Performance of Eigen’s dense kernels measured against BLAS/LAPACK libraries, one machine and one dataset per page, each with the conditions it was taken under: CPU, operating system, compiler and flags, Eigen commit, library versions, thread count and method. Ratios between Eigen and a library are formed on one machine with one build configuration; absolute rates are not comparable across pages.
ab4f7316d.674e4a4e5.674e4a4e5.210e0a609 built for the default Armv8-A target, so every kernel is Eigen’s NEON code.210e0a609.674e4a4e5 built with -mcpu=apple-m4, which selects
its SME kernels.674e4a4e5. Accelerate and Arm Performance
Libraries cannot be held to NEON through documented means; the SME page has those comparisons.674e4a4e5 built for the default Armv8-A
target, so every kernel is Eigen’s NEON code.674e4a4e5. NEON in AArch32 state has no double-precision lanes, so Eigen’s double-precision kernels
there are scalar.210e0a609 built for the default Armv8-A target, so
every kernel is Eigen’s NEON code.-msve-vector-bits=128 -DEIGEN_ARM64_USE_SVE),
against the NEON page’s library measurements, Eigen master 210e0a609.The Xeon, Grace and DGX Spark pages are from September and early October and do not cover the five
operations added in October: TRMM, SYMM, PSTRF (Cholesky with diagonal pivoting, against Eigen’s LDLT),
SYTRF (Bunch-Kaufman) and GELS (least squares through Householder QR).
Every page is produced by the comparison harness under benchmarks/comparison/ in the Eigen source
tree (in review as merge request
!2903), which validates each reference
library’s result against Eigen before timing it and records the full provenance of a run. The charts
are drawn from the raw result files by scripts/benchmarks/plot_comparison.py in the
website repository, where the result files behind
each page are kept beside its images. The plan and progress
are tracked in Eigen issue #3112.
These pages measured Eigen 2 and an early Eigen 3 with the BTL harness, which has since been removed from the tree, against libraries that have all been superseded. They are kept as a record; the numbers say nothing about current hardware or current Eigen.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, TRMM, SYMM, SYRK) and LAPACK (POTRF, PSTRF, SYTRF, GETRF, GEQRF, GELS, SYEV, GESDD, GEEV): Eigen master against OpenBLAS, Intel oneMKL and AMD AOCL on an AMD Ryzen AI MAX+ 395.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, TRMM, SYMM, SYRK) and LAPACK (POTRF, PSTRF, SYTRF, GETRF, GEQRF, GELS, SYEV, GESDD, GEEV): Eigen master against OpenBLAS, Intel oneMKL and AMD AOCL on an AMD Ryzen AI MAX+ 395, every library limited to AVX2 and FMA.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, TRMM, SYMM, SYRK) and LAPACK (POTRF, PSTRF, SYTRF, GETRF, GEQRF, GELS, SYEV, GESDD, GEEV): Eigen master with its SME kernels against Apple Accelerate, Arm Performance Libraries and OpenBLAS on an Apple M4 Mac mini.
Single-threaded float and double BLAS/LAPACK comparisons on an Intel Xeon Gold 6444Y: Eigen against OpenBLAS and oneMKL, with upstream BLIS for BLAS.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, TRMM, SYMM, SYRK) and LAPACK (POTRF, PSTRF, SYTRF, GETRF, GEQRF, GELS, SYEV, GESDD, GEEV): Eigen master built for NEON alone against OpenBLAS on an Apple M4 Mac mini.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, SYRK) and LAPACK (POTRF, GETRF, GEQRF, SYEV, GESDD, GEEV): Eigen master built for NEON against Arm Performance Libraries, NVPL and OpenBLAS on one core of an NVIDIA Grace (Arm Neoverse V2).
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, SYRK) and LAPACK (POTRF, GETRF, GEQRF, SYEV, GESDD, GEEV): Eigen master built for SVE at a 128-bit vector length against Arm Performance Libraries, NVPL and OpenBLAS on one core of an NVIDIA Grace (Arm Neoverse V2).
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, SYRK) and LAPACK (POTRF, GETRF, GEQRF, SYEV, GESDD, GEEV): Eigen master built for NEON against Arm Performance Libraries, NVPL and OpenBLAS on one Arm Cortex-X925 core of an NVIDIA DGX Spark.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, SYRK) and LAPACK (POTRF, GETRF, GEQRF, SYEV, GESDD, GEEV): Eigen master built for SVE at a 128-bit vector length against Arm Performance Libraries, NVPL and OpenBLAS on one Arm Cortex-X925 core of an NVIDIA DGX Spark.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, TRMM, SYMM, SYRK) and LAPACK (POTRF, PSTRF, SYTRF, GETRF, GEQRF, GELS, SYEV, GESDD, GEEV): Eigen master built for 64-bit Arm with NEON against OpenBLAS and Arm Performance Libraries on a Raspberry Pi 5.
Single-threaded BLAS (AXPY, DOT, GEMV, GEMM, TRSM, TRMM, SYMM, SYRK) and LAPACK (POTRF, PSTRF, SYTRF, GETRF, GEQRF, GELS, SYEV, GESDD, GEEV): Eigen master built for 32-bit Arm (armhf) with NEON against OpenBLAS on a Raspberry Pi 5.