NumKong
SIMD-accelerated distances, dot products, matrix ops, geospatial & geometric kernels for 16 numeric types — from 6-bit floats to 64-bit complex — across x86, Arm, RISC-V, and WASM, with bindings for Python, Rust, C, C++, Swift, JS, and Go 📐
Install / Use
/learn @ashvardanian/NumKongREADME
NumKong: Mixed Precision for All
NumKong (previously SimSIMD) is a portable mixed-precision math library with over 2000 kernels for x86, Arm, RISC-V, and WASM. It covers numeric types from 6-bit floats to 64-bit complex numbers, hardened against in-house 118-bit extended-precision baselines. Built alongside the USearch vector-search engine, it provides wider accumulators to avoid the overflow and precision loss typical of naive same-type arithmetic.
Latency, Throughput, & Numerical Stability
Most libraries return dot products in the same type as the input — Float16 × Float16 → Float16, Int8 × Int8 → Int8.
This leads to quiet overflow: a 2048-dimensional i8 dot product can reach ±10 million, but i8 maxes out at 127.
NumKong promotes to wider accumulators — Float16 → Float32, BFloat16 → Float32, Int8 → Int32, Float32 → Float64 — so results stay in range.
Single 2048-d dot product on Intel Sapphire Rapids, single-threaded. Each cell shows gso/s, mean relative error vs higher-precision reference. gso/s = Giga Scalar Operations per Second — a more suitable name than GFLOP/s when counting both integer and floating-point work. NumPy 2.4, PyTorch 2.10, JAX 0.9.
| Input | NumPy + OpenBLAS | PyTorch + MKL | JAX | NumKong |
| :----- | ----------------------: | ----------------------: | ----------------------: | --------------------: |
| | ░░░░░░░░░░░░░░ | ░░░░░░░░░░░░░░ | ░░░░░░░░░░░░░░ | ░░░░░░░░░░░░░░ |
| f64 | 2.0 gso/s, 1e-15 err | 0.6 gso/s, 1e-15 err | 0.4 gso/s, 1e-14 err | 5.8 gso/s, 1e-16 err |
| f32 | 1.5 gso/s, 2e-6 err | 0.6 gso/s, 2e-6 err | 0.4 gso/s, 5e-6 err | 7.1 gso/s, 2e-7 err |
| bf16 | — | 0.5 gso/s, 1.9% err | 0.5 gso/s, 1.9% err | 9.7 gso/s, 1.8% err |
| f16 | 0.2 gso/s, 0.25% err | 0.5 gso/s, 0.25% err | 0.4 gso/s, 0.25% err | 11.5 gso/s, 0.24% err |
| e5m2 | — | 0.7 gso/s, 4.6% err | 0.5 gso/s, 4.6% err | 7.1 gso/s, 0% err |
| i8 | 1.1 gso/s, overflow | 0.5 gso/s, overflow | 0.5 gso/s, overflow | 14.8 gso/s, 0% err |
A fair objection: PyTorch and JAX are designed for throughput, not single-call latency. They lower execution graphs through XLA or vendored BLAS libraries like Intel MKL and Nvidia cuBLAS. So here's the same comparison on a throughput-oriented workload — matrix multiplication:
Matrix multiplication (2048 × 2048) × (2048 × 2048) on Intel Sapphire Rapids, single-threaded. gso/s = Giga Scalar Operations per Second, same format. NumPy 2.4, PyTorch 2.10, JAX 0.9, same versions.
| Input | NumPy + OpenBLAS | PyTorch + MKL | JAX | NumKong |
| :----- | ----------------------: | -----------------------: | -----------------------: | -------------------: |
| | ░░░░░░░░░░░░░░ | ░░░░░░░░░░░░░░ | ░░░░░░░░░░░░░░ | ░░░░░░░░░░░░░░ |
| f64 | 65.5 gso/s, 1e-15 err | 68.2 gso/s, 1e-15 err | ~14.3 gso/s, 1e-15 err | 8.6 gso/s, 1e-16 err |
| f32 | 140 gso/s, 9e-7 err | 145 gso/s, 1e-6 err | ~60.5 gso/s, 1e-6 err | 37.7 gso/s, 4e-7 err |
| bf16 | — | 851 gso/s, 1.8% err | ~25.8 gso/s, 3.4% err | 458 gso/s, 3.6% err |
| f16 | 0.3 gso/s, 0.25% err | 140 gso/s, 0.37% err | ~26.1 gso/s, 0.35% err | 103 gso/s, 0.26% err |
| e5m2 | — | 0.4 gso/s, 4.6% err | ~26.4 gso/s, 4.6% err | 398 gso/s, 0% err |
| i8 | 0.4 gso/s, overflow | 50.0 gso/s, overflow | ~0.0 gso/s, overflow | 1279 gso/s, 0% err |
For f64, compensated "Dot2" summation reduces error by 10–50× compared to naive Float64 accumulation, depending on vector length.
For f32, widening to Float64 gives 5–10× lower error.
The library ships as a relatively small binary:
| Package | Size | Parallelism & Memory | Available For | | :--------------- | -----: | :------------------------------------------------ | :---------------- | | PyTorch + MKL | 705 MB | Vector & Tile SIMD, OpenMP Threads, Hidden Allocs | Python, C++, Java | | JAX + jaxlib | 357 MB | Vector SIMD, XLA Threads, Hidden Allocs | Python | | NumPy + OpenBLAS | 30 MB | Vector SIMD, Built-in Threads, Hidden Allocs | Python | | mathjs | 9 MB | No SIMD, No Threads, Many Allocs | JS | | NumKong | 5 MB | Vector & Tile SIMD, Your Threads, Your Allocs | 7 languages |
Every kernel is validated against 118-bit extended-precision baselines with per-type ULP budgets across log-normal, uniform, and Cauchy input distributions. Tests check triangle inequality, Cauchy-Schwarz bounds, NaN propagation, overflow detection, and probability-simplex constraints for each ISA variant. Results are cross-validated against OpenBLAS, Intel MKL, and Apple Accelerate. A broader throughput comparison is maintained in NumWars.
Quick Start
| Language | Install | Compatible with | Guide |
| :------- | :------------------------- | :----------------------------- | :------------------------------------------- |
| C / C++ | CMake, headers, & prebuilt | Linux, macOS, Windows, Android | include/README.md |
| Python | pip install | Linux, macOS, Windows | python/README.md |
| Rust | cargo add | Linux, macOS, Windows | rust/README.md |
| JS | npm install & import | Node.js, Bun, Deno & browsers | javascript/README.md |
| Swift | Swift Package Manager | macOS, iOS, tvOS, watchOS | swift/README.md |
| Go | go get | Linux, macOS, Windows via cGo | golang/README.md |
What's Inside
NumKong covers 16 numeric types — from 6-bit floats to 64-bit complex numbers — across dozens of operations and 30+ SIMD backends, with hardware-aware defaults: Arm prioritizes f16, x86 prioritizes bf16.
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