diff --git a/loopy/codegen/expression.py b/loopy/codegen/expression.py
index 1ddb9ec30c6b4faec3ddf95413bd7ad5d0ded3a9..5772bf7bcdf01245e496fca28e820c8457dcfc22 100644
--- a/loopy/codegen/expression.py
+++ b/loopy/codegen/expression.py
@@ -77,6 +77,24 @@ class TypeInferenceMapper(CombineMapper):
 
         return result
 
+    def map_sum(self, expr):
+        dtypes = []
+        small_integer_dtypes = []
+        for child in expr.children:
+            dtype = self.rec(child)
+            if isinstance(child, (int, np.integer)) and abs(child) < 1024:
+                small_integer_dtypes.append(dtype)
+            else:
+                dtypes.append(dtype)
+
+        from pytools import all
+        if all(dtype.kind == "i" for dtype in dtypes):
+            dtypes.extend(small_integer_dtypes)
+
+        return self.combine(dtypes)
+
+    map_product = map_sum
+
     def map_quotient(self, expr):
         n_dtype = self.rec(expr.numerator)
         d_dtype = self.rec(expr.denominator)