分类： 数学

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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

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)

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

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Simple ARM NEON optimized sin, cos, log and exp

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：

#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：

mex -output DspMgr 'CFLAGS="\$CFLAGS -std=c99"' '*.c'

v = DspMgr('init')

DspMgr('release',v)

参考链接

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• Nested structures with loadlibrary Matlab
• mex
• matlab调用C程序