OpenBLAS RVV

OpenBLAS 简介

OpenBLAS 是一个开源的 BLAS（Basic Linear Algebra Subprograms）和部分 LAPACK 实现，提供矩阵乘法、向量运算、线性方程求解、矩阵分解等基础数值计算能力。OpenBLAS 被广泛用于 NumPy、SciPy、Eigen、OpenCV、机器学习推理框架以及机器人算法中的线性代数加速场景。

OpenBLAS 的性能与目标 CPU 架构、缓存参数、线程模型和核心算子实现密切相关。对于 GEMM（General Matrix Multiply，通用矩阵乘法）这类计算密集型算子，是否针对具体处理器实现向量化微内核通常会直接影响吞吐。K3 平台搭载的 SpacemiT X100 处理器支持 RISC-V Vector Extension（RVV 1.0），因此在大规模矩阵乘法、矩阵分解等场景中，可以通过 RVV 优化库进一步释放硬件性能。

RVV 加速

K3 系统中可对比两套 OpenBLAS：

对比项	系统 OpenBLAS（libopenblas-pthread-dev）	SpacemiT OpenBLAS（openblas-spacemit）
版本	OpenBLAS 0.3.32	OpenBLAS 0.3.32
安装方式	sudo apt install libopenblas-pthread-dev	sudo apt install openblas-spacemit
头文件路径	/usr/include/riscv64-linux-gnu/openblas-pthread	/opt/openblas-spacemit/include
库文件路径	/usr/lib/riscv64-linux-gnu/openblas-pthread	/opt/openblas-spacemit/lib
目标核心	generic	x100
优化方向	通用 riscv64 OpenBLAS pthread 实现	面向 SpacemiT X100 的 RVV 优化实现
典型用途	兼容系统默认 BLAS/LAPACK 依赖	在 K3 上进行高性能矩阵计算和算法加速

本文后续主要通过相同的 BLAS 接口（如 cblas_sgemm / cblas_dgemm）对比 libopenblas-pthread-dev 与 openblas-spacemit 的性能差异。测试时仅切换头文件与链接库路径，并通过 OPENBLAS_NUM_THREADS、taskset 等方式控制线程数和 CPU 亲和性，从而观察 RVV 优化库在 K3 平台上的加速效果。

使用示例

软硬件环境

• SpacemiT RISCV64 X100 CPU（2.4Ghz）
• Bianbu 4.0.1 操作系统
• 内存：32GB

安装必要依赖

sudo apt update
sudo apt install libopenblas-pthread-dev openblas-spacemit

测试代码

目录结构：

openblas_bench/
├── CMakeLists.txt
└── blas_sgemm_check.cpp

CMakeLists.txt：

cmake_minimum_required(VERSION 3.16)
project(openblas_simple_check LANGUAGES CXX)

set(CMAKE_CXX_STANDARD 17)
set(CMAKE_CXX_STANDARD_REQUIRED ON)

add_executable(openblas_sgemm_check blas_sgemm_check.cpp)

find_package(OpenBLAS REQUIRED)

if(_OpenBLAS_ROOT_DIR STREQUAL "/usr/lib")
	set(OpenBLAS_LIB /usr/lib/riscv64-linux-gnu/openblas-pthread/libopenblas.so)
else()
	set(OpenBLAS_LIB ${OpenBLAS_LIBRARIES})
endif()

message(STATUS "_OpenBLAS_ROOT_DIR: ${_OpenBLAS_ROOT_DIR}")
message(STATUS "OpenBLAS include dir: ${OpenBLAS_INCLUDE_DIRS}")
message(STATUS "OpenBLAS library: ${OpenBLAS_LIB}")

target_include_directories(openblas_sgemm_check PRIVATE ${OpenBLAS_INCLUDE_DIRS})
target_link_libraries(openblas_sgemm_check PRIVATE ${OpenBLAS_LIB})

blas_sgemm_check.cpp

// Test the installed BLAS ABI library by calling cblas_sgemm.
// This validates that the target BLAS library can be linked and used.

#include <algorithm>
#include <chrono>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>

#include <cblas.h>

namespace {

float value_for(int row, int col, int rows) {
  return static_cast<float>(((row + 1) * 17 + (col + 1) * 31 + rows) % 101) / 101.0f;
}

void fill_col_major(std::vector<float>& matrix, int rows, int cols) {
  for (int col = 0; col < cols; ++col) {
    for (int row = 0; row < rows; ++row) {
      matrix[row + col * rows] = value_for(row, col, rows);
    }
  }
}

std::vector<float> reference_gemm(const std::vector<float>& a, const std::vector<float>& b,
                                  int m, int n, int k, float alpha, float beta) {
  std::vector<float> c(static_cast<size_t>(m) * n, 1.0f);
  for (int col = 0; col < n; ++col) {
    for (int row = 0; row < m; ++row) {
      float acc = 0.0f;
      for (int inner = 0; inner < k; ++inner) {
        acc += a[row + inner * m] * b[inner + col * k];
      }
      c[row + col * m] = alpha * acc + beta * c[row + col * m];
    }
  }
  return c;
}

double max_abs_error(const std::vector<float>& x, const std::vector<float>& y) {
  double err = 0.0;
  for (size_t i = 0; i < x.size(); ++i) {
    err = std::max(err, std::abs(static_cast<double>(x[i]) - static_cast<double>(y[i])));
  }
  return err;
}

double checksum(const std::vector<float>& x) {
  double sum = 0.0;
  for (float v : x) sum += v;
  return sum;
}

}  // namespace

int main(int argc, char** argv) {
  int m = 512;
  int n = 512;
  int k = 512;
  int repeats = 20;

  if (argc > 1) m = std::atoi(argv[1]);
  if (argc > 2) n = std::atoi(argv[2]);
  if (argc > 3) k = std::atoi(argv[3]);
  if (argc > 4) repeats = std::atoi(argv[4]);

  if (m <= 0 || n <= 0 || k <= 0 || repeats <= 0) {
    std::cerr << "usage: " << argv[0] << " [m n k repeats]\n";
    return 2;
  }

  std::vector<float> a(static_cast<size_t>(m) * k);
  std::vector<float> b(static_cast<size_t>(k) * n);
  std::vector<float> c(static_cast<size_t>(m) * n, 1.0f);

  fill_col_major(a, m, k);
  fill_col_major(b, k, n);

  float alpha = 1.25f;
  float beta = 0.5f;
  int lda = m;
  int ldb = k;
  int ldc = m;

  const auto expected = reference_gemm(a, b, m, n, k, alpha, beta);

  cblas_sgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, m, n, k, alpha, a.data(), lda, b.data(), ldb,
              beta, c.data(), ldc);

  const double err = max_abs_error(c, expected);
  const double tolerance = 1e-3 * static_cast<double>(k);

  std::cout << std::fixed << std::setprecision(6);
  std::cout << "BLAS symbol: cblas_sgemm\n";
  std::cout << "Problem: m=" << m << ", n=" << n << ", k=" << k << ", repeats=" << repeats << '\n';
  std::cout << "Correctness max_abs_error=" << err << ", tolerance=" << tolerance << '\n';
  std::cout << "Checksum=" << checksum(c) << '\n';

  if (err > tolerance) {
    std::cerr << "BLAS cblas_sgemm result: FAIL - result mismatch\n";
    return 1;
  }

  std::fill(c.begin(), c.end(), 1.0f);
  const auto start = std::chrono::steady_clock::now();
  for (int r = 0; r < repeats; ++r) {
    cblas_sgemm(CblasColMajor, CblasNoTrans, CblasNoTrans, m, n, k, alpha, a.data(), lda, b.data(), ldb,
                beta, c.data(), ldc);
  }
  const auto end = std::chrono::steady_clock::now();
  const double seconds = std::chrono::duration<double>(end - start).count();
  const double avg_seconds = seconds / repeats;
  const double gflops = (2.0 * m * n * k * repeats) / seconds / 1.0e9;

  std::cout << "Time seconds=" << seconds << '\n';
  std::cout << "Average time per SGEMM seconds=" << avg_seconds << '\n';
  std::cout << "Approx GFLOP/s=" << gflops << '\n';
  std::cout << "BLAS cblas_sgemm result: PASS - linked OpenBLAS and computed correctly.\n";
  return 0;
}

编译

# 使用libopenblas-pthread-dev
cmake -S . -B build_system -DCMAKE_BUILD_TYPE=Release
cmake --build build_system

# 使用 openblas-spacemit
cmake -S . -B build_spacemit -DCMAKE_BUILD_TYPE=Release -DOpenBLAS_DIR=/opt/openblas-spacemit/lib/cmake/openblas
cmake --build build_spacemit

终端输出：

测试对比

单核测试

taskset -c 0 ./build_system/openblas_sgemm_check # 系统库

taskset -c 0 ./build_spacemit/openblas_sgemm_check # openblas-spacemit

输出：

可以看出，RVV加速后的sgemm算子性能有所提升（10.18ms -> 8.05ms）

八核测试

taskset -c 0-7 ./build_system/openblas_sgemm_check

taskset -c 0-7 ./build_spacemit/openblas_sgemm_check

输出：

更多性能测试数据

• 使用 taskset -c 限制核数
• 单次测试的计时策略是跑 50 次取平均值，预热10次。本测试重复10次单次测试，取其指标的平均值并计算标准差
• mean 表示 10 次测试的均值，sd 为标准差

测试结果简要说明

本次测评聚焦系统默认 libopenblas-pthread-dev 与面向 SpacemiT X100 处理器优化的 openblas-spacemit，在单核与八核条件下量化 RVV 加速收益，测试均采用统一的计时与重复策略以保证可比性。

主要结论如下：

• BLAS Level-3（矩阵-矩阵运算）：openblas-spacemit 显著提升核心算子性能。单核 sgemm 吞吐由 26.48 GFLOPS 提升至 33.47 GFLOPS（+26.4%），八核 sgemm 吞吐由 150.52 GFLOPS 提升至 183.40 GFLOPS（+22.5%）。ssymm、strmm 等算子普遍获得 15%～23% 的加速；双精度场景（如 dgemm）亦有 5%～10% 的增益。
• BLAS Level-1（向量运算）：数据搬运与缩放类算子（如 scopy、dcopy、sscal、dscal）性能提升 20%～40%；归约类算子（如 sdot、ddot、nrm2）改进有限；部分算子（如 sasum、dasum）仍略逊于系统库。
• BLAS Level-2（矩阵-向量运算）：整体优势不明显，sgemv、dgemv 等算子与系统库相比低约 20%～30%，主要受制于内存带宽及较低的运算密度。

综合来看，openblas-spacemit 在计算密集型矩阵运算中优势突出，适用于机器人感知、SLAM、机器学习推理及科学计算等高度依赖 GEMM 的工作负载；而对内存访问主导的向量与矩阵-向量算子需结合具体场景评估其收益。

单核测试

module	function	api	expression	dtype	input_size	output_size	libopenblas-pthread-dev avg_ms mean±sd	openblas-spacemit avg_ms mean±sd	libopenblas-pthread-dev avg_gflops mean±sd	openblas-spacemit avg_gflops mean±sd	speedup mean±sd	improvement mean±sd
blas1	sasum	cblas_sasum	sum(abs(x))	float32	262144x1	1x1	0.0460 ± 0.0006	0.0516 ± 0.0003	5.7036 ± 0.0745	5.0760 ± 0.0337	0.89x ± 0.01x	-10.96% ± 1.22%
blas1	dasum	cblas_dasum	sum(abs(x))	float64	262144x1	1x1	0.0934 ± 0.0022	0.1066 ± 0.0059	2.8081 ± 0.0625	2.4654 ± 0.1287	0.88x ± 0.04x	-12.18% ± 4.22%
blas1	saxpy	cblas_saxpy	z = alpha*x + z	float32	262144x1	262144x1	0.0951 ± 0.0039	0.0978 ± 0.0034	5.5200 ± 0.2050	5.3671 ± 0.1774	0.97x ± 0.05x	-2.59% ± 5.36%
blas1	daxpy	cblas_daxpy	z = alpha*x + z	float64	262144x1	262144x1	0.4546 ± 0.0208	0.4214 ± 0.0170	1.1555 ± 0.0523	1.2461 ± 0.0493	1.08x ± 0.07x	8.09% ± 7.46%
blas1	scopy	cblas_scopy	z = x	float32	262144x1	262144x1	0.0734 ± 0.0003	0.0593 ± 0.0003	3.5713 ± 0.0140	4.4216 ± 0.0225	1.24x ± 0.01x	23.80% ± 0.70%
blas1	dcopy	cblas_dcopy	z = x	float64	262144x1	262144x1	0.1481 ± 0.0012	0.1239 ± 0.0073	1.7699 ± 0.0145	2.1222 ± 0.1167	1.20x ± 0.06x	19.88% ± 6.03%
blas1	sdot	cblas_sdot	dot(x, y)	float32	262144x1	1x1	0.0771 ± 0.0022	0.0824 ± 0.0073	6.8064 ± 0.1934	6.4044 ± 0.5376	0.94x ± 0.08x	-5.88% ± 7.95%
blas1	ddot	cblas_ddot	dot(x, y)	float64	262144x1	1x1	0.3765 ± 0.0103	0.3628 ± 0.0080	1.3936 ± 0.0387	1.4458 ± 0.0318	1.04x ± 0.03x	3.80% ± 3.00%
blas1	snrm2	cblas_snrm2	sqrt(dot(x, x))	float32	262144x1	1x1	0.6717 ± 0.0014	0.6233 ± 0.0012	0.7805 ± 0.0016	0.8411 ± 0.0016	1.08x ± 0.00x	7.77% ± 0.32%
blas1	dnrm2	cblas_dnrm2	sqrt(dot(x, x))	float64	262144x1	1x1	2.1654 ± 0.0010	2.0484 ± 0.0034	0.2421 ± 0.0001	0.2560 ± 0.0004	1.06x ± 0.00x	5.71% ± 0.15%
blas1	sscal	cblas_sscal	z = alpha*z	float32	262144x1	262144x1	0.0757 ± 0.0003	0.0588 ± 0.0004	3.4646 ± 0.0116	4.4540 ± 0.0255	1.29x ± 0.01x	28.61% ± 0.97%
blas1	dscal	cblas_dscal	z = alpha*z	float64	262144x1	262144x1	0.1662 ± 0.0030	0.1273 ± 0.0110	1.5775 ± 0.0279	2.0720 ± 0.1744	1.31x ± 0.11x	31.39% ± 11.17%
blas2	sgemv	cblas_sgemv	z = alphaAx + beta*z	float32	512x512	512x1	0.0788 ± 0.0002	0.1139 ± 0.0005	6.6556 ± 0.0180	4.6013 ± 0.0198	0.69x ± 0.00x	-30.86% ± 0.29%
blas2	dgemv	cblas_dgemv	z = alphaAx + beta*z	float64	512x512	512x1	0.1611 ± 0.0077	0.2247 ± 0.0100	3.2618 ± 0.1545	2.3368 ± 0.0944	0.72x ± 0.05x	-28.18% ± 4.99%
blas2	ssymv	cblas_ssymv	z = alpha*Sym(A)x + betaz	float32	512x512	512x1	0.0694 ± 0.0006	0.0817 ± 0.0002	7.5572 ± 0.0634	6.4155 ± 0.0158	0.85x ± 0.01x	-15.11% ± 0.72%
blas2	dsymv	cblas_dsymv	z = alpha*Sym(A)x + betaz	float64	512x512	512x1	0.1168 ± 0.0017	0.1331 ± 0.0018	4.4887 ± 0.0640	3.9409 ± 0.0504	0.88x ± 0.01x	-12.18% ± 1.34%
blas2	stbmv	cblas_stbmv	z = TriBand(A)*z	float32	512x512	512x1	0.0109 ± 0.0001	0.0138 ± 0.0003	0.2338 ± 0.0026	0.1857 ± 0.0043	0.79x ± 0.02x	-20.67% ± 2.02%
blas2	dtbmv	cblas_dtbmv	z = TriBand(A)*z	float64	512x512	512x1	0.0112 ± 0.0000	0.0134 ± 0.0006	0.2295 ± 0.0000	0.1914 ± 0.0086	0.84x ± 0.04x	-16.21% ± 3.71%
blas2	stpmv	cblas_stpmv	z = PackedTri(A)*z	float32	512x512	512x1	0.0501 ± 0.0003	0.0499 ± 0.0021	5.2366 ± 0.0354	5.2574 ± 0.2115	1.00x ± 0.04x	0.43% ± 4.11%
blas2	dtpmv	cblas_dtpmv	z = PackedTri(A)*z	float64	512x512	512x1	0.0946 ± 0.0003	0.0889 ± 0.0023	2.7708 ± 0.0102	2.9493 ± 0.0730	1.06x ± 0.02x	6.44% ± 2.37%
blas2	strmv	cblas_strmv	z = Tri(A)*z	float32	512x512	512x1	0.0671 ± 0.0002	0.0732 ± 0.0028	3.9054 ± 0.0111	3.5857 ± 0.1327	0.92x ± 0.03x	-8.21% ± 3.46%
blas2	dtrmv	cblas_dtrmv	z = Tri(A)*z	float64	512x512	512x1	0.1083 ± 0.0012	0.1266 ± 0.0030	2.4214 ± 0.0265	2.0718 ± 0.0481	0.86x ± 0.02x	-14.43% ± 2.07%
blas3	sgemm	cblas_sgemm	C = alphaAB + beta*C	float32	512x512	512x512	10.1364 ± 0.0659	8.0202 ± 0.0188	26.4833 ± 0.1716	33.4701 ± 0.0786	1.26x ± 0.01x	26.39% ± 0.79%
blas3	dgemm	cblas_dgemm	C = alphaAB + beta*C	float64	512x512	512x512	23.3091 ± 0.0797	21.2694 ± 0.0505	11.5165 ± 0.0394	12.6208 ± 0.0300	1.10x ± 0.00x	9.59% ± 0.41%
blas3	ssymm	cblas_ssymm	C = alpha*Sym(A)B + betaC	float32	512x512	512x512	10.1916 ± 0.0355	8.2806 ± 0.0270	26.3392 ± 0.0918	32.4179 ± 0.1055	1.23x ± 0.01x	23.08% ± 0.57%
blas3	dsymm	cblas_dsymm	C = alpha*Sym(A)B + betaC	float64	512x512	512x512	23.0906 ± 0.0821	22.5162 ± 0.0585	11.6255 ± 0.0414	11.9220 ± 0.0310	1.03x ± 0.00x	2.55% ± 0.48%
blas3	strmm	cblas_strmm	C = alpha*Tri(A)*C	float32	512x512	512x512	5.2380 ± 0.0176	4.5287 ± 0.0172	25.6241 ± 0.0857	29.6377 ± 0.1126	1.16x ± 0.01x	15.66% ± 0.51%
blas3	dtrmm	cblas_dtrmm	C = alpha*Tri(A)*C	float64	512x512	512x512	11.3021 ± 0.1004	10.1598 ± 0.0567	11.8763 ± 0.1052	13.2111 ± 0.0736	1.11x ± 0.01x	11.25% ± 0.97%

八核测试

module	function	api	expression	dtype	input_size	output_size	libopenblas-pthread-dev avg_ms mean±sd	openblas-spacemit avg_ms mean±sd	libopenblas-pthread-dev avg_gflops mean±sd	openblas-spacemit avg_gflops mean±sd	speedup mean±sd	improvement mean±sd
blas1	sasum	cblas_sasum	sum(abs(x))	float32	262144x1	1x1	0.0653 ± 0.0063	0.0637 ± 0.0093	4.0463 ± 0.3653	4.1903 ± 0.5812	1.04x ± 0.18x	4.42% ± 17.54%
blas1	dasum	cblas_dasum	sum(abs(x))	float64	262144x1	1x1	0.1100 ± 0.0149	0.1533 ± 0.0097	2.4195 ± 0.2959	1.7163 ± 0.1050	0.72x ± 0.09x	-28.18% ± 8.91%
blas1	saxpy	cblas_saxpy	z = alpha*x + z	float32	262144x1	262144x1	0.0369 ± 0.0053	0.0350 ± 0.0061	14.4811 ± 2.2321	15.4264 ± 2.8504	1.09x ± 0.28x	9.37% ± 28.30%
blas1	daxpy	cblas_daxpy	z = alpha*x + z	float64	262144x1	262144x1	0.0605 ± 0.0079	0.0616 ± 0.0072	8.7922 ± 1.0583	8.6122 ± 0.9870	1.00x ± 0.19x	-0.27% ± 19.23%
blas1	scopy	cblas_scopy	z = x	float32	262144x1	262144x1	0.0733 ± 0.0003	0.0592 ± 0.0004	3.5765 ± 0.0147	4.4264 ± 0.0280	1.24x ± 0.01x	23.78% ± 1.09%
blas1	dcopy	cblas_dcopy	z = x	float64	262144x1	262144x1	0.1706 ± 0.0627	0.1236 ± 0.0060	1.6419 ± 0.3194	2.1261 ± 0.1003	1.39x ± 0.55x	39.07% ± 55.23%
blas1	sdot	cblas_sdot	dot(x, y)	float32	262144x1	1x1	0.1068 ± 0.0360	0.0952 ± 0.0055	5.2162 ± 1.0422	5.5213 ± 0.3114	1.12x ± 0.35x	11.96% ± 34.66%
blas1	ddot	cblas_ddot	dot(x, y)	float64	262144x1	1x1	0.2790 ± 0.0194	0.3266 ± 0.0928	1.8873 ± 0.1318	1.6914 ± 0.3433	0.90x ± 0.21x	-9.77% ± 20.61%
blas1	snrm2	cblas_snrm2	sqrt(dot(x, x))	float32	262144x1	1x1	0.6748 ± 0.0076	0.6434 ± 0.0655	0.7771 ± 0.0086	0.8209 ± 0.0664	1.06x ± 0.08x	5.58% ± 7.69%
blas1	dnrm2	cblas_dnrm2	sqrt(dot(x, x))	float64	262144x1	1x1	2.1886 ± 0.0527	2.0510 ± 0.0056	0.2397 ± 0.0055	0.2556 ± 0.0007	1.07x ± 0.03x	6.71% ± 2.61%
blas1	sscal	cblas_sscal	z = alpha*z	float32	262144x1	262144x1	0.0754 ± 0.0001	0.0590 ± 0.0005	3.4741 ± 0.0038	4.4415 ± 0.0361	1.28x ± 0.01x	27.83% ± 1.18%
blas1	dscal	cblas_dscal	z = alpha*z	float64	262144x1	262144x1	0.1682 ± 0.0057	0.1188 ± 0.0013	1.5604 ± 0.0508	2.2066 ± 0.0233	1.42x ± 0.05x	41.55% ± 5.00%
blas2	sgemv	cblas_sgemv	z = alphaAx + beta*z	float32	512x512	512x1	0.0789 ± 0.0002	0.1140 ± 0.0003	6.6473 ± 0.0137	4.5987 ± 0.0141	0.69x ± 0.00x	-30.81% ± 0.18%
blas2	dgemv	cblas_dgemv	z = alphaAx + beta*z	float64	512x512	512x1	0.1570 ± 0.0064	0.2266 ± 0.0144	3.3446 ± 0.1296	2.3206 ± 0.1279	0.70x ± 0.05x	-30.49% ± 5.15%
blas2	ssymv	cblas_ssymv	z = alpha*Sym(A)x + betaz	float32	512x512	512x1	0.0196 ± 0.0004	0.0242 ± 0.0007	26.8242 ± 0.4924	21.6891 ± 0.5964	0.81x ± 0.03x	-19.09% ± 2.75%
blas2	dsymv	cblas_dsymv	z = alpha*Sym(A)x + betaz	float64	512x512	512x1	0.0310 ± 0.0039	0.0346 ± 0.0007	17.1231 ± 1.6445	15.1380 ± 0.3015	0.89x ± 0.12x	-10.52% ± 11.79%
blas2	stbmv	cblas_stbmv	z = TriBand(A)*z	float32	512x512	512x1	0.0056 ± 0.0003	0.0083 ± 0.0005	0.4546 ± 0.0205	0.3088 ± 0.0176	0.68x ± 0.05x	-31.88% ± 4.96%
blas2	dtbmv	cblas_dtbmv	z = TriBand(A)*z	float64	512x512	512x1	0.0075 ± 0.0003	0.0079 ± 0.0006	0.3409 ± 0.0115	0.3265 ± 0.0225	0.96x ± 0.07x	-4.26% ± 7.18%
blas2	stpmv	cblas_stpmv	z = PackedTri(A)*z	float32	512x512	512x1	0.0133 ± 0.0032	0.0124 ± 0.0003	20.4058 ± 3.0779	21.2088 ± 0.4254	1.07x ± 0.25x	7.29% ± 24.85%
blas2	dtpmv	cblas_dtpmv	z = PackedTri(A)*z	float64	512x512	512x1	0.0227 ± 0.0030	0.0211 ± 0.0008	11.6867 ± 1.2003	12.4503 ± 0.4639	1.07x ± 0.11x	7.46% ± 11.20%
blas2	strmv	cblas_strmv	z = Tri(A)*z	float32	512x512	512x1	0.0312 ± 0.0035	0.0337 ± 0.0015	8.4915 ± 0.8559	7.7875 ± 0.3644	0.93x ± 0.11x	-7.31% ± 10.84%
blas2	dtrmv	cblas_dtrmv	z = Tri(A)*z	float64	512x512	512x1	0.0465 ± 0.0055	0.0661 ± 0.0045	5.7243 ± 0.8369	3.9807 ± 0.2823	0.71x ± 0.10x	-29.33% ± 9.75%
blas3	sgemm	cblas_sgemm	C = alphaAB + beta*C	float32	512x512	512x512	1.7920 ± 0.1311	1.4639 ± 0.0175	150.5191 ± 11.0008	183.4007 ± 2.1639	1.22x ± 0.09x	22.46% ± 9.41%
blas3	dgemm	cblas_dgemm	C = alphaAB + beta*C	float64	512x512	512x512	3.7447 ± 0.1520	3.5579 ± 0.1550	71.7921 ± 2.9347	75.5774 ± 3.3164	1.06x ± 0.08x	5.50% ± 7.52%
blas3	ssymm	cblas_ssymm	C = alpha*Sym(A)B + betaC	float32	512x512	512x512	1.7756 ± 0.0235	1.7004 ± 0.1035	151.2034 ± 1.9713	158.3544 ± 8.9724	1.05x ± 0.05x	4.71% ± 5.47%
blas3	dsymm	cblas_dsymm	C = alpha*Sym(A)B + betaC	float64	512x512	512x512	3.7062 ± 0.0967	3.9785 ± 0.1184	72.4741 ± 1.8827	67.5256 ± 2.0129	0.93x ± 0.04x	-6.76% ± 3.91%
blas3	strmm	cblas_strmm	C = alpha*Tri(A)*C	float32	512x512	512x512	1.2341 ± 0.0619	1.4279 ± 0.0935	108.9822 ± 4.9051	94.3393 ± 5.7967	0.87x ± 0.08x	-13.20% ± 7.73%
blas3	dtrmm	cblas_dtrmm	C = alpha*Tri(A)*C	float64	512x512	512x512	2.4169 ± 0.1800	2.3975 ± 0.0244	55.7853 ± 3.7923	55.9882 ± 0.5670	1.01x ± 0.08x	0.83% ± 7.66%