New expression: find_first_set_exprt

Rather than ad-hoc handling __builtin_ffs (and its variants) in the C
front-end, make find-first-set available across the code base.

Author: tautschnig

regression/cbmc-library/__builtin_ffs-01/main.c renamed to regression/cbmc/__builtin_ffs-01/main.c

@@ -7,9 +7,11 @@ int __builtin_ffsl(long);
 int __builtin_ffsll(long long);
 #endif
 
+#ifdef _MSC_VER
+#  define _Static_assert(x, m) static_assert(x, m)
+#endif
+
 int __VERIFIER_nondet_int();
-long __VERIFIER_nondet_long();
-long long __VERIFIER_nondet_long_long();
 
 // http://graphics.stanford.edu/~seander/bithacks.html#ZerosOnRightMultLookup
 static const int multiply_de_bruijn_bit_position[32] = {
@@ -18,14 +20,14 @@ static const int multiply_de_bruijn_bit_position[32] = {
 
 int main()
 {
-  assert(__builtin_ffs(0) == 0);
-  assert(__builtin_ffs(-1) == 1);
-  assert(__builtin_ffs(INT_MIN) == sizeof(int) * 8);
-  assert(__builtin_ffsl(INT_MIN) == sizeof(int) * 8);
-  assert(__builtin_ffsl(LONG_MIN) == sizeof(long) * 8);
-  assert(__builtin_ffsll(INT_MIN) == sizeof(int) * 8);
-  assert(__builtin_ffsll(LLONG_MIN) == sizeof(long long) * 8);
-  assert(__builtin_ffs(INT_MAX) == 1);
+  _Static_assert(__builtin_ffs(0) == 0, "");
+  _Static_assert(__builtin_ffs(-1) == 1, "");
+  _Static_assert(__builtin_ffs(INT_MIN) == sizeof(int) * 8, "");
+  _Static_assert(__builtin_ffsl(INT_MIN) == sizeof(int) * 8, "");
+  _Static_assert(__builtin_ffsl(LONG_MIN) == sizeof(long) * 8, "");
+  _Static_assert(__builtin_ffsll(INT_MIN) == sizeof(int) * 8, "");
+  _Static_assert(__builtin_ffsll(LLONG_MIN) == sizeof(long long) * 8, "");
+  _Static_assert(__builtin_ffs(INT_MAX) == 1, "");
 
   int i = __VERIFIER_nondet_int();
   __CPROVER_assume(i != 0);

regression/cbmc-library/__builtin_ffs-01/test.desc renamed to regression/cbmc/__builtin_ffs-01/test.desc

@@ -2747,6 +2747,24 @@ exprt c_typecheck_baset::do_special_functions(
 
     return std::move(ctz);
   }
+  else if(
+    identifier == "__builtin_ffs" || identifier == "__builtin_ffsl" ||
+    identifier == "__builtin_ffsll")
+  {
+    if(expr.arguments().size() != 1)
+    {
+      error().source_location = f_op.source_location();
+      error() << identifier << " expects one operand" << eom;
+      throw 0;
+    }
+
+    typecheck_function_call_arguments(expr);
+
+    find_first_set_exprt ffs{expr.arguments().front(), expr.type()};
+    ffs.add_source_location() = source_location;
+
+    return std::move(ffs);
+  }
   else if(identifier==CPROVER_PREFIX "equal")
   {
     if(expr.arguments().size()!=2)

src/ansi-c/c_typecheck_expr.cpp

@@ -3823,6 +3823,7 @@ optionalt<std::string> expr2ct::convert_function(const exprt &src)
     {ID_count_leading_zeros, "__builtin_clz"},
     {ID_count_trailing_zeros, "__builtin_ctz"},
     {ID_dynamic_object, "DYNAMIC_OBJECT"},
+    {ID_find_first_set, "__builtin_ffs"},
     {ID_floatbv_div, "FLOAT/"},
     {ID_floatbv_minus, "FLOAT-"},
     {ID_floatbv_mult, "FLOAT*"},

src/ansi-c/expr2c.cpp

@@ -33,57 +33,6 @@ inline void __sync_synchronize(void)
   #endif
 }
 
-/* FUNCTION: __builtin_ffs */
-
-int __builtin_clz(unsigned int x);
-
-inline int __builtin_ffs(int x)
-{
-  if(x == 0)
-    return 0;
-
-#pragma CPROVER check push
-#pragma CPROVER check disable "conversion"
-  unsigned int u = (unsigned int)x;
-#pragma CPROVER check pop
-
-  return sizeof(int) * 8 - __builtin_clz(u & ~(u - 1));
-}
-
-/* FUNCTION: __builtin_ffsl */
-
-int __builtin_clzl(unsigned long x);
-
-inline int __builtin_ffsl(long x)
-{
-  if(x == 0)
-    return 0;
-
-#pragma CPROVER check push
-#pragma CPROVER check disable "conversion"
-  unsigned long u = (unsigned long)x;
-#pragma CPROVER check pop
-
-  return sizeof(long) * 8 - __builtin_clzl(u & ~(u - 1));
-}
-
-/* FUNCTION: __builtin_ffsll */
-
-int __builtin_clzll(unsigned long long x);
-
-inline int __builtin_ffsll(long long x)
-{
-  if(x == 0)
-    return 0;
-
-#pragma CPROVER check push
-#pragma CPROVER check disable "conversion"
-  unsigned long long u = (unsigned long long)x;
-#pragma CPROVER check pop
-
-  return sizeof(long long) * 8 - __builtin_clzll(u & ~(u - 1));
-}
-
 /* FUNCTION: __atomic_test_and_set */
 
 void __atomic_thread_fence(int memorder);

src/ansi-c/library/gcc.c

@@ -216,6 +216,8 @@ bvt boolbvt::convert_bitvector(const exprt &expr)
     return convert_bv(
       simplify_expr(to_count_trailing_zeros_expr(expr).lower(), ns));
   }
+  else if(expr.id() == ID_find_first_set)
+    return convert_bv(simplify_expr(to_find_first_set_expr(expr).lower(), ns));
 
   return conversion_failed(expr);
 }

src/solvers/flattening/boolbv.cpp

@@ -2042,6 +2042,10 @@ void smt2_convt::convert_expr(const exprt &expr)
   {
     convert_expr(simplify_expr(to_count_trailing_zeros_expr(expr).lower(), ns));
   }
+  else if(expr.id() == ID_find_first_set)
+  {
+    convert_expr(simplify_expr(to_find_first_set_expr(expr).lower(), ns));
+  }
   else
     INVARIANT_WITH_DIAGNOSTICS(
       false,

src/solvers/smt2/smt2_conv.cpp

@@ -142,3 +142,20 @@ exprt count_trailing_zeros_exprt::lower() const
 
   return typecast_exprt::conditional_cast(result, type());
 }
+
+exprt find_first_set_exprt::lower() const
+{
+  exprt x = op();
+  const auto int_width = to_bitvector_type(x.type()).get_width();
+  CHECK_RETURN(int_width >= 1);
+
+  // bitwidth(x) - clz(x & ~((unsigned)x - 1));
+  const unsignedbv_typet ut{int_width};
+  minus_exprt minus_one{typecast_exprt::conditional_cast(x, ut),
+                        from_integer(1, ut)};
+  count_leading_zeros_exprt clz{bitand_exprt{
+    x, bitnot_exprt{typecast_exprt::conditional_cast(minus_one, x.type())}}};
+  minus_exprt result{from_integer(int_width, x.type()), clz.lower()};
+
+  return typecast_exprt::conditional_cast(result, type());
+}

src/util/bitvector_expr.cpp

@@ -1008,4 +1008,81 @@ inline count_trailing_zeros_exprt &to_count_trailing_zeros_expr(exprt &expr)
   return ret;
 }
 
+/// \brief Returns one plus the index of the least-significant one bit, or zero
+/// if the operand is zero.
+class find_first_set_exprt : public unary_exprt
+{
+public:
+  find_first_set_exprt(exprt _op, typet _type)
+    : unary_exprt(ID_find_first_set, std::move(_op), std::move(_type))
+  {
+  }
+
+  explicit find_first_set_exprt(const exprt &_op)
+    : find_first_set_exprt(_op, _op.type())
+  {
+  }
+
+  static void check(
+    const exprt &expr,
+    const validation_modet vm = validation_modet::INVARIANT)
+  {
+    DATA_CHECK(
+      vm,
+      expr.operands().size() == 1,
+      "unary expression must have a single operand");
+    DATA_CHECK(
+      vm,
+      can_cast_type<bitvector_typet>(to_unary_expr(expr).op().type()),
+      "operand must be of bitvector type");
+  }
+
+  static void validate(
+    const exprt &expr,
+    const namespacet &,
+    const validation_modet vm = validation_modet::INVARIANT)
+  {
+    check(expr, vm);
+  }
+
+  /// Lower a find_first_set_exprt to arithmetic and logic expressions.
+  /// \return Semantically equivalent expression
+  exprt lower() const;
+};
+
+template <>
+inline bool can_cast_expr<find_first_set_exprt>(const exprt &base)
+{
+  return base.id() == ID_find_first_set;
+}
+
+inline void validate_expr(const find_first_set_exprt &value)
+{
+  validate_operands(value, 1, "find_first_set must have one operand");
+}
+
+/// \brief Cast an exprt to a \ref find_first_set_exprt
+///
+/// \a expr must be known to be \ref find_first_set_exprt.
+///
+/// \param expr: Source expression
+/// \return Object of type \ref find_first_set_exprt
+inline const find_first_set_exprt &to_find_first_set_expr(const exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_find_first_set);
+  const find_first_set_exprt &ret =
+    static_cast<const find_first_set_exprt &>(expr);
+  validate_expr(ret);
+  return ret;
+}
+
+/// \copydoc to_find_first_set_expr(const exprt &)
+inline find_first_set_exprt &to_find_first_set_expr(exprt &expr)
+{
+  PRECONDITION(expr.id() == ID_find_first_set);
+  find_first_set_exprt &ret = static_cast<find_first_set_exprt &>(expr);
+  validate_expr(ret);
+  return ret;
+}
+
 #endif // CPROVER_UTIL_BITVECTOR_EXPR_H

src/util/bitvector_expr.h

@@ -146,6 +146,8 @@ static std::ostream &format_rec(std::ostream &os, const unary_exprt &src)
     os << "clz";
   else if(src.id() == ID_count_trailing_zeros)
     os << "ctz";
+  else if(src.id() == ID_find_first_set)
+    os << "ffs";
   else
     return os << src.pretty();
 

src/util/format_expr.cpp

@@ -854,6 +854,7 @@ IREP_ID_TWO(vector_gt, vector->)
 IREP_ID_TWO(vector_lt, vector-<)
 IREP_ID_ONE(shuffle_vector)
 IREP_ID_ONE(count_trailing_zeros)
+IREP_ID_ONE(find_first_set)
 
 // Projects depending on this code base that wish to extend the list of
 // available ids should provide a file local_irep_ids.def in their source tree

src/util/irep_ids.def

@@ -197,6 +197,27 @@ simplify_exprt::simplify_ctz(const count_trailing_zeros_exprt &expr)
   return from_integer(n_trailing_zeros, expr.type());
 }
 
+simplify_exprt::resultt<>
+simplify_exprt::simplify_ffs(const find_first_set_exprt &expr)
+{
+  const auto const_bits_opt = expr2bits(
+    expr.op(),
+    config.ansi_c.endianness == configt::ansi_ct::endiannesst::IS_LITTLE_ENDIAN,
+    ns);
+
+  if(!const_bits_opt.has_value())
+    return unchanged(expr);
+
+  // expr2bits generates a bit string starting with the least-significant bit
+  std::size_t first_one_bit = const_bits_opt->find('1');
+  if(first_one_bit == std::string::npos)
+    first_one_bit = 0;
+  else
+    ++first_one_bit;
+
+  return from_integer(first_one_bit, expr.type());
+}
+
 /// Simplify String.endsWith function when arguments are constant
 /// \param expr: the expression to simplify
 /// \param ns: namespace
@@ -2457,6 +2478,10 @@ simplify_exprt::resultt<> simplify_exprt::simplify_node(exprt node)
   {
     r = simplify_ctz(to_count_trailing_zeros_expr(expr));
   }
+  else if(expr.id() == ID_find_first_set)
+  {
+    r = simplify_ffs(to_find_first_set_expr(expr));
+  }
   else if(expr.id() == ID_function_application)
   {
     r = simplify_function_application(to_function_application_expr(expr));

src/util/simplify_expr.cpp

@@ -44,6 +44,7 @@ class div_exprt;
 class exprt;
 class extractbit_exprt;
 class extractbits_exprt;
+class find_first_set_exprt;
 class floatbv_typecast_exprt;
 class function_application_exprt;
 class ieee_float_op_exprt;
@@ -210,6 +211,9 @@ class simplify_exprt
   /// Try to simplify count-trailing-zeros to a constant expression.
   NODISCARD resultt<> simplify_ctz(const count_trailing_zeros_exprt &);
 
+  /// Try to simplify find-first-set to a constant expression.
+  NODISCARD resultt<> simplify_ffs(const find_first_set_exprt &);
+
   // auxiliary
   bool simplify_if_implies(
     exprt &expr, const exprt &cond, bool truth, bool &new_truth);