diff --git a/loopy/target/cuda.py b/loopy/target/cuda.py
index 51ccc301290460c49af73691f2ebe812b8a6da9b..2bdffb5aa69bdc0f72fe12a58faa6d0e78920e0f 100644
--- a/loopy/target/cuda.py
+++ b/loopy/target/cuda.py
@@ -148,7 +148,7 @@ class ExpressionToCudaCExpressionMapper(ExpressionToCExpressionMapper):
     def _get_index_ctype(kernel):
         if kernel.index_dtype.numpy_dtype == np.int32:
             return "int32_t"
-        elif kernel.index_dtype.numpy_dtype == np.int32:
+        elif kernel.index_dtype.numpy_dtype == np.int64:
             return "int64_t"
         else:
             raise LoopyError("unexpected index type")
@@ -318,7 +318,7 @@ class CUDACASTBuilder(CASTBuilder):
                     % scope)
 
     def wrap_global_constant(self, decl):
-        from cgen.opencl import CudaConstant
+        from cgen.cuda import CudaConstant
         return CudaConstant(decl)
 
     def get_global_arg_decl(self, name, shape, dtype, is_written):