diff --git a/loopy/library/reduction.py b/loopy/library/reduction.py
index f435820b23e8da909f0cff14ff5a1272874e865f..c61c052c09d39f0181144200d3fd8ecf3ebef877 100644
--- a/loopy/library/reduction.py
+++ b/loopy/library/reduction.py
@@ -135,13 +135,37 @@ def get_le_neutral(dtype):
     if dtype.numpy_dtype.kind == "f":
         # OpenCL 1.1, section 6.11.2
         return var("INFINITY")
+    elif dtype.numpy_dtype.kind == "i":
+        if dtype.numpy_dtype.itemsize == 4:
+            #32 bit integer
+            return var("INT_MAX")
+        elif dtype.numpy_dtype.itemsize == 8:
+            #64 bit integer
+            return var('LONG_MAX')
     else:
         raise NotImplementedError("less")
 
+def get_ge_neutral(dtype):
+    """Return a number y that satisfies (x >= y) for all y."""
+
+    if dtype.numpy_dtype.kind == "f":
+        # OpenCL 1.1, section 6.11.2
+        return -var("INFINITY")
+    elif dtype.numpy_dtype.kind == "i":
+        if dtype.numpy_dtype.itemsize == 4:
+            #32 bit integer
+            return var("INT_MIN")
+        elif dtype.numpy_dtype.itemsize == 8:
+            #64 bit integer
+            return var('LONG_MIN')
+    else:
+        raise NotImplementedError("less")
+
+
 
 class MaxReductionOperation(ScalarReductionOperation):
     def neutral_element(self, dtype, inames):
-        return -get_le_neutral(dtype)
+        return get_ge_neutral(dtype)
 
     def __call__(self, dtype, operand1, operand2, inames):
         return var("max")(operand1, operand2)
@@ -213,6 +237,8 @@ def get_argext_preamble(kernel, func_id):
 
     c_code_mapper = CCodeMapper()
 
+    neutral = get_ge_neutral if op.neutral_sign < 0 else get_le_neutral
+
     return (prefix, """
     inline %(scalar_t)s %(prefix)s_init(%(index_t)s *index_out)
     {
diff --git a/loopy/target/opencl.py b/loopy/target/opencl.py
index 31cf7c6b648ebf370a17d8beb2538b9748ddb30a..01e56405e30285705be7cb8eb6d75479c8658ef5 100644
--- a/loopy/target/opencl.py
+++ b/loopy/target/opencl.py
@@ -249,6 +249,10 @@ def opencl_symbol_mangler(kernel, name):
             return NumpyType(np.dtype(np.float64)), name
     elif name == "INFINITY":
         return NumpyType(np.dtype(np.float32)), name
+    elif name.startswith("INT_"):
+        return NumpyType(np.dtype(np.int32)), name
+    elif name.startswith("LONG_"):
+        return NumpyType(np.dtype(np.int64)), name
     else:
         return None