diff --git a/drgn/program.py b/drgn/program.py
index e08be749..ea38b0df 100644
--- a/drgn/program.py
+++ b/drgn/program.py
@@ -18,9 +18,17 @@ from drgn.typeindex import TypeIndex
 import functools
 import itertools
 import math
+import operator
 from typing import Any, Callable, Iterable, Optional, Tuple, Union
 
 
+def _c_modulo(a: int, b: int) -> int:
+    if a >= 0:
+        return a % abs(b)
+    else:
+        return -(-a % abs(b))
+
+
 class ProgramObject:
     """
     A ProgramObject either represents an object in the memory of a program (an
@@ -41,20 +49,26 @@ class ProgramObject:
     >>> print(prog['jiffies'])
     (volatile long unsigned int)4326237045
 
-    ProgramObjects try to behave transparently like the object they represent
-    in C. E.g., structure members can be accessed with the dot (".") operator
-    and arrays can be subscripted with "[]".
+    ProgramObjects support C operators wherever possible. E.g., structure
+    members can be accessed with the dot (".") operator, arrays can be
+    subscripted with "[]", arithmetic can be performed, and objects can be
+    compared.
 
     >>> print(prog['init_task'].pid)
     (pid_t)0
     >>> print(prog['init_task'].comm[0])
     (char)115
+    >>> prog['init_task'].nsproxy.mnt_ns.mounts + 1
+    ProgramObject(address=None, type=<unsigned int>, value=34)
+    >>> prog['init_task'].nsproxy.mnt_ns.pending_mounts > 0
+    False
 
     Note that because the structure dereference operator ("->") is not valid
     syntax in Python, "." is also used to access members of pointers to
     structures. Similarly, the indirection operator ("*") is not valid syntax
     in Python, so pointers can be dereferenced with "[0]" (e.g., write "p[0]"
-    instead of "*p").
+    instead of "*p"). The address-of operator ("&") is available as the
+    address_of_() method.
 
     ProgramObject members and methods are named with a trailing underscore to
     avoid conflicting with structure or union members. The helper methods
@@ -263,70 +277,268 @@ class ProgramObject:
                                          self._real_type.qualifiers),
                              address)
 
-    def _check_arithmetic_type(self) -> None:
-        if not isinstance(self._real_type, (ArithmeticType, BitFieldType)):
-            raise TypeError('not an arithmetic type')
+    def _unary_operator(self, op: Callable, op_name: str,
+                        integer: bool = False) -> 'ProgramObject':
+        if ((integer and not self._real_type.is_integer()) or
+                (not integer and not self._real_type.is_arithmetic())):
+            raise TypeError(f"invalid operand to unary {op_name} ('{self.type_}')")
+        type_ = self.program_._type_index.operand_type(self.type_)
+        type_ = self.program_._type_index.integer_promotions(type_)
+        return ProgramObject(self.program_, None, type_, op(self.value_()))
 
-    def _check_integer_type(self) -> None:
-        if not isinstance(self._real_type, (IntType, BitFieldType)):
-            raise TypeError('not an integer type')
+    def _binary_operands(self, lhs: Any, rhs: Any) -> Tuple[Any, Type, Any, Type]:
+        if (isinstance(lhs, ProgramObject) and isinstance(rhs, ProgramObject) and
+                lhs.program_ is not rhs.program_):
+            raise ValueError('operands are from different programs')
+        if isinstance(lhs, ProgramObject):
+            lhs_type = lhs.type_
+            if isinstance(lhs._real_type, ArrayType):
+                lhs = lhs.address_
+            else:
+                lhs = lhs.value_()
+        else:
+            lhs_type = self.program_._type_index.literal_type(lhs)
+        if isinstance(rhs, ProgramObject):
+            rhs_type = rhs.type_
+            if isinstance(rhs._real_type, ArrayType):
+                rhs = rhs.address_
+            else:
+                rhs = rhs.value_()
+        else:
+            rhs_type = self.program_._type_index.literal_type(rhs)
+        return lhs, lhs_type, rhs, rhs_type
 
-    def _unary_type(self, integer: bool = False) -> Type:
-        return self.program_._type_index.integer_promotions(self.type_.unqualified())
+    def _usual_arithmetic_conversions(self, lhs: Any, lhs_type: Type,
+                                      rhs: Any, rhs_type: Type) -> Tuple[Type, Any, Any]:
+        type_ = self.program_._type_index.common_real_type(lhs_type, rhs_type)
+        return type_, type_.convert(lhs), type_.convert(rhs)
+
+    def _arithmetic_operator(self, op: Callable, op_name: str,
+                             lhs: Any, rhs: Any) -> 'ProgramObject':
+        lhs, lhs_type, rhs, rhs_type = self._binary_operands(lhs, rhs)
+        if not lhs_type.is_arithmetic() and not rhs_type.is_arithmetic():
+            raise TypeError(f"invalid operands to binary {op_name} ('{lhs_type}' and '{rhs_type}')")
+        lhs_type = self.program_._type_index.operand_type(lhs_type)
+        rhs_type = self.program_._type_index.operand_type(rhs_type)
+        type_, lhs, rhs = self._usual_arithmetic_conversions(lhs, lhs_type,
+                                                             rhs, rhs_type)
+        return ProgramObject(self.program_, None, type_, op(lhs, rhs))
+
+    def _integer_operator(self, op: Callable, op_name: str,
+                          lhs: Any, rhs: Any) -> 'ProgramObject':
+        lhs, lhs_type, rhs, rhs_type = self._binary_operands(lhs, rhs)
+        if not lhs_type.is_integer() or not rhs_type.is_integer():
+            raise TypeError(f"invalid operands to binary {op_name} ('{lhs_type}' and '{rhs_type}')")
+        lhs_type = self.program_._type_index.operand_type(lhs_type)
+        rhs_type = self.program_._type_index.operand_type(rhs_type)
+        type_, lhs, rhs = self._usual_arithmetic_conversions(lhs, lhs_type,
+                                                             rhs, rhs_type)
+        return ProgramObject(self.program_, None, type_, op(lhs, rhs))
+
+    def _shift_operator(self, op: Callable, op_name: str,
+                        lhs: Any, rhs: Any) -> 'ProgramObject':
+        lhs, lhs_type, rhs, rhs_type = self._binary_operands(lhs, rhs)
+        if not lhs_type.is_integer() or not rhs_type.is_integer():
+            raise TypeError(f"invalid operands to binary {op_name} ('{lhs_type}' and '{rhs_type}')")
+        lhs_type = self.program_._type_index.operand_type(lhs_type)
+        rhs_type = self.program_._type_index.operand_type(rhs_type)
+        lhs_type = self.program_._type_index.integer_promotions(lhs_type)
+        rhs_type = self.program_._type_index.integer_promotions(rhs_type)
+        return ProgramObject(self.program_, None, lhs_type, op(lhs, rhs))
+
+    def _relational_operator(self, op: Callable, op_name: str,
+                             other: Any) -> bool:
+        lhs_pointer = isinstance(self._real_type, (ArrayType, PointerType))
+        rhs_pointer = (isinstance(other, ProgramObject) and
+                       isinstance(other._real_type, (ArrayType, PointerType)))
+        lhs, lhs_type, rhs, rhs_type = self._binary_operands(self, other)
+        if ((lhs_pointer != rhs_pointer) or
+                (not lhs_pointer and
+                 (not lhs_type.is_arithmetic() or not rhs_type.is_arithmetic()))):
+            raise TypeError(f"invalid operands to binary {op_name} ('{lhs_type}' and '{rhs_type}')")
+        lhs_type = self.program_._type_index.operand_type(lhs_type)
+        rhs_type = self.program_._type_index.operand_type(rhs_type)
+        if not lhs_pointer:
+            type_, lhs, rhs = self._usual_arithmetic_conversions(lhs, lhs_type,
+                                                                 rhs, rhs_type)
+        return op(lhs, rhs)
+
+    def _add(self, lhs: Any, rhs: Any) -> 'ProgramObject':
+        lhs_pointer = (isinstance(lhs, ProgramObject) and
+                       isinstance(lhs._real_type, (ArrayType, PointerType)))
+        rhs_pointer = (isinstance(rhs, ProgramObject) and
+                       isinstance(rhs._real_type, (ArrayType, PointerType)))
+        lhs, lhs_type, rhs, rhs_type = self._binary_operands(lhs, rhs)
+        if ((lhs_pointer and rhs_pointer) or
+                (lhs_pointer and not rhs_type.is_integer()) or
+                (rhs_pointer and not lhs_type.is_integer()) or
+                (not lhs_pointer and not rhs_pointer and
+                 (not lhs_type.is_arithmetic() or not rhs_type.is_arithmetic()))):
+            raise TypeError(f"invalid operands to binary + ('{lhs_type}' and '{rhs_type}')")
+        lhs_type = self.program_._type_index.operand_type(lhs_type)
+        rhs_type = self.program_._type_index.operand_type(rhs_type)
+        if lhs_pointer:
+            assert isinstance(lhs_type, PointerType)
+            return ProgramObject(self.program_, None, lhs_type,
+                                 lhs + lhs_type.type.sizeof() * rhs)
+        elif rhs_pointer:
+            assert isinstance(rhs_type, PointerType)
+            return ProgramObject(self.program_, None, rhs_type,
+                                 rhs + rhs_type.type.sizeof() * lhs)
+        else:
+            type_, lhs, rhs = self._usual_arithmetic_conversions(lhs, lhs_type,
+                                                                 rhs, rhs_type)
+            return ProgramObject(self.program_, None, type_, lhs + rhs)
+
+    def _sub(self, lhs: Any, rhs: Any) -> 'ProgramObject':
+        lhs_pointer = (isinstance(lhs, ProgramObject) and
+                       isinstance(lhs._real_type, (ArrayType, PointerType)))
+        if lhs_pointer:
+            lhs_sizeof = lhs._real_type.type.sizeof()
+        rhs_pointer = (isinstance(rhs, ProgramObject) and
+                       isinstance(rhs._real_type, (ArrayType, PointerType)))
+        if rhs_pointer:
+            rhs_sizeof = rhs._real_type.type.sizeof()
+        lhs, lhs_type, rhs, rhs_type = self._binary_operands(lhs, rhs)
+        if ((lhs_pointer and rhs_pointer and lhs_sizeof != rhs_sizeof) or
+                (lhs_pointer and not rhs_pointer and not rhs_type.is_integer()) or
+                (rhs_pointer and not lhs_pointer) or
+                (not lhs_pointer and not rhs_pointer and
+                 (not lhs_type.is_arithmetic() or not rhs_type.is_arithmetic()))):
+            raise TypeError(f"invalid operands to binary - ('{lhs_type}' and '{rhs_type}')")
+        lhs_type = self.program_._type_index.operand_type(lhs_type)
+        rhs_type = self.program_._type_index.operand_type(rhs_type)
+        if lhs_pointer and rhs_pointer:
+            return ProgramObject(self.program_, None,
+                                 self.program_._type_index.ptrdiff_t(),
+                                 (lhs - rhs) // lhs_sizeof)
+        elif lhs_pointer:
+            return ProgramObject(self.program_, None, lhs_type,
+                                 lhs - lhs_sizeof * rhs)
+        else:
+            type_, lhs, rhs = self._usual_arithmetic_conversions(lhs, lhs_type,
+                                                                 rhs, rhs_type)
+            return ProgramObject(self.program_, None, type_, lhs - rhs)
+
+    def __add__(self, other: Any) -> 'ProgramObject':
+        return self._add(self, other)
+
+    def __sub__(self, other: Any) -> 'ProgramObject':
+        return self._sub(self, other)
+
+    def __mul__(self, other: Any) -> 'ProgramObject':
+        return self._arithmetic_operator(operator.mul, '*', self, other)
+
+    def __truediv__(self, other: Any) -> 'ProgramObject':
+        return self._arithmetic_operator(operator.truediv, '/', self, other)
+
+    def __mod__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(_c_modulo, '%', self, other)
+
+    def __lshift__(self, other: Any) -> 'ProgramObject':
+        return self._shift_operator(operator.lshift, '<<', self, other)
+
+    def __rshift__(self, other: Any) -> 'ProgramObject':
+        return self._shift_operator(operator.rshift, '>>', self, other)
+
+    def __and__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(operator.and_, '&', self, other)
+
+    def __xor__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(operator.xor, '^', self, other)
+
+    def __or__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(operator.or_, '|', self, other)
+
+    def __radd__(self, other: Any) -> 'ProgramObject':
+        return self._add(other, self)
+
+    def __rsub__(self, other: Any) -> 'ProgramObject':
+        return self._sub(other, self)
+
+    def __rmul__(self, other: Any) -> 'ProgramObject':
+        return self._arithmetic_operator(operator.mul, '*', other, self)
+
+    def __rtruediv__(self, other: Any) -> 'ProgramObject':
+        return self._arithmetic_operator(operator.truediv, '/', other, self)
+
+    def __rmod__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(_c_modulo, '%', other, self)
+
+    def __rlshift__(self, other: Any) -> 'ProgramObject':
+        return self._shift_operator(operator.lshift, '<<', other, self)
+
+    def __rrshift__(self, other: Any) -> 'ProgramObject':
+        return self._shift_operator(operator.rshift, '>>', other, self)
+
+    def __rand__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(operator.and_, '&', other, self)
+
+    def __rxor__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(operator.xor, '^', other, self)
+
+    def __ror__(self, other: Any) -> 'ProgramObject':
+        return self._integer_operator(operator.or_, '|', other, self)
+
+    def __lt__(self, other: Any) -> bool:
+        return self._relational_operator(operator.lt, '<', other)
+
+    def __le__(self, other: Any) -> bool:
+        return self._relational_operator(operator.le, '<=', other)
+
+    def __eq__(self, other: Any) -> bool:
+        return self._relational_operator(operator.eq, '==', other)
+
+    def __ne__(self, other: Any) -> bool:
+        return self._relational_operator(operator.ne, '!=', other)
+
+    def __gt__(self, other: Any) -> bool:
+        return self._relational_operator(operator.gt, '>', other)
+
+    def __ge__(self, other: Any) -> bool:
+        return self._relational_operator(operator.ge, '>=', other)
 
     def __bool__(self) -> bool:
         if not isinstance(self._real_type, (ArithmeticType, BitFieldType,
                                             PointerType)):
-            raise TypeError('not an arithmetic or pointer type')
+            raise TypeError(f"invalid operand to bool() ('{self.type_}')")
         return bool(self.value_())
 
     def __neg__(self) -> 'ProgramObject':
-        self._check_arithmetic_type()
-        return ProgramObject(self.program_, None, self._unary_type(),
-                             -self.value_())
+        return self._unary_operator(operator.neg, '-')
 
     def __pos__(self) -> 'ProgramObject':
-        self._check_arithmetic_type()
-        return ProgramObject(self.program_, None, self._unary_type(),
-                             +self.value_())
-
-    def __abs__(self) -> 'ProgramObject':
-        self._check_arithmetic_type()
-        return ProgramObject(self.program_, None, self._unary_type(),
-                             abs(self.value_()))
+        return self._unary_operator(operator.pos, '+')
 
     def __invert__(self) -> 'ProgramObject':
-        self._check_integer_type()
-        return ProgramObject(self.program_, None, self._unary_type(),
-                             ~self.value_())
+        return self._unary_operator(operator.invert, '~', True)
 
     def __int__(self) -> int:
-        self._check_arithmetic_type()
+        if not isinstance(self._real_type, (ArithmeticType, BitFieldType)):
+            raise TypeError(f"can't convert {self.type_} to int")
         return int(self.value_())
 
     def __float__(self) -> float:
-        self._check_arithmetic_type()
+        if not isinstance(self._real_type, (ArithmeticType, BitFieldType)):
+            raise TypeError(f"can't convert {self.type_} to float")
         return float(self.value_())
 
     def __index__(self) -> int:
-        self._check_integer_type()
+        if not isinstance(self._real_type, (IntType, BitFieldType)):
+            raise TypeError(f"can't convert {self.type_} to index")
         return self.value_()
 
     def __round__(self, ndigits: Optional[int] = None) -> Union[int, float]:
-        self._check_arithmetic_type()
-        return round(self.value_(), ndigits)
+        return round(self.__float__(), ndigits)
 
     def __trunc__(self) -> int:
-        self._check_arithmetic_type()
-        return math.trunc(self.value_())
+        return math.trunc(self.__float__())
 
     def __floor__(self) -> int:
-        self._check_arithmetic_type()
-        return math.floor(self.value_())
+        return math.floor(self.__float__())
 
     def __ceil__(self) -> int:
-        self._check_arithmetic_type()
-        return math.ceil(self.value_())
+        return math.ceil(self.__float__())
 
 
 class Program:
diff --git a/drgn/typeindex.py b/drgn/typeindex.py
index f257cb9a..499b11cb 100644
--- a/drgn/typeindex.py
+++ b/drgn/typeindex.py
@@ -272,7 +272,7 @@ class TypeIndex:
 
         if (not isinstance(real_type1, (ArithmeticType, BitFieldType)) or
                 not isinstance(real_type2, (ArithmeticType, BitFieldType))):
-            raise TypeError('operands must be arithmetic types or bit fields')
+            raise TypeError('operands must have arithmetic types')
 
         # If either operand is long double, then the result is long double.
         if isinstance(real_type1, FloatType) and real_type1.name == 'long double':
diff --git a/tests/test_program.py b/tests/test_program.py
index 24ce3de7..760ab4d5 100644
--- a/tests/test_program.py
+++ b/tests/test_program.py
@@ -1,4 +1,5 @@
 import math
+import operator
 import unittest
 
 from drgn.program import Program, ProgramObject
@@ -70,7 +71,6 @@ class TestProgramObject(TypeIndexTestCase):
             # _Bool should be the same because of integer promotions.
             self.assertEqual(-obj, ProgramObject(self.program, None, TYPES['int'], -1))
             self.assertEqual(+obj, ProgramObject(self.program, None, TYPES['int'], 1))
-            self.assertEqual(abs(obj), ProgramObject(self.program, None, TYPES['int'], 1))
             self.assertEqual(~obj, ProgramObject(self.program, None, TYPES['int'], -2))
             self.assertEqual(int(obj), 1)
             self.assertEqual(float(obj), 1.0)
@@ -88,7 +88,6 @@ class TestProgramObject(TypeIndexTestCase):
         self.assertTrue(bool(obj))
         self.assertEqual(-obj, ProgramObject(self.program, None, TYPES['double'], -1.5))
         self.assertEqual(+obj, ProgramObject(self.program, None, TYPES['double'], 1.5))
-        self.assertEqual(abs(obj), ProgramObject(self.program, None, TYPES['double'], 1.5))
         with self.assertRaises(TypeError):
             ~obj
         self.assertEqual(int(obj), 1)
@@ -202,3 +201,203 @@ class TestProgramObject(TypeIndexTestCase):
         self.assertEqual(struct_obj.address_, 0xffff0000)
         self.assertEqual(struct_obj.member_('address_'),
                          ProgramObject(self.program, 0xffff0000, TYPES['unsigned long']))
+
+    def test_relational(self):
+        one = self.program.object(None, TYPES['int'], 1)
+        two = self.program.object(None, TYPES['int'], 2)
+        three = self.program.object(None, TYPES['int'], 3)
+        ptr0 = self.program.object(None, self.type_index.pointer(TYPES['int']),
+                                   0xffff0000)
+        ptr1 = self.program.object(None, self.type_index.pointer(TYPES['int']),
+                                   0xffff0004)
+
+        self.assertTrue(one < two)
+        self.assertFalse(two < two)
+        self.assertFalse(three < two)
+        self.assertTrue(ptr0 < ptr1)
+
+        self.assertTrue(one <= two)
+        self.assertTrue(two <= two)
+        self.assertFalse(three <= two)
+        self.assertTrue(ptr0 <= ptr1)
+
+        self.assertTrue(one == one)
+        self.assertFalse(one == two)
+        self.assertFalse(ptr0 == ptr1)
+
+        self.assertFalse(one != one)
+        self.assertTrue(one != two)
+        self.assertTrue(ptr0 != ptr1)
+
+        self.assertFalse(one > two)
+        self.assertFalse(two > two)
+        self.assertTrue(three > two)
+        self.assertFalse(ptr0 > ptr1)
+
+        self.assertFalse(one >= two)
+        self.assertTrue(two >= two)
+        self.assertTrue(three >= two)
+        self.assertFalse(ptr0 >= ptr1)
+
+        negative_one = self.program.object(None, TYPES['int'], -1)
+        unsigned_zero = self.program.object(None, TYPES['unsigned int'], 0)
+        # The usual arithmetic conversions convert -1 to an unsigned int.
+        self.assertFalse(negative_one < unsigned_zero)
+
+        self.assertTrue(self.program.object(None, TYPES['int'], 1) ==
+                        self.program.object(None, TYPES['_Bool'], 1))
+
+        self.assertRaises(TypeError, operator.lt, ptr0, one)
+
+    def _test_arithmetic(self, op, lhs, rhs, result, integral=True,
+                         floating_point=False):
+        def INT(value):
+            return self.program.object(None, TYPES['int'], value)
+        def LONG(value):
+            return self.program.object(None, TYPES['long'], value)
+        def DOUBLE(value):
+            return self.program.object(None, TYPES['double'], value)
+
+        if integral:
+            self.assertEqual(op(INT(lhs), INT(rhs)), INT(result))
+            self.assertEqual(op(INT(lhs), LONG(rhs)), LONG(result))
+            self.assertEqual(op(LONG(lhs), INT(rhs)), LONG(result))
+            self.assertEqual(op(LONG(lhs), LONG(rhs)), LONG(result))
+            self.assertEqual(op(INT(lhs), rhs), INT(result))
+            self.assertEqual(op(LONG(lhs), rhs), LONG(result))
+            self.assertEqual(op(lhs, INT(rhs)), INT(result))
+            self.assertEqual(op(lhs, LONG(rhs)), LONG(result))
+
+        if floating_point:
+            self.assertEqual(op(DOUBLE(lhs), DOUBLE(rhs)), DOUBLE(result))
+            self.assertEqual(op(DOUBLE(lhs), INT(rhs)), DOUBLE(result))
+            self.assertEqual(op(INT(lhs), DOUBLE(rhs)), DOUBLE(result))
+            self.assertEqual(op(DOUBLE(lhs), float(rhs)), DOUBLE(result))
+            self.assertEqual(op(float(lhs), DOUBLE(rhs)), DOUBLE(result))
+            self.assertEqual(op(float(lhs), INT(rhs)), DOUBLE(result))
+            self.assertEqual(op(INT(lhs), float(rhs)), DOUBLE(result))
+
+    def _test_pointer_type_errors(self, op):
+        def INT(value):
+            return self.program.object(None, TYPES['int'], value)
+        def POINTER(value):
+            return self.program.object(None,
+                                       self.type_index.pointer(TYPES['int']),
+                                       value)
+
+        self.assertRaises(TypeError, op, INT(1), POINTER(1))
+        self.assertRaises(TypeError, op, POINTER(1), INT(1))
+        self.assertRaises(TypeError, op, POINTER(1), POINTER(1))
+
+    def _test_floating_type_errors(self, op):
+        def INT(value):
+            return self.program.object(None, TYPES['int'], value)
+        def DOUBLE(value):
+            return self.program.object(None, TYPES['double'], value)
+
+        self.assertRaises(TypeError, op, INT(1), DOUBLE(1))
+        self.assertRaises(TypeError, op, DOUBLE(1), INT(1))
+        self.assertRaises(TypeError, op, DOUBLE(1), DOUBLE(1))
+
+    def _test_shift(self, op, lhs, rhs, result):
+        def BOOL(value):
+            return self.program.object(None, TYPES['_Bool'], value)
+        def INT(value):
+            return self.program.object(None, TYPES['int'], value)
+        def LONG(value):
+            return self.program.object(None, TYPES['long'], value)
+
+        self.assertEqual(op(INT(lhs), INT(rhs)), INT(result))
+        self.assertEqual(op(INT(lhs), LONG(rhs)), INT(result))
+        self.assertEqual(op(LONG(lhs), INT(rhs)), LONG(result))
+        self.assertEqual(op(LONG(lhs), LONG(rhs)), LONG(result))
+        self.assertEqual(op(INT(lhs), rhs), INT(result))
+        self.assertEqual(op(LONG(lhs), rhs), LONG(result))
+        self.assertEqual(op(lhs, INT(rhs)), INT(result))
+        self.assertEqual(op(lhs, LONG(rhs)), INT(result))
+
+        self._test_pointer_type_errors(op)
+        self._test_floating_type_errors(op)
+
+    def test_add(self):
+        self._test_arithmetic(operator.add, 2, 2, 4, floating_point=True)
+
+        one = self.program.object(None, TYPES['int'], 1)
+        ptr = self.program.object(None, self.type_index.pointer(TYPES['int']),
+                                  0xffff0000)
+        ptr1 = self.program.object(None, self.type_index.pointer(TYPES['int']),
+                                   0xffff0004)
+        self.assertEqual(ptr + one, ptr1)
+        self.assertEqual(one + ptr, ptr1)
+        self.assertEqual(ptr + 1, ptr1)
+        self.assertEqual(1 + ptr, ptr1)
+        self.assertRaises(TypeError, operator.add, ptr, ptr)
+        self.assertRaises(TypeError, operator.add, ptr, 2.0)
+        self.assertRaises(TypeError, operator.add, 2.0, ptr)
+
+    def test_sub(self):
+        self._test_arithmetic(operator.sub, 4, 2, 2, floating_point=True)
+
+        ptr = self.program.object(None, self.type_index.pointer(TYPES['int']),
+                                  0xffff0000)
+        ptr1 = self.program.object(None, self.type_index.pointer(TYPES['int']),
+                                   0xffff0004)
+        self.assertEqual(ptr1 - ptr,
+                         ProgramObject(self.program, None, TYPES['ptrdiff_t'], 1))
+        self.assertEqual(ptr - ptr1,
+                         ProgramObject(self.program, None, TYPES['ptrdiff_t'], -1))
+        self.assertEqual(ptr - 0, ptr)
+        self.assertEqual(ptr1 - 1, ptr)
+        self.assertRaises(TypeError, operator.sub, 1, ptr)
+        self.assertRaises(TypeError, operator.sub, ptr, 1.0)
+
+    def test_mul(self):
+        self._test_arithmetic(operator.mul, 2, 3, 6, floating_point=True)
+        self._test_pointer_type_errors(operator.mul)
+
+    def test_div(self):
+        self._test_arithmetic(operator.truediv, 6, 3, 2, floating_point=True)
+
+        # Make sure we do integer division for integer operands.
+        self._test_arithmetic(operator.truediv, 3, 2, 1)
+
+        # Make sure we truncate towards zero (Python truncates towards negative
+        # infinity).
+        self._test_arithmetic(operator.truediv, -1, 2, 0)
+        self._test_arithmetic(operator.truediv, 1, -2, 0)
+
+        self._test_pointer_type_errors(operator.mul)
+
+    def test_mod(self):
+        self._test_arithmetic(operator.mod, 4, 2, 0)
+
+        # Make sure the modulo result has the sign of the dividend (Python uses
+        # the sign of the divisor).
+        self._test_arithmetic(operator.mod, 1, 26, 1)
+        self._test_arithmetic(operator.mod, 1, -26, 1)
+        self._test_arithmetic(operator.mod, -1, 26, -1)
+        self._test_arithmetic(operator.mod, -1, -26, -1)
+
+        self._test_pointer_type_errors(operator.mod)
+        self._test_floating_type_errors(operator.mod)
+
+    def test_lshift(self):
+        self._test_shift(operator.lshift, 2, 3, 16)
+
+    def test_rshift(self):
+        self._test_shift(operator.rshift, 16, 3, 2)
+
+    def test_and(self):
+        self._test_arithmetic(operator.and_, 1, 3, 1)
+        self._test_pointer_type_errors(operator.and_)
+        self._test_floating_type_errors(operator.and_)
+
+    def test_xor(self):
+        self._test_arithmetic(operator.xor, 1, 3, 2)
+        self._test_pointer_type_errors(operator.xor)
+        self._test_floating_type_errors(operator.xor)
+
+    def test_or(self):
+        self._test_arithmetic(operator.or_, 1, 3, 3)
+        self._test_pointer_type_errors(operator.or_)
+        self._test_floating_type_errors(operator.or_)
diff --git a/tests/test_typeindex.py b/tests/test_typeindex.py
index 93d71e6b..e5ba201b 100644
--- a/tests/test_typeindex.py
+++ b/tests/test_typeindex.py
@@ -21,7 +21,7 @@ from drgn.type import (
     VoidType,
 )
 from drgn.typeindex import DwarfTypeIndex, TypeIndex
-from drgn.typename import BasicTypeName, TypeName
+from drgn.typename import BasicTypeName, TypeName, TypedefTypeName
 from tests.test_type import (
     anonymous_point_type,
     const_anonymous_point_type,
@@ -48,7 +48,9 @@ TYPES = {
     'float': FloatType('float', 4),
     'double': FloatType('double', 8),
     'long double': FloatType('long double', 16),
+    'ptrdiff_t': FloatType('long double', 16),
 }
+TYPES['ptrdiff_t'] = TypedefType('ptrdiff_t', TYPES['long'])
 
 
 class MockTypeIndex(TypeIndex):
@@ -56,7 +58,7 @@ class MockTypeIndex(TypeIndex):
         super().__init__(8)
 
     def _find_type(self, type_name: TypeName) -> Type:
-        if isinstance(type_name, BasicTypeName):
+        if isinstance(type_name, (BasicTypeName, TypedefTypeName)):
             try:
                 return TYPES[type_name.name]
             except KeyError: