# Dot Products > NumKong for C Dot products are one of the broadest parts of the native SDK. They include real, complex, packed-binary, mini-float, and mixed-precision forms. ```c nk_f32c_t a[384]; nk_f32c_t b[384]; nk_f64c_t out = {0, 0}; // widened f32c → f64c output nk_dot_f32c_best(a, b, 384, &out, capabilities, NULL); // complex inner product nk_vdot_f32c_best(a, b, 384, &out, capabilities, NULL); // conjugated variant, like numpy.vdot ``` For quantized retrieval pipelines, the storage format often matters more than the nominal math family. The native SDK lets you keep the compact representation and still get a widened output. `#include ` ## nk_dot_*_best Dot product computing the sum of elementwise products between two vectors. ```c nk_status_t nk_dot_f32_best( nk_f32_t const *a, nk_f32_t const *b, nk_size_t n, nk_f64_t *result, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_dot_f32_best`: a, b `nk_f32_t`, result `nk_f64_t` - `nk_dot_f64_best`: a, b `nk_f64_t`, result `nk_f64_t` - `nk_dot_f16_best`: a, b `nk_f16_t`, result `nk_f32_t` - `nk_dot_bf16_best`: a, b `nk_bf16_t`, result `nk_f32_t` - `nk_dot_i8_best`: a, b `nk_i8_t`, result `nk_i32_t` - `nk_dot_u8_best`: a, b `nk_u8_t`, result `nk_u32_t` - `nk_dot_i4_best`: a, b `nk_i4x2_t`, result `nk_i32_t` - `nk_dot_u4_best`: a, b `nk_u4x2_t`, result `nk_u32_t` - `nk_dot_e4m3_best`: a, b `nk_e4m3_t`, result `nk_f32_t` - `nk_dot_e5m2_best`: a, b `nk_e5m2_t`, result `nk_f32_t` - `nk_dot_e2m3_best`: a, b `nk_e2m3_t`, result `nk_f32_t` - `nk_dot_e2m1_best`: a, b `nk_e2m1x2_t`, result `nk_f32_t` - `nk_dot_e3m2_best`: a, b `nk_e3m2_t`, result `nk_f32_t` - `nk_dot_f32` backends: serial, neon, sve, haswell, skylake, rvv, v128relaxed, powervsx, loongsonasx - `nk_dot_f64` backends: serial, neon, sve, haswell, skylake, rvv, v128relaxed, powervsx, loongsonasx - `nk_dot_f16` backends: serial, neon, neonfhm, svehalf, haswell, skylake, diamond, rvv, rvvhalf, v128relaxed, powervsx, loongsonasx - `nk_dot_bf16` backends: serial, neon, neonbfdot, svebfdot, haswell, skylake, genoa, rvv, rvvbf16, v128, v128relaxed, powervsx, loongsonasx - `nk_dot_i8` backends: serial, neonsdot, svesdot, haswell, skylake, icelake, alder, sierra, rvv, v128, v128relaxed, powervsx, loongsonasx - `nk_dot_u8` backends: serial, neonsdot, svesdot, haswell, skylake, icelake, alder, sierra, rvv, v128, v128relaxed, powervsx, loongsonasx - `nk_dot_i4` backends: serial, neonsdot, haswell, icelake, rvv, v128relaxed - `nk_dot_u4` backends: serial, neonsdot, haswell, icelake, rvv, v128relaxed - `nk_dot_e4m3` backends: serial, neon, neonfhm, neonbfdot, neonfp8, haswell, skylake, icelake, diamond, rvv, rvvhalf, rvvbf16, v128relaxed - `nk_dot_e5m2` backends: serial, neon, neonfhm, neonbfdot, neonfp8, haswell, skylake, genoa, diamond, rvv, rvvhalf, rvvbf16, v128relaxed - `nk_dot_e2m3` backends: serial, neon, neonsdot, neonfp8, haswell, skylake, icelake, alder, sierra, rvv, v128relaxed - `nk_dot_e2m1` backends: serial, neonsdot, haswell, skylake, alder, sierra, rvv, v128relaxed - `nk_dot_e3m2` backends: serial, neon, neonsdot, neonfp8, haswell, skylake, icelake, rvv, v128relaxed - `a` (in): The first vector. - `b` (in): The second vector. - `n` (in): Counts dimensions, a multiple of the values per byte. - `result` (out): The output dot product value. - `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: The output value can be negative. Notes: The output value is zero if and only if the two vectors are orthogonal. Notes: Defined for floating-point, integer, and binary data types. 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_dot_u1_best Dot product of two binary vectors, the number of bit positions both set. ```c nk_status_t nk_dot_u1_best( nk_u1x8_t const *a, nk_u1x8_t const *b, nk_size_t n_bits, nk_u32_t *result, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_dot_u1` backends: serial, neon, haswell, icelake, rvv, rvvbb, v128, powervsx - `a` (in): The first vector. - `b` (in): The second vector. - `n_bits` (in): Counts dimensions in bits, a multiple of the bits per byte. - `result` (out): The output dot product value. - `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. 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_dot_*_best Complex dot product computing the sum of elementwise products between two complex vectors. ```c nk_status_t nk_dot_f32c_best( nk_f32c_t const *a_pairs, nk_f32c_t const *b_pairs, nk_size_t count_pairs, nk_f64c_t *result, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_dot_f32c_best`: a_pairs, b_pairs `nk_f32c_t`, result `nk_f64c_t` - `nk_dot_f64c_best`: a_pairs, b_pairs `nk_f64c_t`, result `nk_f64c_t` - `nk_dot_f16c_best`: a_pairs, b_pairs `nk_f16c_t`, result `nk_f32c_t` - `nk_dot_bf16c_best`: a_pairs, b_pairs `nk_bf16c_t`, result `nk_f32c_t` - `nk_dot_f32c` backends: serial, neon, sve, haswell, skylake, rvv, v128relaxed - `nk_dot_f64c` backends: serial, neon, sve, haswell, skylake, rvv, v128relaxed - `nk_dot_f16c` backends: serial, neon, neonfhm, svehalf, haswell - `nk_dot_bf16c` backends: serial, neonbfdot, haswell, genoa - `a_pairs` (in): The first complex vector. - `b_pairs` (in): The second complex vector. - `count_pairs` (in): The number of complex pairs in the vectors. - `result` (out): The output complex value as {real, imag}. - `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. 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_vdot_*_best Complex conjugate dot product between two complex vectors. ```c nk_status_t nk_vdot_f32c_best( nk_f32c_t const *a_pairs, nk_f32c_t const *b_pairs, nk_size_t count_pairs, nk_f64c_t *result, nk_capability_t capabilities, nk_stream_t stream); ``` - `nk_vdot_f32c_best`: a_pairs, b_pairs `nk_f32c_t`, result `nk_f64c_t` - `nk_vdot_f64c_best`: a_pairs, b_pairs `nk_f64c_t`, result `nk_f64c_t` - `nk_vdot_f16c_best`: a_pairs, b_pairs `nk_f16c_t`, result `nk_f32c_t` - `nk_vdot_bf16c_best`: a_pairs, b_pairs `nk_bf16c_t`, result `nk_f32c_t` - `nk_vdot_f32c` backends: serial, neon, sve, haswell, skylake, rvv, v128relaxed - `nk_vdot_f64c` backends: serial, neon, sve, haswell, skylake, rvv, v128relaxed - `nk_vdot_f16c` backends: serial, neon, neonfhm, svehalf, haswell - `nk_vdot_bf16c` backends: serial, neonbfdot, haswell, genoa - `a_pairs` (in): The first complex vector. - `b_pairs` (in): The second complex vector. - `count_pairs` (in): The number of complex pairs in the vectors. - `result` (out): The output complex value as {real, imag}. - `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. 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_dot_output_dtype Returns the output dtype for dot products. ```c nk_dtype_t nk_dot_output_dtype(nk_dtype_t dtype); ``` ## nk_dot_error_bound Returns the error bound of 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_dot_error_bound(nk_dtype_t dtype); ``` ## nk_dot_find_kernel Finds the dot product kernel of `kind` for `dtype`, from the best of `capabilities`. ```c nk_status_t nk_dot_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.