Performance

Benchmarks

Per-call timing for all measured functions across 5 platforms. All figures from the Phase 1 and Phase 2 validation runs on real hardware.

ARM64 M1 Pro

Apple clang 17, -O2

complete

ARM64 M4 Pro

Apple clang 21, -O2

complete

x86-64 i7-13700H

gcc 11.4, Ubuntu 22.04, -O2

complete

ESP32-S3 LX7

ESP-IDF v5.5.2, 240 MHz

complete

Windows x64 MSVC

MSVC 14.51 / VS 2026 Build Tools

complete

Phase 1 — Core functions

linalg, stats, roots, integrate, differentiate, interpolate, poly, ode.

Function	Params	M1 Pro	M4 Pro	x86 i7	ESP32-S3	Win MSVC
numx_vec_dot	n=4	2 ns	—	—	5,456 ns‡	91 ns‡
numx_vec_norm	L2, n=2	7 ns	—	166 ns‡	11,970 ns‡	166 ns‡
numx_vec_cross3	—	1 ns	—	—	332 ns	3 ns
numx_mat_mul	2×2	6 ns	—	—	11,262 ns‡	98 ns‡
numx_mat_det	4×4	5 ns	—	—	5,236 ns	74 ns
numx_mat_transpose	8×8	—	—	—	7,351 ns	79 ns
numx_lu_decompose	4×4	83 ns	142 ns§	29 ns	10,466 ns	110 ns
numx_lu_solve	4×4, pre-factored	—	§	11 ns	4,418 ns	55 ns
numx_stats_mean	n=8	2 ns	2 ns	37 ns†	6,194 ns†	197 ns†
numx_stats_variance	pop, n=8	8 ns	11 ns	395 ns†	69,560 ns†	1,054 ns†
numx_stats_median	n=8	37 ns	67 ns	6,625 ns†	1.11 ms†	18,588 ns†
numx_stats_percentile	p50, n=8	—	32 ns	3,297 ns†	—	9,390 ns†
numx_root_bisect	x²-2, tol=1e-6	108 ns	65 ns	100 ns	11,819 ns	121 ns
numx_root_newton	x²-2, tol=1e-6	9 ns	10 ns	10 ns	5,039 ns	49 ns
numx_root_brent	x²-2, tol=1e-6	70 ns	61 ns	103 ns	19,858 ns	125 ns
numx_integrate_trap	n=100	111 ns	117 ns	139 ns	24,487 ns	—
numx_integrate_simpson	n=100	102 ns	104 ns	183 ns	28,868 ns	—
numx_integrate_gauss	npts=2	4 ns	2 ns	4 ns	1,066 ns	—
numx_diff_forward	—	3 ns	2 ns	3 ns	864 ns	8 ns
numx_diff_central	—	3 ns	2 ns	2 ns	939 ns	7 ns
numx_diff_richardson	—	4 ns	4 ns	4 ns	2,141 ns	11 ns
numx_interp_linear	n=5	2 ns	2 ns	3 ns	1,381 ns	—
numx_interp_spline_eval	n=5, pre-built	3 ns	2 ns	3 ns	2,479 ns	—
numx_interp_chebyshev	n=8	118 ns	137 ns	315 ns	126,311 ns	—
numx_poly_eval	degree=3	3 ns	1 ns	1 ns	407 ns	—
numx_poly_roots	degree=3	78 ns	41 ns	104 ns	20,350 ns	—
numx_ode_rk4	n=1, 100 steps	3,363 ns	—	—	173,201 ns	1,745 ns
numx_ode_rk45	tol=1e-4	470 ns	—	—	39,634 ns	339 ns

† x86 / ESP32 / Win stats benchmarks used n=128; M1 / M4 Pro used n=8. x86 / ESP32 / Win vec_dot and vec_norm used n=64.

‡ ESP32 and Win measured mat_mul and mat_det at 4×4; M1 Pro at 2×2. vec_dot / vec_norm at larger n on non-Apple platforms.

§ M4 Pro lu_decompose time includes lu_solve in a single combined measurement; lu_solve row shows § to indicate this.

Phase 2 — Advanced modules

autodiff, fft, signal, sketch (rsvd), compressed_sensing.

Function	Params	M1 Pro	M4 Pro	x86 i7	ESP32-S3	Win MSVC
numx_dual (fwd)	mul-chain depth=10	8 ns	—¶	20 ns	—	—
numx_tape (rev)	grad x²+y²	667 ns	1,115 ns	1,083 ns	—	—
numx_tape (rev)	grad x²+y²+z²	690 ns	—	1,105 ns	—	—
numx_fft_f32	N=64	2,547 ns	2,767 ns	3,582 ns	2.58 ms⚠	12,420 ns
numx_fft_f32	N=256	13,507 ns	10,429 ns	22,578 ns	13.8 ms⚠	70,745 ns
numx_fft_f32	N=512	30,423 ns	23,218 ns	54,699 ns	31.1 ms⚠	161,765 ns
numx_ifft_f32	N=256	13,470 ns	10,134 ns	22,475 ns	13.8 ms⚠	71,473 ns
numx_fft_q15	N=256	12,981 ns	10,326 ns	23,029 ns	14.3 ms⚠	69,217 ns
numx_fft_magnitude	N=256	19,542 ns	16,349 ns	16,336 ns	3,684 µs⚠	29,800 ns
numx_signal_window_hann	n=512	3,839 ns	3,319 ns	9,058 ns	4,531 ns*	—
numx_signal_convolve	xn=256, hn=32	2,310 ns	1,343 ns	3,241 ns	668 ns*	—
numx_signal_fir	xn=256, ntaps=32	4,892 ns	3,042 ns	3,052 ns	1,344 ns*	—
numx_signal_iir_biquad	n=256	770 ns	334 ns	508 ns	521 ns*	—
numx_signal_ema	n=256, alpha=0.1	540 ns	275 ns	318 ns	303 ns*	—
numx_sketch_rsvd	16×16, rank=4	375,420 ns	242,060 ns	332,972 ns	—	466,460 ns
numx_sketch_rsvd	32×32, rank=8	953,090 ns	606,790 ns	805,758 ns	—	—
numx_sketch_rsvd	64×64, rank=8	1,101,590 ns	667,210 ns	931,322 ns	—	—
numx_cs_spectral_norm	16×32, iter=32	21,910 ns	14,030 ns	20,327 ns	62,570 ns	—
numx_cs_omp	16×32, k=4	1,170 ns	860 ns	1,363 ns	3,670 ns	—
numx_cs_ista	16×32, λ=0.1, iter=500	167,650 ns	111,440 ns	182,629 ns	161,090 ns∥	—

¶ M4 Pro autodiff ran a "dual fwd x2" micro-benchmark; "mul-chain depth=10" result not available for that platform.

⚠ ESP32 FFT timings are ~1000× above expectation due to a software-float bug in the trig kernel (priv_cos/priv_sin calls __divsf3 instead of the hardware FPU). This is a known implementation bug, not a platform limitation.

* ESP32 signal benchmarks used smaller arrays (n=64–128) than the 256-element benchmark on other platforms.

∥ ESP32 ISTA measured at iter=100; other platforms at iter=500.

Methodology

Timer

clock_gettime(CLOCK_MONOTONIC) on Linux/macOS. QueryPerformanceCounter on Windows. esp_timer_get_time() on ESP32 (1 µs resolution). Per-call time = total wall time / N iterations.

Iteration counts

N ranges from 100 (sketch_rsvd, rsvd 64×64) to 100,000 (vec_dot, diff_*). Fast functions use higher N to amortise timer overhead. Slow functions (ODE, sketch) use lower N to keep total run time under a minute.

Build flags

float32 throughout (default build, NUMX_USE_DOUBLE not set). -O2 on all platforms. Apple clang 17 on M1 Pro, Apple clang 21 on M4 Pro, gcc 11.4 on x86-64, MSVC 14.51 on Windows, xtensa-esp32s3-elf-gcc on ESP32-S3.

Isolation

Apple results from a clean-rebooted system with no other user sessions. x86-64 results from a shared Ubuntu lab machine (±10-15% variance). ESP32-S3 at 240 MHz (actual clock; task-watchdog may fire on long loops — results remain valid).