# Sparse Operations > NumKong for C Sparse helpers cover sorted-index intersection and weighted sparse dot products. ```c nk_u32_t a_idx[] = {1, 3, 5, 7}, b_idx[] = {3, 4, 5, 8}; nk_u32_t intersection[4]; nk_size_t count = 0; nk_sparse_intersect_u32_best(a_idx, b_idx, 4, 4, intersection, &count, capabilities, NULL); assert(count == 2 && "indices 3 and 5"); nk_f32_t a_weights[] = {1.0f, 2.0f, 3.0f, 4.0f}; nk_f32_t b_weights[] = {5.0f, 6.0f, 7.0f, 8.0f}; nk_f64_t result = 0; nk_sparse_dot_u32f32_best(a_idx, b_idx, a_weights, b_weights, 4, 4, &result, capabilities, NULL); assert(result > 0 && "weighted dot over shared indices"); ``` This family deserves explicit mention because it is not just sparse dot. Set intersection itself is often the workload. `#include ` ## nk_sparse_intersect_*_best Set intersection between two sorted u16 arrays. ```c nk_status_t nk_sparse_intersect_u16_best( nk_u16_t const *a, nk_u16_t const *b, nk_size_t a_length, nk_size_t b_length, nk_u16_t *result, nk_size_t *count, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_sparse_intersect_u16_best`: a, b, result `nk_u16_t` - `nk_sparse_intersect_u32_best`: a, b, result `nk_u32_t` - `nk_sparse_intersect_u64_best`: a, b, result `nk_u64_t` - `nk_sparse_intersect_u16` backends: serial, neon, sve2, icelake, haswell, turin - `nk_sparse_intersect_u32` backends: serial, neon, sve2, icelake, haswell, turin - `nk_sparse_intersect_u64` backends: serial, neon, sve2, icelake, haswell, turin - `a` (in): The first sorted array of indices. - `b` (in): The second sorted array of indices. - `a_length` (in): The number of elements in the first array. - `b_length` (in): The number of elements in the second array. - `result` (out): Output buffer for intersection elements, or NULL to count only. - `count` (out): The output intersection count. - `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports. - `stream` (in): Null on the CPU, or the GPU stream of that device to queue on. Notes: Inputs must be sorted in ascending order and contain unique elements. Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it. ## nk_sparse_dot_u16bf16_best Sparse dot-product over u16 indices with bf16 weights. ```c nk_status_t nk_sparse_dot_u16bf16_best( nk_u16_t const *a, nk_u16_t const *b, nk_bf16_t const *a_weights, nk_bf16_t const *b_weights, nk_size_t a_length, nk_size_t b_length, nk_f32_t *product, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_sparse_dot_u16bf16` backends: serial, neon, sve2, turin - `a` (in): The first sorted array of indices. - `b` (in): The second sorted array of indices. - `a_weights` (in): The bf16 weights for the first array. - `b_weights` (in): The bf16 weights for the second array. - `a_length` (in): The number of elements in the first array. - `b_length` (in): The number of elements in the second array. - `product` (out): The output dot product. - `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports. - `stream` (in): Null on the CPU, or the GPU stream of that device to queue on. Notes: Inputs must be sorted in ascending order and contain unique elements. Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it. ## nk_sparse_dot_u32f32_best Sparse dot-product over u32 indices with f32 weights. ```c nk_status_t nk_sparse_dot_u32f32_best( nk_u32_t const *a, nk_u32_t const *b, nk_f32_t const *a_weights, nk_f32_t const *b_weights, nk_size_t a_length, nk_size_t b_length, nk_f64_t *product, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_sparse_dot_u32f32` backends: serial, neon, sve2, icelake, haswell, turin - `a` (in): The first sorted array of indices. - `b` (in): The second sorted array of indices. - `a_weights` (in): The f32 weights for the first array. - `b_weights` (in): The f32 weights for the second array. - `a_length` (in): The number of elements in the first array. - `b_length` (in): The number of elements in the second array. - `product` (out): The output dot product. - `capabilities` (in): One device's capabilities, like [`nk_cpu_capabilities_enabled`](https://www.unum.cloud/docs/numkong/c/runtime-dispatch.md#nk_cpu_capabilities_enabled) reports. - `stream` (in): Null on the CPU, or the GPU stream of that device to queue on. Notes: Inputs must be sorted in ascending order and contain unique elements. Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) No capability in `capabilities` has it. ## nk_sparse_dot_output_dtype Returns the output dtype for sparse dot products. ```c nk_dtype_t nk_sparse_dot_output_dtype(nk_dtype_t dtype); ``` ## nk_sparse_dot_error_bound Returns the error bound of sparse dot products, per [`nk_accumulation_error_bound`](https://www.unum.cloud/docs/numkong/c/scalar-types.md#nk_accumulation_error_bound) of their output. ```c nk_f64_t nk_sparse_dot_error_bound(nk_dtype_t dtype); ``` ## nk_sparse_find_kernel Finds the sparse kernel of `kind` for `dtype`, from the best of `capabilities`. ```c nk_status_t nk_sparse_find_kernel( nk_kernel_kind_t kind, nk_dtype_t dtype, nk_capability_t capabilities, nk_kernel_punned_t *kernel, nk_capability_t *capability); ``` - `kind` (in): The verb whose kernel to find. - `dtype` (in): The input type the kernel reads. - `capabilities` (in): The mask to pick the best capability from. - `kernel` (out): The kernel, or null when none of `capabilities` has it. - `capability` (out): The capability the kernel belongs to, or zero. Statuses: - [`nk_missing_kernel_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_kernel_k) - [`nk_missing_library_k`](https://www.unum.cloud/docs/numkong/c/quickstart.md#nk_missing_library_k) Header-only.