Re: Matrix multiplication performance

Thanks, for pointing this out.  You are right.

When stripping out too many special cases from the micro-kernels regarding matrix C (like C is
row/col major, aligned/not-aligned) and alpha=1 I also removed the case for beta=0.  At the moment
I regenerate the websites … and the tar-files

 


On 02 Feb 2016, at 16:32, Karl Rupp <[email protected]> wrote:

> Hi guys,
> 
> I'm sorry to interrupt your performance tuning fun, but please note that the kernel does not work correctly. To verify, consider the case that beta is equal to zero and that C initially consists of NaNs (which may happen in practice if you start if a freshly malloc'ed buffer)...
> 
> Best regards,
> Karli
> 
> 
> 
> 
> On 01/30/2016 05:48 PM, Michael Lehn wrote:
>> Here the same in slightly more general form
>> 
>> template <typename Index>
>> typename std::enable_if<std::is_convertible<Index, std::int64_t>::value
>>                      && BlockSize<double>::MR==4
>>                      && BlockSize<double>::NR==12
>>                      && BlockSize<double>::align==32,
>>          void>::type
>> ugemm(Index kc, double alpha,
>>       const double *A, const double *B,
>>       double beta,
>>       double *C, Index incRowC, Index incColC)
>> {
>>     static const Index MR = BlockSize<double>::MR;
>>     static const Index NR = BlockSize<double>::NR/4;
>>     typedef double vx __attribute__((vector_size (4*sizeof(double))));
>> 
>>     A = (const double*) __builtin_assume_aligned (A, 32);
>>     B = (const double*) __builtin_assume_aligned (B, 32);
>> 
>>     vx P[MR*NR] = {};
>> 
>>     for (Index l=0; l<kc; ++l) {
>>         const vx *b = (const vx *)B;
>> 
>>         for (Index i=0; i<MR; ++i) {
>>             for (Index j=0; j<NR; ++j) {
>>                 P[i*NR+j] += A[i]*b[j];
>>             }
>>         }
>>         A += MR;
>>         B += NR*4;
>>     }
>> 
>>     if (alpha!=double(1)) {
>>         for (Index i=0; i<MR; ++i) {
>>             for (Index j=0; j<NR; ++j) {
>>                 P[i*NR+j] *= alpha;
>>             }
>>         }
>>     }
>> 
>>     for (Index i=0; i<MR; ++i) {
>>         for (Index j=0; j<NR; ++j) {
>>             const double *p = (const double *) &P[i*NR+j];
>>             for (Index j1=0; j1<4; ++j1) {
>>                 C[i*incRowC+(j*4+j1)*incColC] *= beta;
>>                 C[i*incRowC+(j*4+j1)*incColC] += p[j1];
>>             }
>>         }
>>     }
>> }
>> 
>> On 30 Jan 2016, at 13:49, Michael Lehn <[email protected]> wrote:
>> 
>>> Ok, and this version for MR=4, NR=12 even beats the asm kernel on Haswell:
>>> 
>>> //-- Micro Kernel --------------------------------------------------------------
>>> template <typename Index>
>>> typename std::enable_if<std::is_convertible<Index, std::int64_t>::value
>>>                     && BlockSize<double>::MR==4
>>>                     && BlockSize<double>::NR==12
>>>                     && BlockSize<double>::align==32,
>>>         void>::type
>>> ugemm(Index kc, double alpha,
>>>      const double *A, const double *B,
>>>      double beta,
>>>      double *C, Index incRowC, Index incColC)
>>> {
>>>    static const Index MR = BlockSize<double>::MR;
>>>    static const Index NR = BlockSize<double>::NR;
>>>    typedef double vx __attribute__((vector_size (4*sizeof(double))));
>>> 
>>>    A = (const double*) __builtin_assume_aligned (A, 32);
>>>    B = (const double*) __builtin_assume_aligned (B, 32);
>>> 
>>>    vx P0_03 = {}; vx P0_47 = {}; vx P0_811 = {};
>>>    vx P1_03 = {}; vx P1_47 = {}; vx P1_811 = {};
>>>    vx P2_03 = {}; vx P2_47 = {}; vx P2_811 = {};
>>>    vx P3_03 = {}; vx P3_47 = {}; vx P3_811 = {};
>>> 
>>>    for (Index l=0; l<kc; ++l) {
>>>        const vx *b = (const vx *)B;
>>> 
>>>        P0_03 += A[0]*b[0]; P0_47 += A[0]*b[1]; P0_811 += A[0]*b[2];
>>>        P1_03 += A[1]*b[0]; P1_47 += A[1]*b[1]; P1_811 += A[1]*b[2];
>>>        P2_03 += A[2]*b[0]; P2_47 += A[2]*b[1]; P2_811 += A[2]*b[2];
>>>        P3_03 += A[3]*b[0]; P3_47 += A[3]*b[1]; P3_811 += A[3]*b[2];
>>>        A += MR;
>>>        B += NR;
>>>    }
>>> 
>>>    P0_03 *= alpha;  P0_47 *= alpha; P0_811 *= alpha;
>>>    P1_03 *= alpha;  P1_47 *= alpha; P1_811 *= alpha;
>>>    P2_03 *= alpha;  P2_47 *= alpha; P2_811 *= alpha;
>>>    P3_03 *= alpha;  P3_47 *= alpha; P3_811 *= alpha;
>>> 
>>>    if (beta!=double(1)) {
>>>        for (Index i=0; i<MR; ++i) {
>>>            for (Index j=0; j<NR; ++j) {
>>>                C[i*incRowC+j*incColC] *= beta;
>>>            }
>>>        }
>>>    }
>>> 
>>>    const double *p = (const double *) &P0_03;
>>>    C[0*incRowC+0*incColC] += p[0];
>>>    C[0*incRowC+1*incColC] += p[1];
>>>    C[0*incRowC+2*incColC] += p[2];
>>>    C[0*incRowC+3*incColC] += p[3];
>>> 
>>>    p = (const double *) &P0_47;
>>>    C[0*incRowC+4*incColC] += p[0];
>>>    C[0*incRowC+5*incColC] += p[1];
>>>    C[0*incRowC+6*incColC] += p[2];
>>>    C[0*incRowC+7*incColC] += p[3];
>>> 
>>>    p = (const double *) &P0_811;
>>>    C[0*incRowC+8*incColC] += p[0];
>>>    C[0*incRowC+9*incColC] += p[1];
>>>    C[0*incRowC+10*incColC] += p[2];
>>>    C[0*incRowC+11*incColC] += p[3];
>>> 
>>>    p = (const double *) &P1_03;
>>>    C[1*incRowC+0*incColC] += p[0];
>>>    C[1*incRowC+1*incColC] += p[1];
>>>    C[1*incRowC+2*incColC] += p[2];
>>>    C[1*incRowC+3*incColC] += p[3];
>>> 
>>>    p = (const double *) &P1_47;
>>>    C[1*incRowC+4*incColC] += p[0];
>>>    C[1*incRowC+5*incColC] += p[1];
>>>    C[1*incRowC+6*incColC] += p[2];
>>>    C[1*incRowC+7*incColC] += p[3];
>>> 
>>>    p = (const double *) &P1_811;
>>>    C[1*incRowC+8*incColC] += p[0];
>>>    C[1*incRowC+9*incColC] += p[1];
>>>    C[1*incRowC+10*incColC] += p[2];
>>>    C[1*incRowC+11*incColC] += p[3];
>>> 
>>>    p = (const double *) &P2_03;
>>>    C[2*incRowC+0*incColC] += p[0];
>>>    C[2*incRowC+1*incColC] += p[1];
>>>    C[2*incRowC+2*incColC] += p[2];
>>>    C[2*incRowC+3*incColC] += p[3];
>>> 
>>>    p = (const double *) &P2_47;
>>>    C[2*incRowC+4*incColC] += p[0];
>>>    C[2*incRowC+5*incColC] += p[1];
>>>    C[2*incRowC+6*incColC] += p[2];
>>>    C[2*incRowC+7*incColC] += p[3];
>>> 
>>>    p = (const double *) &P2_811;
>>>    C[2*incRowC+8*incColC] += p[0];
>>>    C[2*incRowC+9*incColC] += p[1];
>>>    C[2*incRowC+10*incColC] += p[2];
>>>    C[2*incRowC+11*incColC] += p[3];
>>> 
>>>    p = (const double *) &P3_03;
>>>    C[3*incRowC+0*incColC] += p[0];
>>>    C[3*incRowC+1*incColC] += p[1];
>>>    C[3*incRowC+2*incColC] += p[2];
>>>    C[3*incRowC+3*incColC] += p[3];
>>> 
>>>    p = (const double *) &P3_47;
>>>    C[3*incRowC+4*incColC] += p[0];
>>>    C[3*incRowC+5*incColC] += p[1];
>>>    C[3*incRowC+6*incColC] += p[2];
>>>    C[3*incRowC+7*incColC] += p[3];
>>> 
>>>    p = (const double *) &P3_811;
>>>    C[3*incRowC+8*incColC] += p[0];
>>>    C[3*incRowC+9*incColC] += p[1];
>>>    C[3*incRowC+10*incColC] += p[2];
>>>    C[3*incRowC+11*incColC] += p[3];
>>> 
>>> }
>> 
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