Element-Wise Arithmetic in NumKong

NumKong implements element-wise vector arithmetic: addition, scaling, blending, and fused multiply-add across all supported numeric types. Each operation reads one to three input vectors and writes one output vector of the same length, with scalar coefficients $\alpha$ and $\beta$ controlling linear combinations. Mixed-precision workflows use narrower input types (Float16, BFloat16, Float8) with Float32 intermediate computation and narrowed output.

Sum (addition):

$$\text{result}_i = a_i + b_i$$

Scale:

$$\text{result}_i = \alpha \cdot a_i + \beta$$

Blend:

$$\text{result}_i = \alpha \cdot a_i + \beta \cdot b_i$$

Fused multiply-add:

$$\text{result}_i = \alpha \cdot a_i \cdot b_i + \beta \cdot c_i$$

Reformulating as Python pseudocode:

import numpy as np

def fma(a: np.ndarray, b: np.ndarray, c: np.ndarray,
        alpha: float = 1.0, beta: float = 1.0) -> np.ndarray:
    return alpha * a * b + beta * c

def scale(a: np.ndarray, alpha: float = 1.0, beta: float = 0.0) -> np.ndarray:
    return alpha * a + beta

def add(a: np.ndarray, b: np.ndarray) -> np.ndarray:
    return a + b

def blend(a: np.ndarray, b: np.ndarray,
          alpha: float = 1.0, beta: float = 1.0) -> np.ndarray:
    return alpha * a + beta * b

Input & Output Types

Real and integer element-wise operations:

Input Type	Output Type	Description
f64	f64	64-bit IEEE 754 double precision
f32	f32	32-bit IEEE 754 single precision
f16	f16	16-bit IEEE 754 half precision
bf16	bf16	16-bit brain float
e4m3	e4m3	8-bit Float8: 4 exponent, 3 mantissa bits
e5m2	e5m2	8-bit Float8: 5 exponent, 2 mantissa bits
i8	i8	8-bit signed integers, saturating
u8	u8	8-bit unsigned integers, saturating
i16	i16	16-bit signed integers
u16	u16	16-bit unsigned integers
i32	i32	32-bit signed integers
u32	u32	32-bit unsigned integers
i64	i64	64-bit signed integers
u64	u64	64-bit unsigned integers

Complex element-wise operations:

Input Type	Output Type	Description
f64c	f64c	64-bit complex pairs
f32c	f32c	32-bit complex pairs

Optimizations

Widening-Narrowing Pipeline for Sub-32-bit Types

nk_each_fma_f16_haswell, nk_each_blend_bf16_neonbfdot, nk_each_scale_e4m3_haswell widen inputs to Float32 before arithmetic, then narrow the result back to the original type. The widen-compute-narrow pipeline costs 2 extra conversion instructions per element but guarantees Float32-precision intermediate results — critical for FMA where naive Float16 multiplication would lose 5+ bits of mantissa. Haswell processes 8 Float16 elements per cycle: VCVTPH2PS (widen) -> VFMADD231PS (FMA) -> VCVTPS2PH (narrow), fully pipelined across 3 execution ports.

Saturating Integer Arithmetic

nk_each_sum_i8_haswell, nk_each_sum_u8_neonhalf use saturating addition — clamping to type bounds instead of wrapping on overflow. Haswell uses VPADDSB / VPADDUSB for signed/unsigned 8-bit saturation in a single instruction (32 elements per cycle at YMM width). Serial fallback implements saturation via branch-free min/max: result = min(max(a + b, TYPE_MIN), TYPE_MAX) with overflow detection through sign-bit comparison.

Complex Number Layout

nk_each_fma_f32c_serial, nk_each_blend_f64c_serial operate on interleaved real/imaginary pairs: [re0, im0, re1, im1, ...]. Addition and scaling treat complex vectors as 2N-length real vectors — no special handling needed. FMA requires cross-lane operations for the imaginary part: re(a*b) = re(a)*re(b) - im(a)*im(b), implemented via VFMADDSUB231PS which alternates add/subtract across even/odd lanes.

Performance

The following performance tables are produced by manually re-running nk_test and nk_bench included internal tools to measure both accuracy and throughput at different input shapes. The input size is controlled by the NK_DENSE_DIMENSIONS environment variable and set to 256, 1024, and 4096 elements. The throughput is measured in GB/s as the number of input bytes read per second. Accuracy is reported as mean ULP (units in last place) unless noted otherwise — the average number of representable floating-point values between the result and the exact answer. Rows marked 🧩 use external BLAS baselines rather than NumKong kernels. Each kernel runs for at least 20 seconds per configuration. Benchmark threads are pinned to specific cores; on machines with heterogeneous core types (e.g., Apple P/E cores), only the fastest cores are used. Workloads that significantly degrade CPU frequencies (Intel AMX, Apple SME) run in separate passes to avoid affecting throughput measurements of other kernels.

Intel Sapphire Rapids

Native

Kernel	256	1024	4096
f64	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
sum_f64_with_blas 🧩	12.1 gb/s	8.63 gb/s	6.83 gb/s
each_blend_f64_with_blas 🧩	11.3 gb/s	8.80 gb/s	6.71 gb/s
nk_each_sum_f64_serial	16.7 gb/s, 0 ulp	17.2 gb/s, 0 ulp	10.9 gb/s, 0 ulp
nk_each_sum_f64_haswell	14.7 gb/s, 0 ulp	10.2 gb/s, 0 ulp	7.99 gb/s, 0 ulp
nk_each_sum_f64_skylake	16.4 gb/s, 0 ulp	16.7 gb/s, 0 ulp	8.59 gb/s, 0 ulp
nk_each_scale_f64_serial	11.4 gb/s, 0 ulp	12.5 gb/s, 0 ulp	7.99 gb/s, 0 ulp
nk_each_scale_f64_haswell	9.61 gb/s, 0 ulp	9.22 gb/s, 0 ulp	5.08 gb/s, 0 ulp
nk_each_scale_f64_skylake	11.2 gb/s, 0 ulp	11.9 gb/s, 0 ulp	6.30 gb/s, 0 ulp
nk_each_blend_f64_serial	16.4 gb/s, 1.4 ulp	16.4 gb/s, 1.1 ulp	11.8 gb/s, 1.1 ulp
nk_each_blend_f64_haswell	13.4 gb/s, 1.5 ulp	11.2 gb/s, 1.5 ulp	7.85 gb/s, 1.1 ulp
nk_each_blend_f64_skylake	16.5 gb/s, 1.7 ulp	15.9 gb/s, 1.5 ulp	8.55 gb/s, 1.1 ulp
nk_each_fma_f64_serial	20.1 gb/s, 1.5 ulp	20.8 gb/s, 1.5 ulp	11.7 gb/s, 1.3 ulp
nk_each_fma_f64_haswell	16.8 gb/s, 1.5 ulp	11.1 gb/s, 1.5 ulp	9.42 gb/s, 2.8 ulp
nk_each_fma_f64_skylake	19.8 gb/s, 1.4 ulp	20.4 gb/s, 1.5 ulp	11.6 gb/s, 2.7 ulp
f32	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
sum_f32_with_blas 🧩	11.6 gb/s	12.8 gb/s	7.57 gb/s
each_blend_f32_with_blas 🧩	10.3 gb/s	9.60 gb/s	6.69 gb/s
nk_each_sum_f32_serial	16.9 gb/s, 0 ulp	18.8 gb/s, 0 ulp	15.7 gb/s, 0 ulp
nk_each_sum_f32_haswell	14.6 gb/s, 0 ulp	14.3 gb/s, 0 ulp	8.49 gb/s, 0 ulp
nk_each_sum_f32_skylake	16.7 gb/s, 0 ulp	17.9 gb/s, 0 ulp	16.5 gb/s, 0 ulp
nk_each_scale_f32_serial	10.8 gb/s, 0 ulp	13.0 gb/s, 0 ulp	12.1 gb/s, 0 ulp
nk_each_scale_f32_haswell	9.26 gb/s, 0 ulp	10.2 gb/s, 0 ulp	6.22 gb/s, 0 ulp
nk_each_scale_f32_skylake	12.3 gb/s, 0 ulp	11.9 gb/s, 0 ulp	12.9 gb/s, 0 ulp
nk_each_blend_f32_serial	16.2 gb/s, 351 ulp	18.7 gb/s, 2.0 ulp	17.4 gb/s, 1.4 ulp
nk_each_blend_f32_haswell	14.5 gb/s, 2.3 ulp	14.2 gb/s, 2.1 ulp	8.16 gb/s, 1.3 ulp
nk_each_blend_f32_skylake	15.7 gb/s, 1.9 ulp	17.2 gb/s, 1.8 ulp	15.9 gb/s, 1.3 ulp
nk_each_fma_f32_serial	20.1 gb/s, 1.4 ulp	18.7 gb/s, 2.1 ulp	19.0 gb/s, 1.6 ulp
nk_each_fma_f32_haswell	18.4 gb/s, 1.4 ulp	15.3 gb/s, 1.8 ulp	9.52 gb/s, 1.5 ulp
nk_each_fma_f32_skylake	20.8 gb/s, 1.4 ulp	19.3 gb/s, 1.7 ulp	16.5 gb/s, 1.5 ulp
bf16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_bf16_serial	0.175 gb/s, 0 ulp	0.178 gb/s, 0 ulp	0.173 gb/s, 0 ulp
nk_each_sum_bf16_haswell	7.97 gb/s, 0 ulp	9.33 gb/s, 0 ulp	10.3 gb/s, 0 ulp
nk_each_sum_bf16_skylake	11.4 gb/s, 0 ulp	11.2 gb/s, 0 ulp	14.1 gb/s, 0 ulp
nk_each_scale_bf16_serial	0.128 gb/s, 0 ulp	0.119 gb/s, 0 ulp	0.132 gb/s, 0 ulp
nk_each_scale_bf16_haswell	6.08 gb/s, 0 ulp	6.55 gb/s, 0 ulp	6.92 gb/s, 0 ulp
nk_each_scale_bf16_skylake	7.43 gb/s, 0 ulp	8.04 gb/s, 0 ulp	8.45 gb/s, 0 ulp
nk_each_blend_bf16_serial	0.211 gb/s, 0 ulp	0.204 gb/s, 0 ulp	0.224 gb/s, 0 ulp
nk_each_blend_bf16_haswell	8.58 gb/s, 2.2 ulp	9.44 gb/s, 1.5 ulp	10.2 gb/s, 1.5 ulp
nk_each_blend_bf16_skylake	10.3 gb/s, 2.3 ulp	11.9 gb/s, 1.3 ulp	13.4 gb/s, 1.5 ulp
nk_each_fma_bf16_serial	0.264 gb/s, 0 ulp	0.260 gb/s, 0 ulp	0.256 gb/s, 0 ulp
nk_each_fma_bf16_haswell	10.9 gb/s, 1.5 ulp	10.3 gb/s, 0.9 ulp	11.4 gb/s, 1.0 ulp
nk_each_fma_bf16_skylake	14.1 gb/s, 1.2 ulp	13.0 gb/s, 0.7 ulp	15.8 gb/s, 1.1 ulp
f16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_f16_serial	33.7 gb/s, 0 ulp	16.1 gb/s, 0 ulp	18.8 gb/s, 0 ulp
nk_each_sum_f16_haswell	14.4 gb/s, 0 ulp	11.8 gb/s, 0 ulp	9.84 gb/s, 0 ulp
nk_each_sum_f16_sapphire	39.2 gb/s, 0 ulp	17.0 gb/s, 0 ulp	18.9 gb/s, 0 ulp
nk_each_scale_f16_serial	0.423 gb/s, 0 ulp	0.282 gb/s, 0 ulp	0.409 gb/s, 0 ulp
nk_each_scale_f16_haswell	8.92 gb/s, 0 ulp	8.59 gb/s, 0 ulp	8.15 gb/s, 0 ulp
nk_each_scale_f16_skylake	17.0 gb/s, 0 ulp	10.7 gb/s, 0 ulp	12.1 gb/s, 0 ulp
nk_each_blend_f16_serial	0.769 gb/s, 1.3 ulp	0.669 gb/s, 1.6 ulp	0.792 gb/s, 1.5 ulp
nk_each_blend_f16_haswell	13.5 gb/s, 1.2 ulp	11.0 gb/s, 1.4 ulp	11.7 gb/s, 1.5 ulp
nk_each_blend_f16_skylake	16.9 gb/s, 1.3 ulp	13.9 gb/s, 1.4 ulp	14.2 gb/s, 1.1 ulp
nk_each_fma_f16_serial	0.965 gb/s, 1.0 ulp	0.787 gb/s, 1.1 ulp	0.952 gb/s, 1.2 ulp
nk_each_fma_f16_haswell	15.2 gb/s, 1.4 ulp	13.6 gb/s, 1.0 ulp	15.7 gb/s, 1.1 ulp
nk_each_fma_f16_skylake	16.3 gb/s, 1.3 ulp	16.2 gb/s, 1.3 ulp	15.3 gb/s, 1.1 ulp
e4m3	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e4m3_serial	0.0966 gb/s, 0 ulp	0.0943 gb/s, 0 ulp	0.0946 gb/s, 0 ulp
nk_each_sum_e4m3_haswell	0.895 gb/s, 0 ulp	0.772 gb/s, 0 ulp	0.824 gb/s, 0 ulp
nk_each_sum_e4m3_skylake	1.48 gb/s, 0 ulp	1.34 gb/s, 0 ulp	1.40 gb/s, 0 ulp
nk_each_sum_e4m3_sapphire	2.12 gb/s, 0 ulp	1.89 gb/s, 0 ulp	2.13 gb/s, 0 ulp
nk_each_scale_e4m3_serial	0.0550 gb/s, 0 ulp	0.0543 gb/s, 0 ulp	0.0570 gb/s, 0 ulp
nk_each_scale_e4m3_haswell	0.495 gb/s, 0 ulp	0.532 gb/s, 0 ulp	0.540 gb/s, 0 ulp
nk_each_scale_e4m3_skylake	1.05 gb/s, 0 ulp	1.02 gb/s, 0 ulp	1.10 gb/s, 0 ulp
nk_each_blend_e4m3_serial	0.0889 gb/s, 0 ulp	0.0927 gb/s, 0 ulp	0.0876 gb/s, 0 ulp
nk_each_blend_e4m3_haswell	0.807 gb/s, 0.6 ulp	0.756 gb/s, 0 ulp	0.789 gb/s, 0 ulp
nk_each_blend_e4m3_skylake	1.50 gb/s, 0 ulp	1.44 gb/s, 0 ulp	1.48 gb/s, 0 ulp
nk_each_fma_e4m3_serial	0.120 gb/s, 0 ulp	0.118 gb/s, 0.9 ulp	0.115 gb/s, 0 ulp
nk_each_fma_e4m3_haswell	0.989 gb/s, 0 ulp	0.909 gb/s, 0 ulp	0.967 gb/s, 0.5 ulp
nk_each_fma_e4m3_skylake	1.89 gb/s, 0 ulp	1.74 gb/s, 0 ulp	1.80 gb/s, 0 ulp
e5m2	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e5m2_serial	0.115 gb/s, 0 ulp	0.114 gb/s, 0 ulp	0.110 gb/s, 0 ulp
nk_each_sum_e5m2_haswell	1.04 gb/s, 0 ulp	0.987 gb/s, 0 ulp	0.972 gb/s, 0 ulp
nk_each_sum_e5m2_skylake	1.71 gb/s, 0 ulp	1.76 gb/s, 0 ulp	1.79 gb/s, 0 ulp
nk_each_scale_e5m2_serial	0.0593 gb/s, 0 ulp	0.0630 gb/s, 0 ulp	0.0630 gb/s, 0 ulp
nk_each_scale_e5m2_haswell	0.601 gb/s, 0 ulp	0.611 gb/s, 0 ulp	0.588 gb/s, 0 ulp
nk_each_scale_e5m2_skylake	1.11 gb/s, 0 ulp	1.11 gb/s, 0 ulp	1.12 gb/s, 0 ulp
nk_each_blend_e5m2_serial	0.108 gb/s, 0 ulp	0.113 gb/s, 0 ulp	0.114 gb/s, 50 ulp
nk_each_blend_e5m2_haswell	0.999 gb/s, 0 ulp	0.895 gb/s, 0 ulp	0.951 gb/s, 0 ulp
nk_each_blend_e5m2_skylake	1.77 gb/s, 0 ulp	1.65 gb/s, 0 ulp	1.72 gb/s, 0 ulp
nk_each_fma_e5m2_serial	0.155 gb/s, 5.1 ulp	0.146 gb/s, 0 ulp	0.149 gb/s, 0 ulp
nk_each_fma_e5m2_haswell	1.24 gb/s, 0 ulp	1.19 gb/s, 0 ulp	1.25 gb/s, 0 ulp
nk_each_fma_e5m2_skylake	2.36 gb/s, 0 ulp	2.01 gb/s, 0 ulp	2.11 gb/s, 0 ulp
e2m3	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e2m3_serial	0.109 gb/s, 0 ulp	0.105 gb/s, 0 ulp	0.110 gb/s, 0 ulp
nk_each_scale_e2m3_serial	0.0500 gb/s, 0 ulp	0.0474 gb/s, 0 ulp	0.0495 gb/s, 0 ulp
nk_each_blend_e2m3_serial	0.0864 gb/s, 0 ulp	0.0888 gb/s, 0 ulp	0.0908 gb/s, 0 ulp
nk_each_fma_e2m3_serial	0.133 gb/s, 0 ulp	0.128 gb/s, 0 ulp	0.128 gb/s, 0 ulp
e3m2	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e3m2_serial	0.118 gb/s, 0 ulp	0.115 gb/s, 0 ulp	0.106 gb/s, 0 ulp
nk_each_scale_e3m2_serial	0.0574 gb/s, 0 ulp	0.0555 gb/s, 0 ulp	0.0548 gb/s, 0 ulp
nk_each_blend_e3m2_serial	0.110 gb/s, 0 ulp	0.105 gb/s, 0 ulp	0.0956 gb/s, 0 ulp
nk_each_fma_e3m2_serial	0.151 gb/s, 0 ulp	0.149 gb/s, 0 ulp	0.138 gb/s, 0 ulp
i8	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i8_serial	21.7 gb/s	15.9 gb/s	12.5 gb/s
nk_each_sum_i8_haswell	37.7 gb/s	15.7 gb/s	16.5 gb/s
nk_each_sum_i8_icelake	47.2 gb/s	17.7 gb/s	17.7 gb/s
nk_each_scale_i8_serial	2.34 gb/s	1.50 gb/s	1.70 gb/s
nk_each_scale_i8_haswell	3.91 gb/s	3.93 gb/s	3.64 gb/s
nk_each_scale_i8_skylake	6.74 gb/s	6.70 gb/s	6.93 gb/s
nk_each_scale_i8_sapphire	23.0 gb/s	11.4 gb/s	10.8 gb/s
nk_each_blend_i8_serial	3.66 gb/s	2.23 gb/s	2.60 gb/s
nk_each_blend_i8_haswell	5.95 gb/s	5.37 gb/s	6.37 gb/s
nk_each_blend_i8_sapphire	32.4 gb/s	17.7 gb/s	15.2 gb/s
nk_each_fma_i8_serial	4.49 gb/s	2.63 gb/s	2.98 gb/s
nk_each_fma_i8_haswell	7.36 gb/s	6.84 gb/s	7.15 gb/s
nk_each_fma_i8_skylake	11.2 gb/s	9.45 gb/s	10.1 gb/s
u8	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u8_serial	17.0 gb/s	13.7 gb/s	12.5 gb/s
nk_each_sum_u8_haswell	42.6 gb/s	15.7 gb/s	15.4 gb/s
nk_each_sum_u8_icelake	45.9 gb/s	17.3 gb/s	17.4 gb/s
nk_each_scale_u8_serial	2.11 gb/s	2.03 gb/s	1.86 gb/s
nk_each_scale_u8_haswell	3.91 gb/s	3.89 gb/s	4.27 gb/s
nk_each_scale_u8_skylake	6.93 gb/s	5.99 gb/s	6.70 gb/s
nk_each_scale_u8_sapphire	24.7 gb/s	12.1 gb/s	11.9 gb/s
nk_each_blend_u8_serial	3.23 gb/s	2.62 gb/s	3.43 gb/s
nk_each_blend_u8_haswell	4.87 gb/s	5.10 gb/s	5.61 gb/s
nk_each_blend_u8_sapphire	39.8 gb/s	18.1 gb/s	16.5 gb/s
nk_each_fma_u8_serial	3.19 gb/s	3.92 gb/s	4.54 gb/s
nk_each_fma_u8_haswell	6.98 gb/s	6.29 gb/s	7.62 gb/s
nk_each_fma_u8_skylake	9.66 gb/s	9.21 gb/s	10.3 gb/s
i16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i16_serial	12.0 gb/s	11.6 gb/s	14.2 gb/s
nk_each_sum_i16_haswell	26.1 gb/s	16.2 gb/s	16.8 gb/s
nk_each_sum_i16_icelake	39.3 gb/s	18.2 gb/s	18.0 gb/s
nk_each_scale_i16_serial	3.19 gb/s	4.25 gb/s	3.77 gb/s
nk_each_scale_i16_haswell	7.07 gb/s	7.42 gb/s	7.69 gb/s
nk_each_scale_i16_skylake	12.8 gb/s	8.94 gb/s	10.5 gb/s
nk_each_blend_i16_serial	6.00 gb/s	6.04 gb/s	6.37 gb/s
nk_each_fma_i16_serial	8.37 gb/s	7.64 gb/s	7.07 gb/s
nk_each_fma_i16_haswell	10.7 gb/s	12.5 gb/s	13.4 gb/s
nk_each_fma_i16_skylake	18.3 gb/s	15.7 gb/s	19.0 gb/s
u16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u16_serial	12.2 gb/s	11.8 gb/s	13.7 gb/s
nk_each_sum_u16_haswell	24.1 gb/s	14.4 gb/s	17.7 gb/s
nk_each_sum_u16_icelake	39.7 gb/s	18.2 gb/s	18.4 gb/s
nk_each_scale_u16_serial	4.44 gb/s	5.28 gb/s	5.48 gb/s
nk_each_scale_u16_haswell	7.82 gb/s	7.21 gb/s	7.66 gb/s
nk_each_scale_u16_skylake	15.5 gb/s	11.6 gb/s	9.04 gb/s
nk_each_blend_u16_serial	7.84 gb/s	7.08 gb/s	9.15 gb/s
nk_each_fma_u16_serial	9.01 gb/s	8.19 gb/s	9.37 gb/s
nk_each_fma_u16_haswell	11.2 gb/s	12.2 gb/s	13.9 gb/s
nk_each_fma_u16_skylake	22.6 gb/s	20.8 gb/s	17.5 gb/s
i32	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i32_serial	12.6 gb/s	12.7 gb/s	10.1 gb/s
nk_each_sum_i32_haswell	14.6 gb/s	15.3 gb/s	13.9 gb/s
nk_each_sum_i32_icelake	17.1 gb/s	18.5 gb/s	15.4 gb/s
nk_each_scale_i32_serial	3.04 gb/s	3.28 gb/s	3.44 gb/s
nk_each_scale_i32_haswell	8.94 gb/s	8.72 gb/s	8.09 gb/s
nk_each_scale_i32_skylake	11.1 gb/s	12.6 gb/s	11.3 gb/s
nk_each_blend_i32_serial	4.99 gb/s	5.99 gb/s	5.06 gb/s
nk_each_fma_i32_serial	6.33 gb/s	6.38 gb/s	6.40 gb/s
nk_each_fma_i32_haswell	13.5 gb/s	16.4 gb/s	11.2 gb/s
nk_each_fma_i32_skylake	20.1 gb/s	21.3 gb/s	16.0 gb/s
u32	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u32_serial	13.6 gb/s	11.6 gb/s	9.94 gb/s
nk_each_sum_u32_haswell	16.0 gb/s	17.7 gb/s	12.7 gb/s
nk_each_sum_u32_icelake	17.4 gb/s	19.0 gb/s	14.8 gb/s
nk_each_scale_u32_serial	2.13 gb/s	3.22 gb/s	2.74 gb/s
nk_each_scale_u32_haswell	8.20 gb/s	9.40 gb/s	9.18 gb/s
nk_each_scale_u32_skylake	10.6 gb/s	12.9 gb/s	11.1 gb/s
nk_each_blend_u32_serial	3.76 gb/s	5.22 gb/s	5.78 gb/s
nk_each_fma_u32_serial	4.78 gb/s	5.63 gb/s	8.43 gb/s
nk_each_fma_u32_haswell	13.7 gb/s	16.1 gb/s	12.1 gb/s
nk_each_fma_u32_skylake	20.2 gb/s	21.1 gb/s	15.2 gb/s
i64	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i64_serial	15.9 gb/s	15.8 gb/s	10.3 gb/s
nk_each_sum_i64_icelake	17.7 gb/s	19.2 gb/s	11.1 gb/s
nk_each_scale_i64_serial	7.44 gb/s	9.17 gb/s	8.72 gb/s
nk_each_scale_i64_skylake	11.8 gb/s	13.8 gb/s	9.10 gb/s
nk_each_blend_i64_serial	10.9 gb/s	14.3 gb/s	10.5 gb/s
nk_each_fma_i64_serial	13.5 gb/s	19.0 gb/s	11.8 gb/s
nk_each_fma_i64_skylake	21.7 gb/s	22.2 gb/s	11.8 gb/s
u64	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u64_serial	14.7 gb/s	16.9 gb/s	10.5 gb/s
nk_each_sum_u64_icelake	18.1 gb/s	19.2 gb/s	12.4 gb/s
nk_each_scale_u64_serial	7.99 gb/s	9.79 gb/s	8.82 gb/s
nk_each_scale_u64_skylake	11.6 gb/s	13.9 gb/s	7.24 gb/s
nk_each_blend_u64_serial	11.9 gb/s	16.5 gb/s	13.8 gb/s
nk_each_fma_u64_serial	15.3 gb/s	21.6 gb/s	14.0 gb/s
nk_each_fma_u64_skylake	21.6 gb/s	21.8 gb/s	11.4 gb/s
f64c	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_scale_f64c_serial	10.6 gb/s, 3.4 ulp	7.04 gb/s, 2.6 ulp	5.63 gb/s, 2.0 ulp
nk_each_scale_f64c_haswell	9.89 gb/s, 3.5 ulp	6.45 gb/s, 2.0 ulp	5.90 gb/s, 2.1 ulp
nk_each_scale_f64c_skylake	9.29 gb/s, 3.5 ulp	6.01 gb/s, 2.0 ulp	5.67 gb/s, 2.0 ulp
nk_each_blend_f64c_serial	16.2 gb/s, 2.5 ulp	8.80 gb/s, 2.4 ulp	8.23 gb/s, 2.6 ulp
nk_each_blend_f64c_haswell	14.0 gb/s, 2.5 ulp	8.26 gb/s, 2.4 ulp	8.59 gb/s, 2.7 ulp
nk_each_blend_f64c_skylake	14.3 gb/s, 2.5 ulp	8.82 gb/s, 2.7 ulp	7.33 gb/s, 2.7 ulp
nk_each_fma_f64c_serial	17.4 gb/s, 4.5 ulp	10.1 gb/s, 3.2 ulp	9.45 gb/s, 2.8 ulp
nk_each_fma_f64c_haswell	14.5 gb/s, 4.9 ulp	8.86 gb/s, 3.1 ulp	9.31 gb/s, 2.7 ulp
nk_each_fma_f64c_skylake	16.1 gb/s, 4.0 ulp	8.93 gb/s, 3.4 ulp	10.4 gb/s, 2.8 ulp
f32c	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_scale_f32c_serial	10.1 gb/s, 2.1 ulp	9.28 gb/s, 1.8 ulp	6.20 gb/s, 2.1 ulp
nk_each_scale_f32c_haswell	8.81 gb/s, 2.1 ulp	8.87 gb/s, 1.8 ulp	7.73 gb/s, 2.1 ulp
nk_each_scale_f32c_skylake	9.67 gb/s, 2.2 ulp	7.61 gb/s, 1.8 ulp	7.09 gb/s, 2.1 ulp
nk_each_blend_f32c_serial	14.6 gb/s, 6.9 ulp	10.8 gb/s, 2.8 ulp	8.43 gb/s, 8.7 ulp
nk_each_blend_f32c_haswell	13.0 gb/s, 8.7 ulp	12.1 gb/s, 2.9 ulp	10.5 gb/s, 9.7 ulp
nk_each_blend_f32c_skylake	14.0 gb/s, 7.7 ulp	9.28 gb/s, 2.7 ulp	9.47 gb/s, 10.2 ulp
nk_each_fma_f32c_serial	15.7 gb/s, 8.8 ulp	11.96 gb/s, 3.9 ulp	9.33 gb/s, 8.5 ulp
nk_each_fma_f32c_haswell	14.1 gb/s, 6.6 ulp	10.3 gb/s, 2.9 ulp	9.77 gb/s, 7.2 ulp
nk_each_fma_f32c_skylake	15.5 gb/s, 9.2 ulp	10.3 gb/s, 3.8 ulp	9.95 gb/s, 8.3 ulp

Apple M5

Native

Kernel	256	1024	4096
f64	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_f64_serial	54.7 gb/s, 0 ulp	66.7 gb/s, 0 ulp	51.8 gb/s, 0 ulp
nk_each_sum_f64_neon	53.8 gb/s, 0 ulp	71.3 gb/s, 0 ulp	56.0 gb/s, 0 ulp
nk_each_scale_f64_serial	46.4 gb/s, 0 ulp	58.2 gb/s, 0 ulp	48.2 gb/s, 0 ulp
nk_each_scale_f64_neon	42.1 gb/s, 0 ulp	50.8 gb/s, 0 ulp	52.0 gb/s, 0 ulp
nk_each_blend_f64_serial	75.1 gb/s, 0 ulp	71.8 gb/s, 0 ulp	60.5 gb/s, 0 ulp
nk_each_blend_f64_neon	64.9 gb/s, 1.9 ulp	69.8 gb/s, 2.7 ulp	64.5 gb/s, 1.8 ulp
nk_each_fma_f64_serial	83.7 gb/s, 0 ulp	76.3 gb/s, 0 ulp	66.0 gb/s, 0 ulp
nk_each_fma_f64_neon	71.5 gb/s, 1.4 ulp	71.6 gb/s, 1.6 ulp	69.6 gb/s, 1.6 ulp
f32	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_f32_serial	89.9 gb/s, 0 ulp	67.8 gb/s, 0 ulp	59.6 gb/s, 0 ulp
nk_each_sum_f32_neon	75.5 gb/s, 0 ulp	66.2 gb/s, 0 ulp	55.2 gb/s, 0 ulp
nk_each_scale_f32_serial	66.0 gb/s, 0 ulp	61.5 gb/s, 0 ulp	54.4 gb/s, 0 ulp
nk_each_scale_f32_neon	49.7 gb/s, 0 ulp	44.7 gb/s, 0 ulp	49.2 gb/s, 0 ulp
nk_each_blend_f32_serial	87.1 gb/s, 26 ulp	66.9 gb/s, 26 ulp	52.1 gb/s, 2.0 ulp
nk_each_blend_f32_neon	74.4 gb/s, 1.7 ulp	66.7 gb/s, 1.6 ulp	50.1 gb/s, 1.6 ulp
nk_each_fma_f32_serial	89.4 gb/s, 2.1 ulp	51.3 gb/s, 2.5 ulp	56.2 gb/s, 2.2 ulp
nk_each_fma_f32_neon	82.4 gb/s, 2.1 ulp	55.2 gb/s, 21 ulp	56.1 gb/s, 1.8 ulp
bf16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_bf16_serial	32.8 gb/s, 0 ulp	31.6 gb/s, 0 ulp	33.8 gb/s, 0 ulp
nk_each_sum_bf16_neonbfdot	42.0 gb/s, 0 ulp	41.7 gb/s, 0 ulp	43.3 gb/s, 0 ulp
nk_each_scale_bf16_serial	19.3 gb/s, 0 ulp	17.7 gb/s, 0 ulp	19.8 gb/s, 0 ulp
nk_each_scale_bf16_neonbfdot	26.9 gb/s, 0 ulp	23.8 gb/s, 0 ulp	26.7 gb/s, 0 ulp
nk_each_blend_bf16_serial	25.3 gb/s, 28 ulp	24.0 gb/s, 26 ulp	26.4 gb/s, 2.2 ulp
nk_each_blend_bf16_neonbfdot	34.8 gb/s, 29 ulp	36.1 gb/s, 29 ulp	34.7 gb/s, 2.2 ulp
nk_each_fma_bf16_serial	31.7 gb/s, 2.1 ulp	29.3 gb/s, 2.0 ulp	33.1 gb/s, 33 ulp
nk_each_fma_bf16_neonbfdot	42.8 gb/s, 1.2 ulp	39.8 gb/s, 1.2 ulp	39.3 gb/s, 1.5 ulp
f16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_f16_serial	91.5 gb/s, 0 ulp	68.2 gb/s, 0 ulp	66.1 gb/s, 0 ulp
nk_each_sum_f16_neonhalf	83.2 gb/s, 0 ulp	67.3 gb/s, 0 ulp	61.2 gb/s, 0 ulp
nk_each_scale_f16_serial	37.6 gb/s, 0 ulp	35.9 gb/s, 0 ulp	36.2 gb/s, 0 ulp
nk_each_scale_f16_neonhalf	50.0 gb/s, 87.3K ulp	48.2 gb/s, 84.8K ulp	41.2 gb/s, 87.3K ulp
nk_each_blend_f16_serial	38.3 gb/s, 2.0 ulp	35.8 gb/s, 2.0 ulp	39.1 gb/s, 2.3 ulp
nk_each_blend_f16_neonhalf	78.4 gb/s, 91.6K ulp	59.2 gb/s, 92.6K ulp	66.2 gb/s, 91.9K ulp
nk_each_fma_f16_serial	43.5 gb/s, 2.1 ulp	37.2 gb/s, 1.8 ulp	43.4 gb/s, 2.2 ulp
nk_each_fma_f16_neonhalf	86.5 gb/s, 97.1K ulp	75.4 gb/s, 96.7K ulp	71.2 gb/s, 99.2K ulp
e4m3	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e4m3_serial	0.358 gb/s, 0 ulp	0.332 gb/s, 0 ulp	0.369 gb/s, 0 ulp
nk_each_sum_e4m3_neon	1.59 gb/s, 0 ulp	1.75 gb/s, 0 ulp	1.72 gb/s, 0 ulp
nk_each_scale_e4m3_serial	0.148 gb/s, 0 ulp	0.137 gb/s, 0 ulp	0.153 gb/s, 0 ulp
nk_each_scale_e4m3_neon	0.954 gb/s, 0 ulp	1.07 gb/s, 0 ulp	1.03 gb/s, 0 ulp
nk_each_blend_e4m3_serial	0.253 gb/s, 0.4 ulp	0.239 gb/s, 1.1 ulp	0.259 gb/s, 2.8 ulp
nk_each_blend_e4m3_neon	1.56 gb/s, 0.1 ulp	1.74 gb/s, 0 ulp	1.68 gb/s, 0 ulp
nk_each_fma_e4m3_serial	0.334 gb/s, 0.7 ulp	0.317 gb/s, 0.6 ulp	0.343 gb/s, 2.2 ulp
nk_each_fma_e4m3_neon	1.92 gb/s, 0.1 ulp	2.20 gb/s, 0.6 ulp	2.08 gb/s, 1.0 ulp
e5m2	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e5m2_serial	0.437 gb/s, 0 ulp	0.413 gb/s, 0 ulp	0.445 gb/s, 0 ulp
nk_each_sum_e5m2_neon	3.11 gb/s, 0 ulp	3.48 gb/s, 0 ulp	3.36 gb/s, 0 ulp
nk_each_scale_e5m2_serial	0.180 gb/s, 0 ulp	0.173 gb/s, 0 ulp	0.178 gb/s, 0 ulp
nk_each_scale_e5m2_neon	1.64 gb/s, 0 ulp	1.82 gb/s, 0 ulp	1.75 gb/s, 0 ulp
nk_each_blend_e5m2_serial	0.317 gb/s, 0 ulp	0.322 gb/s, 0 ulp	0.316 gb/s, 4.9 ulp
nk_each_blend_e5m2_neon	3.02 gb/s, 0.7 ulp	3.29 gb/s, 0 ulp	3.20 gb/s, 0 ulp
nk_each_fma_e5m2_serial	0.476 gb/s, 1.9 ulp	0.455 gb/s, 0.9 ulp	0.453 gb/s, 4.0 ulp
nk_each_fma_e5m2_neon	4.14 gb/s, 0 ulp	4.42 gb/s, 1.3 ulp	4.31 gb/s, 0 ulp
e2m3	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e2m3_serial	0.337 gb/s, ? ulp	0.297 gb/s, ? ulp	0.290 gb/s, ? ulp
nk_each_scale_e2m3_serial	0.102 gb/s, ? ulp	0.0925 gb/s, ? ulp	0.0939 gb/s, ? ulp
nk_each_blend_e2m3_serial	0.226 gb/s, ? ulp	0.201 gb/s, ? ulp	0.201 gb/s, ? ulp
nk_each_fma_e2m3_serial	0.368 gb/s, ? ulp	0.331 gb/s, ? ulp	0.331 gb/s, ? ulp
e3m2	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_e3m2_serial	0.544 gb/s, ? ulp	0.472 gb/s, ? ulp	0.458 gb/s, ? ulp
nk_each_scale_e3m2_serial	0.176 gb/s, ? ulp	0.151 gb/s, ? ulp	0.143 gb/s, ? ulp
nk_each_blend_e3m2_serial	0.355 gb/s, ? ulp	0.302 gb/s, ? ulp	0.292 gb/s, ? ulp
nk_each_fma_e3m2_serial	0.506 gb/s, ? ulp	0.433 gb/s, ? ulp	0.436 gb/s, ? ulp
i8	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i8_serial	94.6 gb/s	55.5 gb/s	42.7 gb/s
nk_each_sum_i8_neonhalf	85.5 gb/s	60.5 gb/s	39.6 gb/s
nk_each_scale_i8_serial	0.171 gb/s	0.145 gb/s	0.148 gb/s
nk_each_scale_i8_neonhalf	22.6 gb/s	22.4 gb/s	20.8 gb/s
nk_each_blend_i8_serial	0.302 gb/s	0.254 gb/s	0.272 gb/s
nk_each_blend_i8_neonhalf	26.5 gb/s	27.7 gb/s	27.3 gb/s
nk_each_fma_i8_serial	0.436 gb/s	0.359 gb/s	0.376 gb/s
u8	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u8_serial	13.2 gb/s	12.3 gb/s	12.3 gb/s
nk_each_sum_u8_neonhalf	85.3 gb/s	84.8 gb/s	67.3 gb/s
nk_each_scale_u8_serial	0.135 gb/s	0.120 gb/s	0.119 gb/s
nk_each_scale_u8_neonhalf	23.0 gb/s	21.9 gb/s	21.2 gb/s
nk_each_blend_u8_serial	0.256 gb/s	0.218 gb/s	0.220 gb/s
nk_each_blend_u8_neonhalf	27.4 gb/s	27.0 gb/s	27.4 gb/s
nk_each_fma_u8_serial	0.356 gb/s	0.333 gb/s	0.323 gb/s
i16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i16_serial	100 gb/s	69.6 gb/s	79.2 gb/s
nk_each_sum_i16_neon	75.3 gb/s	65.6 gb/s	66.9 gb/s
nk_each_scale_i16_serial	0.358 gb/s	0.297 gb/s	0.284 gb/s
nk_each_scale_i16_neon	17.6 gb/s	18.5 gb/s	15.5 gb/s
nk_each_blend_i16_serial	0.644 gb/s	0.523 gb/s	0.492 gb/s
nk_each_fma_i16_serial	0.889 gb/s	0.731 gb/s	0.712 gb/s
nk_each_fma_i16_neon	27.9 gb/s	27.7 gb/s	28.1 gb/s
u16	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u16_serial	25.0 gb/s	22.4 gb/s	23.2 gb/s
nk_each_sum_u16_neon	79.2 gb/s	66.8 gb/s	68.1 gb/s
nk_each_scale_u16_serial	0.267 gb/s	0.245 gb/s	0.241 gb/s
nk_each_scale_u16_neon	17.0 gb/s	18.9 gb/s	18.6 gb/s
nk_each_blend_u16_serial	0.520 gb/s	0.432 gb/s	0.444 gb/s
nk_each_fma_u16_serial	0.744 gb/s	0.664 gb/s	0.638 gb/s
nk_each_fma_u16_neon	28.1 gb/s	27.9 gb/s	28.9 gb/s
i32	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i32_serial	68.6 gb/s	62.0 gb/s	71.4 gb/s
nk_each_sum_i32_neon	66.2 gb/s	66.9 gb/s	62.4 gb/s
nk_each_scale_i32_serial	0.672 gb/s	0.613 gb/s	0.589 gb/s
nk_each_scale_i32_neon	18.2 gb/s	19.3 gb/s	18.6 gb/s
nk_each_blend_i32_serial	1.27 gb/s	1.11 gb/s	0.993 gb/s
nk_each_fma_i32_serial	1.71 gb/s	1.54 gb/s	1.47 gb/s
nk_each_fma_i32_neon	28.4 gb/s	28.8 gb/s	27.6 gb/s
u32	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u32_serial	56.2 gb/s	46.0 gb/s	50.0 gb/s
nk_each_sum_u32_neon	84.9 gb/s	69.7 gb/s	55.1 gb/s
nk_each_scale_u32_serial	0.598 gb/s	0.555 gb/s	0.552 gb/s
nk_each_scale_u32_neon	18.4 gb/s	18.8 gb/s	18.5 gb/s
nk_each_blend_u32_serial	1.02 gb/s	0.982 gb/s	0.953 gb/s
nk_each_fma_u32_serial	1.50 gb/s	1.43 gb/s	1.41 gb/s
nk_each_fma_u32_neon	28.2 gb/s	28.9 gb/s	27.0 gb/s
i64	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_i64_serial	55.2 gb/s	41.2 gb/s	53.9 gb/s
nk_each_sum_i64_neon	52.9 gb/s	41.7 gb/s	51.4 gb/s
nk_each_scale_i64_serial	7.90 gb/s	7.64 gb/s	8.13 gb/s
nk_each_scale_i64_neon	39.4 gb/s	22.8 gb/s	34.7 gb/s
nk_each_blend_i64_serial	13.8 gb/s	13.8 gb/s	14.1 gb/s
nk_each_fma_i64_serial	13.3 gb/s	9.94 gb/s	12.8 gb/s
nk_each_fma_i64_neon	57.7 gb/s	34.2 gb/s	49.6 gb/s
u64	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_sum_u64_serial	52.6 gb/s	31.5 gb/s	50.9 gb/s
nk_each_sum_u64_neon	54.3 gb/s	41.3 gb/s	48.8 gb/s
nk_each_scale_u64_serial	9.29 gb/s	9.48 gb/s	9.11 gb/s
nk_each_scale_u64_neon	38.4 gb/s	35.1 gb/s	35.1 gb/s
nk_each_blend_u64_serial	14.3 gb/s	16.1 gb/s	14.1 gb/s
nk_each_fma_u64_serial	14.2 gb/s	13.9 gb/s	15.2 gb/s
nk_each_fma_u64_neon	52.4 gb/s	52.0 gb/s	53.2 gb/s
f64c	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_scale_f64c_serial	28.1 gb/s, 2.2 ulp	39.2 gb/s, 1.9 ulp	37.8 gb/s, 2.2 ulp
nk_each_scale_f64c_neon	25.6 gb/s, 1.5 ulp	51.0 gb/s, 1.5 ulp	42.1 gb/s, 1.3 ulp
nk_each_blend_f64c_serial	44.9 gb/s, 4.2 ulp	35.5 gb/s, 3.0 ulp	48.8 gb/s, 2.6 ulp
nk_each_blend_f64c_neon	43.7 gb/s, 3.2 ulp	46.3 gb/s, 3.0 ulp	48.3 gb/s, 2.2 ulp
nk_each_fma_f64c_serial	58.2 gb/s, 3.4 ulp	43.9 gb/s, 5.2 ulp	52.2 gb/s, 2.5 ulp
nk_each_fma_f64c_neon	56.1 gb/s, 3.2 ulp	52.2 gb/s, 3.0 ulp	53.2 gb/s, 2.4 ulp
f32c	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░	░░░░░░░░░░░░░░░░░░░░░░░░
nk_each_scale_f32c_serial	44.8 gb/s, 17 ulp	37.7 gb/s, 2.4 ulp	44.3 gb/s, 17 ulp
nk_each_scale_f32c_neon	50.8 gb/s, 1.8 ulp	52.7 gb/s, 1.6 ulp	45.7 gb/s, 1.6 ulp
nk_each_blend_f32c_serial	50.3 gb/s, 2.4 ulp	49.0 gb/s, 2.6 ulp	53.5 gb/s, 28 ulp
nk_each_blend_f32c_neon	49.0 gb/s, 2.2 ulp	58.3 gb/s, 2.2 ulp	51.0 gb/s, 3.2 ulp
nk_each_fma_f32c_serial	56.4 gb/s, 3.1 ulp	49.8 gb/s, 78 ulp	51.5 gb/s, 3.5 ulp
nk_each_fma_f32c_neon	62.7 gb/s, 2.9 ulp	62.4 gb/s, 4.1 ulp	58.0 gb/s, 81 ulp