C++ template nontype parameter arithmetic

Question

I am trying to specialize template the following way:

template<size_t _1,size_t _2> // workaround: bool consecutive = (_1 == _2 - 1)>
struct integral_index_ {};
...
template<size_t _1>
struct integral_index_<_1, _1 + 1> { // cannot do arithmetic?
//struct integral_index_<_1, _2, true> { workaround
};

however I get compiler message error

the template argument list of the partial specialization includes a non
-type argument whose type depends on a template parameter.

what do my doing wrong? thanks

I put workaround in comments. Apparently I cannot do arithmetic in template specialization? seems counterintuitive.

here is my final solution in the problem to be solved. Basically, consecutive index requires one multiplication only.

130 template<size_t _1,size_t _2, bool consecutive = (_1 == _2 - 1)>
131 struct integral_index_ {
132     template<typename T, typename U>
133     __device__
134     static T eval(const T (&N)[4], const U &index) {
135         T j = index/N[_1];
136         return ((index - j*N[_1])*range<0,_1>::multiply(N) +
137                 j*range<0,_2>::multiply(N));
138     }
139 };
140
141 template<size_t _1,size_t _2>
142 struct integral_index_<_1, _2, true> {
143     template<typename T, typename U>
144     __device__
145     static T eval(const T (&N)[4], const U &index) {
146         return index*range<0,_1>::multiply(N);
147     }
148 };
149
150 template<size_t _1,size_t _2, typename T, typename U>
151 __device__
152 T integral_index(const T (&N)[4], const U &index) {
153     return integral_index_<_1,_2>::eval(N, index);
154 }

Answer 1

I am posting my solution is suggested by GMan

130 template<size_t _1,size_t _2, bool consecutive = (_1 == _2 - 1)>
131 struct integral_index_ {
132     template<typename T, typename U>
133     __device__
134     static T eval(const T (&N)[4], const U &index) {
135         T j = index/N[_1];
136         return ((index - j*N[_1])*range<0,_1>::multiply(N) +
137                 j*range<0,_2>::multiply(N));
138     }
139 };
140
141 template<size_t _1,size_t _2>
142 struct integral_index_<_1, _2, true> {
143     template<typename T, typename U>
144     __device__
145     static T eval(const T (&N)[4], const U &index) {
146         return index*range<0,_1>::multiply(N);
147     }
148 };
149
150 template<size_t _1,size_t _2, typename T, typename U>
151 __device__
152 T integral_index(const T (&N)[4], const U &index) {
153     return integral_index_<_1,_2>::eval(N, index);
154 }