Eigen vs. BLAS/LAPACK libraries, Intel Xeon Gold 6444Y (September 2026)

Single-threaded float and double BLAS/LAPACK comparisons on an Intel Xeon Gold 6444Y: Eigen against OpenBLAS and oneMKL, with upstream BLIS for BLAS.

Eigen’s dense kernels measured on a bare-metal Intel Xeon Gold 6444Y, using one thread and AVX-512. The twelve operations and all 874 float/double operation-shape cells match the Zen 5 AVX-512 page. OpenBLAS and Intel oneMKL provide both BLAS and LAPACK comparisons; upstream BLIS provides the six BLAS comparisons.

All 30 operation/library runs completed with ten samples per measured cell and no reported validation errors.

Conditions


CPU	Intel Xeon Gold 6444Y, one socket, 16 cores / 32 threads; L1d 48 KiB/core, L2 2 MiB/core, shared L3 45 MiB
OS	Ubuntu 24.04.5 LTS, bare-metal Linux 6.17.0-35-generic
Compiler	GCC 13.3.0, `-O3 -DNDEBUG -mavx512dq -mfma`, C++17
Eigen	Upstream master `ab4f7316d`, fetched before building; the `Eigen/` tree is unchanged. No external BLAS and no OpenMP in the Eigen arm
Harness	MR !2903 at `778e20997`, applied as `11cf0c289`, plus the untimed DOT validation correction described below (`4e0c35ecb`). The first two AXPY runs precede that correction; their kernels and validation are unaffected
OpenBLAS	OpenBLAS 0.3.26 NO_LAPACKE DYNAMIC_ARCH NO_AFFINITY SapphireRapids MAX_THREADS=64; LP64 pthread build, one thread; bundled LAPACK
Intel oneMKL	Intel(R) oneAPI Math Kernel Library Version 2025.3-Product Build 20251007 for Intel(R) 64 architecture applications; sequential LP64, native dispatch
BLIS	2.1; upstream release 2.1, sequential `skx` AVX-512 configuration; BLAS only
Threads and affinity	All library thread caps set to 1; benchmark process pinned to one logical CPU, with its SMT sibling unused
Isolation and frequency	Exclusive node allocation; performance governor; frequency not locked
Method	Google Benchmark 1.8.3, built from source in Release mode; ten repetitions of at least 0.2 seconds of CPU time, median rate per cell
Benchmark runtime	30 completed runs, 312.6 minutes total elapsed runtime, excluding builds; 2026-09-21 08:57 PM PDT to 2026-09-22 03:10 AM PDT

Reading the rates. The harness uses Google Benchmark’s default CPU timer for its GFLOP/s counters; it also retains wall times in the downloadable data. Both implementations use the same nominal flop count, operand shapes, input distribution, and timing protocol. Each benchmark invocation generates fresh random operands outside the timed loop, including between repetitions. Reference results are validated outside the timed loop. Small cells include API and dispatch overhead; Eigen can inline its operation.

Each Eigen/library ratio is formed from the two median rates in the same binary and session. The common Eigen line and table column show the median over its separately measured library builds; the shaded band is the min–max range of those medians. Consequently the common Eigen column divided by a library column need not exactly equal the paired ratio. Within-run variation is summarized below.

Cache markers show where the inputs and outputs of one call fill L1d, L2 or L3; they exclude solver workspace and the harness’s additional copies. Eigenvalue and SVD rates use classical algorithm counts, so they are nominal GFLOP/s rather than executed-instruction throughput.

AXPY

y += alpha * x against ?axpy, alpha = 0.75; (2n) flops. Vector lengths extend through the cache levels into DRAM.

AXPY f64 square

AXPY f32 square

DOT

x.dot(y) against ?dot; (2n) flops. Float and double only.

DOT f64 square

DOT f32 square

GEMV

y.noalias() += A * x against ?gemv, column-major, no transposition; (2mn) flops. Square, short-fat and tall-skinny operands.

GEMV f64 square

GEMV f64 families

GEMV f32 square

GEMV f32 families

GEMM

C.noalias() += A * B against ?gemm, column-major, no transposition; (2mnk) flops. Square sizes through 4097, tall-skinny sweeps and other rectangular shapes.

GEMM f64 square

GEMM f64 families

GEMM f64 shapes

GEMM f32 square

GEMM f32 families

GEMM f32 shapes

TRSM

A.triangularView<Lower>().solveInPlace(X) against ?trsm, left, lower, no transposition, non-unit diagonal; (m(m+1)n) flops. Both arms time one copy of the right-hand side.

TRSM f64 square

TRSM f64 families

TRSM f64 shapes

TRSM f32 square

TRSM f32 families

TRSM f32 shapes

SYRK

C.selfadjointView<Lower>().rankUpdate(A) against ?syrk, lower triangle, no transposition; (n(n+1)k) flops.

SYRK f64 square

SYRK f64 families

SYRK f32 square

SYRK f32 families

POTRF

LLT<Ref<Matrix>> against ?potrf, in-place lower Cholesky factorization. The harness’s shared nominal count is (n(n-1)(n-2)/3 + 2n(n-1)), asymptotically (n^3/3) flops. Both arms time one operand copy.

POTRF f64 square

POTRF f32 square

GETRF

PartialPivLU<Ref<Matrix>> against ?getrf, in-place LU with partial pivoting; (2n^3/3) flops. Both arms time one operand copy.

GETRF f64 square

GETRF f32 square

GEQRF

HouseholderQR<Ref<Matrix>> against ?geqrf, in-place Householder QR with (m \ge n); (2mn^2 - 2n^3/3) flops. Both arms time one operand copy.

GEQRF f64 square

GEQRF f64 families

GEQRF f32 square

GEQRF f32 families

SYEV

SelfAdjointEigenSolver with eigenvectors against ?syev with jobz = 'V', lower triangle; (9n^3) nominal flops. Square sizes through 2048.

SYEV f64 square

SYEV f32 square

GESDD

BDCSVD<Matrix, ComputeThinU | ComputeThinV> against ?gesdd with jobz = 'S'; divide and conquer, with thin singular vectors on both sides. (14mn^2 + 8n^3) nominal flops; square sizes through 2048 plus tall-skinny sweeps.

GESDD f64 square

GESDD f64 families

GESDD f32 square

GESDD f32 families

GEEV

EigenSolver with eigenvectors against ?geev with jobvr = 'V', for a dense random nonsymmetric matrix; (25n^3) nominal flops. Square sizes through 1024.

GEEV f64 square

GEEV f32 square

Summary

Geometric mean of paired Eigen/library rate ratios over square shapes in each size band. Above 1, Eigen is faster.

Operation	Scalar	Library	n ≤ 16	24–128	192–1024	1536–16384	> 16384
AXPY	float	OpenBLAS	3.03	2.85	1.40	1.05	1.00
AXPY	float	Intel oneMKL	2.86	2.31	1.40	1.02	1.00
AXPY	float	BLIS	14.01	9.40	2.58	1.33	0.98
AXPY	double	OpenBLAS	2.53	1.98	1.29	1.02	1.00
AXPY	double	Intel oneMKL	2.88	1.76	0.77	0.92	0.99
AXPY	double	BLIS	13.82	8.86	2.93	1.32	0.99
DOT	float	OpenBLAS	3.49	2.66	1.18	1.02	0.99
DOT	float	Intel oneMKL	4.25	2.70	1.30	1.08	1.01
DOT	float	BLIS	24.89	13.52	3.96	1.72	1.08
DOT	double	OpenBLAS	4.90	2.44	1.10	1.03	1.00
DOT	double	Intel oneMKL	4.99	2.33	1.17	1.06	1.00
DOT	double	BLIS	28.11	10.76	2.79	1.49	1.05
GEMV	float	OpenBLAS	1.39	1.39	1.05	1.06	–
GEMV	float	Intel oneMKL	2.61	1.52	1.05	1.06	–
GEMV	float	BLIS	7.07	2.71	1.16	1.03	–
GEMV	double	OpenBLAS	2.23	1.63	1.08	1.07	–
GEMV	double	Intel oneMKL	2.98	1.48	0.98	1.04	–
GEMV	double	BLIS	7.70	2.28	1.12	1.03	–
GEMM	float	OpenBLAS	1.25	0.86	1.02	0.97	–
GEMM	float	Intel oneMKL	2.57	0.88	0.99	0.96	–
GEMM	float	BLIS	65.54	3.19	1.09	1.00	–
GEMM	double	OpenBLAS	1.11	0.85	1.07	0.94	–
GEMM	double	Intel oneMKL	2.21	0.84	0.98	0.93	–
GEMM	double	BLIS	61.09	2.35	1.04	0.96	–
TRSM	float	OpenBLAS	1.22	3.78	1.96	1.13	–
TRSM	float	Intel oneMKL	1.34	1.12	0.90	0.88	–
TRSM	float	BLIS	38.92	12.21	3.47	1.45	–
TRSM	double	OpenBLAS	1.48	3.60	2.19	1.23	–
TRSM	double	Intel oneMKL	1.45	0.81	0.77	0.88	–
TRSM	double	BLIS	25.21	6.26	1.78	1.13	–
SYRK	float	OpenBLAS	0.62	0.98	1.01	0.98	–
SYRK	float	Intel oneMKL	1.22	1.01	0.98	0.95	–
SYRK	float	BLIS	17.44	3.09	1.08	0.99	–
SYRK	double	OpenBLAS	0.88	1.24	1.08	0.88	–
SYRK	double	Intel oneMKL	1.59	1.02	0.98	0.88	–
SYRK	double	BLIS	21.77	2.43	1.05	0.91	–
POTRF	float	OpenBLAS	1.55	1.12	1.49	1.18	–
POTRF	float	Intel oneMKL	1.06	2.15	0.98	0.99	–
POTRF	double	OpenBLAS	1.38	1.25	1.50	1.25	–
POTRF	double	Intel oneMKL	1.08	1.71	0.99	0.93	–
GETRF	float	OpenBLAS	1.93	1.43	1.31	1.00	–
GETRF	float	Intel oneMKL	1.00	1.33	0.87	0.87	–
GETRF	double	OpenBLAS	1.77	1.53	1.34	0.99	–
GETRF	double	Intel oneMKL	0.97	1.38	1.02	0.93	–
GEQRF	float	OpenBLAS	0.79	1.09	1.15	1.22	–
GEQRF	float	Intel oneMKL	0.40	0.93	0.96	0.94	–
GEQRF	double	OpenBLAS	0.73	0.93	1.03	0.99	–
GEQRF	double	Intel oneMKL	0.35	0.64	0.84	0.81	–
SYEV	float	OpenBLAS	1.51	2.02	3.72	2.99	–
SYEV	float	Intel oneMKL	1.44	1.14	1.02	0.57	–
SYEV	double	OpenBLAS	1.36	1.77	2.33	1.79	–
SYEV	double	Intel oneMKL	1.29	0.95	0.66	0.37	–
GESDD	float	OpenBLAS	1.73	0.72	0.87	0.96	–
GESDD	float	Intel oneMKL	1.63	0.64	0.81	0.92	–
GESDD	double	OpenBLAS	1.34	0.60	0.80	0.90	–
GESDD	double	Intel oneMKL	1.31	0.53	0.69	0.88	–
GEEV	float	OpenBLAS	2.14	1.62	0.48	–	–
GEEV	float	Intel oneMKL	2.01	1.44	0.43	–	–
GEEV	double	OpenBLAS	2.13	1.52	0.45	–	–
GEEV	double	Intel oneMKL	1.13	1.17	0.41	–	–

Variability

Relative IQR is the interquartile range of the ten rates divided by their median. The table pools float and double; Eigen counts include its repeated measurements in each library build. It summarizes dispersion across the measured cells, not a confidence interval. Repetitions use freshly generated random inputs, so the spread includes input variation as well as timing noise.

Operation	Implementation	Measured cells	Median relative IQR	90th percentile relative IQR	Maximum relative IQR
AXPY	eigen	258	0.27%	2.42%	29.15%
AXPY	openblas	86	0.29%	1.37%	8.10%
AXPY	mkl	86	0.31%	0.65%	42.73%
AXPY	blis	86	0.63%	1.54%	10.21%
DOT	eigen	258	0.29%	0.89%	4.08%
DOT	openblas	86	0.36%	1.76%	43.56%
DOT	mkl	86	0.39%	0.86%	4.28%
DOT	blis	86	0.51%	1.29%	2.96%
GEMV	eigen	228	0.27%	0.77%	2.82%
GEMV	openblas	76	0.26%	1.01%	3.27%
GEMV	mkl	76	0.23%	0.89%	1.92%
GEMV	blis	76	0.34%	0.92%	2.36%
GEMM	eigen	300	0.10%	0.36%	1.88%
GEMM	openblas	100	0.06%	0.43%	1.02%
GEMM	mkl	100	0.07%	0.41%	2.64%
GEMM	blis	100	0.13%	0.36%	0.92%
TRSM	eigen	240	0.19%	0.74%	4.58%
TRSM	openblas	80	0.30%	0.71%	2.53%
TRSM	mkl	80	0.14%	0.39%	2.87%
TRSM	blis	80	0.30%	1.02%	2.34%
SYRK	eigen	222	0.14%	0.54%	1.82%
SYRK	openblas	74	0.11%	0.48%	0.71%
SYRK	mkl	74	0.15%	0.45%	1.52%
SYRK	blis	74	0.17%	0.57%	1.12%
POTRF	eigen	120	0.15%	0.64%	2.47%
POTRF	openblas	60	0.21%	0.60%	14.86%
POTRF	mkl	60	0.16%	0.89%	1.85%
GETRF	eigen	120	1.56%	5.29%	10.38%
GETRF	openblas	60	0.38%	2.51%	8.59%
GETRF	mkl	60	0.47%	3.26%	7.48%
GEQRF	eigen	164	0.18%	0.45%	1.99%
GEQRF	openblas	82	0.15%	0.47%	1.61%
GEQRF	mkl	82	0.20%	0.71%	2.21%
SYEV	eigen	108	1.01%	6.53%	14.16%
SYEV	openblas	54	4.44%	9.89%	14.71%
SYEV	mkl	54	4.92%	30.36%	47.16%
GESDD	eigen	132	1.05%	5.52%	13.97%
GESDD	openblas	66	0.41%	4.80%	9.21%
GESDD	mkl	66	0.45%	5.16%	12.54%
GEEV	eigen	100	4.20%	10.77%	22.23%
GEEV	openblas	50	3.27%	8.02%	17.82%
GEEV	mkl	50	4.51%	10.86%	23.35%

The same Eigen cells are also measured in separately linked library builds. Their relative range is (maximum median − minimum median) / median of medians. This includes any differences between binaries and sessions, and is not a confidence interval. A small within-run IQR does not establish agreement between builds.

Operation	Scalar	Cells in multiple builds	Median relative range	90th percentile relative range	Maximum relative range
AXPY	float	43	9.45%	36.90%	68.51%
AXPY	double	43	5.18%	41.48%	67.91%
DOT	float	43	0.75%	5.90%	22.97%
DOT	double	43	0.67%	4.31%	29.30%
GEMV	float	38	0.68%	8.40%	18.81%
GEMV	double	38	0.59%	2.12%	13.90%
GEMM	float	50	0.26%	1.21%	2.84%
GEMM	double	50	0.37%	1.31%	12.49%
TRSM	float	40	0.94%	2.91%	12.73%
TRSM	double	40	1.06%	4.48%	8.58%
SYRK	float	37	0.26%	1.42%	5.31%
SYRK	double	37	0.42%	0.97%	2.35%
POTRF	float	30	0.27%	1.46%	6.41%
POTRF	double	30	0.22%	0.71%	16.10%
GETRF	float	30	0.81%	6.51%	10.30%
GETRF	double	30	1.68%	4.06%	8.05%
GEQRF	float	41	0.31%	1.19%	2.60%
GEQRF	double	41	0.37%	1.82%	2.78%
SYEV	float	27	0.73%	2.08%	6.94%
SYEV	double	27	0.67%	2.06%	13.87%
GESDD	float	33	0.44%	1.19%	1.49%
GESDD	double	33	0.69%	1.49%	2.63%
GEEV	float	25	1.59%	4.22%	7.20%
GEEV	double	25	1.31%	6.30%	9.69%

Caveats

Frequency is not locked; turbo, thermal state and background system services can affect timings. Differences comparable to the observed dispersion are inconclusive.
These are single-threaded measurements on one processor and one compiler configuration. Absolute rates should not be treated as a controlled comparison with the Zen 5 host.
BLIS provides no LAPACK arm here; those entries are explicitly outside its measured scope.
Eigen’s AXPY rates differ substantially between library builds at some cache-resident sizes. The cause was not established; consider paired ratios together with the ranges between builds.
Several single-precision oneMKL SYEV cells have large within-run variation. See the per-implementation IQR table and raw samples.

Full tables

The Eigen column is pooled across builds; ratios retain the within-build comparison.

AXPY float

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2	1.8	0.7	2.40	0.5	3.24	0.1	16.20
3	2.7	1.1	2.51	0.8	3.26	0.2	15.35
4	3.1	1.3	2.45	1.1	2.84	0.2	14.98
6	4.4	1.6	2.72	1.6	2.65	0.3	13.03
8	6.4	1.9	3.39	2.2	2.90	0.5	13.37
12	9.0	2.3	3.92	3.3	2.71	0.7	13.32
16	11.6	2.6	4.45	4.6	2.53	0.9	12.29
24	17.3	3.0	5.86	6.5	2.67	1.4	11.63
32	23.1	10.0	2.31	9.0	2.56	1.9	12.12
48	33.6	6.8	4.97	13.6	2.48	2.8	11.50
64	43.4	19.6	2.22	17.4	2.50	3.8	9.72
96	57.4	23.2	2.47	26.1	2.23	5.6	9.05
100	45.1	21.9	2.08	26.3	1.71	5.6	6.50
128	67.5	35.4	1.99	30.6	2.21	7.4	6.97
192	74.1	42.0	1.78	41.3	1.79	10.6	5.65
256	68.7	53.5	1.29	50.9	1.35	13.7	4.25
384	101.2	65.9	1.54	61.6	1.64	19.2	3.35
512	103.8	70.8	1.47	69.9	1.49	23.1	2.83
768	106.8	79.5	1.34	79.6	1.34	33.3	2.02
1000	104.4	77.9	1.34	84.3	1.24	38.8	1.55
1001	102.9	77.7	1.34	84.5	1.22	38.4	1.51
1024	104.7	86.0	1.22	85.0	1.23	38.2	1.82
1536	108.2	92.3	1.17	92.3	1.17	44.9	1.67
2048	104.8	95.9	1.09	95.9	1.10	48.4	1.49
3072	105.1	94.3	1.12	100.4	1.05	53.2	1.32
4096	101.7	100.9	1.01	102.7	0.99	56.1	1.48
6144	104.3	95.6	1.09	96.1	1.10	44.6	1.87
8192	28.5	26.4	1.01	36.8	0.77	30.6	1.51
10000	26.6	26.2	1.02	26.4	1.01	26.7	1.00
12288	26.6	23.8	0.99	26.4	1.01	26.8	0.99
16384	26.5	24.9	0.97	26.4	1.01	26.9	0.99
32768	26.6	26.5	1.00	26.5	1.00	27.1	0.98
65536	26.6	26.4	1.01	26.6	1.00	27.2	0.96
100000	26.7	26.7	1.00	26.6	1.00	27.3	0.97
131072	26.1	26.3	0.99	26.6	0.98	27.0	0.96
262144	15.9	16.1	1.05	15.5	1.03	16.3	0.94
524288	9.4	9.5	0.99	9.2	1.00	9.7	0.97
1000000	9.3	9.4	1.00	9.2	1.00	9.6	0.98
1048576	9.4	9.4	1.00	9.2	1.00	9.5	0.98
2097152	9.4	9.4	1.00	9.2	0.99	9.5	0.98
4194304	9.2	9.2	1.00	9.1	0.99	9.3	0.99
8388608	7.6	7.6	0.99	7.7	0.99	7.5	1.02
16777216	6.2	6.2	1.00	6.3	0.99	6.1	1.01

AXPY double

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2	1.8	0.7	2.36	0.6	2.94	0.1	15.88
3	2.6	1.1	2.47	0.8	3.28	0.2	16.23
4	3.2	1.3	2.37	1.2	2.74	0.2	13.91
6	4.7	1.8	2.61	1.6	2.95	0.3	14.09
8	5.8	2.2	2.59	2.1	2.82	0.5	12.44
12	8.7	2.7	3.16	3.2	2.65	0.7	12.32
16	11.6	5.1	2.26	4.1	2.85	0.9	12.44
24	17.2	5.0	3.38	6.1	2.82	1.4	12.55
32	21.7	10.4	2.08	7.5	2.60	1.9	11.73
48	29.5	11.6	2.54	11.1	2.09	2.8	10.68
64	32.7	17.8	1.98	14.3	1.72	3.7	8.96
96	37.2	21.5	1.73	20.0	1.34	5.2	7.12
100	33.5	20.9	1.62	21.4	1.26	5.4	6.15
128	33.8	28.0	1.21	23.7	1.17	6.8	6.95
192	50.5	32.3	1.56	30.0	0.97	9.7	5.21
256	51.6	34.8	1.48	37.5	0.81	11.6	4.45
384	53.3	38.2	1.40	41.1	0.76	16.8	3.18
512	52.4	42.6	1.23	43.6	0.73	19.4	2.70
768	54.1	45.0	1.20	46.2	0.75	22.3	2.43
1000	54.4	45.1	1.21	47.4	0.77	23.9	2.28
1001	53.9	44.9	1.20	47.3	0.63	23.8	2.26
1024	52.6	47.3	1.11	47.4	0.77	24.2	2.17
1536	52.5	49.2	1.07	48.7	0.71	26.5	1.98
2048	50.5	50.3	1.01	48.7	0.80	27.9	1.82
3072	51.9	47.5	1.09	48.2	0.83	22.3	2.34
4096	14.5	13.2	1.01	14.5	1.00	15.4	1.50
6144	13.3	11.9	0.98	13.2	1.01	13.4	0.99
8192	13.3	12.4	0.97	13.2	1.01	13.4	0.99
10000	13.3	13.2	1.01	13.3	1.00	13.5	0.99
12288	13.3	13.2	1.00	13.2	1.01	13.5	0.98
16384	13.3	13.3	1.00	13.2	1.01	13.5	0.98
32768	13.3	13.3	1.00	13.2	0.94	13.5	0.98
65536	13.2	13.1	0.99	13.3	1.00	13.6	0.97
100000	12.3	12.7	1.00	12.0	1.00	12.4	1.00
131072	8.1	8.0	1.02	7.8	1.01	8.4	0.97
262144	4.7	4.7	1.00	4.6	1.00	4.8	1.00
524288	4.7	4.7	0.99	4.6	0.99	4.8	0.98
1000000	4.7	4.7	1.00	4.6	1.00	4.8	0.99
1048576	4.7	4.7	1.00	4.6	0.99	4.8	0.98
2097152	4.6	4.6	0.99	4.5	0.99	4.7	0.99
4194304	3.8	3.8	0.99	3.8	1.01	3.7	1.02
8388608	3.1	3.1	0.99	3.1	0.99	3.1	1.02
16777216	2.8	2.8	0.99	2.8	0.99	2.8	1.01

DOT float

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2	4.0	1.2	3.41	0.6	6.43	0.1	32.02
3	6.0	1.6	3.79	0.9	4.98	0.2	33.33
4	7.4	1.9	3.95	1.3	5.11	0.2	32.74
6	8.1	2.6	3.10	1.9	4.13	0.3	24.00
8	8.0	3.0	2.66	2.5	3.30	0.4	18.61
12	8.8	3.5	2.54	3.7	2.26	0.7	13.17
16	24.1	4.0	5.97	4.7	4.97	0.8	28.80
24	12.7	4.4	2.78	7.0	2.17	1.3	10.04
32	39.6	12.4	3.20	9.5	4.15	1.9	20.50
48	49.7	9.6	5.16	14.3	3.46	2.7	18.74
64	56.1	22.8	2.46	18.1	3.07	3.8	14.87
96	71.8	33.4	2.15	28.2	2.42	5.5	13.11
100	52.0	29.1	1.79	28.5	1.96	5.5	9.52
128	84.2	38.9	2.17	36.3	2.31	7.3	11.54
192	91.1	52.8	1.73	49.1	1.86	10.7	8.20
256	93.7	63.5	1.47	58.0	1.58	13.5	6.97
384	99.3	82.1	1.21	70.7	1.41	20.1	4.93
512	102.4	94.0	1.09	75.3	1.34	25.5	4.05
768	106.2	99.4	1.06	85.6	1.25	34.2	3.11
1000	91.1	91.7	0.99	88.8	1.03	36.3	2.49
1001	89.2	86.7	1.02	89.0	1.00	35.9	2.48
1024	105.6	104.7	1.01	90.9	1.16	38.4	2.77
1536	107.6	100.8	1.07	96.0	1.12	44.5	2.42
2048	106.0	104.9	1.01	97.9	1.09	48.5	2.19
3072	107.9	105.5	1.02	102.8	1.05	51.8	2.09
4096	108.9	105.1	1.03	104.6	1.04	52.5	2.09
6144	103.6	98.9	1.05	83.7	1.26	48.6	2.08
8192	48.5	48.4	1.00	46.3	1.05	36.8	1.33
10000	48.1	47.0	1.02	46.5	1.03	37.2	1.30
12288	48.3	48.4	1.00	46.5	1.04	37.5	1.28
16384	48.2	48.6	0.99	46.4	1.03	38.0	1.27
32768	48.4	48.6	1.00	46.7	1.03	38.7	1.25
65536	48.2	48.4	1.00	46.8	1.03	38.9	1.24
100000	48.3	48.6	0.99	46.8	1.03	39.0	1.24
131072	48.2	48.7	0.99	46.9	1.03	39.1	1.24
262144	19.6	19.1	1.01	19.1	1.03	19.6	1.00
524288	10.4	10.4	1.00	10.5	1.00	10.4	1.01
1000000	10.4	10.4	1.00	10.4	1.00	10.3	1.01
1048576	10.3	10.4	1.00	10.4	1.00	10.3	1.01
2097152	10.3	10.4	1.00	10.4	1.00	10.3	1.01
4194304	10.1	10.1	1.00	10.1	0.99	10.0	1.01
8388608	8.1	8.2	0.98	8.3	0.97	7.8	1.04
16777216	6.5	6.6	0.98	6.7	0.97	6.4	1.01

DOT double

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2	5.3	0.9	5.93	0.6	6.72	0.1	42.74
3	6.3	1.1	5.54	1.0	6.26	0.2	35.45
4	7.4	1.5	5.03	1.3	5.69	0.2	32.69
6	8.1	1.9	4.33	1.9	4.16	0.3	24.24
8	13.2	2.4	5.49	2.3	5.60	0.4	29.92
12	11.9	2.6	4.53	3.4	3.17	0.7	18.36
16	20.7	5.4	3.81	4.8	4.34	1.0	21.04
24	26.7	6.0	4.48	7.4	3.64	1.4	19.60
32	29.9	9.7	3.09	9.1	3.30	2.0	15.29
48	35.1	14.8	2.37	14.2	2.48	2.9	12.12
64	44.0	17.2	2.56	18.1	2.41	3.8	11.53
96	47.1	22.7	2.07	24.5	1.93	5.7	8.28
100	40.2	21.6	1.86	24.4	1.65	5.5	7.29
128	47.2	28.6	1.59	29.0	1.63	7.2	6.61
192	48.4	38.3	1.27	34.4	1.41	10.3	4.76
256	50.2	45.1	1.10	37.5	1.35	13.3	3.77
384	52.0	48.5	1.07	43.1	1.21	17.2	3.02
512	52.0	49.8	1.04	45.5	1.14	19.7	2.71
768	52.4	48.7	1.08	48.2	1.09	22.8	2.31
1000	53.1	48.0	1.10	49.3	1.08	23.7	2.24
1001	52.6	48.0	1.09	49.3	1.07	23.7	2.22
1024	53.3	50.0	1.06	48.9	1.09	24.3	2.20
1536	53.6	51.3	1.04	51.5	1.04	25.8	2.08
2048	53.8	52.2	1.03	52.2	1.03	26.6	2.02
3072	51.7	47.7	1.08	40.8	1.30	24.5	2.08
4096	24.4	23.8	1.02	23.3	1.04	18.7	1.31
6144	24.3	23.8	1.02	23.2	1.05	18.8	1.29
8192	24.3	23.7	1.03	23.3	1.04	19.2	1.27
10000	24.1	24.0	1.01	23.2	1.03	19.3	1.25
12288	24.3	23.9	1.02	23.3	1.04	19.3	1.25
16384	24.3	23.9	1.02	23.4	1.04	19.5	1.24
32768	24.3	23.9	1.02	23.4	1.03	19.5	1.24
65536	24.2	24.0	1.01	23.4	1.03	19.6	1.24
100000	19.5	21.3	1.01	15.7	1.01	17.8	1.10
131072	9.7	9.5	1.00	9.8	0.99	9.8	1.01
262144	5.2	5.2	1.00	5.2	1.00	5.2	1.01
524288	5.2	5.2	1.00	5.2	1.00	5.1	1.01
1000000	5.2	5.2	1.00	5.2	1.00	5.1	1.01
1048576	5.2	5.2	1.00	5.2	1.00	5.1	1.01
2097152	5.0	5.1	1.00	5.1	0.99	5.0	1.01
4194304	4.0	4.1	0.98	4.2	0.97	3.9	1.04
8388608	3.2	3.3	0.98	3.3	0.97	3.2	1.01
16777216	2.9	3.0	0.98	3.0	0.98	2.9	1.00

GEMV float

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2	0.7	0.6	1.29	0.3	2.38	0.1	7.04
3x3	1.3	1.3	1.06	0.6	2.29	0.2	6.18
4x4	3.8	1.5	2.58	1.3	3.30	0.4	10.61
6x6	4.5	4.7	0.93	2.2	2.10	0.7	6.33
8x8	14.8	7.8	1.89	4.0	3.73	2.0	7.42
12x12	16.4	16.1	1.01	7.4	2.24	2.9	5.67
16x16	46.6	29.9	1.56	14.5	2.65	6.6	7.19
24x24	51.2	37.1	1.38	18.1	2.52	12.7	4.03
32x32	96.6	68.4	1.41	39.5	2.22	19.6	4.98
48x48	117.9	73.7	1.60	65.2	1.82	32.1	3.66
64x64	132.6	65.0	2.03	82.9	1.60	43.6	3.04
96x96	109.0	76.1	1.43	105.8	1.02	58.2	1.88
100x100	61.1	69.0	0.88	62.5	1.00	39.7	1.54
128x128	79.1	62.2	1.28	70.4	1.12	47.6	1.66
192x192	80.5	64.5	1.25	76.0	1.06	54.4	1.48
200x200	59.0	66.2	0.89	51.8	1.14	55.3	1.07
256x256	83.2	66.5	1.25	77.4	1.07	56.6	1.48
257x257	48.2	46.1	1.04	43.4	1.12	41.3	1.17
384x384	84.0	68.4	1.22	80.4	1.05	60.6	1.39
500x500	50.5	57.1	0.88	49.8	1.02	49.8	1.02
512x512	84.0	69.1	1.22	81.0	1.03	61.7	1.36
768x768	30.1	29.8	0.98	29.6	1.02	32.4	1.01
1000x1000	19.8	20.5	0.96	19.5	1.02	20.4	0.97
1001x1001	19.6	20.2	0.97	19.4	1.01	20.3	0.97
1024x1024	20.2	20.4	0.99	20.1	1.02	20.4	0.99
1536x1536	20.2	20.3	1.00	19.6	1.03	20.1	1.01
2048x2048	20.2	20.0	1.01	19.6	1.03	19.9	1.02
3072x3072	19.6	18.7	1.05	18.5	1.05	19.0	1.03
4096x4096	16.3	14.2	1.15	14.7	1.11	15.1	1.08
4097x4097	15.8	14.5	1.09	14.8	1.07	15.2	1.04
8x10000	28.4	29.4	0.96	8.8	3.41	12.9	2.19
100x10000	20.2	20.0	1.01	18.9	1.07	19.4	1.04
1000x10000	18.7	18.0	1.04	17.9	1.04	18.5	1.01
4000x10000	12.5	11.3	1.11	11.7	1.07	12.1	1.04
10000x8	71.2	71.3	1.01	74.9	0.94	63.2	1.13
10000x100	18.8	19.6	0.96	19.8	0.95	20.0	0.94
10000x1000	18.8	17.7	1.06	18.4	1.02	18.8	1.00
10000x4000	12.5	11.1	1.13	11.8	1.06	12.2	1.02

GEMV double

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2	1.1	0.5	2.43	0.3	3.52	0.1	10.79
3x3	1.7	1.0	1.62	0.7	2.58	0.2	7.67
4x4	4.3	1.5	2.76	1.2	3.50	0.4	10.39
6x6	7.1	3.0	2.36	2.3	2.90	0.8	8.88
8x8	13.2	5.4	2.44	4.1	3.22	1.9	6.89
12x12	16.2	9.7	1.68	7.6	2.13	3.3	4.95
16x16	39.7	15.4	2.59	12.0	3.33	6.4	6.19
24x24	59.2	24.3	2.43	20.0	2.95	12.1	4.91
32x32	69.5	31.7	2.19	28.3	2.46	17.2	4.04
48x48	60.8	39.8	1.53	44.2	1.38	26.5	2.30
64x64	87.1	45.5	1.92	56.3	1.55	30.9	2.81
96x96	43.0	33.0	1.30	39.9	1.08	26.3	1.63
100x100	27.5	22.7	1.21	29.3	0.93	26.8	1.03
128x128	41.3	34.0	1.21	41.2	1.00	28.0	1.48
192x192	42.0	34.6	1.21	42.3	0.99	30.2	1.40
200x200	41.9	34.8	1.21	41.5	1.01	31.0	1.35
256x256	41.9	34.3	1.22	42.9	0.98	31.0	1.35
257x257	23.9	20.0	1.20	25.8	0.92	24.0	1.01
384x384	41.2	34.9	1.17	43.2	0.95	32.0	1.28
500x500	20.1	19.4	1.04	19.2	0.99	21.2	0.98
512x512	18.4	18.9	0.97	17.6	0.98	19.4	1.02
768x768	10.1	10.3	0.99	10.1	1.01	10.1	1.00
1000x1000	9.9	10.2	0.97	10.0	0.99	10.0	0.99
1001x1001	9.8	10.0	0.98	9.8	0.99	9.9	0.99
1024x1024	10.1	10.2	0.99	10.0	1.01	9.9	1.02
1536x1536	10.1	9.7	1.04	9.9	1.03	10.0	1.01
2048x2048	10.0	9.5	1.05	9.3	1.07	9.7	1.02
3072x3072	7.7	7.0	1.11	7.2	1.07	7.3	1.07
4096x4096	6.5	6.0	1.07	6.2	1.04	6.2	1.05
4097x4097	6.3	5.9	1.06	6.2	1.00	6.2	1.01
8x10000	25.3	21.1	1.19	11.0	2.30	11.9	2.13
100x10000	9.8	9.7	1.01	9.8	1.01	9.9	0.99
1000x10000	7.5	7.0	1.07	7.0	1.07	7.0	1.06
4000x10000	5.7	5.4	1.06	5.5	1.03	5.6	1.03
10000x8	33.0	28.9	1.14	32.2	1.03	31.8	1.05
10000x100	8.8	9.3	0.94	9.5	0.92	10.0	0.88
10000x1000	7.2	6.8	1.05	7.1	1.00	7.2	0.99
10000x4000	5.6	5.4	1.04	5.5	1.01	5.6	1.00

GEMM float

m×n×k	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2x2	1.5	0.8	1.79	0.3	5.54	0.0	188.70
3x3x3	4.1	2.2	1.82	0.8	4.91	0.0	151.29
4x4x4	13.3	4.2	3.14	1.8	7.43	0.1	214.48
6x6x6	11.1	9.5	1.17	5.0	2.24	0.2	55.25
8x8x8	16.3	17.4	0.93	9.6	1.69	0.5	36.34
12x12x12	24.5	39.5	0.61	25.3	0.98	1.7	14.61
16x16x16	82.2	114.1	0.72	84.6	0.98	2.8	28.93
24x24x24	85.4	113.2	0.75	82.2	1.05	7.9	10.54
32x32x32	162.0	202.6	0.80	188.6	0.86	19.9	8.15
48x48x48	185.5	197.2	0.94	214.6	0.86	36.9	5.02
64x64x64	171.2	226.2	0.76	212.7	0.80	76.1	2.25
96x96x96	195.4	229.0	0.85	228.2	0.86	135.2	1.44
100x100x100	170.1	209.1	0.82	188.5	0.90	98.2	1.73
128x128x128	202.6	181.2	1.12	230.4	0.88	145.7	1.39
160x160x160	204.8	194.2	1.05	227.3	0.90	163.6	1.25
192x192x192	209.4	201.0	1.04	210.0	0.99	187.0	1.12
200x200x200	197.0	194.8	1.01	199.7	0.98	155.6	1.27
224x224x224	213.2	200.9	1.06	212.7	1.00	184.5	1.16
256x256x256	212.1	205.8	1.03	214.3	0.99	190.0	1.12
257x257x257	193.7	195.5	0.99	197.8	0.98	168.2	1.15
288x288x288	218.4	210.6	1.04	218.6	1.00	200.7	1.09
320x320x320	218.7	206.4	1.06	218.0	1.00	196.0	1.12
384x384x384	217.2	211.2	1.03	216.5	1.00	203.1	1.07
448x448x448	214.5	208.2	1.03	213.3	1.00	201.1	1.07
500x500x500	207.1	208.7	0.99	207.7	1.00	191.4	1.08
512x512x512	215.4	208.8	1.03	214.6	1.00	201.6	1.07
768x768x768	218.2	216.2	1.01	220.6	0.99	212.9	1.02
1000x1000x1000	217.4	219.9	0.99	220.3	0.99	207.1	1.05
1001x1001x1001	211.3	216.7	0.97	215.0	0.98	206.0	1.03
1024x1024x1024	220.1	218.4	1.01	221.7	0.99	213.0	1.03
1536x1536x1536	222.1	224.1	0.99	225.8	0.98	219.6	1.01
2048x2048x2048	222.2	222.7	1.00	226.9	0.98	217.3	1.02
3072x3072x3072	223.1	224.3	1.00	227.8	0.98	218.4	1.02
4096x4096x4096	217.8	225.7	0.97	225.6	0.96	215.5	1.01
4097x4097x4097	196.3	222.3	0.88	217.4	0.90	211.9	0.93
64x64x1024	176.3	156.6	1.13	216.1	0.81	110.0	1.60
64x1024x64	190.0	179.0	1.06	216.7	0.88	147.0	1.29
256x256x1024	208.6	196.2	1.06	201.1	1.04	184.1	1.13
1024x64x64	194.0	180.1	1.08	227.0	0.86	154.4	1.25
1024x256x256	209.2	205.0	1.02	215.9	0.97	198.3	1.06
4096x96x96	175.5	179.6	0.98	220.2	0.80	181.2	0.97
4096x128x128	197.7	185.0	1.07	220.9	0.89	185.6	1.07
4096x144x144	206.2	192.6	1.07	211.9	0.97	195.1	1.06
4096x160x160	208.5	194.9	1.07	202.2	1.03	188.9	1.11
4096x176x176	210.2	196.3	1.07	170.6	1.23	195.4	1.08
8192x128x128	197.9	186.4	1.06	223.0	0.89	183.9	1.08
10000x8x8	89.3	156.4	0.57	178.0	0.50	31.4	2.86
10000x100x100	178.1	184.9	0.97	219.8	0.81	169.9	1.05
10000x1000x1000	219.1	220.7	0.99	221.9	0.99	212.3	1.03
10000x4000x4000	218.4	228.6	0.96	223.0	0.98	215.4	1.01

GEMM double

m×n×k	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2x2	1.5	0.9	1.64	0.5	3.16	0.0	181.35
3x3x3	3.8	2.2	1.74	0.8	4.63	0.0	143.69
4x4x4	13.0	4.3	2.96	1.8	7.32	0.1	206.27
6x6x6	10.6	8.6	1.09	5.0	2.12	0.2	51.92
8x8x8	18.5	30.9	0.60	15.3	1.20	0.5	40.11
12x12x12	23.5	45.4	0.52	24.3	0.97	1.4	16.70
16x16x16	59.7	81.4	0.73	61.5	0.97	3.5	16.99
24x24x24	78.7	92.4	0.85	90.6	0.87	7.9	9.94
32x32x32	83.3	107.4	0.77	97.9	0.85	17.7	4.72
48x48x48	83.5	110.8	0.74	109.4	0.76	36.0	2.32
64x64x64	90.8	112.8	0.81	112.3	0.81	52.3	1.72
96x96x96	96.5	114.7	0.84	114.8	0.84	74.4	1.30
100x100x100	90.6	109.0	0.83	104.7	0.87	66.2	1.37
128x128x128	99.6	84.9	1.17	112.7	0.88	84.6	1.18
160x160x160	103.6	85.5	1.21	115.8	0.89	91.6	1.13
192x192x192	105.5	91.4	1.16	105.5	1.00	96.8	1.09
200x200x200	105.3	94.5	1.11	105.2	1.00	90.9	1.16
224x224x224	105.1	95.7	1.10	104.0	1.01	101.2	1.04
256x256x256	104.8	93.4	1.12	103.8	1.01	96.5	1.09
257x257x257	98.5	91.6	1.08	98.3	1.00	90.9	1.08
288x288x288	104.6	93.5	1.12	103.6	1.01	98.2	1.07
320x320x320	101.2	91.9	1.10	102.5	0.98	100.2	1.01
384x384x384	102.8	93.2	1.10	105.9	0.97	99.3	1.04
448x448x448	105.2	95.6	1.10	106.3	0.99	103.1	1.02
500x500x500	100.9	97.1	1.04	106.0	0.95	100.4	1.00
512x512x512	102.4	98.7	1.04	105.8	0.97	102.5	1.00
768x768x768	105.2	102.9	1.02	109.3	0.96	106.3	0.99
1000x1000x1000	108.7	105.2	1.03	110.9	0.98	106.3	1.03
1001x1001x1001	103.4	104.3	0.99	107.9	0.95	105.5	0.98
1024x1024x1024	106.1	105.3	1.01	110.9	0.96	106.3	1.00
1536x1536x1536	107.9	108.3	1.00	112.4	0.96	107.8	1.00
2048x2048x2048	107.3	109.4	0.98	112.6	0.96	108.0	0.99
3072x3072x3072	104.8	111.3	0.94	112.8	0.93	109.5	0.95
4096x4096x4096	105.1	112.4	0.94	112.6	0.93	108.8	0.97
4097x4097x4097	95.6	111.3	0.86	109.6	0.87	106.0	0.90
64x64x1024	88.8	66.7	1.33	116.2	0.76	67.0	1.33
64x1024x64	97.7	94.4	1.04	113.5	0.86	87.5	1.11
256x256x1024	100.1	87.4	1.15	98.0	1.02	94.0	1.07
1024x64x64	93.2	90.8	1.01	110.3	0.84	80.5	1.16
1024x256x256	101.5	99.6	1.02	103.6	0.98	100.4	1.01
4096x96x96	87.4	94.7	0.92	109.3	0.80	89.1	0.98
4096x128x128	98.0	97.9	1.00	109.6	0.89	89.7	1.10
4096x144x144	102.1	101.0	1.01	109.0	0.94	93.6	1.09
4096x160x160	87.3	99.3	0.88	107.6	0.81	96.5	0.90
4096x176x176	89.3	102.8	0.87	105.3	0.85	99.1	0.90
8192x128x128	98.0	98.3	1.00	109.7	0.89	90.2	1.09
10000x8x8	39.4	65.1	0.57	75.8	0.52	15.1	2.62
10000x100x100	86.4	95.2	0.91	109.2	0.79	84.0	1.03
10000x1000x1000	103.5	111.3	0.93	107.4	0.96	107.7	0.97
10000x4000x4000	106.2	114.4	0.93	109.9	0.97	110.7	0.96

TRSM float

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2	0.1	0.2	0.60	0.1	1.66	0.0	51.05
3x3	0.4	0.5	0.79	0.2	1.69	0.0	45.94
4x4	0.8	1.2	0.70	0.5	1.53	0.0	48.51
6x6	2.2	1.9	1.15	1.5	1.49	0.1	40.88
8x8	4.5	2.8	1.57	3.8	1.18	0.1	37.64
12x12	7.2	4.6	1.58	8.3	0.78	0.4	18.64
16x16	21.9	5.2	4.17	16.5	1.33	0.5	41.43
24x24	32.8	8.1	4.09	28.1	1.17	1.7	19.25
32x32	56.7	9.9	5.74	40.4	1.40	2.7	21.26
48x48	67.3	14.5	4.65	52.8	1.27	3.8	17.95
64x64	64.1	18.2	3.52	60.9	1.03	6.1	10.65
96x96	88.0	25.6	3.44	80.8	1.09	10.7	8.22
100x100	77.4	25.3	3.05	73.7	1.06	7.9	9.80
128x128	87.7	31.7	2.73	97.8	0.90	13.7	6.40
192x192	114.4	41.5	2.76	121.6	0.94	20.6	5.56
200x200	128.6	41.8	3.09	116.8	1.10	18.4	6.97
256x256	119.1	48.8	2.43	137.2	0.87	25.9	4.61
257x257	119.8	46.6	2.58	123.6	0.97	21.7	5.51
384x384	143.9	62.4	2.28	155.7	0.93	35.8	4.02
500x500	151.9	74.3	2.05	152.8	0.99	42.9	3.51
512x512	139.1	75.6	1.83	160.9	0.88	44.9	3.10
768x768	148.1	96.3	1.53	174.8	0.85	61.9	2.39
1000x1000	158.5	110.4	1.44	183.1	0.87	69.8	2.27
1001x1001	148.1	109.3	1.36	176.7	0.84	69.7	2.12
1024x1024	131.3	110.2	1.19	183.2	0.73	74.6	1.76
1536x1536	132.9	133.5	0.99	198.8	0.67	95.2	1.39
2048x2048	189.2	145.7	1.29	206.6	0.93	109.6	1.73
3072x3072	193.7	162.6	1.19	206.8	0.94	129.5	1.49
4096x4096	194.8	171.8	1.13	203.7	0.96	142.9	1.36
4097x4097	184.0	169.9	1.08	198.9	0.92	140.1	1.31
64x4096	50.6	18.4	2.75	65.3	0.77	7.8	6.58
256x4096	90.4	48.3	1.85	127.3	0.71	26.7	3.39
1024x8	62.6	37.4	1.80	68.1	0.87	27.9	2.25
1024x64	134.7	90.2	1.54	157.6	0.85	60.6	2.22
1024x256	151.8	104.6	1.45	179.4	0.85	69.2	2.19
1024x4096	163.1	110.7	1.48	185.7	0.88	74.7	2.18
4096x8	65.7	42.1	1.55	62.0	1.06	43.1	1.52
4096x64	148.6	126.4	1.16	165.7	0.90	108.5	1.38
4096x256	154.3	159.9	0.96	202.4	0.76	133.5	1.16
4096x1024	200.3	172.4	1.16	213.1	0.94	144.3	1.39

TRSM double

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2	0.2	0.2	0.66	0.1	1.81	0.0	35.02
3x3	0.4	0.4	0.95	0.2	1.74	0.0	30.38
4x4	0.9	0.9	0.95	0.6	1.65	0.0	30.94
6x6	2.2	1.8	1.27	1.5	1.47	0.1	24.46
8x8	6.1	2.8	2.18	4.0	1.51	0.2	31.02
12x12	8.6	4.0	2.10	8.4	1.04	0.6	14.05
16x16	19.2	4.3	4.44	17.4	1.15	1.0	18.44
24x24	30.1	6.5	4.52	32.8	0.94	1.9	15.78
32x32	34.7	8.0	4.24	42.1	0.84	3.4	10.14
48x48	42.3	10.7	3.90	47.7	0.89	5.9	7.15
64x64	45.8	13.6	3.36	57.4	0.80	8.5	5.40
96x96	54.9	16.8	3.26	71.7	0.78	13.4	4.03
100x100	51.1	16.5	3.10	67.2	0.73	11.5	4.43
128x128	56.9	18.6	3.06	77.7	0.73	16.6	3.42
192x192	71.1	21.8	3.26	90.1	0.79	24.2	2.93
200x200	74.4	22.3	3.36	88.6	0.83	23.3	3.20
256x256	74.4	23.7	3.10	90.6	0.82	29.8	2.50
257x257	66.8	23.0	2.90	82.9	0.81	28.0	2.39
384x384	78.0	25.7	3.04	87.0	0.89	38.1	2.05
500x500	73.9	33.3	2.21	91.2	0.81	43.5	1.70
512x512	66.3	34.0	1.95	89.5	0.74	40.4	1.64
768x768	69.7	41.4	1.68	96.0	0.73	56.6	1.23
1000x1000	73.2	50.5	1.45	101.6	0.72	63.2	1.16
1001x1001	66.3	50.2	1.32	98.8	0.67	63.3	1.05
1024x1024	69.4	50.7	1.37	101.5	0.68	59.0	1.18
1536x1536	94.8	60.1	1.58	104.4	0.91	69.2	1.37
2048x2048	95.3	67.8	1.41	103.6	0.92	75.5	1.26
3072x3072	90.9	76.3	1.19	102.0	0.89	82.5	1.10
4096x4096	88.9	83.3	1.07	103.3	0.86	87.1	1.02
4097x4097	81.3	82.6	0.98	101.4	0.80	87.5	0.93
64x4096	29.8	13.1	2.27	47.5	0.62	9.4	3.16
256x4096	52.7	23.2	2.27	82.8	0.64	28.9	1.82
1024x8	32.9	21.4	1.59	31.7	0.98	20.1	1.63
1024x64	75.9	43.0	1.78	82.6	0.90	49.3	1.54
1024x256	76.8	48.9	1.57	95.0	0.81	56.3	1.36
1024x4096	83.5	49.3	1.69	98.3	0.85	58.1	1.44
4096x8	31.6	23.8	1.32	25.7	1.23	18.5	1.72
4096x64	69.7	62.4	1.13	78.0	0.89	61.2	1.13
4096x256	73.4	78.7	0.93	98.9	0.74	80.1	0.92
4096x1024	100.3	82.2	1.22	105.7	0.95	86.9	1.16

SYRK float

n×k	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2	0.1	0.2	0.55	0.1	1.31	0.0	21.90
3x3	0.3	0.6	0.55	0.2	1.30	0.0	19.23
4x4	0.9	1.3	0.67	0.6	1.45	0.0	23.88
6x6	1.7	3.1	0.56	1.5	1.12	0.1	15.57
8x8	5.0	7.0	0.71	3.8	1.31	0.2	20.94
12x12	7.9	15.1	0.52	8.1	0.99	0.8	9.34
16x16	22.9	27.5	0.83	19.4	1.16	1.4	16.04
24x24	35.3	41.1	0.86	32.8	1.06	3.8	9.23
32x32	60.3	53.2	1.14	54.1	1.12	9.0	6.68
48x48	79.2	85.3	0.93	81.3	0.97	17.5	4.53
64x64	90.1	83.4	1.08	92.7	0.97	36.4	2.47
96x96	114.4	114.2	1.00	114.3	1.00	74.2	1.54
100x100	101.0	115.7	0.87	103.5	0.98	55.9	1.81
128x128	126.5	121.7	1.04	127.0	0.99	90.6	1.40
192x192	148.0	149.3	0.99	152.3	0.99	134.5	1.10
200x200	142.4	153.5	0.93	150.2	0.95	110.4	1.29
256x256	160.7	157.3	1.02	164.8	0.98	153.2	1.04
257x257	144.3	148.5	0.97	152.8	0.94	129.5	1.12
384x384	179.2	174.4	1.03	183.8	0.97	172.9	1.04
500x500	180.0	178.8	1.01	180.8	1.00	162.7	1.11
512x512	186.7	173.4	1.08	186.9	1.00	170.7	1.09
768x768	192.6	189.2	1.02	196.5	0.98	186.2	1.03
1000x1000	199.7	195.3	1.02	202.6	0.99	187.4	1.06
1001x1001	187.4	190.0	0.98	195.1	0.97	185.9	1.01
1024x1024	198.5	190.7	1.04	198.9	1.00	193.2	1.03
1536x1536	207.0	203.2	1.02	208.4	0.99	202.7	1.02
2048x2048	209.7	205.4	1.02	214.8	0.98	206.4	1.02
3072x3072	206.5	209.2	0.99	217.9	0.95	209.4	0.99
4096x4096	204.5	212.3	0.96	218.9	0.93	209.6	0.98
4097x4097	194.3	209.7	0.93	213.1	0.92	204.2	0.95
64x4096	91.1	97.4	0.94	90.2	1.01	68.8	1.32
256x4096	152.9	153.7	0.99	154.5	0.99	147.7	1.03
1024x4096	198.2	192.1	1.03	198.8	1.00	193.4	1.03
4096x8	90.0	61.5	1.46	88.7	1.00	51.8	1.75
4096x64	169.1	175.9	0.96	188.2	0.90	179.5	0.94
4096x256	205.9	212.9	0.97	221.8	0.93	208.8	0.99
4096x1024	205.6	209.8	0.98	219.9	0.93	208.8	0.99

SYRK double

n×k	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL	BLIS GFLOP/s	Eigen ÷ BLIS
2x2	0.2	0.2	0.83	0.1	1.88	0.0	31.66
3x3	0.4	0.6	0.80	0.3	1.71	0.0	26.01
4x4	1.1	1.3	0.88	0.6	1.83	0.0	30.19
6x6	2.4	3.1	0.75	1.5	1.55	0.1	20.76
8x8	6.3	6.4	0.97	3.8	1.65	0.2	25.42
12x12	9.5	12.1	0.79	7.6	1.25	0.7	13.50
16x16	22.9	18.2	1.26	16.7	1.37	1.8	13.08
24x24	34.0	26.1	1.30	29.4	1.16	3.9	8.62
32x32	43.0	31.4	1.37	40.3	1.07	8.7	4.94
48x48	47.2	39.4	1.20	48.3	0.98	18.5	2.50
64x64	55.1	43.2	1.26	56.4	0.98	28.9	1.91
96x96	65.1	56.6	1.15	67.0	0.97	46.3	1.41
100x100	63.7	58.8	1.08	63.5	1.00	43.0	1.49
128x128	73.2	56.0	1.31	74.3	0.98	61.8	1.19
192x192	82.5	70.3	1.17	86.5	0.96	75.3	1.10
200x200	84.4	80.3	1.05	88.1	0.96	71.9	1.17
256x256	89.8	73.2	1.23	91.7	0.97	83.0	1.08
257x257	83.1	77.8	1.06	86.1	0.97	75.6	1.10
384x384	91.9	81.8	1.12	92.0	1.00	86.8	1.06
500x500	93.0	86.2	1.08	96.5	0.96	88.1	1.05
512x512	93.1	85.6	1.08	94.3	0.99	91.5	1.02
768x768	98.3	94.5	1.04	97.3	1.01	97.3	1.01
1000x1000	102.6	100.3	1.03	103.8	0.99	99.0	1.04
1001x1001	96.6	98.5	0.98	98.9	0.98	98.1	0.98
1024x1024	100.3	98.2	1.02	103.3	0.97	100.1	1.00
1536x1536	101.8	103.6	0.98	107.0	0.96	103.3	0.98
2048x2048	97.4	106.0	0.92	107.5	0.91	103.4	0.94
3072x3072	94.0	108.7	0.86	108.9	0.87	105.3	0.89
4096x4096	93.2	110.2	0.85	109.2	0.85	106.5	0.88
4097x4097	88.6	109.3	0.81	106.6	0.83	103.4	0.86
64x4096	51.6	39.8	1.29	52.4	0.98	39.6	1.31
256x4096	83.6	73.2	1.14	82.3	1.01	80.9	1.03
1024x4096	100.0	98.3	1.02	102.1	0.98	98.7	1.01
4096x8	20.1	31.2	0.65	30.6	0.66	26.0	0.78
4096x64	89.6	96.0	0.93	83.8	1.07	92.8	0.97
4096x256	91.6	110.1	0.83	108.8	0.84	107.3	0.85
4096x1024	92.5	110.2	0.84	109.1	0.85	106.5	0.87

POTRF float

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	0.2	0.1	2.40	0.2	1.31
3	0.6	0.3	2.36	0.6	0.96
4	0.8	0.4	1.89	1.4	0.54
6	1.1	0.8	1.38	0.9	1.19
8	1.7	1.3	1.35	1.4	1.24
12	2.7	2.5	1.07	2.3	1.21
16	4.1	4.0	1.03	3.2	1.26
24	6.4	7.8	0.84	3.8	1.66
32	8.7	9.2	0.94	5.4	1.60
48	14.3	11.4	1.27	7.7	1.83
64	19.8	17.0	1.17	9.5	2.07
96	28.2	24.2	1.17	11.3	2.48
100	25.6	22.6	1.14	11.5	2.21
128	47.7	33.7	1.42	12.5	3.80
192	68.1	43.2	1.58	65.6	1.04
200	65.5	40.3	1.62	69.9	0.94
256	90.5	56.3	1.60	84.2	1.08
257	78.2	52.7	1.48	82.5	0.95
384	116.8	74.3	1.57	113.6	1.03
500	118.9	74.0	1.61	126.5	0.94
512	120.9	82.5	1.47	133.3	0.91
768	132.0	95.4	1.38	137.9	0.96
1000	143.5	101.3	1.42	148.7	0.96
1001	135.9	99.4	1.37	143.3	0.95
1024	137.6	105.0	1.31	133.2	1.03
1536	162.4	125.0	1.30	162.2	1.00
2048	176.5	139.0	1.27	176.4	1.00
3072	175.7	152.7	1.15	180.0	0.98
4096	175.3	158.4	1.11	176.7	0.99
4097	168.8	157.0	1.07	175.9	0.96

POTRF double

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	0.3	0.1	2.38	0.2	1.54
3	0.5	0.3	2.05	0.5	1.02
4	0.7	0.5	1.45	1.2	0.57
6	1.0	1.0	1.01	0.9	1.13
8	1.6	1.5	1.06	1.3	1.23
12	2.9	2.5	1.13	2.5	1.16
16	4.2	3.8	1.10	3.5	1.20
24	7.0	6.1	1.15	3.6	1.92
32	9.0	8.3	1.08	5.4	1.66
48	14.1	9.8	1.43	8.9	1.58
64	16.9	13.4	1.26	11.1	1.52
96	23.4	19.0	1.22	15.1	1.57
100	22.1	18.1	1.22	15.6	1.41
128	34.6	24.5	1.42	13.3	2.58
192	46.0	32.5	1.42	45.1	1.02
200	47.2	29.6	1.60	46.7	1.01
256	55.3	35.6	1.55	56.2	0.99
257	49.7	34.3	1.45	50.4	0.98
384	62.3	40.3	1.55	64.3	0.97
500	62.3	40.5	1.54	67.2	0.93
512	60.6	41.7	1.45	65.1	0.93
768	68.1	47.8	1.43	72.0	0.94
1000	77.4	49.2	1.57	79.2	0.98
1001	72.9	48.6	1.50	67.0	1.09
1024	74.1	50.5	1.47	72.3	1.02
1536	84.0	54.7	1.54	85.4	0.98
2048	82.6	59.2	1.40	85.1	0.97
3072	81.9	65.8	1.24	88.1	0.93
4096	75.4	68.5	1.10	83.0	0.91
4097	72.7	68.4	1.06	82.7	0.88

GETRF float

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	0.2	0.1	1.84	0.3	0.58
3	0.4	0.2	2.03	0.9	0.47
4	0.7	0.4	1.88	2.1	0.31
6	1.2	0.7	1.81	1.0	1.23
8	1.9	0.9	2.03	0.8	2.33
12	3.1	1.5	1.94	1.5	2.08
16	4.6	2.2	2.00	2.4	2.04
24	5.2	4.3	1.26	3.5	1.41
32	8.4	5.8	1.47	5.1	1.62
48	13.7	10.0	1.40	9.1	1.47
64	18.7	12.9	1.47	13.6	1.35
96	28.3	19.2	1.48	23.2	1.21
100	25.9	19.6	1.33	23.1	1.11
128	39.9	24.5	1.66	32.6	1.20
192	58.3	35.7	1.65	50.8	1.14
200	58.0	35.7	1.62	52.8	1.10
256	62.5	44.3	1.41	68.8	0.91
257	62.9	43.1	1.45	65.0	0.97
384	71.7	60.2	1.21	96.9	0.73
500	82.3	67.2	1.22	109.5	0.75
512	78.4	70.2	1.12	115.1	0.68
768	108.0	86.8	1.25	134.5	0.80
1000	122.9	101.1	1.22	142.6	0.86
1001	116.9	99.7	1.18	136.3	0.86
1024	116.9	99.9	1.18	130.0	0.89
1536	133.1	124.7	1.07	158.7	0.84
2048	148.6	138.2	1.07	165.7	0.90
3072	158.5	153.4	1.03	173.8	0.91
4096	156.1	164.1	0.95	177.5	0.88
4097	148.1	162.6	0.91	182.6	0.81

GETRF double

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	0.2	0.1	1.88	0.3	0.68
3	0.5	0.2	1.88	0.8	0.55
4	0.7	0.4	1.68	1.9	0.38
6	1.3	0.8	1.54	1.1	1.21
8	2.1	1.2	1.82	1.2	1.88
12	3.0	1.7	1.83	1.9	1.57
16	4.5	2.6	1.80	2.7	1.59
24	5.8	4.0	1.44	3.7	1.54
32	8.4	5.5	1.53	5.2	1.58
48	13.1	8.5	1.57	8.2	1.58
64	17.4	10.8	1.65	11.7	1.46
96	23.7	15.4	1.56	18.9	1.24
100	22.3	15.3	1.47	19.2	1.15
128	28.7	19.4	1.49	23.4	1.22
192	39.1	26.3	1.49	37.2	1.04
200	41.1	26.1	1.58	38.7	1.06
256	44.8	30.9	1.43	38.5	1.18
257	41.2	30.2	1.34	41.5	1.01
384	49.9	36.8	1.35	53.4	0.94
500	52.0	38.9	1.33	56.5	0.93
512	49.7	40.3	1.24	52.4	0.95
768	59.5	46.9	1.27	58.7	1.01
1000	67.5	52.6	1.28	64.8	1.04
1001	63.8	52.2	1.22	61.7	1.04
1024	65.5	53.0	1.24	62.6	1.05
1536	70.0	63.3	1.10	69.4	1.01
2048	77.2	68.2	1.13	74.8	1.03
3072	75.8	77.6	0.98	70.7	1.07
4096	75.0	83.2	0.90	93.3	0.81
4097	71.7	82.4	0.87	91.6	0.78

GEQRF float

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2x2	0.1	0.1	0.68	0.5	0.16
3x3	0.1	0.2	0.71	0.5	0.26
4x4	0.2	0.3	0.71	0.7	0.30
6x6	0.4	0.6	0.77	0.9	0.50
8x8	0.7	0.9	0.79	1.3	0.54
12x12	1.4	1.6	0.88	2.2	0.63
16x16	2.3	2.3	1.01	3.1	0.74
24x24	4.1	3.5	1.16	4.3	0.94
32x32	5.7	4.6	1.23	6.2	0.92
48x48	9.6	8.3	1.16	9.0	1.07
64x64	8.1	10.2	0.80	11.6	0.69
96x96	17.0	14.8	1.15	16.9	1.00
100x100	13.8	15.6	0.88	16.8	0.82
128x128	23.6	17.5	1.35	20.0	1.18
192x192	41.6	33.1	1.26	37.3	1.11
200x200	38.1	41.5	0.91	37.6	1.02
256x256	53.2	42.5	1.25	51.5	1.03
257x257	42.0	52.3	0.80	58.0	0.72
384x384	79.5	62.6	1.27	81.2	0.98
500x500	88.9	83.1	1.07	108.2	0.82
512x512	93.8	72.3	1.30	92.0	1.02
768x768	115.0	88.5	1.30	112.9	1.01
1000x1000	122.5	105.8	1.16	135.8	0.90
1001x1001	116.6	103.6	1.13	132.0	0.88
1024x1024	117.6	85.6	1.38	100.3	1.17
1536x1536	132.4	100.9	1.31	126.4	1.05
2048x2048	137.1	103.1	1.33	127.5	1.07
3072x3072	136.8	111.1	1.23	137.4	1.00
4096x4096	125.5	108.2	1.15	146.9	0.86
4097x4097	119.9	108.6	1.10	154.6	0.78
4096x8	21.8	20.7	1.05	29.7	0.74
4096x64	33.4	31.9	1.04	46.4	0.72
4096x256	75.3	59.1	1.28	65.4	1.14
4096x1024	124.6	104.5	1.19	122.4	1.02
10000x8	20.2	19.2	1.05	25.2	0.80
10000x100	36.8	20.6	1.81	61.7	0.59
10000x1000	120.3	107.0	1.13	133.1	0.90
10000x4000	112.1	112.6	1.00	155.3	0.72
100000x8	13.9	13.6	1.02	15.4	0.90
100000x64	16.7	15.9	1.06	33.6	0.50
100000x256	41.0	35.5	1.16	56.1	0.73

GEQRF double

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2x2	0.1	0.1	0.65	0.6	0.13
3x3	0.1	0.2	0.67	0.6	0.23
4x4	0.2	0.3	0.71	0.8	0.27
6x6	0.4	0.6	0.73	0.9	0.46
8x8	0.7	0.9	0.76	1.4	0.50
12x12	1.4	1.7	0.80	2.5	0.55
16x16	2.2	2.7	0.83	3.7	0.60
24x24	4.1	4.8	0.85	7.0	0.58
32x32	6.0	6.5	0.92	10.6	0.57
48x48	9.5	10.3	0.91	16.4	0.59
64x64	8.0	13.2	0.60	20.2	0.40
96x96	15.6	14.1	1.09	17.6	0.90
100x100	12.8	14.1	0.91	17.6	0.73
128x128	19.5	13.9	1.39	23.3	0.85
192x192	28.9	25.6	1.13	38.7	0.75
200x200	28.3	32.2	0.87	41.3	0.69
256x256	33.4	30.8	1.08	41.4	0.81
257x257	30.5	36.2	0.84	42.5	0.72
384x384	45.4	40.6	1.11	52.1	0.88
500x500	49.3	48.3	1.02	60.4	0.82
512x512	48.5	43.1	1.13	51.5	0.94
768x768	56.5	51.6	1.09	59.8	0.94
1000x1000	61.1	59.7	1.02	71.2	0.86
1001x1001	58.6	58.3	1.00	68.5	0.86
1024x1024	60.2	52.7	1.15	61.9	0.97
1536x1536	64.9	58.2	1.12	69.5	0.93
2048x2048	66.2	61.4	1.08	72.3	0.92
3072x3072	59.8	62.2	0.96	72.9	0.82
4096x4096	55.0	59.4	0.92	76.6	0.72
4097x4097	53.9	59.6	0.90	78.4	0.69
4096x8	9.1	10.3	0.88	13.7	0.66
4096x64	15.1	12.9	1.17	27.8	0.55
4096x256	35.7	24.0	1.49	44.1	0.81
4096x1024	59.5	55.9	1.07	66.5	0.89
10000x8	9.0	10.0	0.89	13.6	0.67
10000x100	13.0	8.9	1.46	35.7	0.36
10000x1000	47.0	55.0	0.86	62.3	0.76
10000x4000	51.6	62.6	0.83	75.8	0.68
100000x8	5.3	5.9	0.91	6.6	0.81
100000x64	7.3	6.9	1.05	15.5	0.47
100000x256	18.4	15.0	1.22	26.1	0.70

SYEV float

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	0.6	0.4	1.74	0.3	2.00
3	0.6	0.4	1.57	0.4	1.69
4	0.8	0.5	1.49	0.5	1.47
6	1.2	0.8	1.46	0.9	1.41
8	1.7	1.2	1.50	1.3	1.32
12	2.7	1.9	1.39	2.1	1.28
16	3.8	2.6	1.46	3.5	1.07
24	5.9	3.7	1.60	4.7	1.26
32	7.7	4.5	1.74	7.4	1.04
48	11.3	6.5	1.76	10.7	1.05
64	14.6	7.6	1.92	12.8	1.14
96	22.1	9.3	2.41	18.8	1.16
100	20.3	9.1	2.23	18.7	1.08
128	27.6	10.1	2.72	21.3	1.31
192	38.0	11.3	3.36	33.4	1.14
200	37.8	11.4	3.32	30.7	1.22
256	45.5	12.3	3.66	35.6	1.29
257	39.6	12.3	3.22	30.6	1.30
384	55.6	13.6	4.09	38.0	1.47
500	59.6	14.2	4.19	52.5	1.13
512	63.5	14.3	4.43	42.6	1.50
768	68.7	15.0	4.55	76.2	0.91
1000	52.3	15.2	3.43	86.2	0.61
1001	50.8	15.2	3.33	85.0	0.60
1024	49.0	13.6	3.61	74.3	0.66
1536	44.7	15.5	2.89	75.4	0.59
2048	43.7	14.0	3.09	80.1	0.55

SYEV double

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	0.6	0.4	1.54	0.3	1.73
3	0.5	0.3	1.48	0.3	1.31
4	0.6	0.5	1.36	0.5	1.37
6	1.0	0.7	1.37	0.7	1.37
8	1.4	1.0	1.31	1.2	1.14
12	2.1	1.8	1.20	1.8	1.17
16	3.0	2.3	1.31	2.9	1.02
24	4.6	3.3	1.39	4.7	0.97
32	6.0	4.1	1.48	6.5	0.92
48	8.6	5.1	1.69	8.6	1.00
64	10.9	6.4	1.69	12.0	0.92
96	15.2	7.8	1.94	15.6	0.99
100	15.1	7.3	2.08	16.9	0.89
128	18.2	7.9	2.28	18.9	0.96
192	22.3	8.4	2.63	25.7	0.87
200	22.9	9.5	2.39	26.9	0.85
256	25.8	10.0	2.57	29.8	0.87
257	24.7	10.0	2.46	29.3	0.84
384	31.3	10.2	3.05	37.1	0.84
500	29.6	11.4	2.59	41.6	0.71
512	31.8	10.4	3.06	40.1	0.79
768	23.3	11.9	1.96	45.6	0.51
1000	21.1	11.9	1.77	50.3	0.42
1001	20.8	11.9	1.74	48.7	0.43
1024	20.8	11.1	1.87	49.2	0.42
1536	20.2	11.2	1.80	53.3	0.38
2048	20.1	11.3	1.77	55.0	0.37

GESDD float

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2x2	1.9	0.2	9.17	0.3	7.11
3x3	1.4	0.4	3.34	0.4	3.20
4x4	1.4	0.6	2.18	0.6	2.24
6x6	1.4	1.2	1.19	1.1	1.25
8x8	1.7	1.8	0.96	1.8	0.96
12x12	2.1	2.9	0.71	2.8	0.74
16x16	3.2	3.8	0.84	4.7	0.68
24x24	4.7	5.4	0.88	6.0	0.79
32x32	6.4	9.0	0.71	10.6	0.61
48x48	10.4	14.3	0.73	15.9	0.66
64x64	13.0	20.8	0.62	23.8	0.55
96x96	21.9	30.5	0.72	34.9	0.63
100x100	22.4	31.7	0.71	33.6	0.66
128x128	28.8	40.5	0.71	45.5	0.63
192x192	48.8	62.5	0.78	69.3	0.71
200x200	51.0	66.8	0.77	72.1	0.71
256x256	61.3	75.1	0.82	79.8	0.77
257x257	64.0	83.5	0.77	91.5	0.70
384x384	91.6	103.1	0.89	108.0	0.85
500x500	109.9	128.9	0.85	136.2	0.81
512x512	108.1	120.5	0.89	122.7	0.88
768x768	134.6	144.0	0.94	145.2	0.93
1000x1000	131.7	135.4	0.97	153.1	0.86
1001x1001	130.1	143.7	0.91	151.9	0.86
1024x1024	111.6	113.7	0.99	123.7	0.90
1536x1536	123.8	128.6	0.96	137.8	0.90
2048x2048	128.9	133.8	0.96	137.1	0.94
4096x64	104.5	72.1	1.45	124.0	0.84
4096x256	181.8	141.0	1.29	166.7	1.09
4096x1024	176.1	165.1	1.07	184.9	0.95
10000x8	28.6	26.3	1.08	78.1	0.37
10000x100	128.3	59.9	2.13	163.9	0.79
10000x1000	225.9	230.5	0.98	237.6	0.95

GESDD double

m×n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2x2	1.7	0.2	7.92	0.3	6.73
3x3	1.0	0.4	2.50	0.4	2.64
4x4	1.0	0.6	1.72	0.6	1.81
6x6	1.1	1.1	0.99	1.0	1.06
8x8	1.1	1.5	0.72	1.5	0.72
12x12	1.2	2.6	0.48	2.5	0.48
16x16	2.3	3.5	0.66	4.2	0.55
24x24	3.3	4.9	0.68	6.5	0.52
32x32	4.6	8.1	0.57	8.9	0.53
48x48	7.3	11.6	0.62	13.1	0.56
64x64	9.0	17.2	0.53	18.5	0.48
96x96	14.4	23.9	0.60	26.0	0.55
100x100	14.6	24.2	0.60	26.0	0.56
128x128	18.5	29.4	0.64	34.1	0.54
192x192	29.6	41.2	0.72	49.1	0.60
200x200	31.0	45.7	0.68	54.1	0.57
256x256	37.3	49.6	0.75	60.4	0.62
257x257	37.9	53.4	0.71	65.1	0.58
384x384	52.8	64.1	0.82	79.0	0.67
500x500	61.8	73.1	0.84	92.8	0.67
512x512	57.1	67.5	0.84	81.3	0.71
768x768	59.4	67.7	0.88	73.7	0.81
1000x1000	63.2	74.8	0.83	78.1	0.82
1001x1001	62.1	73.4	0.83	76.6	0.82
1024x1024	59.0	67.1	0.88	70.7	0.83
1536x1536	65.1	72.2	0.90	74.6	0.87
2048x2048	68.1	75.6	0.90	76.7	0.89
4096x64	52.1	36.6	1.43	75.7	0.69
4096x256	92.5	66.6	1.39	102.2	0.91
4096x1024	88.0	93.4	0.94	95.8	0.92
10000x8	11.6	20.2	0.58	41.8	0.28
10000x100	50.7	28.5	1.78	92.4	0.55
10000x1000	99.2	120.2	0.82	115.9	0.86

GEEV float

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	2.0	0.2	8.50	0.3	7.15
3	0.9	0.4	2.44	0.4	2.28
4	1.1	0.6	1.95	0.6	1.80
6	1.6	1.0	1.66	1.0	1.53
8	2.3	1.5	1.47	1.6	1.48
12	3.2	2.4	1.34	2.2	1.43
16	4.8	3.1	1.57	3.3	1.41
24	6.2	4.3	1.41	4.3	1.48
32	8.9	5.7	1.55	5.8	1.54
48	12.4	7.3	1.68	8.2	1.51
64	13.7	8.6	1.58	9.8	1.40
96	17.3	9.5	1.81	11.3	1.54
100	16.0	9.7	1.67	11.3	1.40
128	18.6	11.0	1.67	14.9	1.26
192	22.7	22.9	0.99	25.3	0.90
200	21.9	24.9	0.87	25.3	0.88
256	23.7	30.0	0.79	34.0	0.70
257	22.8	30.8	0.73	32.9	0.70
384	20.8	46.0	0.44	51.6	0.41
500	22.7	55.7	0.41	64.5	0.35
512	23.5	34.4	0.68	39.3	0.60
768	23.6	61.5	0.38	71.8	0.33
1000	21.8	83.4	0.26	99.4	0.22
1001	21.8	85.0	0.25	98.0	0.23
1024	14.6	68.0	0.22	77.4	0.19

GEEV double

n	Eigen GFLOP/s	OpenBLAS GFLOP/s	Eigen ÷ OpenBLAS	Intel oneMKL GFLOP/s	Eigen ÷ Intel oneMKL
2	2.1	0.2	9.63	0.6	3.41
3	0.8	0.3	2.29	0.7	1.17
4	1.1	0.5	1.95	1.0	1.04
6	1.3	0.9	1.53	1.6	0.81
8	2.0	1.2	1.54	2.3	0.90
12	2.7	2.0	1.38	3.2	0.82
16	4.0	2.8	1.43	4.2	0.95
24	5.8	4.0	1.41	5.6	1.05
32	7.0	4.8	1.41	6.5	1.12
48	9.3	5.9	1.57	8.1	1.14
64	10.0	6.6	1.52	9.1	1.09
96	11.6	6.8	1.68	10.3	1.15
100	10.7	6.9	1.56	10.5	1.02
128	11.8	7.5	1.55	6.9	1.72
192	12.3	14.4	0.87	16.9	0.72
200	13.8	15.5	0.88	17.1	0.81
256	13.4	17.4	0.77	17.9	0.75
257	12.8	18.4	0.70	21.4	0.59
384	13.5	26.4	0.51	30.3	0.45
500	12.2	32.5	0.37	39.6	0.31
512	11.4	20.1	0.57	19.4	0.58
768	10.3	31.6	0.33	31.7	0.32
1000	10.2	46.4	0.22	53.8	0.19
1001	10.1	45.6	0.22	52.9	0.19
1024	9.2	38.9	0.24	38.4	0.24

Reproducibility

The MR !2903 harness, original commit 778e20997982c76c7a803d4c958574aa98418ae8, was applied without conflicts onto upstream master ab4f7316dc90a936ba06463d241a765d9ce9e0ba. The first two AXPY runs use combined commit 11cf0c2899fab5c25593e3ef76315dfd9eb1a63b. Subsequent runs use 4e0c35ecbfcc0e0039d4b77d6bfca4ab72ad1da7, which adds only the DOT validation correction and its regression check; the complete Eigen header tree matches that upstream master in every run. The result files retain all ten samples, compiler flags, library versions, thread caps, affinity and run conditions. Machine identifiers and installation paths have been anonymized; numerical samples are unchanged.

BLIS was built from upstream release 2.1, commit caf0db6be1202d9c83c79b51e75eceb96aa8b556, with --disable-threading --enable-shared --disable-static skx. The runtime configuration query also reports skx.

Download the machine profile, shape grid, and the result files:

The DOT check originally scaled its allowance by the dot-product result, which can nearly cancel. A 16-element float case was falsely rejected even though both implementations agreed with a 256-bit MPFR reference to within one float epsilon times the sum of absolute products. The correction uses the larger of the original allowance and 64 * epsilon * sum(abs(x_i * y_i)) in the untimed check; the timed kernels are unchanged. Regression checks cover the captured cancellation case, an incorrect result, zero, and non-finite values. The MPFR reproducer retains the exact operands.

Result	Value	Absolute error against MPFR
MPFR, 256 bits	-0.001443878941188359	—
Eigen, float	-0.001443922519683838	4.36e-8
OpenBLAS, float	-0.001443852204829454	2.67e-8

To reconstruct the measured source, check out upstream master ab4f7316dc90a936ba06463d241a765d9ce9e0ba and cherry-pick the harness commit 778e20997982c76c7a803d4c958574aa98418ae8, then apply the DOT validation patch with git am dot-validation.patch so the benchmark worktree is clean. Install Google Benchmark 1.8.3 built with CMAKE_BUILD_TYPE=Release and the listed libraries. Put the downloaded profile in a directory named profiles and the shape grid in shapes.json. Configure library discovery as described in the profile; build on an idle machine, then wait for compilation load to subside before timing.

For example, from the Eigen checkout, select exactly the published GEMM shapes below. First run the command with --dry-run -j JOBS in place of --no-build to build and list the cells, choosing JOBS for the available memory and CPUs. Once compilation load subsides, run it as shown to measure:

filter=$(python3 -c 'import json,re; g=json.load(open("shapes.json")); print("/(?:f32|f64)/(?:" + "|".join(map(re.escape,g["GEMM"])) + ")$")')
python3 benchmarks/comparison/run.py --machine xeon-gold-6444y \
  --machines-dir profiles --arms openblas --ops GEMM --scalars f32,f64 \
  --threads 1 --repetitions 10 --min-time 0.2s --filter "$filter" --no-build

Repeat the build and measurement steps with each operation’s shape list and each library; restrict BLIS to AXPY, DOT, GEMV, GEMM, TRSM and SYRK. The profile pins CPU 2; adapt this to an available physical core on another machine.

Regenerate the charts from the downloaded result files with scripts/benchmarks/plot_comparison.py --out-dir OUTPUT --cache L1=48K --cache L2=2M --cache L3=45M data/*.json from the website repository.