diff --git a/paddle/fluid/operators/math/math_function.cc b/paddle/fluid/operators/math/math_function.cc
index 44fd739fb1d161c6c7d6ab1cc611c59220280a4e..b5ae41c8f9d7aeb8e410b795fb9fbbd57ec69d4b 100644
--- a/paddle/fluid/operators/math/math_function.cc
+++ b/paddle/fluid/operators/math/math_function.cc
@@ -13,6 +13,7 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #include "paddle/fluid/operators/math/math_function.h"
+#include <vector>
 #include "paddle/fluid/framework/data_type.h"
 #include "paddle/fluid/operators/math/math_function_impl.h"
 #include "paddle/fluid/platform/float16.h"
@@ -161,7 +162,8 @@ void batched_gemm<platform::CPUDeviceContext, float16>(
     const platform::CPUDeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const float16 alpha, const float16* A, const float16* B, const float16 beta,
-    float16* C, const int batchCount, const int strideA, const int strideB) {
+    float16* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
   PADDLE_THROW("float16 batched_gemm not supported on CPU");
 }
 
@@ -172,7 +174,8 @@ void batched_gemm<platform::CPUDeviceContext, float>(
     const platform::CPUDeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const float alpha, const float* A, const float* B, const float beta,
-    float* C, const int batchCount, const int strideA, const int strideB) {
+    float* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
   int lda = (transA == CblasNoTrans) ? K : M;
   int ldb = (transB == CblasNoTrans) ? N : K;
   int ldc = N;
@@ -194,7 +197,8 @@ void batched_gemm<platform::CPUDeviceContext, double>(
     const platform::CPUDeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const double alpha, const double* A, const double* B, const double beta,
-    double* C, const int batchCount, const int strideA, const int strideB) {
+    double* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
   int lda = (transA == CblasNoTrans) ? K : M;
   int ldb = (transB == CblasNoTrans) ? N : K;
   int ldc = N;
@@ -220,7 +224,8 @@ void batched_gemm<platform::CPUDeviceContext, float>(
     const platform::CPUDeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const float alpha, const float* A, const float* B, const float beta,
-    float* C, const int batchCount, const int strideA, const int strideB) {
+    float* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
   for (int k = 0; k < batchCount; ++k) {
     const float* Ak = &A[k * strideA];
     const float* Bk = &B[k * strideB];
@@ -235,7 +240,8 @@ void batched_gemm<platform::CPUDeviceContext, double>(
     const platform::CPUDeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const double alpha, const double* A, const double* B, const double beta,
-    double* C, const int batchCount, const int strideA, const int strideB) {
+    double* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
   for (int k = 0; k < batchCount; ++k) {
     const double* Ak = &A[k * strideA];
     const double* Bk = &B[k * strideB];
diff --git a/paddle/fluid/operators/math/math_function.cu b/paddle/fluid/operators/math/math_function.cu
index 9badf26c9bb80acad029be3d1b63377cef63d929..2aa819625e0f5213a6001908e715bcc73d4747c3 100644
--- a/paddle/fluid/operators/math/math_function.cu
+++ b/paddle/fluid/operators/math/math_function.cu
@@ -13,6 +13,7 @@ See the License for the specific language governing permissions and
 limitations under the License. */
 
 #define EIGEN_USE_GPU
+#include <vector>
 #include "paddle/fluid/framework/data_type.h"
 #include "paddle/fluid/operators/math/math_function.h"
 #include "paddle/fluid/operators/math/math_function_impl.h"
@@ -267,7 +268,8 @@ void batched_gemm<platform::CUDADeviceContext, float16>(
     const platform::CUDADeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const float16 alpha, const float16* A, const float16* B, const float16 beta,
-    float16* C, const int batchCount, const int strideA, const int strideB) {
+    float16* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
 #if CUDA_VERSION >= 8000
   // Note that cublas follows fortran order, so the order is different from
   // the cblas convention.
@@ -278,7 +280,7 @@ void batched_gemm<platform::CUDADeviceContext, float16>(
       (transA == CblasNoTrans) ? CUBLAS_OP_N : CUBLAS_OP_T;
   cublasOperation_t cuTransB =
       (transB == CblasNoTrans) ? CUBLAS_OP_N : CUBLAS_OP_T;
-  const int strideC = M * N;
+  const int64_t strideC = M * N;
 
   const half h_alpha = static_cast<const half>(alpha);
   const half h_beta = static_cast<const half>(beta);
@@ -303,7 +305,8 @@ void batched_gemm<platform::CUDADeviceContext, float>(
     const platform::CUDADeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const float alpha, const float* A, const float* B, const float beta,
-    float* C, const int batchCount, const int strideA, const int strideB) {
+    float* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
 #if CUDA_VERSION >= 8000
   // Note that cublas follows fortran order, so the order is different from
   // the cblas convention.
@@ -314,7 +317,7 @@ void batched_gemm<platform::CUDADeviceContext, float>(
       (transA == CblasNoTrans) ? CUBLAS_OP_N : CUBLAS_OP_T;
   cublasOperation_t cuTransB =
       (transB == CblasNoTrans) ? CUBLAS_OP_N : CUBLAS_OP_T;
-  const int strideC = M * N;
+  const int64_t strideC = M * N;
 
   PADDLE_ENFORCE(platform::dynload::cublasSgemmStridedBatched(
       context.cublas_handle(), cuTransB, cuTransA, N, M, K, &alpha, B, ldb,
@@ -329,7 +332,8 @@ void batched_gemm<platform::CUDADeviceContext, double>(
     const platform::CUDADeviceContext& context, const CBLAS_TRANSPOSE transA,
     const CBLAS_TRANSPOSE transB, const int M, const int N, const int K,
     const double alpha, const double* A, const double* B, const double beta,
-    double* C, const int batchCount, const int strideA, const int strideB) {
+    double* C, const int batchCount, const int64_t strideA,
+    const int64_t strideB) {
 #if CUDA_VERSION >= 8000
   // Note that cublas follows fortran order, so the order is different from
   // the cblas convention.
@@ -340,7 +344,7 @@ void batched_gemm<platform::CUDADeviceContext, double>(
       (transA == CblasNoTrans) ? CUBLAS_OP_N : CUBLAS_OP_T;
   cublasOperation_t cuTransB =
       (transB == CblasNoTrans) ? CUBLAS_OP_N : CUBLAS_OP_T;
-  const int strideC = M * N;
+  const int64_t strideC = M * N;
 
   PADDLE_ENFORCE(platform::dynload::cublasDgemmStridedBatched(
       context.cublas_handle(), cuTransB, cuTransA, N, M, K, &alpha, B, ldb,
diff --git a/paddle/fluid/operators/math/math_function.h b/paddle/fluid/operators/math/math_function.h
index cdbc7bfb37e83c6c2b696ba010277c9eec49f2a8..cdd02974722045457aacdfa517c147751185f332 100644
--- a/paddle/fluid/operators/math/math_function.h
+++ b/paddle/fluid/operators/math/math_function.h
@@ -26,7 +26,7 @@ limitations under the License. */
 
 #ifndef LAPACK_FOUND
 extern "C" {
-#include <cblas.h>
+#include <cblas.h>  // NOLINT
 int LAPACKE_sgetrf(int matrix_layout, int m, int n, float* a, int lda,
                    int* ipiv);
 int LAPACKE_dgetrf(int matrix_layout, int m, int n, double* a, int lda,
@@ -39,6 +39,7 @@ int LAPACKE_dgetri(int matrix_layout, int n, double* a, int lda,
 #endif
 
 #include <cmath>
+#include <vector>
 
 #include "paddle/fluid/framework/eigen.h"
 #include "paddle/fluid/framework/tensor.h"
@@ -78,8 +79,8 @@ template <typename DeviceContext, typename T>
 void batched_gemm(const DeviceContext& context, const CBLAS_TRANSPOSE transA,
                   const CBLAS_TRANSPOSE transB, const int M, const int N,
                   const int K, const T alpha, const T* A, const T* B,
-                  const T beta, T* C, const int batchCount, const int strideA,
-                  const int strideB);
+                  const T beta, T* C, const int batchCount,
+                  const int64_t strideA, const int64_t strideB);
 
 template <typename DeviceContext, typename T>
 void gemv(const DeviceContext& context, const bool trans_a, const int M,