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| template<typename... Xs>  | 
| __host__ constexpr __device__ auto  | ck::make_multi_index (Xs &&... xs) | 
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| template<index_t NSize>  | 
| __host__ constexpr __device__ auto  | ck::make_zero_multi_index () | 
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| template<typename T >  | 
| __host__ constexpr __device__ auto  | ck::to_multi_index (const T &x) | 
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| template<index_t NSize, typename X >  | 
| __host__ constexpr __device__ auto  | ck::operator+= (MultiIndex< NSize > &y, const X &x) | 
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| template<index_t NSize, typename X >  | 
| __host__ constexpr __device__ auto  | ck::operator-= (MultiIndex< NSize > &y, const X &x) | 
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| template<index_t NSize, typename T >  | 
| __host__ constexpr __device__ auto  | ck::operator+ (const MultiIndex< NSize > &a, const T &b) | 
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| template<index_t NSize, typename T >  | 
| __host__ constexpr __device__ auto  | ck::operator- (const MultiIndex< NSize > &a, const T &b) | 
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| template<index_t NSize, typename T >  | 
| __host__ constexpr __device__ auto  | ck::operator* (const MultiIndex< NSize > &a, const T &b) | 
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