	 NAME = NAME2 & CST2.

	 Extract CST2 from the and.

	 Also handle
	 NAME = (unsigned) NAME2;
	 casts where NAME's type is unsigned and has smaller precision
	 than NAME2's type as if it was NAME = NAME2 & MASK.  */
      names[0] = NULL_TREE;
      names[1] = NULL_TREE;
      cst2 = NULL_TREE;
      if (rhs_code == BIT_AND_EXPR
	  || (CONVERT_EXPR_CODE_P (rhs_code)
	      && INTEGRAL_TYPE_P (TREE_TYPE (val))
	      && TYPE_UNSIGNED (TREE_TYPE (val))
	      && TYPE_PRECISION (TREE_TYPE (gimple_assign_rhs1 (def_stmt)))
		 > prec))
	{
	  name2 = gimple_assign_rhs1 (def_stmt);
	  if (rhs_code == BIT_AND_EXPR)
	    cst2 = gimple_assign_rhs2 (def_stmt);
	  else
	    {
	      cst2 = TYPE_MAX_VALUE (TREE_TYPE (val));
	      nprec = TYPE_PRECISION (TREE_TYPE (name2));
	    }
	  if (TREE_CODE (name2) == SSA_NAME
	      && INTEGRAL_TYPE_P (TREE_TYPE (name2))
	      && TREE_CODE (cst2) == INTEGER_CST
	      && !integer_zerop (cst2)
	      && (nprec > 1
		  || TYPE_UNSIGNED (TREE_TYPE (val))))
	    {
	      gimple *def_stmt2 = SSA_NAME_DEF_STMT (name2);
	      if (gimple_assign_cast_p (def_stmt2))
		{
		  names[1] = gimple_assign_rhs1 (def_stmt2);
		  if (!CONVERT_EXPR_CODE_P (gimple_assign_rhs_code (def_stmt2))
		      || TREE_CODE (names[1]) != SSA_NAME
		      || !INTEGRAL_TYPE_P (TREE_TYPE (names[1]))
		      || (TYPE_PRECISION (TREE_TYPE (name2))
			  != TYPE_PRECISION (TREE_TYPE (names[1]))))
		    names[1] = NULL_TREE;
		}
	      names[0] = name2;
	    }
	}
      if (names[0] || names[1])
	{
	  wide_int minv, maxv, valv, cst2v;
	  wide_int tem, sgnbit;
	  bool valid_p = false, valn, cst2n;
	  enum tree_code ccode = comp_code;

	  valv = wide_int::from (wi::to_wide (val), nprec, UNSIGNED);
	  cst2v = wide_int::from (wi::to_wide (cst2), nprec, UNSIGNED);
	  valn = wi::neg_p (valv, TYPE_SIGN (TREE_TYPE (val)));
	  cst2n = wi::neg_p (cst2v, TYPE_SIGN (TREE_TYPE (val)));
	  /* If CST2 doesn't have most significant bit set,
	     but VAL is negative, we have comparison like
	     if ((x & 0x123) > -4) (always true).  Just give up.  */
	  if (!cst2n && valn)
	    ccode = ERROR_MARK;
	  if (cst2n)
	    sgnbit = wi::set_bit_in_zero (nprec - 1, nprec);
	  else
	    sgnbit = wi::zero (nprec);
	  minv = valv & cst2v;
	  switch (ccode)
	    {
	    case EQ_EXPR:
	      /* Minimum unsigned value for equality is VAL & CST2
		 (should be equal to VAL, otherwise we probably should
		 have folded the comparison into false) and
		 maximum unsigned value is VAL | ~CST2.  */
	      maxv = valv | ~cst2v;
	      valid_p = true;
	      break;

	    case NE_EXPR:
	      tem = valv | ~cst2v;
	      /* If VAL is 0, handle (X & CST2) != 0 as (X & CST2) > 0U.  */
	      if (valv == 0)
		{
		  cst2n = false;
		  sgnbit = wi::zero (nprec);
		  goto gt_expr;
		}
	      /* If (VAL | ~CST2) is all ones, handle it as
		 (X & CST2) < VAL.  */
	      if (tem == -1)
		{
		  cst2n = false;
		  valn = false;
		  sgnbit = wi::zero (nprec);
		  goto lt_expr;
		}
	      if (!cst2n && wi::neg_p (cst2v))
		sgnbit = wi::set_bit_in_zero (nprec - 1, nprec);
	      if (sgnbit != 0)
		{
		  if (valv == sgnbit)
		    {
		      cst2n = true;
		      valn = true;
		      goto gt_expr;
		    }
		  if (tem == wi::mask (nprec - 1, false, nprec))
		    {
		      cst2n = true;
		      goto lt_expr;
		    }
		  if (!cst2n)
		    sgnbit = wi::zero (nprec);
		}
	      break;

	    case GE_EXPR:
	      /* Minimum unsigned value for >= if (VAL & CST2) == VAL
		 is VAL and maximum unsigned value is ~0.  For signed
		 comparison, if CST2 doesn't have most significant bit
		 set, handle it similarly.  If CST2 has MSB set,
		 the minimum is the same, and maximum is ~0U/2.  */
	      if (minv != valv)
		{
		  /* If (VAL & CST2) != VAL, X & CST2 can't be equal to
		     VAL.  */
		  minv = masked_increment (valv, cst2v, sgnbit, nprec);
		  if (minv == valv)
		    break;
		}
	      maxv = wi::mask (nprec - (cst2n ? 1 : 0), false, nprec);
	      valid_p = true;
	      break;

	    case GT_EXPR:
	    gt_expr:
	      /* Find out smallest MINV where MINV > VAL
		 && (MINV & CST2) == MINV, if any.  If VAL is signed and
		 CST2 has MSB set, compute it biased by 1 << (nprec - 1).  */
	      minv = masked_increment (valv, cst2v, sgnbit, nprec);
	      if (minv == valv)
		break;
	      maxv = wi::mask (nprec - (cst2n ? 1 : 0), false, nprec);
	      valid_p = true;
	      break;

	    case LE_EXPR:
	      /* Minimum unsigned value for <= is 0 and maximum
		 unsigned value is VAL | ~CST2 if (VAL & CST2) == VAL.
		 Otherwise, find smallest VAL2 where VAL2 > VAL
		 && (VAL2 & CST2) == VAL2 and use (VAL2 - 1) | ~CST2
		 as maximum.
		 For signed comparison, if CST2 doesn't have most
		 significant bit set, handle it similarly.  If CST2 has
		 MSB set, the maximum is the same and minimum is INT_MIN.  */
	      if (minv == valv)
		maxv = valv;
	      else
		{
		  maxv = masked_increment (valv, cst2v, sgnbit, nprec);
		  if (maxv == valv)
		    break;
		  maxv -= 1;
		}
	      maxv |= ~cst2v;
	      minv = sgnbit;
	      valid_p = true;
	      break;

	    case LT_EXPR:
	    lt_expr:
	      /* Minimum unsigned value for < is 0 and maximum
		 unsigned value is (VAL-1) | ~CST2 if (VAL & CST2) == VAL.
		 Otherwise, find smallest VAL2 where VAL2 > VAL
		 && (VAL2 & CST2) == VAL2 and use (VAL2 - 1) | ~CST2
		 as maximum.
		 For signed comparison, if CST2 doesn't have most
		 significant bit set, handle it similarly.  If CST2 has
		 MSB set, the maximum is the same and minimum is INT_MIN.  */
	      if (minv == valv)
		{
		  if (valv == sgnbit)
		    break;
		  maxv = valv;
		}
	      else
		{
		  maxv = masked_increment (valv, cst2v, sgnbit, nprec);
		  if (maxv == valv)
		    break;
		}
	      maxv -= 1;
	      maxv |= ~cst2v;
	      minv = sgnbit;
	      valid_p = true;
	      break;

	    default:
	      break;
	    }
	  if (valid_p
	      && (maxv - minv) != -1)
	    {
	      tree tmp, new_val, type;
	      int i;

	      for (i = 0; i < 2; i++)
		if (names[i])
		  {
		    wide_int maxv2 = maxv;
		    tmp = names[i];
		    type = TREE_TYPE (names[i]);
		    if (!TYPE_UNSIGNED (type))
		      {
			type = build_nonstandard_integer_type (nprec, 1);
			tmp = build1 (NOP_EXPR, type, names[i]);
		      }
		    if (minv != 0)
		      {
			tmp = build2 (PLUS_EXPR, type, tmp,
				      wide_int_to_tree (type, -minv));
			maxv2 = maxv - minv;
		      }
		    new_val = wide_int_to_tree (type, maxv2);
		    add_assert_info (asserts, names[i], tmp, LE_EXPR, new_val);
		  }
	    }
	}
    }
}

/* OP is an operand of a truth value expression which is known to have
   a particular value.  Register any asserts for OP and for any
   operands in OP's defining statement.

   If CODE is EQ_EXPR, then we want to register OP is zero (false),
   if CODE is NE_EXPR, then we want to register OP is nonzero (true).   */

static void
register_edge_assert_for_1 (tree op, enum tree_code code,
			    edge e, vec<assert_info> &asserts)
{
  gimple *op_def;
  tree val;
  enum tree_code rhs_code;

  /* We only care about SSA_NAMEs.  */
  if (TREE_CODE (op) != SSA_NAME)
    return;

  /* We know that OP will have a zero or nonzero value.  */
  val = build_int_cst (TREE_TYPE (op), 0);
  add_assert_info (asserts, op, op, code, val);

  /* Now look at how OP is set.  If it's set from a comparison,
     a truth operation or some bit operations, then we may be able
     to register information about the operands of that assignment.  */
  op_def = SSA_NAME_DEF_STMT (op);
  if (gimple_code (op_def) != GIMPLE_ASSIGN)
    return;

  rhs_code = gimple_assign_rhs_code (op_def);

  if (TREE_CODE_CLASS (rhs_code) == tcc_comparison)
    {
      bool invert = (code == EQ_EXPR ? true : false);
      tree op0 = gimple_assign_rhs1 (op_def);
      tree op1 = gimple_assign_rhs2 (op_def);

      if (TREE_CODE (op0) == SSA_NAME)
        register_edge_assert_for_2 (op0, e, rhs_code, op0, op1, invert, asserts);
      if (TREE_CODE (op1) == SSA_NAME)
        register_edge_assert_for_2 (op1, e, rhs_code, op0, op1, invert, asserts);
    }
  else if ((code == NE_EXPR
	    && gimple_assign_rhs_code (op_def) == BIT_AND_EXPR)
	   || (code == EQ_EXPR
	       && gimple_assign_rhs_code (op_def) == BIT_IOR_EXPR))
    {
      /* Recurse on each operand.  */
      tree op0 = gimple_assign_rhs1 (op_def);
      tree op1 = gimple_assign_rhs2 (op_def);
      if (TREE_CODE (op0) == SSA_NAME
	  && has_single_use (op0))
	register_edge_assert_for_1 (op0, code, e, asserts);
      if (TREE_CODE (op1) == SSA_NAME
	  && has_single_use (op1))
	register_edge_assert_for_1 (op1, code, e, asserts);
    }
  else if (gimple_assign_rhs_code (op_def) == BIT_NOT_EXPR
	   && TYPE_PRECISION (TREE_TYPE (gimple_assign_lhs (op_def))) == 1)
    {
      /* Recurse, flipping CODE.  */
      code = invert_tree_comparison (code, false);
      register_edge_assert_for_1 (gimple_assign_rhs1 (op_def), code, e, asserts);
    }
  else if (gimple_assign_rhs_code (op_def) == SSA_NAME)
    {
      /* Recurse through the copy.  */
      register_edge_assert_for_1 (gimple_assign_rhs1 (op_def), code, e, asserts);
    }
  else if (CONVERT_EXPR_CODE_P (gimple_assign_rhs_code (op_def)))
    {
      /* Recurse through the type conversion, unless it is a narrowing
	 conversion or conversion from non-integral type.  */
      tree rhs = gimple_assign_rhs1 (op_def);
      if (INTEGRAL_TYPE_P (TREE_TYPE (rhs))
	  && (TYPE_PRECISION (TREE_TYPE (rhs))
	      <= TYPE_PRECISION (TREE_TYPE (op))))
	register_edge_assert_for_1 (rhs, code, e, asserts);
    }
}

/* Check if comparison
     NAME COND_OP INTEGER_CST
   has a form of
     (X & 11...100..0) COND_OP XX...X00...0
   Such comparison can yield assertions like
     X >= XX...X00...0
     X <= XX...X11...1
   in case of COND_OP being EQ_EXPR or
     X < XX...X00...0
     X > XX...X11...1
   in case of NE_EXPR.  */

static bool
is_masked_range_test (tree name, tree valt, enum tree_code cond_code,
		      tree *new_name, tree *low, enum tree_code *low_code,
		      tree *high, enum tree_code *high_code)
{
  gimple *def_stmt = SSA_NAME_DEF_STMT (name);

  if (!is_gimple_assign (def_stmt)
      || gimple_assign_rhs_code (def_stmt) != BIT_AND_EXPR)
    return false;

  tree t = gimple_assign_rhs1 (def_stmt);
  tree maskt = gimple_assign_rhs2 (def_stmt);
  if (TREE_CODE (t) != SSA_NAME || TREE_CODE (maskt) != INTEGER_CST)
    return false;

  wi::tree_to_wide_ref mask = wi::to_wide (maskt);
  wide_int inv_mask = ~mask;
  /* Must have been removed by now so don't bother optimizing.  */
  if (mask == 0 || inv_mask == 0)
    return false;

  /* Assume VALT is INTEGER_CST.  */
  wi::tree_to_wide_ref val = wi::to_wide (valt);

  if ((inv_mask & (inv_mask + 1)) != 0
      || (val & mask) != val)
    return false;

  bool is_range = cond_code == EQ_EXPR;

  tree type = TREE_TYPE (t);
  wide_int min = wi::min_value (type),
    max = wi::max_value (type);

  if (is_range)
    {
      *low_code = val == min ? ERROR_MARK : GE_EXPR;
      *high_code = val == max ? ERROR_MARK : LE_EXPR;
    }
  else
    {
      /* We can still generate assertion if one of alternatives
	 is known to always be false.  */
      if (val == min)
	{
	  *low_code = (enum tree_code) 0;
	  *high_code = GT_EXPR;
	}
      else if ((val | inv_mask) == max)
	{
	  *low_code = LT_EXPR;
	  *high_code = (enum tree_code) 0;
	}
      else
	return false;
    }

  *new_name = t;
  *low = wide_int_to_tree (type, val);
  *high = wide_int_to_tree (type, val | inv_mask);

  return true;
}

/* Try to register an edge assertion for SSA name NAME on edge E for
   the condition COND contributing to the conditional jump pointed to by
   SI.  */

void
register_edge_assert_for (tree name, edge e,
			  enum tree_code cond_code, tree cond_op0,
			  tree cond_op1, vec<assert_info> &asserts)
{
  tree val;
  enum tree_code comp_code;
  bool is_else_edge = (e->flags & EDGE_FALSE_VALUE) != 0;

  /* Do not attempt to infer anything in names that flow through
     abnormal edges.  */
  if (SSA_NAME_OCCURS_IN_ABNORMAL_PHI (name))
    return;

  if (!extract_code_and_val_from_cond_with_ops (name, cond_code,
						cond_op0, cond_op1,
						is_else_edge,
						&comp_code, &val))
    return;

  /* Register ASSERT_EXPRs for name.  */
  register_edge_assert_for_2 (name, e, cond_code, cond_op0,
			      cond_op1, is_else_edge, asserts);


  /* If COND is effectively an equality test of an SSA_NAME against
     the value zero or one, then we may be able to assert values
     for SSA_NAMEs which flow into COND.  */

  /* In the case of NAME == 1 or NAME != 0, for BIT_AND_EXPR defining
     statement of NAME we can assert both operands of the BIT_AND_EXPR
     have nonzero value.  */
  if ((comp_code == EQ_EXPR && integer_onep (val))
      || (comp_code == NE_EXPR && integer_zerop (val)))
    {
      gimple *def_stmt = SSA_NAME_DEF_STMT (name);

      if (is_gimple_assign (def_stmt)
	  && gimple_assign_rhs_code (def_stmt) == BIT_AND_EXPR)
	{
	  tree op0 = gimple_assign_rhs1 (def_stmt);
	  tree op1 = gimple_assign_rhs2 (def_stmt);
	  register_edge_assert_for_1 (op0, NE_EXPR, e, asserts);
	  register_edge_assert_for_1 (op1, NE_EXPR, e, asserts);
	}
      else if (is_gimple_assign (def_stmt)
	       && (TREE_CODE_CLASS (gimple_assign_rhs_code (def_stmt))
		   == tcc_comparison))
	register_edge_assert_for_1 (name, NE_EXPR, e, asserts);
    }

  /* In the case of NAME == 0 or NAME != 1, for BIT_IOR_EXPR defining
     statement of NAME we can assert both operands of the BIT_IOR_EXPR
     have zero value.  */
  if ((comp_code == EQ_EXPR && integer_zerop (val))
      || (comp_code == NE_EXPR
	  && integer_onep (val)
	  && TYPE_PRECISION (TREE_TYPE (name)) == 1))
    {
      gimple *def_stmt = SSA_NAME_DEF_STMT (name);

      /* For BIT_IOR_EXPR only if NAME == 0 both operands have
	 necessarily zero value, or if type-precision is one.  */
      if (is_gimple_assign (def_stmt)
	  && gimple_assign_rhs_code (def_stmt) == BIT_IOR_EXPR)
	{
	  tree op0 = gimple_assign_rhs1 (def_stmt);
	  tree op1 = gimple_assign_rhs2 (def_stmt);
	  register_edge_assert_for_1 (op0, EQ_EXPR, e, asserts);
	  register_edge_assert_for_1 (op1, EQ_EXPR, e, asserts);
	}
      else if (is_gimple_assign (def_stmt)
	       && (TREE_CODE_CLASS (gimple_assign_rhs_code (def_stmt))
		   == tcc_comparison))
	register_edge_assert_for_1 (name, EQ_EXPR, e, asserts);
    }

  /* Sometimes we can infer ranges from (NAME & MASK) == VALUE.  */
  if ((comp_code == EQ_EXPR || comp_code == NE_EXPR)
      && TREE_CODE (val) == INTEGER_CST)
    {
      enum tree_code low_code, high_code;
      tree low, high;
      if (is_masked_range_test (name, val, comp_code, &name, &low,
				&low_code, &high, &high_code))
	{
	  if (low_code != ERROR_MARK)
	    register_edge_assert_for_2 (name, e, low_code, name,
					low, /*invert*/false, asserts);
	  if (high_code != ERROR_MARK)
	    register_edge_assert_for_2 (name, e, high_code, name,
					high, /*invert*/false, asserts);
	}
    }
}

/* Handle
   _4 = x_3 & 31;
   if (_4 != 0)
     goto <bb 6>;
   else
     goto <bb 7>;
   <bb 6>:
   __builtin_unreachable ();
   <bb 7>:
   x_5 = ASSERT_EXPR <x_3, ...>;
   If x_3 has no other immediate uses (checked by caller),
   var is the x_3 var from ASSERT_EXPR, we can clear low 5 bits
   from the non-zero bitmask.  */

void
maybe_set_nonzero_bits (edge e, tree var)
{
  basic_block cond_bb = e->src;
  gimple *stmt = last_stmt (cond_bb);
  tree cst;

  if (stmt == NULL
      || gimple_code (stmt) != GIMPLE_COND
      || gimple_cond_code (stmt) != ((e->flags & EDGE_TRUE_VALUE)
				     ? EQ_EXPR : NE_EXPR)
      || TREE_CODE (gimple_cond_lhs (stmt)) != SSA_NAME
      || !integer_zerop (gimple_cond_rhs (stmt)))
    return;

  stmt = SSA_NAME_DEF_STMT (gimple_cond_lhs (stmt));
  if (!is_gimple_assign (stmt)
      || gimple_assign_rhs_code (stmt) != BIT_AND_EXPR
      || TREE_CODE (gimple_assign_rhs2 (stmt)) != INTEGER_CST)
    return;
  if (gimple_assign_rhs1 (stmt) != var)
    {
      gimple *stmt2;

      if (TREE_CODE (gimple_assign_rhs1 (stmt)) != SSA_NAME)
	return;
      stmt2 = SSA_NAME_DEF_STMT (gimple_assign_rhs1 (stmt));
      if (!gimple_assign_cast_p (stmt2)
	  || gimple_assign_rhs1 (stmt2) != var
	  || !CONVERT_EXPR_CODE_P (gimple_assign_rhs_code (stmt2))
	  || (TYPE_PRECISION (TREE_TYPE (gimple_assign_rhs1 (stmt)))
			      != TYPE_PRECISION (TREE_TYPE (var))))
	return;
    }
  cst = gimple_assign_rhs2 (stmt);
  set_nonzero_bits (var, wi::bit_and_not (get_nonzero_bits (var),
					  wi::to_wide (cst)));
}

/* Return true if STMT is interesting for VRP.  */

bool
stmt_interesting_for_vrp (gimple *stmt)
{
  if (gimple_code (stmt) == GIMPLE_PHI)
    {
      tree res = gimple_phi_result (stmt);
      return (!virtual_operand_p (res)
	      && (INTEGRAL_TYPE_P (TREE_TYPE (res))
		  || POINTER_TYPE_P (TREE_TYPE (res))));
    }
  else if (is_gimple_assign (stmt) || is_gimple_call (stmt))
    {
      tree lhs = gimple_get_lhs (stmt);

      /* In general, assignments with virtual operands are not useful
	 for deriving ranges, with the obvious exception of calls to
	 builtin functions.  */
      if (lhs && TREE_CODE (lhs) == SSA_NAME
	  && (INTEGRAL_TYPE_P (TREE_TYPE (lhs))
	      || POINTER_TYPE_P (TREE_TYPE (lhs)))
	  && (is_gimple_call (stmt)
	      || !gimple_vuse (stmt)))
	return true;
      else if (is_gimple_call (stmt) && gimple_call_internal_p (stmt))
	switch (gimple_call_internal_fn (stmt))
	  {
	  case IFN_ADD_OVERFLOW:
	  case IFN_SUB_OVERFLOW:
	  case IFN_MUL_OVERFLOW:
	  case IFN_ATOMIC_COMPARE_EXCHANGE:
	    /* These internal calls return _Complex integer type,
	       but are interesting to VRP nevertheless.  */
	    if (lhs && TREE_CODE (lhs) == SSA_NAME)
	      return true;
	    break;
	  default:
	    break;
	  }
    }
  else if (gimple_code (stmt) == GIMPLE_COND
	   || gimple_code (stmt) == GIMPLE_SWITCH)
    return true;

  return false;
}

/* Searches the case label vector VEC for the index *IDX of the CASE_LABEL
   that includes the value VAL.  The search is restricted to the range
   [START_IDX, n - 1] where n is the size of VEC.

   If there is a CASE_LABEL for VAL, its index is placed in IDX and true is
   returned.

   If there is no CASE_LABEL for VAL and there is one that is larger than VAL,
   it is placed in IDX and false is returned.

   If VAL is larger than any CASE_LABEL, n is placed on IDX and false is
   returned. */

bool
find_case_label_index (gswitch *stmt, size_t start_idx, tree val, size_t *idx)
{
  size_t n = gimple_switch_num_labels (stmt);
  size_t low, high;

  /* Find case label for minimum of the value range or the next one.
     At each iteration we are searching in [low, high - 1]. */

  for (low = start_idx, high = n; high != low; )
    {
      tree t;
      int cmp;
      /* Note that i != high, so we never ask for n. */
      size_t i = (high + low) / 2;
      t = gimple_switch_label (stmt, i);

      /* Cache the result of comparing CASE_LOW and val.  */
      cmp = tree_int_cst_compare (CASE_LOW (t), val);

      if (cmp == 0)
	{
	  /* Ranges cannot be empty. */
	  *idx = i;
	  return true;
	}
      else if (cmp > 0)
        high = i;
      else
	{
	  low = i + 1;
	  if (CASE_HIGH (t) != NULL
	      && tree_int_cst_compare (CASE_HIGH (t), val) >= 0)
	    {
	      *idx = i;
	      return true;
	    }
        }
    }

  *idx = high;
  return false;
}

/* Searches the case label vector VEC for the range of CASE_LABELs that is used
   for values between MIN and MAX. The first index is placed in MIN_IDX. The
   last index is placed in MAX_IDX. If the range of CASE_LABELs is empty
   then MAX_IDX < MIN_IDX.
   Returns true if the default label is not needed. */

bool
find_case_label_range (gswitch *stmt, tree min, tree max, size_t *min_idx,
		       size_t *max_idx)
{
  size_t i, j;
  bool min_take_default = !find_case_label_index (stmt, 1, min, &i);
  bool max_take_default = !find_case_label_index (stmt, i, max, &j);

  if (i == j
      && min_take_default
      && max_take_default)
    {
      /* Only the default case label reached.
         Return an empty range. */
      *min_idx = 1;
      *max_idx = 0;
      return false;
    }
  else
    {
      bool take_default = min_take_default || max_take_default;
      tree low, high;
      size_t k;

      if (max_take_default)
	j--;

      /* If the case label range is continuous, we do not need
	 the default case label.  Verify that.  */
      high = CASE_LOW (gimple_switch_label (stmt, i));
      if (CASE_HIGH (gimple_switch_label (stmt, i)))
	high = CASE_HIGH (gimple_switch_label (stmt, i));
      for (k = i + 1; k <= j; ++k)
	{
	  low = CASE_LOW (gimple_switch_label (stmt, k));
	  if (!integer_onep (int_const_binop (MINUS_EXPR, low, high)))
	    {
	      take_default = true;
	      break;
	    }
	  high = low;
	  if (CASE_HIGH (gimple_switch_label (stmt, k)))
	    high = CASE_HIGH (gimple_switch_label (stmt, k));
	}

      *min_idx = i;
      *max_idx = j;
      return !take_default;
    }
}

/* Given a SWITCH_STMT, return the case label that encompasses the
   known possible values for the switch operand.  RANGE_OF_OP is a
   range for the known values of the switch operand.  */

tree
find_case_label_range (gswitch *switch_stmt, const irange *range_of_op)
{
  if (range_of_op->undefined_p ()
      || range_of_op->varying_p ()
      || range_of_op->symbolic_p ())
    return NULL_TREE;

  size_t i, j;
  tree op = gimple_switch_index (switch_stmt);
  tree type = TREE_TYPE (op);
  tree tmin = wide_int_to_tree (type, range_of_op->lower_bound ());
  tree tmax = wide_int_to_tree (type, range_of_op->upper_bound ());
  find_case_label_range (switch_stmt, tmin, tmax, &i, &j);
  if (i == j)
    {
      /* Look for exactly one label that encompasses the range of
	 the operand.  */
      tree label = gimple_switch_label (switch_stmt, i);
      tree case_high
	= CASE_HIGH (label) ? CASE_HIGH (label) : CASE_LOW (label);
      int_range_max label_range (CASE_LOW (label), case_high);
      if (!types_compatible_p (label_range.type (), range_of_op->type ()))
	range_cast (label_range, range_of_op->type ());
      label_range.intersect (range_of_op);
      if (label_range == *range_of_op)
	return label;
    }
  else if (i > j)
    {
      /* If there are no labels at all, take the default.  */
      return gimple_switch_label (switch_stmt, 0);
    }
  else
    {
      /* Otherwise, there are various labels that can encompass
	 the range of operand.  In which case, see if the range of
	 the operand is entirely *outside* the bounds of all the
	 (non-default) case labels.  If so, take the default.  */
      unsigned n = gimple_switch_num_labels (switch_stmt);
      tree min_label = gimple_switch_label (switch_stmt, 1);
      tree max_label = gimple_switch_label (switch_stmt, n - 1);
      tree case_high = CASE_HIGH (max_label);
      if (!case_high)
	case_high = CASE_LOW (max_label);
      int_range_max label_range (CASE_LOW (min_label), case_high);
      if (!types_compatible_p (label_range.type (), range_of_op->type ()))
	range_cast (label_range, range_of_op->type ());
      label_range.intersect (range_of_op);
      if (label_range.undefined_p ())
	return gimple_switch_label (switch_stmt, 0);
    }
  return NULL_TREE;
}

struct case_info
{
  tree expr;
  basic_block bb;
};

/* Location information for ASSERT_EXPRs.  Each instance of this
   structure describes an ASSERT_EXPR for an SSA name.  Since a single
   SSA name may have more than one assertion associated with it, these
   locations are kept in a linked list attached to the corresponding
   SSA name.  */
struct assert_locus
{
  /* Basic block where the assertion would be inserted.  */
  basic_block bb;

  /* Some assertions need to be inserted on an edge (e.g., assertions
     generated by COND_EXPRs).  In those cases, BB will be NULL.  */
  edge e;

  /* Pointer to the statement that generated this assertion.  */
  gimple_stmt_iterator si;

  /* Predicate code for the ASSERT_EXPR.  Must be COMPARISON_CLASS_P.  */
  enum tree_code comp_code;

  /* Value being compared against.  */
  tree val;

  /* Expression to compare.  */
  tree expr;

  /* Next node in the linked list.  */
  assert_locus *next;
};

/* Class to traverse the flowgraph looking for conditional jumps to
   insert ASSERT_EXPR range expressions.  These range expressions are
   meant to provide information to optimizations that need to reason
   in terms of value ranges.  They will not be expanded into RTL.  */

class vrp_asserts
{
public:
  vrp_asserts (struct function *fn) : fun (fn) { }

  void insert_range_assertions ();

  /* Convert range assertion expressions into the implied copies and
     copy propagate away the copies.  */
  void remove_range_assertions ();

  /* Dump all the registered assertions for all the names to FILE.  */
  void dump (FILE *);

  /* Dump all the registered assertions for NAME to FILE.  */
  void dump (FILE *file, tree name);

  /* Dump all the registered assertions for NAME to stderr.  */
  void debug (tree name)
  {
    dump (stderr, name);
  }

  /* Dump all the registered assertions for all the names to stderr.  */
  void debug ()
  {
    dump (stderr);
  }

private:
  /* Set of SSA names found live during the RPO traversal of the function
     for still active basic-blocks.  */
  live_names live;

  /* Function to work on.  */
  struct function *fun;

  /* If bit I is present, it means that SSA name N_i has a list of
     assertions that should be inserted in the IL.  */
  bitmap need_assert_for;

  /* Array of locations lists where to insert assertions.  ASSERTS_FOR[I]
     holds a list of ASSERT_LOCUS_T nodes that describe where
     ASSERT_EXPRs for SSA name N_I should be inserted.  */
  assert_locus **asserts_for;

  /* Finish found ASSERTS for E and register them at GSI.  */
  void finish_register_edge_assert_for (edge e, gimple_stmt_iterator gsi,
					vec<assert_info> &asserts);

  /* Determine whether the outgoing edges of BB should receive an
     ASSERT_EXPR for each of the operands of BB's LAST statement.  The
     last statement of BB must be a SWITCH_EXPR.

     If any of the sub-graphs rooted at BB have an interesting use of
     the predicate operands, an assert location node is added to the
     list of assertions for the corresponding operands.  */
  void find_switch_asserts (basic_block bb, gswitch *last);

  /* Do an RPO walk over the function computing SSA name liveness
     on-the-fly and deciding on assert expressions to insert.  */
  void find_assert_locations ();

  /* Traverse all the statements in block BB looking for statements that
     may generate useful assertions for the SSA names in their operand.
     See method implementation comentary for more information.  */
  void find_assert_locations_in_bb (basic_block bb);

  /* Determine whether the outgoing edges of BB should receive an
     ASSERT_EXPR for each of the operands of BB's LAST statement.
     The last statement of BB must be a COND_EXPR.

     If any of the sub-graphs rooted at BB have an interesting use of
     the predicate operands, an assert location node is added to the
     list of assertions for the corresponding operands.  */
  void find_conditional_asserts (basic_block bb, gcond *last);

  /* Process all the insertions registered for every name N_i registered
     in NEED_ASSERT_FOR.  The list of assertions to be inserted are
     found in ASSERTS_FOR[i].  */
  void process_assert_insertions ();

  /* If NAME doesn't have an ASSERT_EXPR registered for asserting
     'EXPR COMP_CODE VAL' at a location that dominates block BB or
     E->DEST, then register this location as a possible insertion point
     for ASSERT_EXPR <NAME, EXPR COMP_CODE VAL>.

     BB, E and SI provide the exact insertion point for the new
     ASSERT_EXPR.  If BB is NULL, then the ASSERT_EXPR is to be inserted
     on edge E.  Otherwise, if E is NULL, the ASSERT_EXPR is inserted on
     BB.  If SI points to a COND_EXPR or a SWITCH_EXPR statement, then E
     must not be NULL.  */
  void register_new_assert_for (tree name, tree expr,
				enum tree_code comp_code,
				tree val, basic_block bb,
				edge e, gimple_stmt_iterator si);

  /* Given a COND_EXPR COND of the form 'V OP W', and an SSA name V,
     create a new SSA name N and return the assertion assignment
     'N = ASSERT_EXPR <V, V OP W>'.  */
  gimple *build_assert_expr_for (tree cond, tree v);

  /* Create an ASSERT_EXPR for NAME and insert it in the location
     indicated by LOC.  Return true if we made any edge insertions.  */
  bool process_assert_insertions_for (tree name, assert_locus *loc);

  /* Qsort callback for sorting assert locations.  */
  template <bool stable> static int compare_assert_loc (const void *,
							const void *);

  /* Return false if EXPR is a predicate expression involving floating
     point values.  */
  bool fp_predicate (gimple *stmt)
  {
    GIMPLE_CHECK (stmt, GIMPLE_COND);
    return FLOAT_TYPE_P (TREE_TYPE (gimple_cond_lhs (stmt)));
  }

  bool all_imm_uses_in_stmt_or_feed_cond (tree var, gimple *stmt,
					  basic_block cond_bb);

  static int compare_case_labels (const void *, const void *);
};

/* Given a COND_EXPR COND of the form 'V OP W', and an SSA name V,
   create a new SSA name N and return the assertion assignment
   'N = ASSERT_EXPR <V, V OP W>'.  */

gimple *
vrp_asserts::build_assert_expr_for (tree cond, tree v)
{
  tree a;
  gassign *assertion;

  gcc_assert (TREE_CODE (v) == SSA_NAME
	      && COMPARISON_CLASS_P (cond));

  a = build2 (ASSERT_EXPR, TREE_TYPE (v), v, cond);
  assertion = gimple_build_assign (NULL_TREE, a);

  /* The new ASSERT_EXPR, creates a new SSA name that replaces the
     operand of the ASSERT_EXPR.  Create it so the new name and the old one
     are registered in the replacement table so that we can fix the SSA web
     after adding all the ASSERT_EXPRs.  */
  tree new_def = create_new_def_for (v, assertion, NULL);
  /* Make sure we preserve abnormalness throughout an ASSERT_EXPR chain
     given we have to be able to fully propagate those out to re-create
     valid SSA when removing the asserts.  */
  if (SSA_NAME_OCCURS_IN_ABNORMAL_PHI (v))
    SSA_NAME_OCCURS_IN_ABNORMAL_PHI (new_def) = 1;

  return assertion;
}

/* Dump all the registered assertions for NAME to FILE.  */

void
vrp_asserts::dump (FILE *file, tree name)
{
  assert_locus *loc;

  fprintf (file, "Assertions to be inserted for ");
  print_generic_expr (file, name);
  fprintf (file, "\n");

  loc = asserts_for[SSA_NAME_VERSION (name)];
  while (loc)
    {
      fprintf (file, "\t");
      print_gimple_stmt (file, gsi_stmt (loc->si), 0);
      fprintf (file, "\n\tBB #%d", loc->bb->index);
      if (loc->e)
	{
	  fprintf (file, "\n\tEDGE %d->%d", loc->e->src->index,
	           loc->e->dest->index);
	  dump_edge_info (file, loc->e, dump_flags, 0);
	}
      fprintf (file, "\n\tPREDICATE: ");
      print_generic_expr (file, loc->expr);
      fprintf (file, " %s ", get_tree_code_name (loc->comp_code));
      print_generic_expr (file, loc->val);
      fprintf (file, "\n\n");
      loc = loc->next;
    }

  fprintf (file, "\n");
}

/* Dump all the registered assertions for all the names to FILE.  */

void
vrp_asserts::dump (FILE *file)
{
  unsigned i;
  bitmap_iterator bi;

  fprintf (file, "\nASSERT_EXPRs to be inserted\n\n");
  EXECUTE_IF_SET_IN_BITMAP (need_assert_for, 0, i, bi)
    dump (file, ssa_name (i));
  fprintf (file, "\n");
}

/* If NAME doesn't have an ASSERT_EXPR registered for asserting
   'EXPR COMP_CODE VAL' at a location that dominates block BB or
   E->DEST, then register this location as a possible insertion point
   for ASSERT_EXPR <NAME, EXPR COMP_CODE VAL>.

   BB, E and SI provide the exact insertion point for the new
   ASSERT_EXPR.  If BB is NULL, then the ASSERT_EXPR is to be inserted
   on edge E.  Otherwise, if E is NULL, the ASSERT_EXPR is inserted on
   BB.  If SI points to a COND_EXPR or a SWITCH_EXPR statement, then E
   must not be NULL.  */

void
vrp_asserts::register_new_assert_for (tree name, tree expr,
				      enum tree_code comp_code,
				      tree val,
				      basic_block bb,
				      edge e,
				      gimple_stmt_iterator si)
{
  assert_locus *n, *loc, *last_loc;
  basic_block dest_bb;

  gcc_checking_assert (bb == NULL || e == NULL);

  if (e == NULL)
    gcc_checking_assert (gimple_code (gsi_stmt (si)) != GIMPLE_COND
			 && gimple_code (gsi_stmt (si)) != GIMPLE_SWITCH);

  /* Never build an assert comparing against an integer constant with
     TREE_OVERFLOW set.  This confuses our undefined overflow warning
     machinery.  */
  if (TREE_OVERFLOW_P (val))
    val = drop_tree_overflow (val);

  /* The new assertion A will be inserted at BB or E.  We need to
     determine if the new location is dominated by a previously
     registered location for A.  If we are doing an edge insertion,
     assume that A will be inserted at E->DEST.  Note that this is not
     necessarily true.

     If E is a critical edge, it will be split.  But even if E is
     split, the new block will dominate the same set of blocks that
     E->DEST dominates.

     The reverse, however, is not true, blocks dominated by E->DEST
     will not be dominated by the new block created to split E.  So,
     if the insertion location is on a critical edge, we will not use
     the new location to move another assertion previously registered
     at a block dominated by E->DEST.  */
  dest_bb = (bb) ? bb : e->dest;

  /* If NAME already has an ASSERT_EXPR registered for COMP_CODE and
     VAL at a block dominating DEST_BB, then we don't need to insert a new
     one.  Similarly, if the same assertion already exists at a block
     dominated by DEST_BB and the new location is not on a critical
     edge, then update the existing location for the assertion (i.e.,
     move the assertion up in the dominance tree).

     Note, this is implemented as a simple linked list because there
     should not be more than a handful of assertions registered per
     name.  If this becomes a performance problem, a table hashed by
     COMP_CODE and VAL could be implemented.  */
  loc = asserts_for[SSA_NAME_VERSION (name)];
  last_loc = loc;
  while (loc)
    {
      if (loc->comp_code == comp_code
	  && (loc->val == val
	      || operand_equal_p (loc->val, val, 0))
	  && (loc->expr == expr
	      || operand_equal_p (loc->expr, expr, 0)))
	{
	  /* If E is not a critical edge and DEST_BB
	     dominates the existing location for the assertion, move
	     the assertion up in the dominance tree by updating its
	     location information.  */
	  if ((e == NULL || !EDGE_CRITICAL_P (e))
	      && dominated_by_p (CDI_DOMINATORS, loc->bb, dest_bb))
	    {
	      loc->bb = dest_bb;
	      loc->e = e;
	      loc->si = si;
	      return;
	    }
	}

      /* Update the last node of the list and move to the next one.  */
      last_loc = loc;
      loc = loc->next;
    }

  /* If we didn't find an assertion already registered for
     NAME COMP_CODE VAL, add a new one at the end of the list of
     assertions associated with NAME.  */
  n = XNEW (struct assert_locus);
  n->bb = dest_bb;
  n->e = e;
  n->si = si;
  n->comp_code = comp_code;
  n->val = val;
  n->expr = expr;
  n->next = NULL;

  if (last_loc)
    last_loc->next = n;
  else
    asserts_for[SSA_NAME_VERSION (name)] = n;

  bitmap_set_bit (need_assert_for, SSA_NAME_VERSION (name));
}

/* Finish found ASSERTS for E and register them at GSI.  */

void
vrp_asserts::finish_register_edge_assert_for (edge e,
					      gimple_stmt_iterator gsi,
					      vec<assert_info> &asserts)
{
  for (unsigned i = 0; i < asserts.length (); ++i)
    /* Only register an ASSERT_EXPR if NAME was found in the sub-graph
       reachable from E.  */
    if (live.live_on_edge_p (asserts[i].name, e))
      register_new_assert_for (asserts[i].name, asserts[i].expr,
			       asserts[i].comp_code, asserts[i].val,
			       NULL, e, gsi);
}

/* Determine whether the outgoing edges of BB should receive an
   ASSERT_EXPR for each of the operands of BB's LAST statement.
   The last statement of BB must be a COND_EXPR.

   If any of the sub-graphs rooted at BB have an interesting use of
   the predicate operands, an assert location node is added to the
   list of assertions for the corresponding operands.  */

void
vrp_asserts::find_conditional_asserts (basic_block bb, gcond *last)
{
  gimple_stmt_iterator bsi;
  tree op;
  edge_iterator ei;
  edge e;
  ssa_op_iter iter;

  bsi = gsi_for_stmt (last);

  /* Look for uses of the operands in each of the sub-graphs
     rooted at BB.  We need to check each of the outgoing edges
     separately, so that we know what kind of ASSERT_EXPR to
     insert.  */
  FOR_EACH_EDGE (e, ei, bb->succs)
    {
      if (e->dest == bb)
	continue;

      /* Register the necessary assertions for each operand in the
	 conditional predicate.  */
      auto_vec<assert_info, 8> asserts;
      FOR_EACH_SSA_TREE_OPERAND (op, last, iter, SSA_OP_USE)
	register_edge_assert_for (op, e,
				  gimple_cond_code (last),
				  gimple_cond_lhs (last),
				  gimple_cond_rhs (last), asserts);
      finish_register_edge_assert_for (e, bsi, asserts);
    }
}

/* Compare two case labels sorting first by the destination bb index
   and then by the case value.  */

int
vrp_asserts::compare_case_labels (const void *p1, const void *p2)
{
  const struct case_info *ci1 = (const struct case_info *) p1;
  const struct case_info *ci2 = (const struct case_info *) p2;
  int idx1 = ci1->bb->index;
  int idx2 = ci2->bb->index;

  if (idx1 < idx2)
    return -1;
  else if (idx1 == idx2)
    {
      /* Make sure the default label is first in a group.  */
      if (!CASE_LOW (ci1->expr))
	return -1;
      else if (!CASE_LOW (ci2->expr))
	return 1;
      else
	return tree_int_cst_compare (CASE_LOW (ci1->expr),
				     CASE_LOW (ci2->expr));
    }
  else
    return 1;
}

/* Determine whether the outgoing edges of BB should receive an
   ASSERT_EXPR for each of the operands of BB's LAST statement.
   The last statement of BB must be a SWITCH_EXPR.

   If any of the sub-graphs rooted at BB have an interesting use of
   the predicate operands, an assert location node is added to the
   list of assertions for the corresponding operands.  */

void
vrp_asserts::find_switch_asserts (basic_block bb, gswitch *last)
{
  gimple_stmt_iterator bsi;
  tree op;
  edge e;
  struct case_info *ci;
  size_t n = gimple_switch_num_labels (last);
#if GCC_VERSION >= 4000
  unsigned int idx;
#else
  /* Work around GCC 3.4 bug (PR 37086).  */
  volatile unsigned int idx;
#endif

  bsi = gsi_for_stmt (last);
  op = gimple_switch_index (last);
  if (TREE_CODE (op) != SSA_NAME)
    return;

  /* Build a vector of case labels sorted by destination label.  */
  ci = XNEWVEC (struct case_info, n);
  for (idx = 0; idx < n; ++idx)
    {
      ci[idx].expr = gimple_switch_label (last, idx);
      ci[idx].bb = label_to_block (fun, CASE_LABEL (ci[idx].expr));
    }
  edge default_edge = find_edge (bb, ci[0].bb);
  qsort (ci, n, sizeof (struct case_info), compare_case_labels);

  for (idx = 0; idx < n; ++idx)
    {
      tree min, max;
      tree cl = ci[idx].expr;
      basic_block cbb = ci[idx].bb;

      min = CASE_LOW (cl);
      max = CASE_HIGH (cl);

      /* If there are multiple case labels with the same destination
	 we need to combine them to a single value range for the edge.  */
      if (idx + 1 < n && cbb == ci[idx + 1].bb)
	{
	  /* Skip labels until the last of the group.  */
	  do {
	    ++idx;
	  } while (idx < n && cbb == ci[idx].bb);
	  --idx;

	  /* Pick up the maximum of the case label range.  */
	  if (CASE_HIGH (ci[idx].expr))
	    max = CASE_HIGH (ci[idx].expr);
	  else
	    max = CASE_LOW (ci[idx].expr);
	}

      /* Can't extract a useful assertion out of a range that includes the
	 default label.  */
      if (min == NULL_TREE)
	continue;

      /* Find the edge to register the assert expr on.  */
      e = find_edge (bb, cbb);

      /* Register the necessary assertions for the operand in the
	 SWITCH_EXPR.  */
      auto_vec<assert_info, 8> asserts;
      register_edge_assert_for (op, e,
				max ? GE_EXPR : EQ_EXPR,
				op, fold_convert (TREE_TYPE (op), min),
				asserts);
      if (max)
	register_edge_assert_for (op, e, LE_EXPR, op,
				  fold_convert (TREE_TYPE (op), max),
				  asserts);
      finish_register_edge_assert_for (e, bsi, asserts);
    }

  XDELETEVEC (ci);

  if (!live.live_on_edge_p (op, default_edge))
    return;

  /* Now register along the default label assertions that correspond to the
     anti-range of each label.  */
  int insertion_limit = param_max_vrp_switch_assertions;
  if (insertion_limit == 0)
    return;

  /* We can't do this if the default case shares a label with another case.  */
  tree default_cl = gimple_switch_default_label (last);
  for (idx = 1; idx < n; idx++)
    {
      tree min, max;
      tree cl = gimple_switch_label (last, idx);
      if (CASE_LABEL (cl) == CASE_LABEL (default_cl))
	continue;

      min = CASE_LOW (cl);
      max = CASE_HIGH (cl);

      /* Combine contiguous case ranges to reduce the number of assertions
	 to insert.  */
      for (idx = idx + 1; idx < n; idx++)
	{
	  tree next_min, next_max;
	  tree next_cl = gimple_switch_label (last, idx);
	  if (CASE_LABEL (next_cl) == CASE_LABEL (default_cl))
	    break;

	  next_min = CASE_LOW (next_cl);
	  next_max = CASE_HIGH (next_cl);

	  wide_int difference = (wi::to_wide (next_min)
				 - wi::to_wide (max ? max : min));
	  if (wi::eq_p (difference, 1))
	    max = next_max ? next_max : next_min;
	  else
	    break;
	}
      idx--;

      if (max == NULL_TREE)
	{
	  /* Register the assertion OP != MIN.  */
	  auto_vec<assert_info, 8> asserts;
	  min = fold_convert (TREE_TYPE (op), min);
	  register_edge_assert_for (op, default_edge, NE_EXPR, op, min,
				    asserts);
	  finish_register_edge_assert_for (default_edge, bsi, asserts);
	}
      else
	{
	  /* Register the assertion (unsigned)OP - MIN > (MAX - MIN),
	     which will give OP the anti-range ~[MIN,MAX].  */
	  tree uop = fold_convert (unsigned_type_for (TREE_TYPE (op)), op);
	  min = fold_convert (TREE_TYPE (uop), min);
	  max = fold_convert (TREE_TYPE (uop), max);

	  tree lhs = fold_build2 (MINUS_EXPR, TREE_TYPE (uop), uop, min);
	  tree rhs = int_const_binop (MINUS_EXPR, max, min);
	  register_new_assert_for (op, lhs, GT_EXPR, rhs,
				   NULL, default_edge, bsi);
	}

      if (--insertion_limit == 0)
	break;
    }
}

/* Traverse all the statements in block BB looking for statements that
   may generate useful assertions for the SSA names in their operand.
   If a statement produces a useful assertion A for name N_i, then the
   list of assertions already generated for N_i is scanned to
   determine if A is actually needed.

   If N_i already had the assertion A at a location dominating the
   current location, then nothing needs to be done.  Otherwise, the
   new location for A is recorded instead.

   1- For every statement S in BB, all the variables used by S are
      added to bitmap FOUND_IN_SUBGRAPH.

   2- If statement S uses an operand N in a way that exposes a known
      value range for N, then if N was not already generated by an
      ASSERT_EXPR, create a new assert location for N.  For instance,
      if N is a pointer and the statement dereferences it, we can
      assume that N is not NULL.

   3- COND_EXPRs are a special case of #2.  We can derive range
      information from the predicate but need to insert different
      ASSERT_EXPRs for each of the sub-graphs rooted at the
      conditional block.  If the last statement of BB is a conditional
      expression of the form 'X op Y', then

      a) Remove X and Y from the set FOUND_IN_SUBGRAPH.

      b) If the conditional is the only entry point to the sub-graph
	 corresponding to the THEN_CLAUSE, recurse into it.  On
	 return, if X and/or Y are marked in FOUND_IN_SUBGRAPH, then
	 an ASSERT_EXPR is added for the corresponding variable.

      c) Repeat step (b) on the ELSE_CLAUSE.

      d) Mark X and Y in FOUND_IN_SUBGRAPH.

      For instance,

	    if (a == 9)
	      b = a;
	    else
	      b = c + 1;

      In this case, an assertion on the THEN clause is useful to
      determine that 'a' is always 9 on that edge.  However, an assertion
      on the ELSE clause would be unnecessary.

   4- If BB does not end in a conditional expression, then we recurse
      into BB's dominator children.

   At the end of the recursive traversal, every SSA name will have a
   list of locations where ASSERT_EXPRs should be added.  When a new
   location for name N is found, it is registered by calling
   register_new_assert_for.  That function keeps track of all the
   registered assertions to prevent adding unnecessary assertions.
   For instance, if a pointer P_4 is dereferenced more than once in a
   dominator tree, only the location dominating all the dereference of
   P_4 will receive an ASSERT_EXPR.  */

void
vrp_asserts::find_assert_locations_in_bb (basic_block bb)
{
  gimple *last;

  last = last_stmt (bb);

  /* If BB's last statement is a conditional statement involving integer
     operands, determine if we need to add ASSERT_EXPRs.  */
  if (last
      && gimple_code (last) == GIMPLE_COND
      && !fp_predicate (last)
      && !ZERO_SSA_OPERANDS (last, SSA_OP_USE))
    find_conditional_asserts (bb, as_a <gcond *> (last));

  /* If BB's last statement is a switch statement involving integer
     operands, determine if we need to add ASSERT_EXPRs.  */
  if (last
      && gimple_code (last) == GIMPLE_SWITCH
      && !ZERO_SSA_OPERANDS (last, SSA_OP_USE))
    find_switch_asserts (bb, as_a <gswitch *> (last));

  /* Traverse all the statements in BB marking used names and looking
     for statements that may infer assertions for their used operands.  */
  for (gimple_stmt_iterator si = gsi_last_bb (bb); !gsi_end_p (si);
       gsi_prev (&si))
    {
      gimple *stmt;
      tree op;
      ssa_op_iter i;

      stmt = gsi_stmt (si);

      if (is_gimple_debug (stmt))
	continue;

      /* See if we can derive an assertion for any of STMT's operands.  */
      FOR_EACH_SSA_TREE_OPERAND (op, stmt, i, SSA_OP_USE)
	{
	  tree value;
	  enum tree_code comp_code;

	  /* If op is not live beyond this stmt, do not bother to insert
	     asserts for it.  */
	  if (!live.live_on_block_p (op, bb))
	    continue;

	  /* If OP is used in such a way that we can infer a value
	     range for it, and we don't find a previous assertion for
	     it, create a new assertion location node for OP.  */
	  if (infer_value_range (stmt, op, &comp_code, &value))
	    {
	      /* If we are able to infer a nonzero value range for OP,
		 then walk backwards through the use-def chain to see if OP
		 was set via a typecast.

		 If so, then we can also infer a nonzero value range
		 for the operand of the NOP_EXPR.  */
	      if (comp_code == NE_EXPR && integer_zerop (value))
		{
		  tree t = op;
		  gimple *def_stmt = SSA_NAME_DEF_STMT (t);

		  while (is_gimple_assign (def_stmt)
			 && CONVERT_EXPR_CODE_P
			     (gimple_assign_rhs_code (def_stmt))
			 && TREE_CODE
			     (gimple_assign_rhs1 (def_stmt)) == SSA_NAME
			 && POINTER_TYPE_P
			     (TREE_TYPE (gimple_assign_rhs1 (def_stmt))))
		    {
		      t = gimple_assign_rhs1 (def_stmt);
		      def_stmt = SSA_NAME_DEF_STMT (t);

		      /* Note we want to register the assert for the
			 operand of the NOP_EXPR after SI, not after the
			 conversion.  */
		      if (live.live_on_block_p (t, bb))
			register_new_assert_for (t, t, comp_code, value,
						 bb, NULL, si);
		    }
		}

	      register_new_assert_for (op, op, comp_code, value, bb, NULL, si);
	    }
	}

      /* Update live.  */
      FOR_EACH_SSA_TREE_OPERAND (op, stmt, i, SSA_OP_USE)
	live.set (op, bb);
      FOR_EACH_SSA_TREE_OPERAND (op, stmt, i, SSA_OP_DEF)
	live.clear (op, bb);
    }

  /* Traverse all PHI nodes in BB, updating live.  */
  for (gphi_iterator si = gsi_start_phis (bb); !gsi_end_p (si);
       gsi_next (&si))
    {
      use_operand_p arg_p;
      ssa_op_iter i;
      gphi *phi = si.phi ();
      tree res = gimple_phi_result (phi);

      if (virtual_operand_p (res))
	continue;

      FOR_EACH_PHI_ARG (arg_p, phi, i, SSA_OP_USE)
	{
	  tree arg = USE_FROM_PTR (arg_p);
	  if (TREE_CODE (arg) == SSA_NAME)
	    live.set (arg, bb);
	}

      live.clear (res, bb);
    }
}

/* Do an RPO walk over the function computing SSA name liveness
   on-the-fly and deciding on assert expressions to insert.  */

void
vrp_asserts::find_assert_locations (void)
{
  int *rpo = XNEWVEC (int, last_basic_block_for_fn (fun));
  int *bb_rpo = XNEWVEC (int, last_basic_block_for_fn (fun));
  int *last_rpo = XCNEWVEC (int, last_basic_block_for_fn (fun));
  int rpo_cnt, i;

  rpo_cnt = pre_and_rev_post_order_compute (NULL, rpo, false);
  for (i = 0; i < rpo_cnt; ++i)
    bb_rpo[rpo[i]] = i;

  /* Pre-seed loop latch liveness from loop header PHI nodes.  Due to
     the order we compute liveness and insert asserts we otherwise
     fail to insert asserts into the loop latch.  */
  for (auto loop : loops_list (cfun, 0))
    {
      i = loop->latch->index;
      unsigned int j = single_succ_edge (loop->latch)->dest_idx;
      for (gphi_iterator gsi = gsi_start_phis (loop->header);
	   !gsi_end_p (gsi); gsi_next (&gsi))
	{
	  gphi *phi = gsi.phi ();
	  if (virtual_operand_p (gimple_phi_result (phi)))
	    continue;
	  tree arg = gimple_phi_arg_def (phi, j);
	  if (TREE_CODE (arg) == SSA_NAME)
	    live.set (arg, loop->latch);
	}
    }

  for (i = rpo_cnt - 1; i >= 0; --i)
    {
      basic_block bb = BASIC_BLOCK_FOR_FN (fun, rpo[i]);
      edge e;
      edge_iterator ei;

      /* Process BB and update the live information with uses in
         this block.  */
      find_assert_locations_in_bb (bb);

      /* Merge liveness into the predecessor blocks and free it.  */
      if (!live.block_has_live_names_p (bb))
	{
	  int pred_rpo = i;
	  FOR_EACH_EDGE (e, ei, bb->preds)
	    {
	      int pred = e->src->index;
	      if ((e->flags & EDGE_DFS_BACK) || pred == ENTRY_BLOCK)
		continue;

	      live.merge (e->src, bb);

	      if (bb_rpo[pred] < pred_rpo)
		pred_rpo = bb_rpo[pred];
	    }

	  /* Record the RPO number of the last visited block that needs
	     live information from this block.  */
	  last_rpo[rpo[i]] = pred_rpo;
	}
      else
	live.clear_block (bb);

      /* We can free all successors live bitmaps if all their
         predecessors have been visited already.  */
      FOR_EACH_EDGE (e, ei, bb->succs)
	if (last_rpo[e->dest->index] == i)
	  live.clear_block (e->dest);
    }

  XDELETEVEC (rpo);
  XDELETEVEC (bb_rpo);
  XDELETEVEC (last_rpo);
}

/* Create an ASSERT_EXPR for NAME and insert it in the location
   indicated by LOC.  Return true if we made any edge insertions.  */

bool
vrp_asserts::process_assert_insertions_for (tree name, assert_locus *loc)
{
  /* Build the comparison expression NAME_i COMP_CODE VAL.  */
  gimple *stmt;
  tree cond;
  gimple *assert_stmt;
  edge_iterator ei;
  edge e;

  /* If we have X <=> X do not insert an assert expr for that.  */
  if (loc->expr == loc->val)
    return false;

  cond = build2 (loc->comp_code, boolean_type_node, loc->expr, loc->val);
  assert_stmt = build_assert_expr_for (cond, name);
  if (loc->e)
    {
      /* We have been asked to insert the assertion on an edge.  This
	 is used only by COND_EXPR and SWITCH_EXPR assertions.  */
      gcc_checking_assert (gimple_code (gsi_stmt (loc->si)) == GIMPLE_COND
			   || (gimple_code (gsi_stmt (loc->si))
			       == GIMPLE_SWITCH));

      gsi_insert_on_edge (loc->e, assert_stmt);
      return true;
    }

  /* If the stmt iterator points at the end then this is an insertion
     at the beginning of a block.  */
  if (gsi_end_p (loc->si))
    {
      gimple_stmt_iterator si = gsi_after_labels (loc->bb);
      gsi_insert_before (&si, assert_stmt, GSI_SAME_STMT);
      return false;

    }
  /* Otherwise, we can insert right after LOC->SI iff the
     statement must not be the last statement in the block.  */
  stmt = gsi_stmt (loc->si);
  if (!stmt_ends_bb_p (stmt))
    {
      gsi_insert_after (&loc->si, assert_stmt, GSI_SAME_STMT);
      return false;
    }

  /* If STMT must be the last statement in BB, we can only insert new
     assertions on the non-abnormal edge out of BB.  Note that since
     STMT is not control flow, there may only be one non-abnormal/eh edge
     out of BB.  */
  FOR_EACH_EDGE (e, ei, loc->bb->succs)
    if (!(e->flags & (EDGE_ABNORMAL|EDGE_EH)))
      {
	gsi_insert_on_edge (e, assert_stmt);
	return true;
      }

  gcc_unreachable ();
}

/* Qsort helper for sorting assert locations.  If stable is true, don't
   use iterative_hash_expr because it can be unstable for -fcompare-debug,
   on the other side some pointers might be NULL.  */

template <bool stable>
int
vrp_asserts::compare_assert_loc (const void *pa, const void *pb)
{
  assert_locus * const a = *(assert_locus * const *)pa;
  assert_locus * const b = *(assert_locus * const *)pb;

  /* If stable, some asserts might be optimized away already, sort
     them last.  */
  if (stable)
    {
      if (a == NULL)
	return b != NULL;
      else if (b == NULL)
	return -1;
    }

  if (a->e == NULL && b->e != NULL)
    return 1;
  else if (a->e != NULL && b->e == NULL)
    return -1;

  /* After the above checks, we know that (a->e == NULL) == (b->e == NULL),
     no need to test both a->e and b->e.  */

  /* Sort after destination index.  */
  if (a->e == NULL)
    ;
  else if (a->e->dest->index > b->e->dest->index)
    return 1;
  else if (a->e->dest->index < b->e->dest->index)
    return -1;

  /* Sort after comp_code.  */
  if (a->comp_code > b->comp_code)
    return 1;
  else if (a->comp_code < b->comp_code)
    return -1;

  hashval_t ha, hb;

  /* E.g. if a->val is ADDR_EXPR of a VAR_DECL, iterative_hash_expr
     uses DECL_UID of the VAR_DECL, so sorting might differ between
     -g and -g0.  When doing the removal of redundant assert exprs
     and commonization to successors, this does not matter, but for
     the final sort needs to be stable.  */
  if (stable)
    {
      ha = 0;
      hb = 0;
    }
  else
    {
      ha = iterative_hash_expr (a->expr, iterative_hash_expr (a->val, 0));
      hb = iterative_hash_expr (b->expr, iterative_hash_expr (b->val, 0));
    }

  /* Break the tie using hashing and source/bb index.  */
  if (ha == hb)
    return (a->e != NULL
	    ? a->e->src->index - b->e->src->index
	    : a->bb->index - b->bb->index);
  return ha > hb ? 1 : -1;
}

/* Process all the insertions registered for every name N_i registered
   in NEED_ASSERT_FOR.  The list of assertions to be inserted are
   found in ASSERTS_FOR[i].  */

void
vrp_asserts::process_assert_insertions ()
{
  unsigned i;
  bitmap_iterator bi;
  bool update_edges_p = false;
  int num_asserts = 0;

  if (dump_file && (dump_flags & TDF_DETAILS))
    dump (dump_file);

  EXECUTE_IF_SET_IN_BITMAP (need_assert_for, 0, i, bi)
    {
      assert_locus *loc = asserts_for[i];
      gcc_assert (loc);

      auto_vec<assert_locus *, 16> asserts;
      for (; loc; loc = loc->next)
	asserts.safe_push (loc);
      asserts.qsort (compare_assert_loc<false>);

      /* Push down common asserts to successors and remove redundant ones.  */
      unsigned ecnt = 0;
      assert_locus *common = NULL;
      unsigned commonj = 0;
      for (unsigned j = 0; j < asserts.length (); ++j)
	{
	  loc = asserts[j];
	  if (! loc->e)
	    common = NULL;
	  else if (! common
		   || loc->e->dest != common->e->dest
		   || loc->comp_code != common->comp_code
		   || ! operand_equal_p (loc->val, common->val, 0)
		   || ! operand_equal_p (loc->expr, common->expr, 0))
	    {
	      commonj = j;
	      common = loc;
	      ecnt = 1;
	    }
	  else if (loc->e == asserts[j-1]->e)
	    {
	      /* Remove duplicate asserts.  */
	      if (commonj == j - 1)
		{
		  commonj = j;
		  common = loc;
		}
	      free (asserts[j-1]);
	      asserts[j-1] = NULL;
	    }
	  else
	    {
	      ecnt++;
	      if (EDGE_COUNT (common->e->dest->preds) == ecnt)
		{
		  /* We have the same assertion on all incoming edges of a BB.
		     Insert it at the beginning of that block.  */
		  loc->bb = loc->e->dest;
		  loc->e = NULL;
		  loc->si = gsi_none ();
		  common = NULL;
		  /* Clear asserts commoned.  */
		  for (; commonj != j; ++commonj)
		    if (asserts[commonj])
		      {
			free (asserts[commonj]);
			asserts[commonj] = NULL;
		      }
		}
	    }
	}

      /* The asserts vector sorting above might be unstable for
	 -fcompare-debug, sort again to ensure a stable sort.  */
      asserts.qsort (compare_assert_loc<true>);
      for (unsigned j = 0; j < asserts.length (); ++j)
	{
	  loc = asserts[j];
	  if (! loc)
	    break;
	  update_edges_p |= process_assert_insertions_for (ssa_name (i), loc);
	  num_asserts++;
	  free (loc);
	}
    }

  if (update_edges_p)
    gsi_commit_edge_inserts ();

  statistics_counter_event (fun, "Number of ASSERT_EXPR expressions inserted",
			    num_asserts);
}

/* Traverse the flowgraph looking for conditional jumps to insert range
   expressions.  These range expressions are meant to provide information
   to optimizations that need to reason in terms of value ranges.  They
   will not be expanded into RTL.  For instance, given:

   x = ...
   y = ...
   if (x < y)
     y = x - 2;
   else
     x = y + 3;

   this pass will transform the code into:

   x = ...
   y = ...
   if (x < y)
    {
      x = ASSERT_EXPR <x, x < y>
      y = x - 2
    }
   else
    {
      y = ASSERT_EXPR <y, x >= y>
      x = y + 3
    }

   The idea is that once copy and constant propagation have run, other
   optimizations will be able to determine what ranges of values can 'x'
   take in different paths of the code, simply by checking the reaching
   definition of 'x'.  */

void
vrp_asserts::insert_range_assertions (void)
{
  need_assert_for = BITMAP_ALLOC (NULL);
  asserts_for = XCNEWVEC (assert_locus *, num_ssa_names);

  calculate_dominance_info (CDI_DOMINATORS);

  find_assert_locations ();
  if (!bitmap_empty_p (need_assert_for))
    {
      process_assert_insertions ();
      update_ssa (TODO_update_ssa_no_phi);
    }

  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fprintf (dump_file, "\nSSA form after inserting ASSERT_EXPRs\n");
      dump_function_to_file (current_function_decl, dump_file, dump_flags);
    }

  free (asserts_for);
  BITMAP_FREE (need_assert_for);
}

/* Return true if all imm uses of VAR are either in STMT, or
   feed (optionally through a chain of single imm uses) GIMPLE_COND
   in basic block COND_BB.  */

bool
vrp_asserts::all_imm_uses_in_stmt_or_feed_cond (tree var,
						gimple *stmt,
						basic_block cond_bb)
{
  use_operand_p use_p, use2_p;
  imm_use_iterator iter;

  FOR_EACH_IMM_USE_FAST (use_p, iter, var)
    if (USE_STMT (use_p) != stmt)
      {
	gimple *use_stmt = USE_STMT (use_p), *use_stmt2;
	if (is_gimple_debug (use_stmt))
	  continue;
	while (is_gimple_assign (use_stmt)
	       && TREE_CODE (gimple_assign_lhs (use_stmt)) == SSA_NAME
	       && single_imm_use (gimple_assign_lhs (use_stmt),
				  &use2_p, &use_stmt2))
	  use_stmt = use_stmt2;
	if (gimple_code (use_stmt) != GIMPLE_COND
	    || gimple_bb (use_stmt) != cond_bb)
	  return false;
      }
  return true;
}

/* Convert range assertion expressions into the implied copies and
   copy propagate away the copies.  Doing the trivial copy propagation
   here avoids the need to run the full copy propagation pass after
   VRP.

   FIXME, this will eventually lead to copy propagation removing the
   names that had useful range information attached to them.  For
   instance, if we had the assertion N_i = ASSERT_EXPR <N_j, N_j > 3>,
   then N_i will have the range [3, +INF].

   However, by converting the assertion into the implied copy
   operation N_i = N_j, we will then copy-propagate N_j into the uses
   of N_i and lose the range information.  We may want to hold on to
   ASSERT_EXPRs a little while longer as the ranges could be used in
   things like jump threading.

   The problem with keeping ASSERT_EXPRs around is that passes after
   VRP need to handle them appropriately.

   Another approach would be to make the range information a first
   class property of the SSA_NAME so that it can be queried from
   any pass.  This is made somewhat more complex by the need for
   multiple ranges to be associated with one SSA_NAME.  */

void
vrp_asserts::remove_range_assertions ()
{
  basic_block bb;
  gimple_stmt_iterator si;
  /* 1 if looking at ASSERT_EXPRs immediately at the beginning of
     a basic block preceeded by GIMPLE_COND branching to it and
     __builtin_trap, -1 if not yet checked, 0 otherwise.  */
  int is_unreachable;

  /* Note that the BSI iterator bump happens at the bottom of the
     loop and no bump is necessary if we're removing the statement
     referenced by the current BSI.  */
  FOR_EACH_BB_FN (bb, fun)
    for (si = gsi_after_labels (bb), is_unreachable = -1; !gsi_end_p (si);)
      {
	gimple *stmt = gsi_stmt (si);

	if (is_gimple_assign (stmt)
	    && gimple_assign_rhs_code (stmt) == ASSERT_EXPR)
	  {
	    tree lhs = gimple_assign_lhs (stmt);
	    tree rhs = gimple_assign_rhs1 (stmt);
	    tree var;

	    var = ASSERT_EXPR_VAR (rhs);

	    if (TREE_CODE (var) == SSA_NAME
		&& !POINTER_TYPE_P (TREE_TYPE (lhs))
		&& SSA_NAME_RANGE_INFO (lhs))
	      {
		if (is_unreachable == -1)
		  {
		    is_unreachable = 0;
		    if (single_pred_p (bb)
			&& assert_unreachable_fallthru_edge_p
						    (single_pred_edge (bb)))
		      is_unreachable = 1;
		  }
		/* Handle
		   if (x_7 >= 10 && x_7 < 20)
		     __builtin_unreachable ();
		   x_8 = ASSERT_EXPR <x_7, ...>;
		   if the only uses of x_7 are in the ASSERT_EXPR and
		   in the condition.  In that case, we can copy the
		   range info from x_8 computed in this pass also
		   for x_7.  */
		if (is_unreachable
		    && all_imm_uses_in_stmt_or_feed_cond (var, stmt,
							  single_pred (bb)))
		  {
		    set_range_info (var, SSA_NAME_RANGE_TYPE (lhs),
				    SSA_NAME_RANGE_INFO (lhs)->get_min (),
				    SSA_NAME_RANGE_INFO (lhs)->get_max ());
		    maybe_set_nonzero_bits (single_pred_edge (bb), var);
		  }
	      }

	    /* Propagate the RHS into every use of the LHS.  For SSA names
	       also propagate abnormals as it merely restores the original
	       IL in this case (an replace_uses_by would assert).  */
	    if (TREE_CODE (var) == SSA_NAME)
	      {
		imm_use_iterator iter;
		use_operand_p use_p;
		gimple *use_stmt;
		FOR_EACH_IMM_USE_STMT (use_stmt, iter, lhs)
		  FOR_EACH_IMM_USE_ON_STMT (use_p, iter)
		    SET_USE (use_p, var);
	      }
	    else
	      replace_uses_by (lhs, var);

	    /* And finally, remove the copy, it is not needed.  */
	    gsi_remove (&si, true);
	    release_defs (stmt);
	  }
	else
	  {
	    if (!is_gimple_debug (gsi_stmt (si)))
	      is_unreachable = 0;
	    gsi_next (&si);
	  }
      }
}

class vrp_prop : public ssa_propagation_engine
{
public:
  vrp_prop (vr_values *v)
    : ssa_propagation_engine (),
      m_vr_values (v) { }

  void initialize (struct function *);
  void finalize ();

private:
  enum ssa_prop_result visit_stmt (gimple *, edge *, tree *) FINAL OVERRIDE;
  enum ssa_prop_result visit_phi (gphi *) FINAL OVERRIDE;

  struct function *fun;
  vr_values *m_vr_values;
};

/* Initialization required by ssa_propagate engine.  */

void
vrp_prop::initialize (struct function *fn)
{
  basic_block bb;
  fun = fn;

  FOR_EACH_BB_FN (bb, fun)
    {
      for (gphi_iterator si = gsi_start_phis (bb); !gsi_end_p (si);
	   gsi_next (&si))
	{
	  gphi *phi = si.phi ();
	  if (!stmt_interesting_for_vrp (phi))
	    {
	      tree lhs = PHI_RESULT (phi);
	      m_vr_values->set_def_to_varying (lhs);
	      prop_set_simulate_again (phi, false);
	    }
	  else
	    prop_set_simulate_again (phi, true);
	}

      for (gimple_stmt_iterator si = gsi_start_bb (bb); !gsi_end_p (si);
	   gsi_next (&si))
        {
	  gimple *stmt = gsi_stmt (si);

 	  /* If the statement is a control insn, then we do not
 	     want to avoid simulating the statement once.  Failure
 	     to do so means that those edges will never get added.  */
	  if (stmt_ends_bb_p (stmt))
	    prop_set_simulate_again (stmt, true);
	  else if (!stmt_interesting_for_vrp (stmt))
	    {
	      m_vr_values->set_defs_to_varying (stmt);
	      prop_set_simulate_again (stmt, false);
	    }
	  else
	    prop_set_simulate_again (stmt, true);
	}
    }
}

/* Evaluate statement STMT.  If the statement produces a useful range,
   return SSA_PROP_INTERESTING and record the SSA name with the
   interesting range into *OUTPUT_P.

   If STMT is a conditional branch and we can determine its truth
   value, the taken edge is recorded in *TAKEN_EDGE_P.

   If STMT produces a varying value, return SSA_PROP_VARYING.  */

enum ssa_prop_result
vrp_prop::visit_stmt (gimple *stmt, edge *taken_edge_p, tree *output_p)
{
  tree lhs = gimple_get_lhs (stmt);
  value_range_equiv vr;
  m_vr_values->extract_range_from_stmt (stmt, taken_edge_p, output_p, &vr);

  if (*output_p)
    {
      if (m_vr_values->update_value_range (*output_p, &vr))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fprintf (dump_file, "Found new range for ");
	      print_generic_expr (dump_file, *output_p);
	      fprintf (dump_file, ": ");
	      dump_value_range (dump_file, &vr);
	      fprintf (dump_file, "\n");
	    }

	  if (vr.varying_p ())
	    return SSA_PROP_VARYING;

	  return SSA_PROP_INTERESTING;
	}
      return SSA_PROP_NOT_INTERESTING;
    }

  if (is_gimple_call (stmt) && gimple_call_internal_p (stmt))
    switch (gimple_call_internal_fn (stmt))
      {
      case IFN_ADD_OVERFLOW:
      case IFN_SUB_OVERFLOW:
      case IFN_MUL_OVERFLOW:
      case IFN_ATOMIC_COMPARE_EXCHANGE:
	/* These internal calls return _Complex integer type,
	   which VRP does not track, but the immediate uses
	   thereof might be interesting.  */
	if (lhs && TREE_CODE (lhs) == SSA_NAME)
	  {
	    imm_use_iterator iter;
	    use_operand_p use_p;
	    enum ssa_prop_result res = SSA_PROP_VARYING;

	    m_vr_values->set_def_to_varying (lhs);

	    FOR_EACH_IMM_USE_FAST (use_p, iter, lhs)
	      {
		gimple *use_stmt = USE_STMT (use_p);
		if (!is_gimple_assign (use_stmt))
		  continue;
		enum tree_code rhs_code = gimple_assign_rhs_code (use_stmt);
		if (rhs_code != REALPART_EXPR && rhs_code != IMAGPART_EXPR)
		  continue;
		tree rhs1 = gimple_assign_rhs1 (use_stmt);
		tree use_lhs = gimple_assign_lhs (use_stmt);
		if (TREE_CODE (rhs1) != rhs_code
		    || TREE_OPERAND (rhs1, 0) != lhs
		    || TREE_CODE (use_lhs) != SSA_NAME
		    || !stmt_interesting_for_vrp (use_stmt)
		    || (!INTEGRAL_TYPE_P (TREE_TYPE (use_lhs))
			|| !TYPE_MIN_VALUE (TREE_TYPE (use_lhs))
			|| !TYPE_MAX_VALUE (TREE_TYPE (use_lhs))))
		  continue;

		/* If there is a change in the value range for any of the
		   REALPART_EXPR/IMAGPART_EXPR immediate uses, return
		   SSA_PROP_INTERESTING.  If there are any REALPART_EXPR
		   or IMAGPART_EXPR immediate uses, but none of them have
		   a change in their value ranges, return
		   SSA_PROP_NOT_INTERESTING.  If there are no
		   {REAL,IMAG}PART_EXPR uses at all,
		   return SSA_PROP_VARYING.  */
		value_range_equiv new_vr;
		m_vr_values->extract_range_basic (&new_vr, use_stmt);
		const value_range_equiv *old_vr
		  = m_vr_values->get_value_range (use_lhs);
		if (!old_vr->equal_p (new_vr, /*ignore_equivs=*/false))
		  res = SSA_PROP_INTERESTING;
		else
		  res = SSA_PROP_NOT_INTERESTING;
		new_vr.equiv_clear ();
		if (res == SSA_PROP_INTERESTING)
		  {
		    *output_p = lhs;
		    return res;
		  }
	      }

	    return res;
	  }
	break;
      default:
	break;
      }

  /* All other statements produce nothing of interest for VRP, so mark
     their outputs varying and prevent further simulation.  */
  m_vr_values->set_defs_to_varying (stmt);

  return (*taken_edge_p) ? SSA_PROP_INTERESTING : SSA_PROP_VARYING;
}

/* Visit all arguments for PHI node PHI that flow through executable
   edges.  If a valid value range can be derived from all the incoming
   value ranges, set a new range for the LHS of PHI.  */

enum ssa_prop_result
vrp_prop::visit_phi (gphi *phi)
{
  tree lhs = PHI_RESULT (phi);
  value_range_equiv vr_result;
  m_vr_values->extract_range_from_phi_node (phi, &vr_result);
  if (m_vr_values->update_value_range (lhs, &vr_result))
    {
      if (dump_file && (dump_flags & TDF_DETAILS))
	{
	  fprintf (dump_file, "Found new range for ");
	  print_generic_expr (dump_file, lhs);
	  fprintf (dump_file, ": ");
	  dump_value_range (dump_file, &vr_result);
	  fprintf (dump_file, "\n");
	}

      if (vr_result.varying_p ())
	return SSA_PROP_VARYING;

      return SSA_PROP_INTERESTING;
    }

  /* Nothing changed, don't add outgoing edges.  */
  return SSA_PROP_NOT_INTERESTING;
}

/* Traverse all the blocks folding conditionals with known ranges.  */

void
vrp_prop::finalize ()
{
  size_t i;

  /* We have completed propagating through the lattice.  */
  m_vr_values->set_lattice_propagation_complete ();

  if (dump_file)
    {
      fprintf (dump_file, "\nValue ranges after VRP:\n\n");
      m_vr_values->dump (dump_file);
      fprintf (dump_file, "\n");
    }

  /* Set value range to non pointer SSA_NAMEs.  */
  for (i = 0; i < num_ssa_names; i++)
    {
      tree name = ssa_name (i);
      if (!name)
	continue;

      const value_range_equiv *vr = m_vr_values->get_value_range (name);
      if (!name || vr->varying_p () || !vr->constant_p ())
	continue;

      if (POINTER_TYPE_P (TREE_TYPE (name))
	  && range_includes_zero_p (vr) == 0)
	set_ptr_nonnull (name);
      else if (!POINTER_TYPE_P (TREE_TYPE (name)))
	set_range_info (name, *vr);
    }
}

class vrp_folder : public substitute_and_fold_engine
{
 public:
  vrp_folder (vr_values *v)
    : substitute_and_fold_engine (/* Fold all stmts.  */ true),
      m_vr_values (v), simplifier (v)
    {  }

private:
  tree value_of_expr (tree name, gimple *stmt) OVERRIDE
    {
      return m_vr_values->value_of_expr (name, stmt);
    }
  bool fold_stmt (gimple_stmt_iterator *) FINAL OVERRIDE;
  bool fold_predicate_in (gimple_stmt_iterator *);

  vr_values *m_vr_values;
  simplify_using_ranges simplifier;
};

/* If the statement pointed by SI has a predicate whose value can be
   computed using the value range information computed by VRP, compute
   its value and return true.  Otherwise, return false.  */

bool
vrp_folder::fold_predicate_in (gimple_stmt_iterator *si)
{
  bool assignment_p = false;
  tree val;
  gimple *stmt = gsi_stmt (*si);

  if (is_gimple_assign (stmt)
      && TREE_CODE_CLASS (gimple_assign_rhs_code (stmt)) == tcc_comparison)
    {
      assignment_p = true;
      val = simplifier.vrp_evaluate_conditional (gimple_assign_rhs_code (stmt),
						 gimple_assign_rhs1 (stmt),
						 gimple_assign_rhs2 (stmt),
						 stmt);
    }
  else if (gcond *cond_stmt = dyn_cast <gcond *> (stmt))
    val = simplifier.vrp_evaluate_conditional (gimple_cond_code (cond_stmt),
					       gimple_cond_lhs (cond_stmt),
					       gimple_cond_rhs (cond_stmt),
					       stmt);
  else
    return false;

  if (val)
    {
      if (assignment_p)
	val = fold_convert (TREE_TYPE (gimple_assign_lhs (stmt)), val);

      if (dump_file)
	{
	  fprintf (dump_file, "Folding predicate ");
	  print_gimple_expr (dump_file, stmt, 0);
	  fprintf (dump_file, " to ");
	  print_generic_expr (dump_file, val);
	  fprintf (dump_file, "\n");
	}

      if (is_gimple_assign (stmt))
	gimple_assign_set_rhs_from_tree (si, val);
      else
	{
	  gcc_assert (gimple_code (stmt) == GIMPLE_COND);
	  gcond *cond_stmt = as_a <gcond *> (stmt);
	  if (integer_zerop (val))
	    gimple_cond_make_false (cond_stmt);
	  else if (integer_onep (val))
	    gimple_cond_make_true (cond_stmt);
	  else
	    gcc_unreachable ();
	}

      return true;
    }

  return false;
}

/* Callback for substitute_and_fold folding the stmt at *SI.  */

bool
vrp_folder::fold_stmt (gimple_stmt_iterator *si)
{
  if (fold_predicate_in (si))
    return true;

  return simplifier.simplify (si);
}

/* STMT is a conditional at the end of a basic block.

   If the conditional is of the form SSA_NAME op constant and the SSA_NAME
   was set via a type conversion, try to replace the SSA_NAME with the RHS
   of the type conversion.  Doing so makes the conversion dead which helps
   subsequent passes.  */

static void
vrp_simplify_cond_using_ranges (range_query *query, gcond *stmt)
{
  tree op0 = gimple_cond_lhs (stmt);
  tree op1 = gimple_cond_rhs (stmt);

  /* If we have a comparison of an SSA_NAME (OP0) against a constant,
     see if OP0 was set by a type conversion where the source of
     the conversion is another SSA_NAME with a range that fits
     into the range of OP0's type.

     If so, the conversion is redundant as the earlier SSA_NAME can be
     used for the comparison directly if we just massage the constant in the
     comparison.  */
  if (TREE_CODE (op0) == SSA_NAME
      && TREE_CODE (op1) == INTEGER_CST)
    {
      gimple *def_stmt = SSA_NAME_DEF_STMT (op0);
      tree innerop;

      if (!is_gimple_assign (def_stmt))
	return;

      switch (gimple_assign_rhs_code (def_stmt))
	{
	CASE_CONVERT:
	  innerop = gimple_assign_rhs1 (def_stmt);
	  break;
	case VIEW_CONVERT_EXPR:
	  innerop = TREE_OPERAND (gimple_assign_rhs1 (def_stmt), 0);
	  if (!INTEGRAL_TYPE_P (TREE_TYPE (innerop)))
	    return;
	  break;
	default:
	  return;
	}

      if (TREE_CODE (innerop) == SSA_NAME
	  && !POINTER_TYPE_P (TREE_TYPE (innerop))
	  && !SSA_NAME_OCCURS_IN_ABNORMAL_PHI (innerop)
	  && desired_pro_or_demotion_p (TREE_TYPE (innerop), TREE_TYPE (op0)))
	{
	  const value_range *vr = query->get_value_range (innerop);

	  if (range_int_cst_p (vr)
	      && range_fits_type_p (vr,
				    TYPE_PRECISION (TREE_TYPE (op0)),
				    TYPE_SIGN (TREE_TYPE (op0)))
	      && int_fits_type_p (op1, TREE_TYPE (innerop)))
	    {
	      tree newconst = fold_convert (TREE_TYPE (innerop), op1);
	      gimple_cond_set_lhs (stmt, innerop);
	      gimple_cond_set_rhs (stmt, newconst);
	      update_stmt (stmt);
	      if (dump_file && (dump_flags & TDF_DETAILS))
		{
		  fprintf (dump_file, "Folded into: ");
		  print_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
		  fprintf (dump_file, "\n");
		}
	    }
	}
    }
}

/* A comparison of an SSA_NAME against a constant where the SSA_NAME
   was set by a type conversion can often be rewritten to use the RHS
   of the type conversion.  Do this optimization for all conditionals
   in FUN.

   However, doing so inhibits jump threading through the comparison.
   So that transformation is not performed until after jump threading
   is complete.  */

static void
simplify_casted_conds (function *fun, range_query *query)
{
  basic_block bb;
  FOR_EACH_BB_FN (bb, fun)
    {
      gimple *last = last_stmt (bb);
      if (last && gimple_code (last) == GIMPLE_COND)
	vrp_simplify_cond_using_ranges (query, as_a <gcond *> (last));
    }
}

/* Main entry point to VRP (Value Range Propagation).  This pass is
   loosely based on J. R. C. Patterson, ``Accurate Static Branch
   Prediction by Value Range Propagation,'' in SIGPLAN Conference on
   Programming Language Design and Implementation, pp. 67-78, 1995.
   Also available at http://citeseer.ist.psu.edu/patterson95accurate.html

   This is essentially an SSA-CCP pass modified to deal with ranges
   instead of constants.

   While propagating ranges, we may find that two or more SSA name
   have equivalent, though distinct ranges.  For instance,

     1	x_9 = p_3->a;
     2	p_4 = ASSERT_EXPR <p_3, p_3 != 0>
     3	if (p_4 == q_2)
     4	  p_5 = ASSERT_EXPR <p_4, p_4 == q_2>;
     5	endif
     6	if (q_2)

   In the code above, pointer p_5 has range [q_2, q_2], but from the
   code we can also determine that p_5 cannot be NULL and, if q_2 had
   a non-varying range, p_5's range should also be compatible with it.

   These equivalences are created by two expressions: ASSERT_EXPR and
   copy operations.  Since p_5 is an assertion on p_4, and p_4 was the
   result of another assertion, then we can use the fact that p_5 and
   p_4 are equivalent when evaluating p_5's range.

   Together with value ranges, we also propagate these equivalences
   between names so that we can take advantage of information from
   multiple ranges when doing final replacement.  Note that this
   equivalency relation is transitive but not symmetric.

   In the example above, p_5 is equivalent to p_4, q_2 and p_3, but we
   cannot assert that q_2 is equivalent to p_5 because q_2 may be used
   in contexts where that assertion does not hold (e.g., in line 6).

   TODO, the main difference between this pass and Patterson's is that
   we do not propagate edge probabilities.  We only compute whether
   edges can be taken or not.  That is, instead of having a spectrum
   of jump probabilities between 0 and 1, we only deal with 0, 1 and
   DON'T KNOW.  In the future, it may be worthwhile to propagate
   probabilities to aid branch prediction.  */

static unsigned int
execute_vrp (struct function *fun, bool warn_array_bounds_p)
{
  loop_optimizer_init (LOOPS_NORMAL | LOOPS_HAVE_RECORDED_EXITS);
  rewrite_into_loop_closed_ssa (NULL, TODO_update_ssa);
  scev_initialize ();

  /* ???  This ends up using stale EDGE_DFS_BACK for liveness computation.
     Inserting assertions may split edges which will invalidate
     EDGE_DFS_BACK.  */
  vrp_asserts assert_engine (fun);
  assert_engine.insert_range_assertions ();

  /* For visiting PHI nodes we need EDGE_DFS_BACK computed.  */
  mark_dfs_back_edges ();

  vr_values vrp_vr_values;

  class vrp_prop vrp_prop (&vrp_vr_values);
  vrp_prop.initialize (fun);
  vrp_prop.ssa_propagate ();

  /* Instantiate the folder here, so that edge cleanups happen at the
     end of this function.  */
  vrp_folder folder (&vrp_vr_values);
  vrp_prop.finalize ();

  /* If we're checking array refs, we want to merge information on
     the executability of each edge between vrp_folder and the
     check_array_bounds_dom_walker: each can clear the
     EDGE_EXECUTABLE flag on edges, in different ways.

     Hence, if we're going to call check_all_array_refs, set
     the flag on every edge now, rather than in
     check_array_bounds_dom_walker's ctor; vrp_folder may clear
     it from some edges.  */
  if (warn_array_bounds && warn_array_bounds_p)
    set_all_edges_as_executable (fun);

  folder.substitute_and_fold ();

  if (warn_array_bounds && warn_array_bounds_p)
    {
      array_bounds_checker array_checker (fun, &vrp_vr_values);
      array_checker.check ();
    }

  simplify_casted_conds (fun, &vrp_vr_values);

  free_numbers_of_iterations_estimates (fun);

  /* ASSERT_EXPRs must be removed before finalizing jump threads
     as finalizing jump threads calls the CFG cleanup code which
     does not properly handle ASSERT_EXPRs.  */
  assert_engine.remove_range_assertions ();

  scev_finalize ();
  loop_optimizer_finalize ();
  return 0;
}

namespace {

const pass_data pass_data_vrp =
{
  GIMPLE_PASS, /* type */
  "vrp", /* name */
  OPTGROUP_NONE, /* optinfo_flags */
  TV_TREE_VRP, /* tv_id */
  PROP_ssa, /* properties_required */
  0, /* properties_provided */
  0, /* properties_destroyed */
  0, /* todo_flags_start */
  ( TODO_cleanup_cfg | TODO_update_ssa ), /* todo_flags_finish */
};

class pass_vrp : public gimple_opt_pass
{
public:
  pass_vrp (gcc::context *ctxt)
    : gimple_opt_pass (pass_data_vrp, ctxt), warn_array_bounds_p (false)
  {}

  /* opt_pass methods: */
  opt_pass * clone () { return new pass_vrp (m_ctxt); }
  void set_pass_param (unsigned int n, bool param)
    {
      gcc_assert (n == 0);
      warn_array_bounds_p = param;
    }
  virtual bool gate (function *) { return flag_tree_vrp != 0; }
  virtual unsigned int execute (function *fun)
    { return execute_vrp (fun, warn_array_bounds_p); }

 private:
  bool warn_array_bounds_p;
}; // class pass_vrp

} // anon namespace

gimple_opt_pass *
make_pass_vrp (gcc::context *ctxt)
{
  return new pass_vrp (ctxt);
}

// This is the dom walker for the hybrid threader.  The reason this is
// here, as opposed to the generic threading files, is because the
// other client would be DOM, and they have their own custom walker.

class hybrid_threader : public dom_walker
{
public:
  hybrid_threader ();
  ~hybrid_threader ();

  void thread_jumps (function *fun)
  {
    walk (fun->cfg->x_entry_block_ptr);
  }
  bool thread_through_all_blocks ()
  {
    return m_threader->thread_through_all_blocks (false);
  }

private:
  edge before_dom_children (basic_block) override;
  void after_dom_children (basic_block bb) override;

  hybrid_jt_simplifier *m_simplifier;
  jump_threader *m_threader;
  jt_state *m_state;
  gimple_ranger *m_ranger;
  path_range_query *m_query;
};

hybrid_threader::hybrid_threader () : dom_walker (CDI_DOMINATORS, REACHABLE_BLOCKS)
{
  loop_optimizer_init (LOOPS_NORMAL | LOOPS_HAVE_RECORDED_EXITS);
  scev_initialize ();
  calculate_dominance_info (CDI_DOMINATORS);
  mark_dfs_back_edges ();

  m_ranger = new gimple_ranger;
  m_query = new path_range_query (*m_ranger, /*resolve=*/true);
  m_simplifier = new hybrid_jt_simplifier (m_ranger, m_query);
  m_state = new hybrid_jt_state;
  m_threader = new jump_threader (m_simplifier, m_state);
}

hybrid_threader::~hybrid_threader ()
{
  delete m_simplifier;
  delete m_threader;
  delete m_state;
  delete m_ranger;
  delete m_query;

  scev_finalize ();
  loop_optimizer_finalize ();
}

edge
hybrid_threader::before_dom_children (basic_block bb)
{
  gimple_stmt_iterator gsi;
  int_range<2> r;

  for (gsi = gsi_start_nondebug_bb (bb); !gsi_end_p (gsi); gsi_next (&gsi))
    {
      gimple *stmt = gsi_stmt (gsi);
      m_ranger->range_of_stmt (r, stmt);
    }
  return NULL;
}

void
hybrid_threader::after_dom_children (basic_block bb)
{
  m_threader->thread_outgoing_edges (bb);
}

static unsigned int
execute_vrp_threader (function *fun)
{
  hybrid_threader threader;
  threader.thread_jumps (fun);
  if (threader.thread_through_all_blocks ())
    return (TODO_cleanup_cfg | TODO_update_ssa);
  return 0;
}

namespace {

const pass_data pass_data_vrp_threader =
{
  GIMPLE_PASS, /* type */
  "vrp-thread", /* name */
  OPTGROUP_NONE, /* optinfo_flags */
  TV_TREE_VRP_THREADER, /* tv_id */
  PROP_ssa, /* properties_required */
  0, /* properties_provided */
  0, /* properties_destroyed */
  0, /* todo_flags_start */
  0 /* todo_flags_finish */
};

class pass_vrp_threader : public gimple_opt_pass
{
public:
  pass_vrp_threader (gcc::context *ctxt)
    : gimple_opt_pass (pass_data_vrp_threader, ctxt)
  {}

  /* opt_pass methods: */
  opt_pass * clone () { return new pass_vrp_threader (m_ctxt); }
  virtual bool gate (function *) { return flag_tree_vrp != 0; }
  virtual unsigned int execute (function *fun)
    { return execute_vrp_threader (fun); }
};

} // namespace {

gimple_opt_pass *
make_pass_vrp_threader (gcc::context *ctxt)
{
  return new pass_vrp_threader (ctxt);
}