--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/gcc/wide-int-range.cc	Thu Oct 25 10:21:07 2018 +0900
@@ -0,0 +1,834 @@
+/* Support routines for range operations on wide ints.
+   Copyright (C) 2018 Free Software Foundation, Inc.
+
+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 "tree.h"
+#include "function.h"
+#include "fold-const.h"
+#include "wide-int-range.h"
+
+/* Wrapper around wide_int_binop that adjusts for overflow.
+
+   Return true if we can compute the result; i.e. if the operation
+   doesn't overflow or if the overflow is undefined.  In the latter
+   case (if the operation overflows and overflow is undefined), then
+   adjust the result to be -INF or +INF depending on CODE, VAL1 and
+   VAL2.  Return the value in *RES.
+
+   Return false for division by zero, for which the result is
+   indeterminate.  */
+
+static bool
+wide_int_binop_overflow (wide_int &res,
+			 enum tree_code code,
+			 const wide_int &w0, const wide_int &w1,
+			 signop sign, bool overflow_undefined)
+{
+  wi::overflow_type overflow;
+  if (!wide_int_binop (res, code, w0, w1, sign, &overflow))
+    return false;
+
+  /* If the operation overflowed return -INF or +INF depending on the
+     operation and the combination of signs of the operands.  */
+  if (overflow && overflow_undefined)
+    {
+      switch (code)
+	{
+	case MULT_EXPR:
+	  /* For multiplication, the sign of the overflow is given
+	     by the comparison of the signs of the operands.  */
+	  if (sign == UNSIGNED || w0.sign_mask () == w1.sign_mask ())
+	    res = wi::max_value (w0.get_precision (), sign);
+	  else
+	    res = wi::min_value (w0.get_precision (), sign);
+	  return true;
+
+	case TRUNC_DIV_EXPR:
+	case FLOOR_DIV_EXPR:
+	case CEIL_DIV_EXPR:
+	case EXACT_DIV_EXPR:
+	case ROUND_DIV_EXPR:
+	  /* For division, the only case is -INF / -1 = +INF.  */
+	  res = wi::max_value (w0.get_precision (), sign);
+	  return true;
+
+	default:
+	  gcc_unreachable ();
+	}
+    }
+  return !overflow;
+}
+
+/* For range [LB, UB] compute two wide_int bit masks.
+
+   In the MAY_BE_NONZERO bit mask, if some bit is unset, it means that
+   for all numbers in the range the bit is 0, otherwise it might be 0
+   or 1.
+
+   In the MUST_BE_NONZERO bit mask, if some bit is set, it means that
+   for all numbers in the range the bit is 1, otherwise it might be 0
+   or 1.  */
+
+void
+wide_int_range_set_zero_nonzero_bits (signop sign,
+				      const wide_int &lb, const wide_int &ub,
+				      wide_int &may_be_nonzero,
+				      wide_int &must_be_nonzero)
+{
+  may_be_nonzero = wi::minus_one (lb.get_precision ());
+  must_be_nonzero = wi::zero (lb.get_precision ());
+
+  if (wi::eq_p (lb, ub))
+    {
+      may_be_nonzero = lb;
+      must_be_nonzero = may_be_nonzero;
+    }
+  else if (wi::ge_p (lb, 0, sign) || wi::lt_p (ub, 0, sign))
+    {
+      wide_int xor_mask = lb ^ ub;
+      may_be_nonzero = lb | ub;
+      must_be_nonzero = lb & ub;
+      if (xor_mask != 0)
+	{
+	  wide_int mask = wi::mask (wi::floor_log2 (xor_mask), false,
+				    may_be_nonzero.get_precision ());
+	  may_be_nonzero = may_be_nonzero | mask;
+	  must_be_nonzero = wi::bit_and_not (must_be_nonzero, mask);
+	}
+    }
+}
+
+/* Order 2 sets of wide int ranges (w0/w1, w2/w3) and set MIN/MAX
+   accordingly.  */
+
+static void
+wide_int_range_order_set (wide_int &min, wide_int &max,
+			  wide_int &w0, wide_int &w1,
+			  wide_int &w2, wide_int &w3,
+			  signop sign)
+{
+  /* Order pairs w0,w1 and w2,w3.  */
+  if (wi::gt_p (w0, w1, sign))
+    std::swap (w0, w1);
+  if (wi::gt_p (w2, w3, sign))
+    std::swap (w2, w3);
+
+  /* Choose min and max from the ordered pairs.  */
+  min = wi::min (w0, w2, sign);
+  max = wi::max (w1, w3, sign);
+}
+
+/* Calculate the cross product of two sets of ranges (VR0 and VR1) and
+   store the result in [RES_LB, RES_UB].
+
+   CODE is the operation to perform with sign SIGN.
+
+   OVERFLOW_UNDEFINED is set if overflow is undefined for the operation type.
+
+   Return TRUE if we were able to calculate the cross product.  */
+
+bool
+wide_int_range_cross_product (wide_int &res_lb, wide_int &res_ub,
+			      enum tree_code code, signop sign,
+			      const wide_int &vr0_lb, const wide_int &vr0_ub,
+			      const wide_int &vr1_lb, const wide_int &vr1_ub,
+			      bool overflow_undefined)
+{
+  wide_int cp1, cp2, cp3, cp4;
+
+  /* Compute the 4 cross operations, bailing if we get an overflow we
+     can't handle.  */
+
+  if (!wide_int_binop_overflow (cp1, code, vr0_lb, vr1_lb, sign,
+				overflow_undefined))
+    return false;
+
+  if (wi::eq_p (vr0_lb, vr0_ub))
+    cp3 = cp1;
+  else if (!wide_int_binop_overflow (cp3, code, vr0_ub, vr1_lb, sign,
+				     overflow_undefined))
+    return false;
+
+  if (wi::eq_p (vr1_lb, vr1_ub))
+    cp2 = cp1;
+  else if (!wide_int_binop_overflow (cp2, code, vr0_lb, vr1_ub, sign,
+				     overflow_undefined))
+    return false;
+
+  if (wi::eq_p (vr0_lb, vr0_ub))
+    cp4 = cp2;
+  else if (!wide_int_binop_overflow (cp4, code, vr0_ub, vr1_ub, sign,
+				     overflow_undefined))
+    return false;
+
+  wide_int_range_order_set (res_lb, res_ub, cp1, cp2, cp3, cp4, sign);
+  return true;
+}
+
+/* Multiply two ranges when TYPE_OVERFLOW_WRAPS:
+
+     [RES_LB, RES_UB] = [MIN0, MAX0] * [MIN1, MAX1]
+
+   This is basically fancy code so we don't drop to varying with an
+   unsigned [-3,-1]*[-3,-1].
+
+   Return TRUE if we were able to perform the operation.  */
+
+bool
+wide_int_range_mult_wrapping (wide_int &res_lb,
+			      wide_int &res_ub,
+			      signop sign,
+			      unsigned prec,
+			      const wide_int &min0_,
+			      const wide_int &max0_,
+			      const wide_int &min1_,
+			      const wide_int &max1_)
+{
+  /* This test requires 2*prec bits if both operands are signed and
+     2*prec + 2 bits if either is not.  Therefore, extend the values
+     using the sign of the result to PREC2.  From here on out,
+     everthing is just signed math no matter what the input types
+     were.  */
+  widest2_int min0 = widest2_int::from (min0_, sign);
+  widest2_int max0 = widest2_int::from (max0_, sign);
+  widest2_int min1 = widest2_int::from (min1_, sign);
+  widest2_int max1 = widest2_int::from (max1_, sign);
+  widest2_int sizem1 = wi::mask <widest2_int> (prec, false);
+  widest2_int size = sizem1 + 1;
+
+  /* Canonicalize the intervals.  */
+  if (sign == UNSIGNED)
+    {
+      if (wi::ltu_p (size, min0 + max0))
+	{
+	  min0 -= size;
+	  max0 -= size;
+	}
+
+      if (wi::ltu_p (size, min1 + max1))
+	{
+	  min1 -= size;
+	  max1 -= size;
+	}
+    }
+
+  widest2_int prod0 = min0 * min1;
+  widest2_int prod1 = min0 * max1;
+  widest2_int prod2 = max0 * min1;
+  widest2_int prod3 = max0 * max1;
+
+  /* Sort the 4 products so that min is in prod0 and max is in
+     prod3.  */
+  /* min0min1 > max0max1 */
+  if (prod0 > prod3)
+    std::swap (prod0, prod3);
+
+  /* min0max1 > max0min1 */
+  if (prod1 > prod2)
+    std::swap (prod1, prod2);
+
+  if (prod0 > prod1)
+    std::swap (prod0, prod1);
+
+  if (prod2 > prod3)
+    std::swap (prod2, prod3);
+
+  /* diff = max - min.  */
+  prod2 = prod3 - prod0;
+  if (wi::geu_p (prod2, sizem1))
+    /* The range covers all values.  */
+    return false;
+
+  res_lb = wide_int::from (prod0, prec, sign);
+  res_ub = wide_int::from (prod3, prec, sign);
+  return true;
+}
+
+/* Perform multiplicative operation CODE on two ranges:
+
+     [RES_LB, RES_UB] = [VR0_LB, VR0_UB] .CODE. [VR1_LB, VR1_LB]
+
+   Return TRUE if we were able to perform the operation.
+
+   NOTE: If code is MULT_EXPR and !TYPE_OVERFLOW_UNDEFINED, the resulting
+   range must be canonicalized by the caller because its components
+   may be swapped.  */
+
+bool
+wide_int_range_multiplicative_op (wide_int &res_lb, wide_int &res_ub,
+				  enum tree_code code,
+				  signop sign,
+				  unsigned prec,
+				  const wide_int &vr0_lb,
+				  const wide_int &vr0_ub,
+				  const wide_int &vr1_lb,
+				  const wide_int &vr1_ub,
+				  bool overflow_undefined)
+{
+  /* Multiplications, divisions and shifts are a bit tricky to handle,
+     depending on the mix of signs we have in the two ranges, we
+     need to operate on different values to get the minimum and
+     maximum values for the new range.  One approach is to figure
+     out all the variations of range combinations and do the
+     operations.
+
+     However, this involves several calls to compare_values and it
+     is pretty convoluted.  It's simpler to do the 4 operations
+     (MIN0 OP MIN1, MIN0 OP MAX1, MAX0 OP MIN1 and MAX0 OP MAX0 OP
+     MAX1) and then figure the smallest and largest values to form
+     the new range.  */
+  if (code == MULT_EXPR && !overflow_undefined)
+    return wide_int_range_mult_wrapping (res_lb, res_ub,
+					 sign, prec,
+					 vr0_lb, vr0_ub, vr1_lb, vr1_ub);
+  return wide_int_range_cross_product (res_lb, res_ub,
+				       code, sign,
+				       vr0_lb, vr0_ub, vr1_lb, vr1_ub,
+				       overflow_undefined);
+}
+
+/* Perform a left shift operation on two ranges:
+
+     [RES_LB, RES_UB] = [VR0_LB, VR0_UB] << [VR1_LB, VR1_LB]
+
+   Return TRUE if we were able to perform the operation.
+
+   NOTE: The resulting range must be canonicalized by the caller
+   because its contents components may be swapped.  */
+
+bool
+wide_int_range_lshift (wide_int &res_lb, wide_int &res_ub,
+		       signop sign, unsigned prec,
+		       const wide_int &vr0_lb, const wide_int &vr0_ub,
+		       const wide_int &vr1_lb, const wide_int &vr1_ub,
+		       bool overflow_undefined)
+{
+  /* Transform left shifts by constants into multiplies.  */
+  if (wi::eq_p (vr1_lb, vr1_ub))
+    {
+      unsigned shift = vr1_ub.to_uhwi ();
+      wide_int tmp = wi::set_bit_in_zero (shift, prec);
+      return wide_int_range_multiplicative_op (res_lb, res_ub,
+					       MULT_EXPR, sign, prec,
+					       vr0_lb, vr0_ub, tmp, tmp,
+					       /*overflow_undefined=*/false);
+    }
+
+  int overflow_pos = prec;
+  if (sign == SIGNED)
+    overflow_pos -= 1;
+  int bound_shift = overflow_pos - vr1_ub.to_shwi ();
+  /* If bound_shift == HOST_BITS_PER_WIDE_INT, the llshift can
+     overflow.  However, for that to happen, vr1.max needs to be
+     zero, which means vr1 is a singleton range of zero, which
+     means it should be handled by the previous LSHIFT_EXPR
+     if-clause.  */
+  wide_int bound = wi::set_bit_in_zero (bound_shift, prec);
+  wide_int complement = ~(bound - 1);
+  wide_int low_bound, high_bound;
+  bool in_bounds = false;
+  if (sign == UNSIGNED)
+    {
+      low_bound = bound;
+      high_bound = complement;
+      if (wi::ltu_p (vr0_ub, low_bound))
+	{
+	  /* [5, 6] << [1, 2] == [10, 24].  */
+	  /* We're shifting out only zeroes, the value increases
+	     monotonically.  */
+	  in_bounds = true;
+	}
+      else if (wi::ltu_p (high_bound, vr0_lb))
+	{
+	  /* [0xffffff00, 0xffffffff] << [1, 2]
+	     == [0xfffffc00, 0xfffffffe].  */
+	  /* We're shifting out only ones, the value decreases
+	     monotonically.  */
+	  in_bounds = true;
+	}
+    }
+  else
+    {
+      /* [-1, 1] << [1, 2] == [-4, 4].  */
+      low_bound = complement;
+      high_bound = bound;
+      if (wi::lts_p (vr0_ub, high_bound)
+	  && wi::lts_p (low_bound, vr0_lb))
+	{
+	  /* For non-negative numbers, we're shifting out only
+	     zeroes, the value increases monotonically.
+	     For negative numbers, we're shifting out only ones, the
+	     value decreases monotomically.  */
+	  in_bounds = true;
+	}
+    }
+  if (in_bounds)
+    return wide_int_range_multiplicative_op (res_lb, res_ub,
+					     LSHIFT_EXPR, sign, prec,
+					     vr0_lb, vr0_ub,
+					     vr1_lb, vr1_ub,
+					     overflow_undefined);
+  return false;
+}
+
+/* Return TRUE if a bit operation on two ranges can be easily
+   optimized in terms of a mask.
+
+   Basically, for BIT_AND_EXPR or BIT_IOR_EXPR see if we can optimize:
+
+	[LB, UB] op Z
+   into:
+	[LB op Z, UB op Z]
+
+   It is up to the caller to perform the actual folding above.  */
+
+static bool
+wide_int_range_can_optimize_bit_op (tree_code code,
+				    const wide_int &lb, const wide_int &ub,
+				    const wide_int &mask)
+
+{
+  if (code != BIT_AND_EXPR && code != BIT_IOR_EXPR)
+    return false;
+  /* If Z is a constant which (for op | its bitwise not) has n
+     consecutive least significant bits cleared followed by m 1
+     consecutive bits set immediately above it and either
+     m + n == precision, or (x >> (m + n)) == (y >> (m + n)).
+
+     The least significant n bits of all the values in the range are
+     cleared or set, the m bits above it are preserved and any bits
+     above these are required to be the same for all values in the
+     range.  */
+
+  wide_int w = mask;
+  int m = 0, n = 0;
+  if (code == BIT_IOR_EXPR)
+    w = ~w;
+  if (wi::eq_p (w, 0))
+    n = w.get_precision ();
+  else
+    {
+      n = wi::ctz (w);
+      w = ~(w | wi::mask (n, false, w.get_precision ()));
+      if (wi::eq_p (w, 0))
+	m = w.get_precision () - n;
+      else
+	m = wi::ctz (w) - n;
+    }
+  wide_int new_mask = wi::mask (m + n, true, w.get_precision ());
+  if ((new_mask & lb) == (new_mask & ub))
+    return true;
+
+  return false;
+}
+
+/* Helper function for wide_int_range_optimize_bit_op.
+
+   Calculates bounds and mask for a pair of ranges.  The mask is the
+   singleton range among the ranges, if any.  The bounds are the
+   bounds for the remaining range.  */
+
+bool
+wide_int_range_get_mask_and_bounds (wide_int &mask,
+				    wide_int &lower_bound,
+				    wide_int &upper_bound,
+				    const wide_int &vr0_min,
+				    const wide_int &vr0_max,
+				    const wide_int &vr1_min,
+				    const wide_int &vr1_max)
+{
+  if (wi::eq_p (vr1_min, vr1_max))
+    {
+      mask = vr1_min;
+      lower_bound = vr0_min;
+      upper_bound = vr0_max;
+      return true;
+    }
+  else if (wi::eq_p (vr0_min, vr0_max))
+    {
+      mask = vr0_min;
+      lower_bound = vr1_min;
+      upper_bound = vr1_max;
+      return true;
+    }
+  return false;
+}
+
+/* Optimize a bit operation (BIT_AND_EXPR or BIT_IOR_EXPR) if
+   possible.  If so, return TRUE and store the result in
+   [RES_LB, RES_UB].  */
+
+bool
+wide_int_range_optimize_bit_op (wide_int &res_lb, wide_int &res_ub,
+				enum tree_code code,
+				signop sign,
+				const wide_int &vr0_min,
+				const wide_int &vr0_max,
+				const wide_int &vr1_min,
+				const wide_int &vr1_max)
+{
+  gcc_assert (code == BIT_AND_EXPR || code == BIT_IOR_EXPR);
+
+  wide_int lower_bound, upper_bound, mask;
+  if (!wide_int_range_get_mask_and_bounds (mask, lower_bound, upper_bound,
+					   vr0_min, vr0_max, vr1_min, vr1_max))
+    return false;
+  if (wide_int_range_can_optimize_bit_op (code,
+					  lower_bound, upper_bound, mask))
+    {
+      wi::overflow_type ovf;
+      wide_int_binop (res_lb, code, lower_bound, mask, sign, &ovf);
+      wide_int_binop (res_ub, code, upper_bound, mask, sign, &ovf);
+      return true;
+    }
+  return false;
+}
+
+/* Calculate the XOR of two ranges and store the result in [WMIN,WMAX].
+   The two input ranges are described by their MUST_BE_NONZERO and
+   MAY_BE_NONZERO bit masks.
+
+   Return TRUE if we were able to successfully calculate the new range.  */
+
+bool
+wide_int_range_bit_xor (wide_int &wmin, wide_int &wmax,
+			signop sign,
+			unsigned prec,
+			const wide_int &must_be_nonzero0,
+			const wide_int &may_be_nonzero0,
+			const wide_int &must_be_nonzero1,
+			const wide_int &may_be_nonzero1)
+{
+  wide_int result_zero_bits = ((must_be_nonzero0 & must_be_nonzero1)
+			       | ~(may_be_nonzero0 | may_be_nonzero1));
+  wide_int result_one_bits
+    = (wi::bit_and_not (must_be_nonzero0, may_be_nonzero1)
+       | wi::bit_and_not (must_be_nonzero1, may_be_nonzero0));
+  wmax = ~result_zero_bits;
+  wmin = result_one_bits;
+  /* If the range has all positive or all negative values, the result
+     is better than VARYING.  */
+  if (wi::lt_p (wmin, 0, sign) || wi::ge_p (wmax, 0, sign))
+    return true;
+  wmin = wi::min_value (prec, sign);
+  wmax = wi::max_value (prec, sign);
+  return false;
+}
+
+/* Calculate the IOR of two ranges and store the result in [WMIN,WMAX].
+   Return TRUE if we were able to successfully calculate the new range.  */
+
+bool
+wide_int_range_bit_ior (wide_int &wmin, wide_int &wmax,
+			signop sign,
+			const wide_int &vr0_min,
+			const wide_int &vr0_max,
+			const wide_int &vr1_min,
+			const wide_int &vr1_max,
+			const wide_int &must_be_nonzero0,
+			const wide_int &may_be_nonzero0,
+			const wide_int &must_be_nonzero1,
+			const wide_int &may_be_nonzero1)
+{
+  if (wide_int_range_optimize_bit_op (wmin, wmax, BIT_IOR_EXPR, sign,
+				      vr0_min, vr0_max,
+				      vr1_min, vr1_max))
+    return true;
+  wmin = must_be_nonzero0 | must_be_nonzero1;
+  wmax = may_be_nonzero0 | may_be_nonzero1;
+  /* If the input ranges contain only positive values we can
+     truncate the minimum of the result range to the maximum
+     of the input range minima.  */
+  if (wi::ge_p (vr0_min, 0, sign)
+      && wi::ge_p (vr1_min, 0, sign))
+    {
+      wmin = wi::max (wmin, vr0_min, sign);
+      wmin = wi::max (wmin, vr1_min, sign);
+    }
+  /* If either input range contains only negative values
+     we can truncate the minimum of the result range to the
+     respective minimum range.  */
+  if (wi::lt_p (vr0_max, 0, sign))
+    wmin = wi::max (wmin, vr0_min, sign);
+  if (wi::lt_p (vr1_max, 0, sign))
+    wmin = wi::max (wmin, vr1_min, sign);
+  /* If the limits got swapped around, indicate error so we can adjust
+     the range to VARYING.  */
+  if (wi::gt_p (wmin, wmax,sign))
+    return false;
+  return true;
+}
+
+/* Calculate the bitwise AND of two ranges and store the result in [WMIN,WMAX].
+   Return TRUE if we were able to successfully calculate the new range.  */
+
+bool
+wide_int_range_bit_and (wide_int &wmin, wide_int &wmax,
+			signop sign,
+			unsigned prec,
+			const wide_int &vr0_min,
+			const wide_int &vr0_max,
+			const wide_int &vr1_min,
+			const wide_int &vr1_max,
+			const wide_int &must_be_nonzero0,
+			const wide_int &may_be_nonzero0,
+			const wide_int &must_be_nonzero1,
+			const wide_int &may_be_nonzero1)
+{
+  if (wide_int_range_optimize_bit_op (wmin, wmax, BIT_AND_EXPR, sign,
+				      vr0_min, vr0_max,
+				      vr1_min, vr1_max))
+    return true;
+  wmin = must_be_nonzero0 & must_be_nonzero1;
+  wmax = may_be_nonzero0 & may_be_nonzero1;
+  /* If both input ranges contain only negative values we can
+     truncate the result range maximum to the minimum of the
+     input range maxima.  */
+  if (wi::lt_p (vr0_max, 0, sign) && wi::lt_p (vr1_max, 0, sign))
+    {
+      wmax = wi::min (wmax, vr0_max, sign);
+      wmax = wi::min (wmax, vr1_max, sign);
+    }
+  /* If either input range contains only non-negative values
+     we can truncate the result range maximum to the respective
+     maximum of the input range.  */
+  if (wi::ge_p (vr0_min, 0, sign))
+    wmax = wi::min (wmax, vr0_max, sign);
+  if (wi::ge_p (vr1_min, 0, sign))
+    wmax = wi::min (wmax, vr1_max, sign);
+  /* PR68217: In case of signed & sign-bit-CST should
+     result in [-INF, 0] instead of [-INF, INF].  */
+  if (wi::gt_p (wmin, wmax, sign))
+    {
+      wide_int sign_bit = wi::set_bit_in_zero (prec - 1, prec);
+      if (sign == SIGNED
+	  && ((wi::eq_p (vr0_min, vr0_max)
+	       && !wi::cmps (vr0_min, sign_bit))
+	      || (wi::eq_p (vr1_min, vr1_max)
+		  && !wi::cmps (vr1_min, sign_bit))))
+	{
+	  wmin = wi::min_value (prec, sign);
+	  wmax = wi::zero (prec);
+	}
+    }
+  /* If the limits got swapped around, indicate error so we can adjust
+     the range to VARYING.  */
+  if (wi::gt_p (wmin, wmax,sign))
+    return false;
+  return true;
+}
+
+/* Calculate TRUNC_MOD_EXPR on two ranges and store the result in
+   [WMIN,WMAX].  */
+
+void
+wide_int_range_trunc_mod (wide_int &wmin, wide_int &wmax,
+			  signop sign,
+			  unsigned prec,
+			  const wide_int &vr0_min,
+			  const wide_int &vr0_max,
+			  const wide_int &vr1_min,
+			  const wide_int &vr1_max)
+{
+  wide_int tmp;
+
+  /* ABS (A % B) < ABS (B) and either
+     0 <= A % B <= A or A <= A % B <= 0.  */
+  wmax = vr1_max - 1;
+  if (sign == SIGNED)
+    {
+      tmp = -1 - vr1_min;
+      wmax = wi::smax (wmax, tmp);
+    }
+
+  if (sign == UNSIGNED)
+    wmin = wi::zero (prec);
+  else
+    {
+      wmin = -wmax;
+      tmp = vr0_min;
+      if (wi::gts_p (tmp, 0))
+	tmp = wi::zero (prec);
+      wmin = wi::smax (wmin, tmp);
+    }
+  tmp = vr0_max;
+  if (sign == SIGNED && wi::neg_p (tmp))
+    tmp = wi::zero (prec);
+  wmax = wi::min (wmax, tmp, sign);
+}
+
+/* Calculate ABS_EXPR on a range and store the result in [MIN, MAX].  */
+
+bool
+wide_int_range_abs (wide_int &min, wide_int &max,
+		    signop sign, unsigned prec,
+		    const wide_int &vr0_min, const wide_int &vr0_max,
+		    bool overflow_undefined)
+{
+  /* Pass through VR0 the easy cases.  */
+  if (sign == UNSIGNED || wi::ge_p (vr0_min, 0, sign))
+    {
+      min = vr0_min;
+      max = vr0_max;
+      return true;
+    }
+
+  /* -TYPE_MIN_VALUE = TYPE_MIN_VALUE with flag_wrapv so we can't get a
+     useful range.  */
+  wide_int min_value = wi::min_value (prec, sign);
+  wide_int max_value = wi::max_value (prec, sign);
+  if (!overflow_undefined && wi::eq_p (vr0_min, min_value))
+    return false;
+
+  /* ABS_EXPR may flip the range around, if the original range
+     included negative values.  */
+  if (wi::eq_p (vr0_min, min_value))
+    min = max_value;
+  else
+    min = wi::abs (vr0_min);
+  if (wi::eq_p (vr0_max, min_value))
+    max = max_value;
+  else
+    max = wi::abs (vr0_max);
+
+  /* If the range contains zero then we know that the minimum value in the
+     range will be zero.  */
+  if (wi::le_p (vr0_min, 0, sign) && wi::ge_p (vr0_max, 0, sign))
+    {
+      if (wi::gt_p (min, max, sign))
+	max = min;
+      min = wi::zero (prec);
+    }
+  else
+    {
+      /* If the range was reversed, swap MIN and MAX.  */
+      if (wi::gt_p (min, max, sign))
+	std::swap (min, max);
+    }
+
+  /* If the new range has its limits swapped around (MIN > MAX), then
+     the operation caused one of them to wrap around.  The only thing
+     we know is that the result is positive.  */
+  if (wi::gt_p (min, max, sign))
+    {
+      min = wi::zero (prec);
+      max = max_value;
+    }
+  return true;
+}
+
+/* Convert range in [VR0_MIN, VR0_MAX] with INNER_SIGN and INNER_PREC,
+   to a range in [MIN, MAX] with OUTER_SIGN and OUTER_PREC.
+
+   Return TRUE if we were able to successfully calculate the new range.
+
+   Caller is responsible for canonicalizing the resulting range.  */
+
+bool
+wide_int_range_convert (wide_int &min, wide_int &max,
+			signop inner_sign,
+			unsigned inner_prec,
+			signop outer_sign,
+			unsigned outer_prec,
+			const wide_int &vr0_min,
+			const wide_int &vr0_max)
+{
+  /* If the conversion is not truncating we can convert the min and
+     max values and canonicalize the resulting range.  Otherwise we
+     can do the conversion if the size of the range is less than what
+     the precision of the target type can represent.  */
+  if (outer_prec >= inner_prec
+      || wi::rshift (wi::sub (vr0_max, vr0_min),
+		     wi::uhwi (outer_prec, inner_prec),
+		     inner_sign) == 0)
+    {
+      min = wide_int::from (vr0_min, outer_prec, inner_sign);
+      max = wide_int::from (vr0_max, outer_prec, inner_sign);
+      return (!wi::eq_p (min, wi::min_value (outer_prec, outer_sign))
+	      || !wi::eq_p (max, wi::max_value (outer_prec, outer_sign)));
+    }
+  return false;
+}
+
+/* Calculate a division operation on two ranges and store the result in
+   [WMIN, WMAX] U [EXTRA_MIN, EXTRA_MAX].
+
+   If EXTRA_RANGE_P is set upon return, EXTRA_MIN/EXTRA_MAX hold
+   meaningful information, otherwise they should be ignored.
+
+   Return TRUE if we were able to successfully calculate the new range.  */
+
+bool
+wide_int_range_div (wide_int &wmin, wide_int &wmax,
+		    tree_code code, signop sign, unsigned prec,
+		    const wide_int &dividend_min, const wide_int &dividend_max,
+		    const wide_int &divisor_min, const wide_int &divisor_max,
+		    bool overflow_undefined,
+		    bool &extra_range_p,
+		    wide_int &extra_min, wide_int &extra_max)
+{
+  extra_range_p = false;
+
+  /* If we know we won't divide by zero, just do the division.  */
+  if (!wide_int_range_includes_zero_p (divisor_min, divisor_max, sign))
+    return wide_int_range_multiplicative_op (wmin, wmax, code, sign, prec,
+					     dividend_min, dividend_max,
+					     divisor_min, divisor_max,
+					     overflow_undefined);
+
+  /* If flag_non_call_exceptions, we must not eliminate a division
+     by zero.  */
+  if (cfun->can_throw_non_call_exceptions)
+    return false;
+
+  /* If we're definitely dividing by zero, there's nothing to do.  */
+  if (wide_int_range_zero_p (divisor_min, divisor_max, prec))
+    return false;
+
+  /* Perform the division in 2 parts, [LB, -1] and [1, UB],
+     which will skip any division by zero.
+
+     First divide by the negative numbers, if any.  */
+  if (wi::neg_p (divisor_min, sign))
+    {
+      if (!wide_int_range_multiplicative_op (wmin, wmax,
+					     code, sign, prec,
+					     dividend_min, dividend_max,
+					     divisor_min, wi::minus_one (prec),
+					     overflow_undefined))
+	return false;
+      extra_range_p = true;
+    }
+  /* Then divide by the non-zero positive numbers, if any.  */
+  if (wi::gt_p (divisor_max, wi::zero (prec), sign))
+    {
+      if (!wide_int_range_multiplicative_op (extra_range_p ? extra_min : wmin,
+					     extra_range_p ? extra_max : wmax,
+					     code, sign, prec,
+					     dividend_min, dividend_max,
+					     wi::one (prec), divisor_max,
+					     overflow_undefined))
+	return false;
+    }
+  else
+    extra_range_p = false;
+  return true;
+}