numx

A portable, scientific-grade numerical computing library in pure C99 for resource-constrained embedded systems.

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Why numx

Most numerical libraries assume a heap, an OS, and a math coprocessor. numx assumes none of those things. It targets the processors where computation is hardest: ESP32, ARM Cortex-M/A, AVR, RISC-V — and it brings algorithms previously considered out of reach (automatic differentiation, compressed sensing, post-quantum NTT) to those platforms.

Every function is reentrant, allocation-free, and returns a typed status code. The entire precision of the library — float32 or float64 — is switchable with a single compile flag.

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Module status

Module	Functions	Status
linalg	dot, norm, cross, mat_mul, transpose, det, LU	✅ complete
stats	mean, variance, median, percentile	✅ complete
roots	bisect, newton, brent	✅ complete
integrate	trap, simpson, gauss	✅ complete
differentiate	forward, central, richardson	✅ complete
interpolate	linear, cubic spline, chebyshev	✅ complete
poly	eval (Horner), roots (Newton + deflation)	✅ complete
ode	rk4, rk45 (adaptive)	✅ complete
signal	windows, FIR, IIR, convolve, correlate, peaks, EMA	✅ complete
fft	Cooley-Tukey f32, Q15, IFFT, magnitude	✅ complete
autodiff	forward-mode (dual numbers), reverse-mode (static tape)	✅ complete
compressed_sensing	OMP, ISTA	✅ complete
sketch	randomized SVD (Halko-Martinsson-Tropp)	✅ complete
ntt	Number Theoretic Transform (constant-time, Kyber/Dilithium params)	🔧 planned

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Hardware validation

All results are device-run, per-formula values with measured error margins — not simulation. Full tables: validation/results/.

Platform	Toolchain	Modules	Tests
x86-64 — Intel i7-13700H / Ubuntu 22.04	gcc 11.4.0 -O2 / float32	13 / 13	300 / 300 ✅
ARM64 — Apple M4 Pro / macOS 26.2	Apple clang 21.0.0 -O2 / float32	13 / 13	300 / 300 ✅
ARM64 — Apple M1 Pro / macOS 26.2	Apple clang 17.0.0 -O2 / float32	13 / 13	300 / 300 ✅
Windows x64 — MSVC 14.51 (VS 2026 Build Tools)	MSVC /O2 / float32	13 / 13	295 / 295 ✅
Windows x64 — MSVC 14.51 (VS 2026 Build Tools)	MSVC /O2 / float64	13 / 13	294 / 294 ✅
ESP32-S3 — Xtensa LX7 / ESP-IDF v5.5.2	xtensa-esp32s3-elf-gcc -O2 / float32	13 / 13	548 / 550 ✅

ESP32-S3: 2 sketch test cases fail due to rand() seed portability across libc implementations — the RSVD algorithm is correct; the test fixture is not portable. See FLAG S-01 in validation/results/sketch/sketch.md.

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Quick start

Option A — FetchContent (recommended)

include(FetchContent)
FetchContent_Declare(numx
  GIT_REPOSITORY https://github.com/NIKX-Tech/numx.git
  GIT_TAG        v0.1.0
)
FetchContent_MakeAvailable(numx)
target_link_libraries(my_target PRIVATE numx::numx)

Option B — clone and build locally

git clone https://github.com/NIKX-Tech/numx.git
cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build --parallel
ctest --test-dir build --output-on-failure

Switch to double precision:

cmake -B build -DCMAKE_BUILD_TYPE=Release -DNUMX_USE_DOUBLE=1

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Usage example

#include "numx/numx.h"

int main(void) {
    /* Switch precision via -DNUMX_USE_DOUBLE at compile time.      */
    /* All functions return numx_status_t — always check it.        */
    numx_real_t result;
    numx_status_t s = numx_integrate_simpson(my_func, 0.0f, 1.0f, 100, &result);
    if (s != NUMX_OK) {
        /* handle error */
        return 1;
    }
    return 0;
}

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Benchmarks

Per-call averages measured on physical hardware. Full tables: validation/results/.

Function	x86-64 (gcc -O2)	ESP32-S3 (240 MHz)
numx_vec_dot n=64	15 ns	5.5 µs
numx_mat_mul 4×4	26 ns	11 µs
numx_lu_decompose 4×4	29 ns	10 µs
numx_integrate_gauss npts=8	11 ns	2.7 µs
numx_root_brent tol=1e-6	103 ns	20 µs
numx_ode_rk45 tol=1e-4	239 ns	40 µs
numx_stats_median n=128	6.6 µs	1.1 ms
numx_fft_f32 N=64	3.6 µs	2.6 ms
numx_autodiff fwd chain-10	20 ns	358 ns

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Contributing

See CONTRIBUTING.md for the rules, templates, and the exact prompt pattern to use with Claude Code when adding a new algorithm.

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License

MIT — see LICENSE.

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Citation

Once the accompanying paper is published, cite as:

@software{numx2026,
  author  = {NIKX Technologies},
  title   = {numx: Scientific Numerical Computing for Embedded Systems},
  year    = {2026},
  url     = {https://github.com/NIKX-Tech/numx},
  license = {MIT}
}