diff --git a/paddle/fluid/framework/ddim.cc b/paddle/fluid/framework/ddim.cc
index 95078093e5905a47cd363815b62a1ed0db089bf2..37544e97eb655287860f8b113e0e1f1ed298474b 100644
--- a/paddle/fluid/framework/ddim.cc
+++ b/paddle/fluid/framework/ddim.cc
@@ -42,7 +42,8 @@ struct DDimEqualityVisitor {
 };
 
 bool DDim::operator==(const DDim& d) const {
-  return rank_ == d.rank_ && this->apply_visitor(DDimEqualityVisitor(d.Get()));
+  return size() == d.size() &&
+         this->apply_visitor(DDimEqualityVisitor(d.Get()));
 }
 
 bool DDim::operator!=(const DDim& d) const { return !(*this == d); }
@@ -61,7 +62,7 @@ struct DDimPlusVisitor {
 };
 
 DDim DDim::operator+(const DDim& d) const {
-  PADDLE_ENFORCE(rank_ == d.rank_);
+  PADDLE_ENFORCE(size() == d.size());
   DDim ret;
   ret.rank_ = rank_;
   ret.apply_visitor(DDimPlusVisitor(Get(), d.Get()));
@@ -82,7 +83,7 @@ struct DDimMulVisitor {
 };
 
 DDim DDim::operator*(const DDim& d) const {
-  PADDLE_ENFORCE(rank_ == d.rank_);
+  PADDLE_ENFORCE(size() == d.size());
   DDim ret;
   ret.rank_ = rank_;
   ret.apply_visitor(DDimMulVisitor(Get(), d.Get()));
@@ -121,13 +122,11 @@ int64_t product(const DDim& ddim) {
 }
 
 DDim slice_ddim(const DDim& dim, int begin, int end) {
-  PADDLE_ENFORCE(begin >= 0,
-                 "Begin index can't be less than zero in ddim slice.");
-  int len = end - begin;
-  DDim ret;
-  ret.rank_ = len;
-  dynamic_dim_assign(dim.Get() + begin, ret.GetMutable(), ret.rank_);
-  return ret;
+  PADDLE_ENFORCE(begin >= 0 && end <= dim.size(),
+                 "[begin(%d), end(%d)) must be inside [0, %d) in ddim slice.",
+                 begin, end, dim.size());
+  // Constructor of DDim would check whether end - begin is valid
+  return DDim(dim.Get() + begin, end - begin);
 }
 
 int arity(const DDim& d) { return d.size(); }
@@ -138,8 +137,8 @@ struct DDimPrinter {
   std::ostream& os;
   explicit DDimPrinter(std::ostream& os_) : os(os_) {}
 
-  template <typename T>
-  void operator()(const T& t) {
+  template <int D>
+  void operator()(const Dim<D>& t) {
     os << t;
   }
 };
@@ -152,12 +151,11 @@ std::ostream& operator<<(std::ostream& os, const DDim& ddim) {
 }
 
 DDim flatten_to_2d(const DDim& src, int num_col_dims) {
-  int rank = src.size();
-  return make_ddim({product(slice_ddim(src, 0, num_col_dims)),
-                    product(slice_ddim(src, num_col_dims, rank))});
+  return DDim({product(slice_ddim(src, 0, num_col_dims)),
+               product(slice_ddim(src, num_col_dims, src.size()))});
 }
 
-DDim flatten_to_1d(const DDim& src) { return make_ddim({product(src)}); }
+DDim flatten_to_1d(const DDim& src) { return DDim({product(src)}); }
 
 DDim stride(const DDim& ddim) {
   DDim strides;
diff --git a/paddle/fluid/framework/ddim.h b/paddle/fluid/framework/ddim.h
index 0d7b12120525b538ac714e8f89156f8d79f8c41d..452072a58762d9a5668e351e98eb6e7c8e38f4b3 100644
--- a/paddle/fluid/framework/ddim.h
+++ b/paddle/fluid/framework/ddim.h
@@ -124,16 +124,16 @@ class DDim {
   inline int size() const { return rank_; }
 
  private:
-  template <int M>
-  inline Dim<M>& UnsafeCast() {
-    return const_cast<Dim<M>&>(const_cast<const DDim*>(this)->UnsafeCast<M>());
+  template <int D>
+  inline Dim<D>& UnsafeCast() {
+    return const_cast<Dim<D>&>(const_cast<const DDim*>(this)->UnsafeCast<D>());
   }
 
-  template <int M>
-  inline const Dim<M>& UnsafeCast() const {
-    static_assert(M >= 0 && M <= kMaxRank, "Invalid rank");
+  template <int D>
+  inline const Dim<D>& UnsafeCast() const {
+    static_assert(D >= 0 && D <= kMaxRank, "Invalid rank");
     auto* p = static_cast<const void*>(&dim_);
-    return *reinterpret_cast<const Dim<M>*>(p);
+    return *reinterpret_cast<const Dim<D>*>(p);
   }
 
   friend DDim slice_ddim(const DDim& dim, int begin, int end);
diff --git a/paddle/fluid/framework/dim.h b/paddle/fluid/framework/dim.h
index 21d91167a4475466ec77fce7f47edb5800e74dca..88aee8379d835ce88b6b348aca99eb4a35bbeb5c 100644
--- a/paddle/fluid/framework/dim.h
+++ b/paddle/fluid/framework/dim.h
@@ -28,17 +28,17 @@ namespace paddle {
 namespace framework {
 
 // Statically sized, statically indexed dimension
-template <int N>
-class Dim : public Array<int64_t, N> {
+template <int D>
+class Dim : public Array<int64_t, D> {
  public:
-  static_assert(N >= 0, "N must be not less than 0");
+  static_assert(D >= 0, "D must be not less than 0");
 
-  static constexpr int kRank = N;
-  using BaseClass = Array<int64_t, N>;
+  static constexpr int kRank = D;
+  using BaseClass = Array<int64_t, D>;
 
-  inline Dim(int64_t head, const Dim<N - 1>& tail) {
+  inline Dim(int64_t head, const Dim<D - 1>& tail) {
     (*this)[0] = head;
-    new (this->GetMutable() + 1) Dim<N - 1>(tail);
+    new (this->GetMutable() + 1) Dim<D - 1>(tail);
   }
 
   template <typename... Args>
@@ -47,7 +47,7 @@ class Dim : public Array<int64_t, N> {
 
   /** Construct a Dim from a linear index and size.  Uses Fortran order
    * indexing. */
-  HOSTDEVICE Dim(int64_t idx, const Dim<N>& size);
+  HOSTDEVICE Dim(int64_t idx, const Dim<D>& size);
 
   /** Construct a Dim with each dimension set to the given index */
   HOSTDEVICE explicit Dim(int64_t idx) { this->Fill(idx); }
@@ -77,42 +77,42 @@ struct FortranOrderIndexingConstructorFunctor<kStart, kEnd, true> {
 };
 }  // namespace detail
 
-template <int N>
-HOSTDEVICE Dim<N>::Dim(int64_t idx, const Dim<N>& size) {
-  detail::FortranOrderIndexingConstructorFunctor<0, N, N == 0>::Run(
+template <int D>
+HOSTDEVICE Dim<D>::Dim(int64_t idx, const Dim<D>& size) {
+  detail::FortranOrderIndexingConstructorFunctor<0, D, D == 0>::Run(
       size.Get(), &idx, this->GetMutable());
 }
 
-template <int idx, int N>
-HOSTDEVICE inline int64_t get(const Dim<N>& dim) {
+template <int idx, int D>
+HOSTDEVICE inline int64_t get(const Dim<D>& dim) {
   return dim[idx];
 }
 
-template <int idx, int N>
-HOSTDEVICE inline int64_t& get(Dim<N>& dim) {  // NOLINT
+template <int idx, int D>
+HOSTDEVICE inline int64_t& get(Dim<D>& dim) {  // NOLINT
   return dim[idx];
 }
 
-template <int N>
-HOSTDEVICE inline int64_t get(const Dim<N>& dim, int idx) {
+template <int D>
+HOSTDEVICE inline int64_t get(const Dim<D>& dim, int idx) {
   return dim[idx];
 }
 
-template <int N>
-HOSTDEVICE inline int64_t& get(Dim<N>& dim, int idx) {  // NOLINT
+template <int D>
+HOSTDEVICE inline int64_t& get(Dim<D>& dim, int idx) {  // NOLINT
   return dim[idx];
 }
 
 // Dot product of two dims
-template <int N>
-HOSTDEVICE inline int64_t linearize(const Dim<N>& a, const Dim<N>& b) {
-  return UnrollProduct<N>::Run(a.Get(), b.Get());
+template <int D>
+HOSTDEVICE inline int64_t linearize(const Dim<D>& a, const Dim<D>& b) {
+  return UnrollProduct<D>::Run(a.Get(), b.Get());
 }
 
 // Product of a Dim
-template <int N>
-HOSTDEVICE inline int64_t product(const Dim<N>& a) {
-  return UnrollProduct<N>::Run(a.Get());
+template <int D>
+HOSTDEVICE inline int64_t product(const Dim<D>& a) {
+  return UnrollProduct<D>::Run(a.Get());
 }
 
 // Is 0 <= idx_i < size_i for all i?
@@ -135,9 +135,9 @@ struct ContainedFunctor<kStart, kEnd, true> {
 };
 }  // namespace detail
 
-template <int N>
-HOSTDEVICE inline bool contained(const Dim<N>& idx, const Dim<N>& size) {
-  return detail::ContainedFunctor<0, N, N == 0>::Run(idx.Get(), size.Get());
+template <int D>
+HOSTDEVICE inline bool contained(const Dim<D>& idx, const Dim<D>& size) {
+  return detail::ContainedFunctor<0, D, D == 0>::Run(idx.Get(), size.Get());
 }
 
 /**
@@ -160,40 +160,40 @@ struct ExPrefixMulFunctor<kStart, kEnd, true> {
 };
 }  // namespace detail
 
-template <int N>
-HOSTDEVICE inline Dim<N> ex_prefix_mul(const Dim<N>& src) {
-  Dim<N> ret;
-  detail::ExPrefixMulFunctor<0, N, N == 0>::Run(src.Get(), ret.GetMutable());
+template <int D>
+HOSTDEVICE inline Dim<D> ex_prefix_mul(const Dim<D>& src) {
+  Dim<D> ret;
+  detail::ExPrefixMulFunctor<0, D, D == 0>::Run(src.Get(), ret.GetMutable());
   return ret;
 }
 
 /**
  * Add two dimensions together
  */
-template <int N>
-HOSTDEVICE inline Dim<N> dim_plus(const Dim<N>& a, const Dim<N>& b) {
-  Dim<N> ret;
-  UnrollAdd<N>::Run(a.Get(), b.Get(), ret.GetMutable());
+template <int D>
+HOSTDEVICE inline Dim<D> dim_plus(const Dim<D>& a, const Dim<D>& b) {
+  Dim<D> ret;
+  UnrollAdd<D>::Run(a.Get(), b.Get(), ret.GetMutable());
   return ret;
 }
 
-template <int N>
-HOSTDEVICE inline Dim<N> operator+(const Dim<N>& lhs, const Dim<N>& rhs) {
+template <int D>
+HOSTDEVICE inline Dim<D> operator+(const Dim<D>& lhs, const Dim<D>& rhs) {
   return dim_plus(lhs, rhs);
 }
 
 /**
  * Multiply two dimensions together
  */
-template <int N>
-HOSTDEVICE inline Dim<N> dim_mult(const Dim<N>& a, const Dim<N>& b) {
-  Dim<N> ret;
-  UnrollMul<N>::Run(a.Get(), b.Get(), ret.GetMutable());
+template <int D>
+HOSTDEVICE inline Dim<D> dim_mult(const Dim<D>& a, const Dim<D>& b) {
+  Dim<D> ret;
+  UnrollMul<D>::Run(a.Get(), b.Get(), ret.GetMutable());
   return ret;
 }
 
-template <int i>
-HOSTDEVICE Dim<i> operator*(const Dim<i>& lhs, const Dim<i>& rhs) {
+template <int D>
+HOSTDEVICE Dim<D> operator*(const Dim<D>& lhs, const Dim<D>& rhs) {
   return dim_mult(lhs, rhs);
 }
 
@@ -224,10 +224,10 @@ struct NormalizeStridesFunctor<kStart, kEnd, true> {
 };
 }  // namespace detail
 
-template <int N>
-HOSTDEVICE Dim<N> normalize_strides(const Dim<N>& size, const Dim<N>& stride) {
-  Dim<N> ret;
-  detail::NormalizeStridesFunctor<0, N, N == 0>::Run(size.Get(), stride.Get(),
+template <int D>
+HOSTDEVICE Dim<D> normalize_strides(const Dim<D>& size, const Dim<D>& stride) {
+  Dim<D> ret;
+  detail::NormalizeStridesFunctor<0, D, D == 0>::Run(size.Get(), stride.Get(),
                                                      ret.GetMutable());
   return ret;
 }
@@ -245,10 +245,10 @@ HOSTDEVICE inline Dim<sizeof...(Args)> make_dim(Args... idxes) {
 }
 
 // Allows us to output a Dim
-template <int N>
-inline std::ostream& operator<<(std::ostream& os, const Dim<N>& d) {
+template <int D>
+inline std::ostream& operator<<(std::ostream& os, const Dim<D>& d) {
   os << d[0];
-  for (int i = 1; i < N; ++i) {
+  for (int i = 1; i < D; ++i) {
     os << ", " << d[i];
   }
   return os;
@@ -258,23 +258,23 @@ inline std::ostream& operator<<(std::ostream& os, const Dim<0>& d) {
   return os;
 }
 
-template <int N>
-HOST std::string Dim<N>::to_string() const {
+template <int D>
+HOST std::string Dim<D>::to_string() const {
   std::stringstream stream;
   stream << *this;
   return stream.str();
 }
 
-template <int N>
-HOSTDEVICE Dim<N> linear_to_dimension(int linear_index, const Dim<N>& extents) {
-  Dim<N> result;
+template <int D>
+HOSTDEVICE Dim<D> linear_to_dimension(int linear_index, const Dim<D>& extents) {
+  Dim<D> result;
 
-  for (int i = 0; i < N - 1; ++i) {
+  for (int i = 0; i < D - 1; ++i) {
     result[i] = linear_index % extents[i];
     linear_index /= extents[i];
   }
 
-  result[N - 1] = linear_index;
+  result[D - 1] = linear_index;
 
   return result;
 }