introduce zero_extend expression

This introduces the zero_extend expression, which, given a bit-vector
operand and a type, either

a) pads the given operand with zeros from the left if the given type is
wider than the type of the operand, or

b) truncates the operand to the width of the given type if the given type is
smaller than the operand, or

c) reinterprets the operand as having the given type if the width of the
type and the width of the operand match.  This may differ from conversion if
the types have different bit representations.

This is easier to read and less prone to error than the current pattern, in
which the operand is 1) converted to an unsigned type of the same width, and
then 2) casted to an unsigned type of the wider width, and 3) finally casted
to the target type.

src/solvers/flattening/boolbv.cpp

@@ -165,6 +165,8 @@ bvt boolbvt::convert_bitvector(const exprt &expr)
     return convert_replication(to_replication_expr(expr));
   else if(expr.id()==ID_extractbits)
     return convert_extractbits(to_extractbits_expr(expr));
+  else if(expr.id() == ID_zero_extend)
+    return convert_bitvector(to_zero_extend_expr(expr).lower());
   else if(expr.id()==ID_bitnot || expr.id()==ID_bitand ||
           expr.id()==ID_bitor || expr.id()==ID_bitxor ||
           expr.id()==ID_bitxnor || expr.id()==ID_bitnor ||

src/solvers/floatbv/float_bv.cpp

@@ -692,8 +692,10 @@ exprt float_bvt::mul(
 
   // zero-extend the fractions (unpacked fraction has the hidden bit)
   typet new_fraction_type=unsignedbv_typet((spec.f+1)*2);
-  const exprt fraction1=typecast_exprt(unpacked1.fraction, new_fraction_type);
-  const exprt fraction2=typecast_exprt(unpacked2.fraction, new_fraction_type);
+  const exprt fraction1 =
+    zero_extend_exprt{unpacked1.fraction, new_fraction_type};
+  const exprt fraction2 =
+    zero_extend_exprt{unpacked2.fraction, new_fraction_type};
 
   // multiply the fractions
   unbiased_floatt result;
@@ -750,7 +752,7 @@ exprt float_bvt::div(
     unsignedbv_typet(div_width));
 
   // zero-extend fraction2 to match fraction1
-  const typecast_exprt fraction2(unpacked2.fraction, fraction1.type());
+  const zero_extend_exprt fraction2{unpacked2.fraction, fraction1.type()};
 
   // divide fractions
   unbiased_floatt result;

src/solvers/smt2/smt2_conv.cpp

@@ -2456,6 +2456,10 @@ void smt2_convt::convert_expr(const exprt &expr)
   {
     convert_expr(simplify_expr(to_bitreverse_expr(expr).lower(), ns));
   }
+  else if(expr.id() == ID_zero_extend)
+  {
+    convert_expr(to_zero_extend_expr(expr).lower());
+  }
   else if(expr.id() == ID_function_application)
   {
     const auto &function_application_expr = to_function_application_expr(expr);

src/solvers/smt2_incremental/convert_expr_to_smt.cpp

@@ -1470,6 +1470,15 @@ static smt_termt convert_expr_to_smt(
     count_trailing_zeros.pretty());
 }
 
+static smt_termt convert_expr_to_smt(
+  const zero_extend_exprt &zero_extend,
+  const sub_expression_mapt &converted)
+{
+  UNREACHABLE_BECAUSE(
+    "zero_extend expression should have been lowered by the decision "
+    "procedure before conversion to smt terms");
+}
+
 static smt_termt convert_expr_to_smt(
   const prophecy_r_or_w_ok_exprt &prophecy_r_or_w_ok,
   const sub_expression_mapt &converted)
@@ -1823,6 +1832,12 @@ static smt_termt dispatch_expr_to_smt_conversion(
   {
     return convert_expr_to_smt(*count_trailing_zeros, converted);
   }
+  if(
+    const auto zero_extend =
+      expr_try_dynamic_cast<zero_extend_exprt>(expr))
+  {
+    return convert_expr_to_smt(*zero_extend, converted);
+  }
   if(
     const auto prophecy_r_or_w_ok =
       expr_try_dynamic_cast<prophecy_r_or_w_ok_exprt>(expr))

src/solvers/smt2_incremental/smt2_incremental_decision_procedure.cpp

@@ -3,6 +3,7 @@
 #include "smt2_incremental_decision_procedure.h"
 
 #include <util/arith_tools.h>
+#include <util/bitvector_expr.h>
 #include <util/byte_operators.h>
 #include <util/c_types.h>
 #include <util/range.h>
@@ -296,6 +297,19 @@ static exprt lower_rw_ok_pointer_in_range(exprt expr, const namespacet &ns)
   return expr;
 }
 
+static exprt lower_zero_extend(exprt expr, const namespacet &ns)
+{
+  expr.visit_pre([](exprt &expr) {
+    if(
+      auto zero_extend =
+        expr_try_dynamic_cast<zero_extend_exprt>(expr))
+    {
+      expr = zero_extend->lower();
+    }
+  });
+  return expr;
+}
+
 void smt2_incremental_decision_proceduret::ensure_handle_for_expr_defined(
   const exprt &in_expr)
 {
@@ -677,9 +691,9 @@ void smt2_incremental_decision_proceduret::define_object_properties()
 
 exprt smt2_incremental_decision_proceduret::lower(exprt expression) const
 {
-  const exprt lowered = struct_encoding.encode(lower_enum(
+  const exprt lowered = struct_encoding.encode(lower_zero_extend(lower_enum(
     lower_byte_operators(lower_rw_ok_pointer_in_range(expression, ns), ns),
-    ns));
+    ns), ns));
   log.conditional_output(log.debug(), [&](messaget::mstreamt &debug) {
     if(lowered != expression)
       debug << "lowered to -\n  " << lowered.pretty(2, 0) << messaget::eom;

src/util/bitvector_expr.cpp

@@ -54,8 +54,7 @@ exprt update_bit_exprt::lower() const
     typecast_exprt(src(), src_bv_type), bitnot_exprt(mask_shifted));
 
   // zero-extend the replacement bit to match src
-  auto new_value_casted = typecast_exprt(
-    typecast_exprt(new_value(), unsignedbv_typet(width)), src_bv_type);
+  auto new_value_casted = zero_extend_exprt{new_value(), src_bv_type};
 
   // shift the replacement bits
   auto new_value_shifted = shl_exprt(new_value_casted, index());
@@ -85,7 +84,7 @@ exprt update_bits_exprt::lower() const
     bitand_exprt(typecast_exprt(src(), src_bv_type), mask_shifted);
 
   // zero-extend or shrink the replacement bits to match src
-  auto new_value_casted = typecast_exprt(new_value(), src_bv_type);
+  auto new_value_casted = zero_extend_exprt{new_value(), src_bv_type};
 
   // shift the replacement bits
   auto new_value_shifted = shl_exprt(new_value_casted, index());
@@ -279,3 +278,19 @@ exprt find_first_set_exprt::lower() const
 
   return typecast_exprt::conditional_cast(result, type());
 }
+
+exprt zero_extend_exprt::lower() const
+{
+  const auto old_width = to_bitvector_type(op().type()).get_width();
+  const auto new_width = to_bitvector_type(type()).get_width();
+
+  if(new_width > old_width)
+  {
+    return concatenation_exprt{
+      bv_typet{new_width - old_width}.all_zeros_expr(), op(), type()};
+  }
+  else // new_width <= old_width
+  {
+    return extractbits_exprt{op(), integer_typet{}.zero_expr(), type()};
+  }
+}

src/util/bitvector_expr.h

@@ -1663,4 +1663,48 @@ inline find_first_set_exprt &to_find_first_set_expr(exprt &expr)
   return ret;
 }
 
+/// \brief zero extension
+/// The operand is converted to the given type by either
+/// a) truncating if the new type is shorter, or
+/// b) padding with most-significant zero bits if the new type is larger, or
+/// c) reinterprets the operand as the given type if their widths match.
+class zero_extend_exprt : public unary_exprt
+{
+public:
+  zero_extend_exprt(exprt _op, typet _type)
+    : unary_exprt(ID_zero_extend, std::move(_op), std::move(_type))
+  {
+  }
+
+  // a lowering to extraction or concatenation
+  exprt lower() const;
+};
+
+template <>
+inline bool can_cast_expr<zero_extend_exprt>(const exprt &base)
+{
+  return base.id() == ID_zero_extend;
+}
+
+/// \brief Cast an exprt to a \ref zero_extend_exprt
+///
+/// \a expr must be known to be \ref zero_extend_exprt.
+///
+/// \param expr: Source expression
+/// \return Object of type \ref zero_extend_exprt
+inline const zero_extend_exprt &to_zero_extend_expr(const exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_zero_extend);
+  zero_extend_exprt::check(expr);
+  return static_cast<const zero_extend_exprt &>(expr);
+}
+
+/// \copydoc to_zero_extend_expr(const exprt &)
+inline zero_extend_exprt &to_zero_extend_expr(exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_zero_extend);
+  zero_extend_exprt::check(expr);
+  return static_cast<zero_extend_exprt &>(expr);
+}
+
 #endif // CPROVER_UTIL_BITVECTOR_EXPR_H

src/util/format_expr.cpp

@@ -363,6 +363,12 @@ void format_expr_configt::setup()
               << format(expr.type()) << ')';
   };
 
+  expr_map[ID_zero_extend] =
+    [](std::ostream &os, const exprt &expr) -> std::ostream & {
+    return os << "zero_extend(" << format(to_zero_extend_expr(expr).op())
+              << ", " << format(expr.type()) << ')';
+  };
+
   expr_map[ID_floatbv_typecast] =
     [](std::ostream &os, const exprt &expr) -> std::ostream & {
     const auto &floatbv_typecast_expr = to_floatbv_typecast_expr(expr);

src/util/irep_ids.def

@@ -188,6 +188,7 @@ IREP_ID_ONE(extractbit)
 IREP_ID_ONE(extractbits)
 IREP_ID_ONE(update_bit)
 IREP_ID_ONE(update_bits)
+IREP_ID_ONE(zero_extend)
 IREP_ID_TWO(C_reference, #reference)
 IREP_ID_TWO(C_rvalue_reference, #rvalue_reference)
 IREP_ID_ONE(true)

src/util/lower_byte_operators.cpp

@@ -2491,10 +2491,7 @@ static exprt lower_byte_update(
     exprt zero_extended;
     if(bit_width > update_size_bits)
     {
-      zero_extended = concatenation_exprt{
-        bv_typet{bit_width - update_size_bits}.all_zeros_expr(),
-        value,
-        bv_typet{bit_width}};
+      zero_extended = zero_extend_exprt{value, bv_typet{bit_width}};
 
       if(!is_little_endian)
         to_concatenation_expr(zero_extended)