From 47f0c3d1cb0d77a4724f232b9f1d0ec764b98460 Mon Sep 17 00:00:00 2001 From: jiayaozhang Date: Fri, 11 Feb 2022 21:23:38 +0800 Subject: [PATCH] finish hw07 yeah! --- .../index/alignalloc.h.61C002AA54843252.idx | Bin 0 -> 4410 bytes .../index/main.cpp.D4B0CBCBF15E99F4.idx | Bin 0 -> 3858 bytes .../index/ndarray.h.D2E81DB3AE0CDD83.idx | Bin 0 -> 3810 bytes .../index/ticktock.h.DA79E8F882CB1FB0.idx | Bin 0 -> 242 bytes .../index/wangsrng.h.FA1F5931EA52ADFF.idx | Bin 0 -> 2656 bytes ANSWER.md | 136 ++++++++++++++++-- CMakeLists.txt | 4 +- main.cpp | 122 +++++++++++++--- 8 files changed, 227 insertions(+), 35 deletions(-) create mode 100644 .cache/clangd/index/alignalloc.h.61C002AA54843252.idx create mode 100644 .cache/clangd/index/main.cpp.D4B0CBCBF15E99F4.idx create mode 100644 .cache/clangd/index/ndarray.h.D2E81DB3AE0CDD83.idx create mode 100644 .cache/clangd/index/ticktock.h.DA79E8F882CB1FB0.idx create mode 100644 .cache/clangd/index/wangsrng.h.FA1F5931EA52ADFF.idx diff --git 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+matrix_trace: 0.000323195s +1.00156e+08 +test_func: 0.519699s +t=2: n=1024 +matrix_randomize: 0.00063783s +matrix_randomize: 0.000629075s +matrix_transpose: 0.00313033s +matrix_multiply: 0.358542s +matrix_multiply: 0.359807s +matrix_RtAR: 0.721592s +matrix_trace: 5.6674e-05s +1.34324e+08 +test_func: 0.728255s +t=3: n=1056 +matrix_randomize: 0.000902491s +matrix_randomize: 0.000780195s +matrix_transpose: 0.00387635s +matrix_multiply: 0.3977s +matrix_multiply: 0.406229s +matrix_RtAR: 0.808082s +matrix_trace: 8.5799e-05s +1.47405e+08 +test_func: 0.816765s +overall: 3.07871s ``` # 改进后 ``` -这里贴改进后的运行结果。 -matrix_randomize: 0.01s +t=0: n=1120 +matrix_randomize: 0.00347719s +matrix_randomize: 0.00243836s +matrix_transpose: 0.00556866s +matrix_multiply: 0.106349s +matrix_multiply: 0.0895811s +matrix_RtAR: 0.208163s +matrix_trace: 0.000257071s +1.76466e+08 +test_func: 0.223656s +t=1: n=928 +matrix_randomize: 0.00487382s +matrix_randomize: 0.00245537s +matrix_transpose: 0.00080515s +matrix_multiply: 0.0597233s +matrix_multiply: 0.0543553s +matrix_RtAR: 0.115015s +matrix_trace: 0.000258041s +1.00585e+08 +test_func: 0.127455s +t=2: n=1024 +matrix_randomize: 0.000620257s +matrix_randomize: 0.00175319s +matrix_transpose: 0.00213852s +matrix_multiply: 0.0661278s +matrix_multiply: 0.065029s +matrix_RtAR: 0.133401s +matrix_trace: 0.000278096s +1.34691e+08 +test_func: 0.143559s +t=3: n=1056 +matrix_randomize: 0.00101717s +matrix_randomize: 0.00216396s +matrix_transpose: 0.00102147s +matrix_multiply: 0.0686898s +matrix_multiply: 0.0643553s +matrix_RtAR: 0.134125s +matrix_trace: 0.000949931s +1.47779e+08 +test_func: 0.146622s +overall: 0.643736s ``` # 加速比 -matrix_randomize: 10000x -matrix_transpose: 10000x -matrix_multiply: 10000x -matrix_RtAR: 10000x +matrix_randomize: 10x +matrix_transpose: 3x +matrix_multiply: 7x +matrix_RtAR: 8x > 如果记录了多种优化方法，可以做表格比较 @@ -27,20 +105,54 @@ matrix_RtAR: 10000x > matrix_randomize -请回答。 - + answer: + 这是因为 YX 序的数组，X 方向在内存空间中的排布是连续的 + YX 序的循环，其 X 是内层循环体，因此在先后执行的时间上是连续的。 + 对于 YX 序（列主序，C/C++）的数组，请用 YX 序遍历（x变量做内层循环体） + + answer: + _mm_stream_ps 可以一次性写入 16 字节到挂起队列，更加高效了 + 他的第二参数是一个 __m128 类型，可以配合其他手写的 SIMD 指令使用 + 不过，_mm_stream_ps 写入的地址必须对齐到 16 字节，否则会产生段错误等异常 + 需要注意，stream 系列指令写入的地址，必须是连续的，中间不能有跨步，否则无法合并写入，会产生有中间数据读的带宽 + > matrix_transpose -请回答。 + answer: + 循环是 XY 序的，虽然 out 也是 XY 序的没问题，但是 in 相当于一个 YX 序的二维数组， + 从而在内存看来访存是跳跃的，违背了空间局域性。因为每次跳跃了 ny，所以只要缓存容量小于 ny 就无法命中。 + 解决方法当然还是循环分块。 + 这样只需要块的大小 blockSize^2 小于缓存容量，即可保证全部命中。 + + answer: + tbb::simple_partitioner 自带莫顿序遍历功能 + 保证对齐到16字节 > matrix_multiply -请回答。 + answer: + out(x, y) 始终在一个地址不动（一般）。 + lhs(x, t) 每次跳跃 n 间隔的访问（坏）。 + rhs(t, y) 连续的顺序访问（好）。 + 因为存在不连续的 lhs 和一直不动的 out，导致矢量化失败，一次只能处理一个标量，CPU也无法启动指令级并行（ILP） + + answer: + #pragma omp unroll + + answer: + out(i, j) 连续 32 次顺序访问（好）。 + lhs(i, t) 连续 32 次顺序访问（好）。 + rhs(t, j) 32 次在一个地址不动（一般）。 + 这样就消除不连续的访问了，从而内部的 i 循环可以顺利矢量化，且多个循环体之间没有依赖关系，CPU得以启动指令级并行，缓存预取也能正常工作，快好多！ + > matrix_RtAR +static 预先分配好空间 + 请回答。 # 我的创新点 如果有，请说明。 + diff --git a/CMakeLists.txt b/CMakeLists.txt index 5d76276..3cd661c 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -11,8 +11,8 @@ add_executable(main main.cpp) find_package(OpenMP REQUIRED) target_link_libraries(main PUBLIC OpenMP::OpenMP_CXX) -#find_package(TBB REQUIRED) -#target_link_libraries(main PUBLIC TBB::tbb) +find_package(TBB REQUIRED) +target_link_libraries(main PUBLIC TBB::tbb) if (MSVC) target_compile_options(main PUBLIC /fp:fast /arch:AVX) diff --git a/main.cpp b/main.cpp index d5af053..1d464b9 100644 --- a/main.cpp +++ b/main.cpp @@ -7,16 +7,28 @@ // 作业中有很多个问句，请通过注释回答问题，并改进其代码，以使其更快 // 并行可以用 OpenMP 也可以用 TBB +#include #include -//#include // _mm 系列指令都来自这个头文件 -//#include // 如果上面那个不行，试试这个 +#include // _mm 系列指令都来自这个头文件 +#include +#include +#include +#include +// #include // 如果上面那个不行，试试这个 +#include +#include #include "ndarray.h" #include "wangsrng.h" #include "ticktock.h" // Matrix 是 YX 序的二维浮点数组：mat(x, y) = mat.data()[y * mat.shape(0) + x] -using Matrix = ndarray<2, float>; +// using Matrix = ndarray<2, float>; +using Matrix = ndarray<2, float, 0, 0, AlignedAllocator >; // 注意：默认对齐到 64 字节，如需 4096 字节，请用 ndarray<2, float, AlignedAllocator<4096, float>> +// 4096 那么大，即64个缓存行。 +// 这样一次随机访问之后会伴随着64次顺序访问，能被CPU检测到，从而启动缓存行预取，避免了等待数据抵达前空转浪费时间 + + static void matrix_randomize(Matrix &out) { TICK(matrix_randomize); @@ -24,11 +36,30 @@ static void matrix_randomize(Matrix &out) { size_t ny = out.shape(1); // 这个循环为什么不够高效？如何优化？ 10 分 -#pragma omp parallel for collapse(2) - for (int x = 0; x < nx; x++) { - for (int y = 0; y < ny; y++) { - float val = wangsrng(x, y).next_float(); - out(x, y) = val; + // answer: 这是因为 YX 序的数组，X 方向在内存空间中的排布是连续的 + // YX 序的循环，其 X 是内层循环体，因此在先后执行的时间上是连续的。 + // 对于 YX 序（列主序，C/C++）的数组，请用 YX 序遍历（x变量做内层循环体） + + // #pragma omp parallel for collapse(2) + // for (int x = 0; x < nx; x++) { + // for (int y = 0; y < ny; y++) { + // float val = wangsrng(x, y).next_float(); + // out(x, y) = val; + // } + // } + + +// _mm_stream_ps 可以一次性写入 16 字节到挂起队列，更加高效了 +// 他的第二参数是一个 __m128 类型，可以配合其他手写的 SIMD 指令使用 +// 不过，_mm_stream_ps 写入的地址必须对齐到 16 字节，否则会产生段错误等异常 +// 需要注意，stream 系列指令写入的地址，必须是连续的，中间不能有跨步，否则无法合并写入，会产生有中间数据读的带宽 + #pragma omp parallel for collapse(2) + for (int y = 0; y < ny; y++) { + for (int x = 0; x < nx; x+=4) { + + __m128 tmp = {wangsrng(x, y).next_float(), wangsrng(x+1, y).next_float(), wangsrng(x+2, y).next_float(), wangsrng(x+3, y).next_float()}; + _mm_stream_ps(&out(x,y), tmp); + } } TOCK(matrix_randomize); @@ -41,12 +72,32 @@ static void matrix_transpose(Matrix &out, Matrix const &in) { out.reshape(ny, nx); // 这个循环为什么不够高效？如何优化？ 15 分 -#pragma omp parallel for collapse(2) - for (int x = 0; x < nx; x++) { - for (int y = 0; y < ny; y++) { - out(y, x) = in(x, y); - } - } + // answer: 循环是 XY 序的，虽然 out 也是 XY 序的没问题，但是 in 相当于一个 YX 序的二维数组， + // 从而在内存看来访存是跳跃的，违背了空间局域性。因为每次跳跃了 ny，所以只要缓存容量小于 ny 就无法命中。 + + // #pragma omp parallel for collapse(2) + // for (int x = 0; x < nx; x++) { + // for (int y = 0; y < ny; y++) { + // out(y, x) = in(x, y); + // } + // } + + // 解决方法当然还是循环分块。 + // 这样只需要块的大小 blockSize^2 小于缓存容量，即可保证全部命中。 + constexpr int block_size = 64; + tbb::parallel_for(tbb::blocked_range2d(0,ny, block_size, 0, nx, block_size), + [&](const tbb::blocked_range2d &r){ + for(size_t y=r.cols().begin(); y{1024, 1024}), RtA(std::array{1024, 1024}); + matrix_transpose(Rt, R); matrix_multiply(RtA, Rt, A); matrix_multiply(RtAR, RtA, R); @@ -106,6 +184,7 @@ static void test_func(size_t n) { Matrix RtAR; matrix_RtAR(RtAR, R, A); + std::cout << matrix_trace(RtAR) << std::endl; TOCK(test_func); @@ -116,6 +195,7 @@ int main() { TICK(overall); for (int t = 0; t < 4; t++) { size_t n = 32 * (rng.next_uint64() % 16 + 24); + // size_t n = 1<<13; std::cout << "t=" << t << ": n=" << n << std::endl; test_func(n); }