Performance Characterization of Mobile GP-GPUs
继续阅读Performance Characterization of Mobile GP-GPUs
继续阅读Performance Characterization of Mobile GP-GPUs
分类： 数学
Matrix Multiplication with OpenCL
Matrix Multiplication with OpenCL
继续阅读Matrix Multiplication with OpenCL
继续阅读Matrix Multiplication with OpenCL
macOS Mojave(10.14.4)系统Octave 5.1.0使用pause()函数无法响应按键事件
目前 ( 2019/04/24 )，在 macOS Mojave (10.14.4)系统上使用 brew install octave ，安装 Octave 5.1.0 之后，使用 pause() 函数无法在点击键盘之后继续执行，除了 Ctrl + C 之外任意键都不响应。正常情况下，点击任意按键之后，应该继续执行后续的代码。
这个是目前使用 brew 安装的 Octave 5.1.0 在编译的时候，关联的库是 glibc 2.28 之后的版本。这个版本上 glibc 2.28 的某些行为发生变动。具体的讨论信息，参考 bug #55029: pause() with no arguments does not return like kbhit() with glibc 2.28 上的讨论。本质就是 glibc 2.28 之后的版本要求应用程序在接收信息结束（ EOF ）之后，主动调用 clearerr (stdin); ，否则会收不到后续的按键通知。这个 BUG 在 Octave 5.2 版本被修复，但是这个版本何时发布，暂时不定。
目前的修复方式为要求 brew 从最新版本的代码编译安装，而不是安装已发布版本，如下：
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$ brew uninstall --ignore-dependencies octave # 安装编译依赖 $ brew install texinfo $ wget https://raw.githubusercontent.com/Homebrew/homebrew-core/master/Formula/octave.rb $ sed -i "" "s/\"--enable-shared\"/\"--enable-shared\",\"--disable-docs\"/g" octave.rb $ brew install --build-from-source --HEAD -v octave.rb |
修改下载的编译配置文件,并且关闭文档编译( 目前文档编译会失败），也就是增加 --disable-docs 这个编译参数。
调整之后的编译脚本如下：
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class Octave < Formula desc "High-level interpreted language for numerical computing" homepage "https://www.gnu.org/software/octave/index.html" url "https://ftp.gnu.org/gnu/octave/octave-5.1.0.tar.xz" mirror "https://ftpmirror.gnu.org/octave/octave-5.1.0.tar.xz" sha256 "87b4df6dfa28b1f8028f69659f7a1cabd50adfb81e1e02212ff22c863a29454e" revision 2 bottle do sha256 "6bb8497839d6f7872efcd6acad0216f443420e097a9b7fad44835823e1c0e735" => :mojave sha256 "d1de53a30f002d8b7ec3a6065994c46d8cbd4830aa7e199f572baff48723c6e6" => :high_sierra sha256 "7a648cff129ec85a5ee9417a0339a3b804756f7958585b707c015d322d220b15" => :sierra end head do url "https://hg.savannah.gnu.org/hgweb/octave", :branch => "default", :using => :hg depends_on "autoconf" => :build depends_on "automake" => :build depends_on "bison" => :build depends_on "icoutils" => :build depends_on "librsvg" => :build end # Complete list of dependencies at https://wiki.octave.org/Building depends_on "gnu-sed" => :build # https://lists.gnu.org/archive/html/octave-maintainers/2016-09/msg00193.html depends_on :java => ["1.6+", :build] depends_on "pkg-config" => :build depends_on "arpack" depends_on "epstool" depends_on "fftw" depends_on "fig2dev" depends_on "fltk" depends_on "fontconfig" depends_on "freetype" depends_on "gcc" # for gfortran depends_on "ghostscript" depends_on "gl2ps" depends_on "glpk" depends_on "gnuplot" depends_on "graphicsmagick" depends_on "hdf5" depends_on "libsndfile" depends_on "libtool" depends_on "pcre" depends_on "portaudio" depends_on "pstoedit" depends_on "qhull" depends_on "qrupdate" depends_on "qt" depends_on "readline" depends_on "suite-sparse" depends_on "sundials" depends_on "texinfo" depends_on "veclibfort" # Dependencies use Fortran, leading to spurious messages about GCC cxxstdlib_check :skip def install # Default configuration passes all linker flags to mkoctfile, to be # inserted into every oct/mex build. This is unnecessary and can cause # cause linking problems. inreplace "src/mkoctfile.in.cc", /%OCTAVE_CONF_OCT(AVE)?_LINK_(DEPS|OPTS)%/, '""' # Qt 5.12 compatibility # https://savannah.gnu.org/bugs/?55187 ENV["QCOLLECTIONGENERATOR"] = "qhelpgenerator" # These "shouldn't" be necessary, but the build breaks without them. # https://savannah.gnu.org/bugs/?55883 ENV["QT_CPPFLAGS"]="-I#{Formula["qt"].opt_include}" ENV.append "CPPFLAGS", "-I#{Formula["qt"].opt_include}" ENV["QT_LDFLAGS"]="-F#{Formula["qt"].opt_lib}" ENV.append "LDFLAGS", "-F#{Formula["qt"].opt_lib}" system "./bootstrap" if build.head? system "./configure", "--prefix=#{prefix}", "--disable-dependency-tracking", "--disable-silent-rules", "--enable-link-all-dependencies", "--enable-shared","--disable-docs", "--disable-static", "--with-hdf5-includedir=#{Formula["hdf5"].opt_include}", "--with-hdf5-libdir=#{Formula["hdf5"].opt_lib}", "--with-x=no", "--with-blas=-L#{Formula["veclibfort"].opt_lib} -lvecLibFort", "--with-portaudio", "--with-sndfile" system "make", "all" # Avoid revision bumps whenever fftw's or gcc's Cellar paths change inreplace "src/mkoctfile.cc" do |s| s.gsub! Formula["fftw"].prefix.realpath, Formula["fftw"].opt_prefix s.gsub! Formula["gcc"].prefix.realpath, Formula["gcc"].opt_prefix end # Make sure that Octave uses the modern texinfo at run time rcfile = buildpath/"scripts/startup/site-rcfile" rcfile.append_lines "makeinfo_program(\"#{Formula["texinfo"].opt_bin}/makeinfo\");" system "make", "install" end test do system bin/"octave", "--eval", "(22/7 - pi)/pi" # This is supposed to crash octave if there is a problem with veclibfort system bin/"octave", "--eval", "single ([1+i 2+i 3+i]) * single ([ 4+i ; 5+i ; 6+i])" end end |
参考链接
Simple ARM NEON optimized sin, cos, log and exp
This is the sequel of the single precision SSE optimized sin, cos, log and exp that I wrote some time ago. Adapted to the NEON fpu of my pandaboard. Precision and range are exactly the same than the SSE version, so I won't repeat them.
The code
The functions below are licensed under the zlib license, so you can do basically what you want with them.
- neon_mathfun.h source code for sin_ps, cos_ps, sincos_ps, exp_ps, log_ps, as straight C.
- neon_mathfun_test.c Validation+Bench program for those function. Do not forget to run it once.
Performance
Results on a pandaboard with a 1GHz dual-core ARM Cortex A9 (OMAP4), using gcc 4.6.1
command line: gcc -O3 -mfloat-abi=softfp -mfpu=neon -march=armv7-a -mtune=cortex-a9 -Wall -W neon_mathfun_test.c -lm
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exp([ -1000, -100, 100, 1000]) = [ 0, 0, 2.4061436e+38, 2.4061436e+38] exp([ -nan, inf, -inf, nan]) = [ nan, 2.4061436e+38, 0, nan] log([ 0, -10, 1e+30, 1.0005271e-42]) = [ -nan, -nan, 69.077553, -nan] log([ -nan, inf, -inf, nan]) = [ 89.128304, 88.722839, -nan, 89.128304] sin([ -nan, inf, -inf, nan]) = [ nan, nan, -nan, nan] cos([ -nan, inf, -inf, nan]) = [ nan, nan, nan, nan] sin([ -1e+30, -100000, 1e+30, 100000]) = [ inf, -0.035749275, -inf, 0.035749275] cos([ -1e+30, -100000, 1e+30, 100000]) = [ nan, -0.9993608, nan, -0.9993608] benching sinf .. -> 2.0 millions of vector evaluations/second -> 121 cycles/value on a 1000MHz computer benching cosf .. -> 1.8 millions of vector evaluations/second -> 132 cycles/value on a 1000MHz computer benching expf .. -> 1.1 millions of vector evaluations/second -> 221 cycles/value on a 1000MHz computer benching logf .. -> 1.7 millions of vector evaluations/second -> 141 cycles/value on a 1000MHz computer benching cephes_sinf .. -> 2.4 millions of vector evaluations/second -> 103 cycles/value on a 1000MHz computer benching cephes_cosf .. -> 2.0 millions of vector evaluations/second -> 123 cycles/value on a 1000MHz computer benching cephes_expf .. -> 1.6 millions of vector evaluations/second -> 153 cycles/value on a 1000MHz computer benching cephes_logf .. -> 1.5 millions of vector evaluations/second -> 156 cycles/value on a 1000MHz computer benching sin_ps .. -> 5.8 millions of vector evaluations/second -> 43 cycles/value on a 1000MHz computer benching cos_ps .. -> 5.9 millions of vector evaluations/second -> 42 cycles/value on a 1000MHz computer benching sincos_ps .. -> 6.0 millions of vector evaluations/second -> 41 cycles/value on a 1000MHz computer benching exp_ps .. -> 5.6 millions of vector evaluations/second -> 44 cycles/value on a 1000MHz computer benching log_ps .. -> 5.3 millions of vector evaluations/second -> 47 cycles/value on a 1000MHz computer |
So performance is not stellar. I recommend to use gcc 4.6.1 or newer as it generates much better code than previous (gcc 4.5) versions -- almost 20% faster here. I believe rewriting these functions in assembly would improve the performance by 30%, and should not be very hard as the ARM and NEON asm is quite nice and easy to write -- maybe I'll do it. Computing two SIMD vectors at once would also help to improve a lot the performance as there are enough registers on NEON, and it would reduce the dependancies between neon instructions.
Note also that I have no idea of the performance on a Cortex A8 -- it may be extremely bad, I don't know.
Comparison with an Intel Atom
For comparison purposes, here is the performance of the SSE version on a single core Intel Atom N270 running at 1.66GHz
command line: cl.exe /arch:SSE /O2 /TP /MD sse_mathfun_test.c (this is msvc 2010)
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benching sinf .. -> 1.3 millions of vector evaluations/second -> 303 cycles/value on a 1600MHz computer benching cosf .. -> 1.3 millions of vector evaluations/second -> 305 cycles/value on a 1600MHz computer benching sincos (x87) .. -> 1.2 millions of vector evaluations/second -> 314 cycles/value on a 1600MHz computer benching expf .. -> 1.6 millions of vector evaluations/second -> 244 cycles/value on a 1600MHz computer benching logf .. -> 1.4 millions of vector evaluations/second -> 276 cycles/value on a 1600MHz computer benching cephes_sinf .. -> 1.4 millions of vector evaluations/second -> 280 cycles/value on a 1600MHz computer benching cephes_cosf .. -> 1.5 millions of vector evaluations/second -> 265 cycles/value on a 1600MHz computer benching cephes_expf .. -> 0.7 millions of vector evaluations/second -> 548 cycles/value on a 1600MHz computer benching cephes_logf .. -> 0.8 millions of vector evaluations/second -> 489 cycles/value on a 1600MHz computer benching sin_ps .. -> 9.2 millions of vector evaluations/second -> 43 cycles/value on a 1600MHz computer benching cos_ps .. -> 9.5 millions of vector evaluations/second -> 42 cycles/value on a 1600MHz computer benching sincos_ps .. -> 8.8 millions of vector evaluations/second -> 45 cycles/value on a 1600MHz computer benching exp_ps .. -> 9.8 millions of vector evaluations/second -> 41 cycles/value on a 1600MHz computer benching log_ps .. -> 8.6 millions of vector evaluations/second -> 46 cycles/value on a 1600MHz computer |
The number of cycles is quite similar -- but the atom has a higher clock..
Last modified: 2011/05/29
参考链接
Matlab调用C程序
有时需要用Matlab调试某些C语言开发的函数库，需要在Matlab里面查看执行效果。
整个的参考例子如下：
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#include <mex.h> // Check if some command is really some givent one static bool commandIs(const mxArray* mxCommand, const char* command) { double result; mxArray* plhs1[1]; mxArray* prhs1[1]; mxArray* plhs2[1]; mxArray* prhs2[2]; if (mxCommand == NULL) { mexErrMsgTxt("'mxCommand' is null"); return false; } if (command == NULL) { mexErrMsgTxt("'command' is null"); return false; } if (!mxIsChar(mxCommand)) { mexErrMsgTxt("'mxCommand' is not a string"); return false; } // First trim prhs1[0] = (mxArray*)mxCommand; mexCallMATLAB(1, plhs1, 1, prhs1, "strtrim"); // Then compare prhs2[0] = mxCreateString(command); prhs2[1] = plhs1[0]; mexCallMATLAB(1, plhs2, 2, prhs2, "strcmpi"); // Return comparison result result = mxGetScalar(plhs2[0]); return (result != 0.0); } static void processHelpMessageCommand(void) { mexPrintf("DspMgr('init') init return Handle,return nil if failed. use 'release' free memory\n"); mexPrintf("DspMgr('release',handle) free memory\n"); } static void processInitCommand(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { char* example_buffer = malloc(512); plhs[0] = mxCreateNumericMatrix(1,1,mxUINT64_CLASS,mxREAL); long long *ip = (long long *) mxGetData(plhs[0]); *ip = (long long)example_buffer; } static void processReleaseCommand(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { if(nrhs != 2) { mexErrMsgTxt("release need 1 params"); } else { if(!mxIsUint64(prhs[1])) { mexErrMsgTxt("release handle must be UINT64 format"); return; } int M=mxGetM(prhs[1]); //获得矩阵的行数 int N=mxGetN(prhs[1]); //获得矩阵的列数 if((1 != M) &&(1 != N)) { mexErrMsgTxt("release handle must be 1*1 array format"); return; } long long ip = mxGetScalar(prhs[1]); char* example_buffer = (char*)ip; free(example_buffer); //return true avoid warnning plhs[0] = mxCreateNumericMatrix(1,1,mxINT8_CLASS,mxREAL); char* mx_data = (char *) mxGetData(plhs[0]); mx_data[0] = 1; } } // Mex entry point void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) { // Arguments parsing if (nrhs < 1) { mexErrMsgTxt("Not enough input arguments. use 'DspMgr help' for help message."); return; } if (!mxIsChar(prhs[0])) { mexErrMsgTxt("First parameter must be a string."); return; } // Command selection if (commandIs(prhs[0], "HELP")) { processHelpMessageCommand(); } else if (commandIs(prhs[0], "init")) { processInitCommand(nlhs, plhs, nrhs, prhs); } else if (commandIs(prhs[0], "release")) { processReleaseCommand(nlhs, plhs, nrhs, prhs); } else { mexErrMsgTxt("Unknown command or command not implemented yet."); } } |
尤其注意上面例子里我们如何隐藏一个C里申请的指针并传递给Matlab。
Matlab的调用例子如下：
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mex -output DspMgr 'CFLAGS="\$CFLAGS -std=c99"' '*.c' v = DspMgr('init') DspMgr('release',v) |
参考链接
泰勒公式
泰勒公式是将一个在x=x0处具有n阶导数的函数f(x)利用关于(x-x0)的n次多项式来逼近函数的方法。
若函数f(x)在包含x0的某个闭区间[a,b]上具有n阶导数，且在开区间(a,b)上具有(n+1)阶导数，则对闭区间[a,b]上任意一点x，成立下式：
其中，
表示f(x)的n阶导数，等号后的多项式称为函数f(x)在x0处的泰勒展开式，剩余的Rn(x)是泰勒公式的余项，是(x-x0)n的高阶无穷小。
这里需要注意的是，我们规定0的阶乘 " 0！=1 "。
参考链接
卡尔曼滤波原论文 A New Approach to Linear Filtering and Prediction Problems
卡尔曼滤波原论文 A New Approach to Linear Filtering and Prediction Problems
继续阅读卡尔曼滤波原论文 A New Approach to Linear Filtering and Prediction Problems
高斯函数
下载Word文档 高斯函数
常用数学符号希腊字母表
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希腊字母表
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序号
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大写
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小写
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英文注音
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国际音标注音
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中文读音
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意义
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1
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Α
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α
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alpha
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a:lf
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阿尔法
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角度；系数
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2
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Β
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β
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beta
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bet
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贝塔
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磁通系数；角度；系数
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3
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Γ
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γ
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gamma
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ga:m
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伽马
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电导系数（小写）
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4
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Δ
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δ
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delta
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delt
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德尔塔
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变动；密度；屈光度
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5
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Ε
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ε
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epsilon
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ep
silon |
艾普西龙
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对数之基数
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6
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Ζ
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ζ
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zeta
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zat
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截塔
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系数；方位角；阻抗；相对粘度；原子序数
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7
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Η
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η
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eta
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eit
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艾塔
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磁滞系数；效率（小写）
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8
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Θ
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θ
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thet
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θit
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西塔
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温度；相位角
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9
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Ι
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ι
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iot
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aiot
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约塔
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微小，一点儿
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10
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Κ
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κ
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kappa
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kap
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卡帕
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介质常数
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11
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Λ
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λ
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lambda
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lambd
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兰布达
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波长（小写）；体积
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12
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Μ
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μ
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mu
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mju
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缪
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磁导系数微（千分之一）放大因数（小写）
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13
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Ν
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ν
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nu
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nju
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纽
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磁阻系数
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14
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Ξ
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ξ
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xi
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ksi
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克西
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数学上的随机变量
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15
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Ο
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ο
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omicron
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omikron
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奥密克戎
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|
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16
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Π
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π
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pi
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pai
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派
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圆周率=圆周÷直径=3.14159 26535 89793
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17
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Ρ
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ρ
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rho
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rou
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肉
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电阻系数（小写）
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18
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Σ
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σ
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sigma
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sigma |
西格马
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总和（大写），表面密度；跨导（小写）
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19
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Τ
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τ
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tau
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tau
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套
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时间常数
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20
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Υ
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υ
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upsilon
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jupsilon
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伊普西龙
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位移
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21
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Φ
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φ
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phi
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fai
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佛爱
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磁通；角
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22
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Χ
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χ
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chi
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phai
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西
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|
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23
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Ψ
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ψ
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psi
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psai
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普西
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角速；介质电通量（静电力线）；角
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24
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Ω
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ω
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omega
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o`miga
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欧米伽
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欧姆（大写）；角速（小写）；角
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