--- /dev/null
+// { dg-do compile }
+// { dg-options "-std=c++14 -O2 -ftemplate-depth=1000000" }
+
+template <class T, int Dim0, int Dim1, int Dim2> struct Tensor3;
+template <class A, class T, int Dim0, int Dim1, int Dim2, char i, char j,
+ char k>
+struct Tensor3_Expr;
+
+template <class T, int Dim0, int Dim1, int Dim2, int Dim3> struct Tensor4;
+template <class A, class T, int Dim0, int Dim1, int Dim2, int Dim3, char i,
+ char j, char k, char l>
+struct Tensor4_Expr;
+
+template <char i, int Dim> struct Index
+{};
+template <const int N> struct Number
+{
+ Number(){};
+ operator int() const { return N; }
+};
+
+template <class T, int Tensor_Dim0, int Tensor_Dim1, int Tensor_Dim2>
+struct Tensor3
+{
+ T data[Tensor_Dim0][Tensor_Dim1][Tensor_Dim2];
+
+ T operator()(const int N1, const int N2, const int N3) const
+ {
+ return data[N1][N2][N3];
+ }
+
+ template <char i, char j, char k, int Dim0, int Dim1, int Dim2>
+ Tensor3_Expr<const Tensor3<T, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2>, T,
+ Dim0, Dim1, Dim2, i, j, k>
+ operator()(const Index<i, Dim0>, const Index<j, Dim1>,
+ const Index<k, Dim2>) const
+ {
+ return Tensor3_Expr<const Tensor3<T, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2>,
+ T, Dim0, Dim1, Dim2, i, j, k>(*this);
+ }
+};
+
+template <class A, class T, int Dim0, int Dim1, int Dim2, char i, char j,
+ char k>
+struct Tensor3_Expr
+{
+ A iter;
+
+ Tensor3_Expr(const A &a) : iter(a) {}
+ T operator()(const int N1, const int N2, const int N3) const
+ {
+ return iter(N1, N2, N3);
+ }
+};
+
+template <class A, class T, int Tensor_Dim0, int Tensor_Dim1, int Tensor_Dim2,
+ int Dim0, int Dim1, int Dim2, char i, char j, char k>
+struct Tensor3_Expr<Tensor3<A, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2>, T, Dim0,
+ Dim1, Dim2, i, j, k>
+{
+ Tensor3<A, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2> &iter;
+
+ Tensor3_Expr(Tensor3<A, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2> &a) : iter(a)
+ {}
+ T operator()(const int N1, const int N2, const int N3) const
+ {
+ return iter(N1, N2, N3);
+ }
+};
+
+template <class A, class B, class T, class U, int Dim0, int Dim1, int Dim23,
+ int Dim4, int Dim5, char i, char j, char k, char l, char m>
+struct Tensor3_times_Tensor3_21
+{
+ Tensor3_Expr<A, T, Dim0, Dim1, Dim23, i, j, k> iterA;
+ Tensor3_Expr<B, U, Dim23, Dim4, Dim5, k, l, m> iterB;
+
+ template <int CurrentDim>
+ T eval(const int N1, const int N2, const int N3, const int N4,
+ const Number<CurrentDim> &) const
+ {
+ return iterA(N1, N2, CurrentDim - 1) * iterB(CurrentDim - 1, N3, N4)
+ + eval(N1, N2, N3, N4, Number<CurrentDim - 1>());
+ }
+ T eval(const int N1, const int N2, const int N3, const int N4,
+ const Number<1> &) const
+ {
+ return iterA(N1, N2, 0) * iterB(0, N3, N4);
+ }
+
+ Tensor3_times_Tensor3_21(
+ const Tensor3_Expr<A, T, Dim0, Dim1, Dim23, i, j, k> &a,
+ const Tensor3_Expr<B, U, Dim23, Dim4, Dim5, k, l, m> &b)
+ : iterA(a), iterB(b)
+ {}
+ T operator()(const int &N1, const int &N2, const int &N3,
+ const int &N4) const
+ {
+ return eval(N1, N2, N3, N4, Number<Dim23>());
+ }
+};
+
+template <class A, class B, class T, class U, int Dim0, int Dim1, int Dim23,
+ int Dim4, int Dim5, char i, char j, char k, char l, char m>
+Tensor4_Expr<Tensor3_times_Tensor3_21<A, B, T, U, Dim0, Dim1, Dim23, Dim4,
+ Dim5, i, j, k, l, m>,
+ T, Dim0, Dim1, Dim4, Dim5, i, j, l, m>
+operator*(const Tensor3_Expr<A, T, Dim0, Dim1, Dim23, i, j, k> &a,
+ const Tensor3_Expr<B, U, Dim23, Dim4, Dim5, k, l, m> &b)
+{
+ using TensorExpr = Tensor3_times_Tensor3_21<A, B, T, U, Dim0, Dim1, Dim23,
+ Dim4, Dim5, i, j, k, l, m>;
+ return Tensor4_Expr<TensorExpr, T, Dim0, Dim1, Dim4, Dim5, i, j, l, m>(
+ TensorExpr(a, b));
+};
+
+template <class T, int Tensor_Dim0, int Tensor_Dim1, int Tensor_Dim2,
+ int Tensor_Dim3>
+struct Tensor4
+{
+ T data[Tensor_Dim0][Tensor_Dim1][Tensor_Dim2][Tensor_Dim3];
+
+ Tensor4() {}
+ T &operator()(const int N1, const int N2, const int N3, const int N4)
+ {
+ return data[N1][N2][N3][N4];
+ }
+
+ template <char i, char j, char k, char l, int Dim0, int Dim1, int Dim2,
+ int Dim3>
+ Tensor4_Expr<Tensor4<T, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2, Tensor_Dim3>,
+ T, Dim0, Dim1, Dim2, Dim3, i, j, k, l>
+ operator()(const Index<i, Dim0>, const Index<j, Dim1>, const Index<k, Dim2>,
+ const Index<l, Dim3>)
+ {
+ return Tensor4_Expr<
+ Tensor4<T, Tensor_Dim0, Tensor_Dim1, Tensor_Dim2, Tensor_Dim3>, T, Dim0,
+ Dim1, Dim2, Dim3, i, j, k, l>(*this);
+ };
+};
+
+template <class A, class T, int Dim0, int Dim1, int Dim2, int Dim3, char i,
+ char j, char k, char l>
+struct Tensor4_Expr
+{
+ A iter;
+
+ Tensor4_Expr(const A &a) : iter(a) {}
+ T operator()(const int N1, const int N2, const int N3, const int N4) const
+ {
+ return iter(N1, N2, N3, N4);
+ }
+};
+
+template <class A, class T, int Dim0, int Dim1, int Dim2, int Dim3, char i,
+ char j, char k, char l>
+struct Tensor4_Expr<Tensor4<A, Dim0, Dim1, Dim2, Dim3>, T, Dim0, Dim1, Dim2,
+ Dim3, i, j, k, l>
+{
+ Tensor4<A, Dim0, Dim1, Dim2, Dim3> &iter;
+
+ Tensor4_Expr(Tensor4<A, Dim0, Dim1, Dim2, Dim3> &a) : iter(a) {}
+ T operator()(const int N1, const int N2, const int N3, const int N4) const
+ {
+ return iter(N1, N2, N3, N4);
+ }
+
+ template <class B, class U, int Dim1_0, int Dim1_1, int Dim1_2, int Dim1_3,
+ char i_1, char j_1, char k_1, char l_1>
+ auto &operator=(const Tensor4_Expr<B, U, Dim1_0, Dim1_1, Dim1_2, Dim1_3, i_1,
+ j_1, k_1, l_1> &rhs)
+ {
+ for(int ii = 0; ii < Dim0; ++ii)
+ for(int jj = 0; jj < Dim1; ++jj)
+ for(int kk = 0; kk < Dim2; ++kk)
+ for(int ll = 0; ll < Dim3; ++ll)
+ {
+ iter(ii, jj, kk, ll) = rhs(ii, jj, kk, ll);
+ }
+ return *this;
+ }
+};
+
+int main()
+{
+ Tensor3<float, 100, 100, 1000> t1;
+ Tensor3<float, 1000, 100, 100> t2;
+
+ Index<'l', 100> l;
+ Index<'m', 100> m;
+ Index<'k', 1000> k;
+ Index<'n', 100> n;
+ Index<'o', 100> o;
+
+ Tensor4<float, 100, 100, 100, 100> res;
+ res(l, m, n, o) = t1(l, m, k) * t2(k, n, o);
+ return 0;
+}
+