GEMM Micro Kernel für AVX

#  void
#  gemm_micro(long   k,
#             double alpha,
#             double *A,
#             double *B,
#             double beta,
#             double *C, long incRowC, long incColC);
.globl ugemm_4_8
ugemm_4_8:

#  Arguments:
#           %rdi     long           k
#           %xmm0    double         alpha
#           %rsi     double         *A
#           %rdx     double         *B
#           %xmm1    double         beta
#           %rcx     double         *C
#           %r8      long           incRowC
#           %r9      long           incColC


#
#       ... code for function ...
#


        retq

    leaq (,%r8,2)   %r10

        vmovlpd                 %xmm0,       -8(%rsp)
        vmovlpd                 %xmm1,      -16(%rsp)

        movq                    %rax,       -24(%rsp)
        movq                    %rbx,       -32(%rsp)

        vbroadcastsd         -8(%rsp),         %ymm6

        leaq                    (,%r8,8),       %r8
        leaq                    (,%r9,8),       %r9     # 1*incCol

        leaq                    (,%r9,2),       %r10     # 2*incCol
        leaq                    (%r10,%r9),     %r11     # 3*incCol
        leaq                    (%rcx,%r10,2),  %rdx     # 4*incCol

        vbroadcastsd         -16(%rsp),         %ymm7

        vextractf128            $1,             %ymm8,          %xmm4

#
#       Update C(0,:)
#
        vmovlpd                 (%rcx),         %xmm0,          %xmm0
        vmovhpd                 (%rcx,%r9),     %xmm0,          %xmm0
        vmovlpd                 (%rcx,%r10),    %xmm1,          %xmm1
        vmovhpd                 (%rcx,%r11),    %xmm1,          %xmm1
        vmovlpd                 (%rdx),         %xmm2,          %xmm2
        vmovhpd                 (%rdx,%r9),     %xmm2,          %xmm2
        vmovlpd                 (%rdx,%r10),    %xmm3,          %xmm3
        vmovhpd                 (%rdx,%r11),    %xmm3,          %xmm3

        vmulpd                  %xmm7,          %xmm0,          %xmm0
        vmulpd                  %xmm7,          %xmm1,          %xmm1
        vmulpd                  %xmm7,          %xmm2,          %xmm2
        vmulpd                  %xmm7,          %xmm3,          %xmm3

        vextractf128            $1,             %ymm8,          %xmm4
        vextractf128            $1,             %ymm9,          %xmm5

        vaddpd                  %xmm0,          %xmm8,          %xmm0
        vaddpd                  %xmm1,          %xmm4,          %xmm1
        vaddpd                  %xmm2,          %xmm9,          %xmm2
        vaddpd                  %xmm3,          %xmm5,          %xmm3

        vmovlpd                 %xmm0,          (%rcx)
        vmovhpd                 %xmm0,          (%rcx,%r9)
        vmovlpd                 %xmm1,          (%rcx,%r10)
        vmovhpd                 %xmm1,          (%rcx,%r11)
        vmovlpd                 %xmm2,          (%rdx)
        vmovhpd                 %xmm2,          (%rdx,%r9)
        vmovlpd                 %xmm3,          (%rdx,%r10)
        vmovhpd                 %xmm3,          (%rdx,%r11)

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <sys/times.h>
#include <unistd.h>
#include <stdint.h>

//-- setup and print matrices --------------------------------------------------
double
walltime()
{
   struct tms    ts;
   static double ClockTick=0.0;

   if (ClockTick==0.0) {
        ClockTick = 1.0 / ((double) sysconf(_SC_CLK_TCK));
   }
   return ((double) times(&ts)) * ClockTick;
}

void
initGeMatrix(int m, int n, double *A, int incRowA, int incColA)
{
    int i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            A[i*incRowA+j*incColA] = i*n + j + 1;
        }
    }
}

void
randGeMatrix(int m, int n, double *A, int incRowA, int incColA)
{
    int i, j;
    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            A[i*incRowA+j*incColA] = ((double)rand()-RAND_MAX/2)*200/RAND_MAX;
        }
    }
}


void
printGeMatrix(int m, int n, const double *A, int incRowA, int incColA)
{
    int i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            printf("%10.4lf ", A[i*incRowA+j*incColA]);
        }
        printf("\n");
    }
    printf("\n\n");
}

void
dgemm_ref(int m, int n, int k,
          double alpha,
          const double *A, int incRowA, int incColA,
          const double *B, int incRowB, int incColB,
          double beta,
          double *C, int incRowC, int incColC)
{
    int i, j, l;

    if (beta!=1) {
        for (i=0; i<m; ++i) {
            for (j=0; j<n; ++j) {
                if (beta!=0) {
                    C[i*incRowC+j*incColC] *= beta;
                } else {
                    C[i*incRowC+j*incColC] = 0;
                }
            }
        }
    }
    if (alpha!=0) {
        for (i=0; i<m; ++i) {
            for (j=0; j<n; ++j) {
                for (l=0; l<k; ++l) {
                    C[i*incRowC+j*incColC] += alpha*A[i*incRowA+l*incColA]
                                                   *B[l*incRowB+j*incColB];
                }
            }
        }
    }
}

double
dgenrm1(int m, int n, const double *A, int incRowA, int incColA)
{
    int     i, j;
    double  result = 0;

    for (j=0; j<n; ++j) {
        double sum = 0;
        for (i=0; i<m; ++i) {
            sum += fabs(A[i*incRowA+j*incColA]);
        }
        if (sum>result) {
            result = sum;
        }
    }
    return result;
}

void
dgecopy(int m, int n,
        const double *X, int incRowX, int incColX,
        double *Y, int incRowY, int incColY)
{
    int i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            Y[i*incRowY+j*incColY] = X[i*incRowX+j*incColX];
        }
    }
}

void
dgescal(int m, int n, double alpha,
        double *X, int incRowX, int incColX)
{
    int i, j;

    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            X[i*incRowX+j*incColX] *= alpha;
        }
    }
}

void
dgeaxpy(int m, int n, double alpha,
        const double *X, int incRowX, int incColX,
        double *Y, int incRowY, int incColY)
{
    int i, j;

    if (alpha==0 || m==0 || n==0) {
        return;
    }
    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            Y[i*incRowY+j*incColY] += alpha*X[i*incRowX+j*incColX];
        }
    }
}

#define MIN(X,Y)   ((X)<(Y) ? (X) : (Y))
#define MAX(X,Y)   ((X)>(Y) ? (X) : (Y))

double
err_dgemm(int m, int n, int k,
          double alpha,
          const double *A, int incRowA, int incColA,
          const double *B, int incRowB, int incColB,
          double beta,
          const double *C0, int incRowC0, int incColC0,
          double *C, int incRowC, int incColC)
{
    double normA = dgenrm1(m, k, A, incRowA, incColA);
    double normB = dgenrm1(k, n, B, incRowB, incColB);
    double normC = dgenrm1(m, n, C, incRowC0, incColC0);
    double normD;
    int    mn    = (m>n)  ? m  : n;
    int    mnk   = (mn>k) ? mn : k;

    normA = MAX(normA, fabs(alpha)*normA);
    normC = MAX(normC, fabs(beta)*normC);

    dgeaxpy(m, n, -1.0, C0, incRowC0, incColC0, C, incRowC, incColC);
    normD = dgenrm1(m, n, C, incRowC, incColC);

    return normD/(mnk*normA*normB*normC);
}

//------------------------------------------------------------------------------
//-- new with alignment --------------------------------------------------------
void *
malloc_(size_t alignment, size_t size)
{
    size     += alignment;

    void *ptr  = malloc(size);
    void *ptr2 = (void *)(((size_t)ptr + alignment) & ~(alignment-1));
    void **vp  = (void**) ptr2 - 1;
    *vp        = ptr;
    return ptr2;
}

void
free_(void *ptr)
{
    free(*((void**)ptr-1));
}
//------------------------------------------------------------------------------

#define DGEMM_MC 256
#define DGEMM_NC 512
#define DGEMM_KC 256

#define DGEMM_MR 4
#define DGEMM_NR 8

//------------------------------------------------------------------------------

void
dpack_A(int m, int k, const double *A, int incRowA, int incColA, double *p)
{
    int i, i0, j, l, nu;
    int mp = (m+DGEMM_MR-1) / DGEMM_MR;

    for (j=0; j<k; ++j) {
        for (l=0; l<mp; ++l) {
            for (i0=0; i0<DGEMM_MR; ++i0) {
                i     = l*DGEMM_MR + i0;
                nu    = l*DGEMM_MR*k + j*DGEMM_MR + i0;
                p[nu] = (i<m) ? A[i*incRowA+j*incColA]
                              : 0;
            }
        }
    }
}

void
dpack_B(int k, int n, const double *B, int incRowB, int incColB, double *p)
{
    int i, j, j0, l, nu;
    int np = (n+DGEMM_NR-1) / DGEMM_NR;

    for (l=0; l<np; ++l) {
        for (j0=0; j0<DGEMM_NR; ++j0) {
            j = l*DGEMM_NR + j0;
            for (i=0; i<k; ++i) {
                nu    = l*DGEMM_NR*k + i*DGEMM_NR + j0;
                p[nu] = (j<n) ? B[i*incRowB+j*incColB]
                              : 0;
            }
        }
    }
}

void
ugemm_4_8(int64_t k,
          double alpha,
          const double *A,
          const double *B,
          double beta,
          double *C, int64_t incRowC, int64_t incColC);

void
dgemm_macro(int m, int n, int k,
            double alpha,
            const double *A,
            const double *B,
            double beta,
            double *C, int incRowC, int incColC)
{
    double C_[DGEMM_MR*DGEMM_NR];
    int i, j;

    const int MR = DGEMM_MR;
    const int NR = DGEMM_NR;

    for (j=0; j<n; j+=NR) {
        int nr = (j+NR<n) ? NR
                          : n - j;

        for (i=0; i<m; i+=MR) {
            int mr = (i+MR<m) ? MR
                              : m - i;

            if (mr==MR && nr==NR) {
                ugemm_4_8(k, alpha,
                          &A[i*k], &B[j*k],
                          beta,
                          &C[i*incRowC+j*incColC], incRowC, incColC);
            } else {
                ugemm_4_8(k, alpha,
                          &A[i*k], &B[j*k],
                          0.,
                          C_, 1, MR);
                dgescal(mr, nr, beta,
                        &C[i*incRowC+j*incColC], incRowC, incColC);
                dgeaxpy(mr, nr, 1., C_, 1, MR,
                        &C[i*incRowC+j*incColC], incRowC, incColC);
            }
        }
    }
}

void
dgemm(int m, int n, int k,
      double alpha,
      const double *A, int incRowA, int incColA,
      const double *B, int incRowB, int incColB,
      double beta,
      double *C, int incRowC, int incColC)
{
    int i, j, l;

    const int MC = DGEMM_MC;
    const int NC = DGEMM_NC;
    const int KC = DGEMM_KC;

    if (alpha==0.0 || k==0) {
        dgescal(m, n, beta, C, incRowC, incColC);
    } else {

        double *A_ = (double *)malloc_(32, sizeof(double)*DGEMM_MC*DGEMM_KC);
        double *B_ = (double *)malloc_(32, sizeof(double)*DGEMM_KC*DGEMM_NC);

        for (j=0; j<n; j+=NC) {
            int nc = (j+NC<=n) ? NC
                               : n - j;

            for (l=0; l<k; l+=KC) {
                int    kc    = (l+KC<=k) ? KC
                                         : k - l;
                double beta_ = (l==0) ? beta
                                      : 1;

                dpack_B(kc, nc,
                        &B[l*incRowB+j*incColB], incRowB, incColB,
                        B_);

                for (i=0; i<m; i+=MC) {
                    int mc = (i+MC<=m) ? MC
                                       : m - i;
                    dpack_A(mc, kc,
                            &A[i*incRowA+l*incColA], incRowA, incColA,
                            A_);

                    dgemm_macro(mc, nc, kc,
                                alpha,
                                A_, B_,
                                beta_,
                                &C[i*incRowC+j*incColC], incRowC, incColC);
                }
            }
        }

        free_(A_);
        free_(B_);
    }
}

//------------------------------------------------------------------------------
#ifndef ALPHA
#define ALPHA 2
#endif

#ifndef BETA
#define BETA 2
#endif

#ifndef MIN_N
#define MIN_N 100
#endif

#ifndef MAX_N
#define MAX_N 1500
#endif

#ifndef INC_N
#define INC_N 100
#endif

#ifndef MIN_M
#define MIN_M 100
#endif

#ifndef MAX_M
#define MAX_M 1500
#endif

#ifndef INC_M
#define INC_M 100
#endif

#ifndef MIN_K
#define MIN_K 100
#endif

#ifndef MAX_K
#define MAX_K 1500
#endif

#ifndef INC_K
#define INC_K 100
#endif

#ifndef ROWMAJOR_A
#define ROWMAJOR_A 0
#endif

#ifndef ROWMAJOR_B
#define ROWMAJOR_B 0
#endif

#ifndef ROWMAJOR_C
#define ROWMAJOR_C 0
#endif

#if (ROWMAJOR_A==1)
#   define INCROW_A  MAX_K
#   define INCCOL_A  1
#else
#   define INCROW_A  1
#   define INCCOL_A  MAX_M
#endif

#if (ROWMAJOR_B==1)
#   define INCROW_B  MAX_N
#   define INCCOL_B  1
#else
#   define INCROW_B  1
#   define INCCOL_B  MAX_K
#endif

#if (ROWMAJOR_C==1)
#   define INCROW_C  MAX_N
#   define INCCOL_C  1
#else
#   define INCROW_C  1
#   define INCCOL_C  MAX_M
#endif


double A_[MAX_M*MAX_K*MIN(INCROW_A,INCCOL_A)];
double B_[MAX_K*MAX_N*MIN(INCROW_B,INCCOL_B)];
double C_[MAX_M*MAX_N];

double C_0[MAX_M*MAX_N*MIN(INCROW_A,INCCOL_A)];
double C_1[MAX_M*MAX_N*MIN(INCROW_A,INCCOL_A)];

int
main()
{
    int m, n, k;

    randGeMatrix(MAX_M, MAX_K, A_, INCROW_A, INCCOL_A);
    randGeMatrix(MAX_K, MAX_N, B_, INCROW_B, INCCOL_B);
    randGeMatrix(MAX_M, MAX_N, C_, 1, MAX_M);

    printf("#%9s %9s %9s", "m", "n", "k");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf("\n");

    for (m=MIN_M, n=MIN_N, k=MIN_K;
         n<=MAX_N && m<=MAX_M && k<=MAX_K;
         m+=INC_M, n+=INC_N, k+=INC_K)
    {
        double t, dt, err;
        int    runs  = 1;
        double ops   = 2.0*m/1000*n/1000*k;

        printf(" %9d %9d %9d", m, n, k);

        // compute reference solution
        dgecopy(m, n, C_, 1, MAX_M, C_0, INCROW_C, INCCOL_C);
        dgemm_ref(m, n, k,
                  ALPHA,
                  A_, INCROW_A, INCCOL_A,
                  B_, INCROW_B, INCCOL_B,
                  BETA,
                  C_0, INCROW_C, INCCOL_C);

        // bench dgemm

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, C_, 1, MAX_M, C_1, INCROW_C, INCCOL_C);
            dt = walltime();
            dgemm(m, n, k,
                  ALPHA,
                  A_, INCROW_A, INCCOL_A,
                  B_, INCROW_B, INCCOL_B,
                  BETA,
                  C_1, INCROW_C, INCCOL_C);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_dgemm(m, n, k,
                        ALPHA,
                        A_, INCROW_A, INCCOL_A,
                        B_, INCROW_B, INCCOL_B,
                        BETA,
                        C_0, INCROW_C, INCCOL_C,
                        C_1, INCROW_C, INCCOL_C);

        printf(" %12.2e %12.2lf %12.2e", t, ops/t, err);

        printf("\n");
    }

    return 0;
}