xref: /petsc/src/mat/impls/baij/seq/baijfact11.c (revision 78bb40077513d5120f4c52e0fb25a84efb280004)

#define PETSCMAT_DLL

/*
    Factorization code for BAIJ format.
*/
#include "../src/mat/impls/baij/seq/baij.h"
#include "../src/mat/blockinvert.h"

/* ------------------------------------------------------------*/
/*
      Version for when blocks are 4 by 4
*/
#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4(Mat C,Mat A,const MatFactorInfo *info)
{
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
  IS             isrow = b->row,isicol = b->icol;
  PetscErrorCode ierr;
  const PetscInt *r,*ic;
  PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
  PetscInt       *ajtmpold,*ajtmp,nz,row;
  PetscInt       *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
  MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
  MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
  MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
  MatScalar      p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
  MatScalar      m13,m14,m15,m16;
  MatScalar      *ba = b->a,*aa = a->a;
  PetscTruth     pivotinblocks = b->pivotinblocks;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
  ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
  ierr = PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);

  for (i=0; i<n; i++) {
    nz    = bi[i+1] - bi[i];
    ajtmp = bj + bi[i];
    for  (j=0; j<nz; j++) {
      x = rtmp+16*ajtmp[j];
      x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
      x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
    }
    /* load in initial (unfactored row) */
    idx      = r[i];
    nz       = ai[idx+1] - ai[idx];
    ajtmpold = aj + ai[idx];
    v        = aa + 16*ai[idx];
    for (j=0; j<nz; j++) {
      x    = rtmp+16*ic[ajtmpold[j]];
      x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
      x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
      x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
      x[14] = v[14]; x[15] = v[15];
      v    += 16;
    }
    row = *ajtmp++;
    while (row < i) {
      pc  = rtmp + 16*row;
      p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
      p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
      p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
      p15 = pc[14]; p16 = pc[15];
      if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
          p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
          p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
          || p16 != 0.0) {
        pv = ba + 16*diag_offset[row];
        pj = bj + diag_offset[row] + 1;
        x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
        x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
        x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
        x15 = pv[14]; x16 = pv[15];
        pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
        pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
        pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
        pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;

        pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
        pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
        pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
        pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;

        pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
        pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
        pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
        pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;

        pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
        pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
        pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
        pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;

        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 16;
        for (j=0; j<nz; j++) {
          x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
          x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
          x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
          x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
          x    = rtmp + 16*pj[j];
          x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
          x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
          x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
          x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;

          x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
          x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
          x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
          x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;

          x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
          x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
          x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
          x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;

          x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
          x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
          x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
          x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;

          pv   += 16;
        }
        ierr = PetscLogFlops(128.0*nz+112.0);CHKERRQ(ierr);
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 16*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for (j=0; j<nz; j++) {
      x      = rtmp+16*pj[j];
      pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
      pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
      pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
      pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
      pv   += 16;
    }
    /* invert diagonal block */
    w    = ba + 16*diag_offset[i];
    if (pivotinblocks) {
      ierr = Kernel_A_gets_inverse_A_4(w,shift);CHKERRQ(ierr);
    } else {
      ierr = Kernel_A_gets_inverse_A_4_nopivot(w);CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
  C->ops->solve          = MatSolve_SeqBAIJ_4;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
  PetscFunctionReturn(0);
}

/* MatLUFactorNumeric_SeqBAIJ_4_newdatastruct -
     copied from MatLUFactorNumeric_SeqBAIJ_N_newdatastruct() and manually re-implemented
       Kernel_A_gets_A_times_B()
       Kernel_A_gets_A_minus_B_times_C()
       Kernel_A_gets_inverse_A()
*/
#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_newdatastruct"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat            C=B;
  Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
  IS             isrow = b->row,isicol = b->icol;
  PetscErrorCode ierr;
  const PetscInt *r,*ic,*ics;
  PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
  PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
  MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
  PetscInt       bs2 = a->bs2,flg;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
  ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);

  /* generate work space needed by the factorization */
  ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  mwork = rtmp + bs2*n;
  ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
  ics  = ic;

  for (i=0; i<n; i++){
    /* zero rtmp */
    /* L part */
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* U part */
    nz = bi[2*n-i+1] - bi[2*n-i];
    bjtmp = bj + bi[2*n-i];
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* load in initial (unfactored row) */
    nz    = ai[r[i]+1] - ai[r[i]];
    ajtmp = aj + ai[r[i]];
    v     = aa + bs2*ai[r[i]];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i+1] - bi[i];
    for(k=0;k < nzL;k++) {
      row = bjtmp[k];
      pc = rtmp + bs2*row;
      for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
      if (flg) {
        pv = b->a + bs2*bdiag[row];
        /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        ierr = Kernel_A_gets_A_times_B_4(pc,pv,mwork);CHKERRQ(ierr);

        pj = b->j + bi[2*n-row]; /* begining of U(row,:) */
        pv = b->a + bs2*bi[2*n-row];
        nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
        for (j=0; j<nz; j++) {
          /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          v    = rtmp + bs2*pj[j];
          ierr = Kernel_A_gets_A_minus_B_times_C_4(v,pc,pv);CHKERRQ(ierr);
          pv  += bs2;
        }
        ierr = PetscLogFlops(128*nz+112);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv   = b->a + bs2*bi[i] ;
    pj   = b->j + bi[i] ;
    nz   = bi[i+1] - bi[i];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* Mark diagonal and invert diagonal for simplier triangular solves */
    pv   = b->a + bs2*bdiag[i];
    pj   = b->j + bdiag[i];
    ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
    ierr = Kernel_A_gets_inverse_A_4(pv,shift);CHKERRQ(ierr);

    /* U part */
    pv = b->a + bs2*bi[2*n-i];
    pj = b->j + bi[2*n-i];
    nz = bi[2*n-i+1] - bi[2*n-i] - 1;
    for (j=0; j<nz; j++){
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);

  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_newdatastruct_v2"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat            C=B;
  Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
  IS             isrow = b->row,isicol = b->icol;
  PetscErrorCode ierr;
  const PetscInt *r,*ic,*ics;
  PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
  PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
  MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
  PetscInt       bs2 = a->bs2,flg;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
  ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);

  /* generate work space needed by the factorization */
  ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  mwork = rtmp + bs2*n;
  ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
  ics  = ic;

  for (i=0; i<n; i++){
    /* zero rtmp */
    /* L part */
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* U part */
    nz = bdiag[i]-bdiag[i+1];
    bjtmp = bj + bdiag[i+1]+1;
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* load in initial (unfactored row) */
    nz    = ai[r[i]+1] - ai[r[i]];
    ajtmp = aj + ai[r[i]];
    v     = aa + bs2*ai[r[i]];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i+1] - bi[i];
    for(k=0;k < nzL;k++) {
      row = bjtmp[k];
      pc = rtmp + bs2*row;
      for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
      if (flg) {
        pv = b->a + bs2*bdiag[row];
        /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        ierr = Kernel_A_gets_A_times_B_4(pc,pv,mwork);CHKERRQ(ierr);

        pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
        pv = b->a + bs2*(bdiag[row+1]+1);
        nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
        for (j=0; j<nz; j++) {
          /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          v    = rtmp + bs2*pj[j];
          ierr = Kernel_A_gets_A_minus_B_times_C_4(v,pc,pv);CHKERRQ(ierr);
          pv  += bs2;
        }
        ierr = PetscLogFlops(128*nz+112);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv   = b->a + bs2*bi[i] ;
    pj   = b->j + bi[i] ;
    nz   = bi[i+1] - bi[i];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* Mark diagonal and invert diagonal for simplier triangular solves */
    pv   = b->a + bs2*bdiag[i];
    pj   = b->j + bdiag[i];
    ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
    ierr = Kernel_A_gets_inverse_A_4(pv,shift);CHKERRQ(ierr);

    /* U part */
    pv = b->a + bs2*(bdiag[i+1]+1);
    pj = b->j + bdiag[i+1]+1;
    nz = bdiag[i] - bdiag[i+1] - 1;
    for (j=0; j<nz; j++){
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
  ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);

  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
{
/*
    Default Version for when blocks are 4 by 4 Using natural ordering
*/
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
  PetscErrorCode ierr;
  PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
  PetscInt       *ajtmpold,*ajtmp,nz,row;
  PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
  MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
  MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
  MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
  MatScalar      p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
  MatScalar      m13,m14,m15,m16;
  MatScalar      *ba = b->a,*aa = a->a;
  PetscTruth     pivotinblocks = b->pivotinblocks;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  ierr = PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);

  for (i=0; i<n; i++) {
    nz    = bi[i+1] - bi[i];
    ajtmp = bj + bi[i];
    for  (j=0; j<nz; j++) {
      x = rtmp+16*ajtmp[j];
      x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
      x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
    }
    /* load in initial (unfactored row) */
    nz       = ai[i+1] - ai[i];
    ajtmpold = aj + ai[i];
    v        = aa + 16*ai[i];
    for (j=0; j<nz; j++) {
      x    = rtmp+16*ajtmpold[j];
      x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
      x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
      x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
      x[14] = v[14]; x[15] = v[15];
      v    += 16;
    }
    row = *ajtmp++;
    while (row < i) {
      pc  = rtmp + 16*row;
      p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
      p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
      p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
      p15 = pc[14]; p16 = pc[15];
      if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
          p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
          p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
          || p16 != 0.0) {
        pv = ba + 16*diag_offset[row];
        pj = bj + diag_offset[row] + 1;
        x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
        x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
        x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
        x15 = pv[14]; x16 = pv[15];
        pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
        pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
        pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
        pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;

        pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
        pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
        pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
        pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;

        pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
        pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
        pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
        pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;

        pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
        pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
        pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
        pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 16;
        for (j=0; j<nz; j++) {
          x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
          x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
          x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
          x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
          x    = rtmp + 16*pj[j];
          x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
          x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
          x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
          x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;

          x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
          x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
          x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
          x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;

          x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
          x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
          x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
          x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;

          x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
          x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
          x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
          x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;

          pv   += 16;
        }
        ierr = PetscLogFlops(128.0*nz+112.0);CHKERRQ(ierr);
      }
      row = *ajtmp++;
    }
    /* finished row so stick it into b->a */
    pv = ba + 16*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];
    for (j=0; j<nz; j++) {
      x      = rtmp+16*pj[j];
      pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
      pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
      pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
      pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
      pv   += 16;
    }
    /* invert diagonal block */
    w = ba + 16*diag_offset[i];
    if (pivotinblocks) {
      ierr = Kernel_A_gets_inverse_A_4(w,shift);CHKERRQ(ierr);
    } else {
      ierr = Kernel_A_gets_inverse_A_4_nopivot(w);CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
  PetscFunctionReturn(0);
}
/*
  MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_newdatastruct -
    copied from MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_newdatastruct()
*/
#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_newdatastruct"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat            C=B;
  Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
  PetscErrorCode ierr;
  PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
  PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
  MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
  PetscInt       bs2 = a->bs2,flg;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  /* generate work space needed by the factorization */
  ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  mwork = rtmp + bs2*n;
  ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);

  for (i=0; i<n; i++){
    /* zero rtmp */
    /* L part */
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* U part */
    nz = bi[2*n-i+1] - bi[2*n-i];
    bjtmp = bj + bi[2*n-i];
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* load in initial (unfactored row) */
    nz    = ai[i+1] - ai[i];
    ajtmp = aj + ai[i];
    v     = aa + bs2*ai[i];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i+1] - bi[i];
    for(k=0;k < nzL;k++) {
      row = bjtmp[k];
      pc = rtmp + bs2*row;
      for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
      if (flg) {
        pv = b->a + bs2*bdiag[row];
        /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        ierr = Kernel_A_gets_A_times_B_4(pc,pv,mwork);CHKERRQ(ierr);

        pj = b->j + bi[2*n-row]; /* begining of U(row,:) */
        pv = b->a + bs2*bi[2*n-row];
        nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
        for (j=0; j<nz; j++) {
          /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          v    = rtmp + bs2*pj[j];
          ierr = Kernel_A_gets_A_minus_B_times_C_4(v,pc,pv);CHKERRQ(ierr);
          pv  += bs2;
        }
        ierr = PetscLogFlops(128*nz+112);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv   = b->a + bs2*bi[i] ;
    pj   = b->j + bi[i] ;
    nz   = bi[i+1] - bi[i];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* Mark diagonal and invert diagonal for simplier triangular solves */
    pv   = b->a + bs2*bdiag[i];
    pj   = b->j + bdiag[i];
    ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
    ierr = Kernel_A_gets_inverse_A_4(pv,shift);CHKERRQ(ierr);

    /* U part */
    pv = b->a + bs2*bi[2*n-i];
    pj = b->j + bi[2*n-i];
    nz = bi[2*n-i+1] - bi[2*n-i] - 1;
    for (j=0; j<nz; j++){
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_newdatastruct_v2"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat            C=B;
  Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
  PetscErrorCode ierr;
  PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
  PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
  MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
  PetscInt       bs2 = a->bs2,flg;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  /* generate work space needed by the factorization */
  ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  mwork = rtmp + bs2*n;
  ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);

  for (i=0; i<n; i++){
    /* zero rtmp */
    /* L part */
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* U part */
    nz = bdiag[i] - bdiag[i+1];
    bjtmp = bj + bdiag[i+1]+1;
    for  (j=0; j<nz; j++){
      ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* load in initial (unfactored row) */
    nz    = ai[i+1] - ai[i];
    ajtmp = aj + ai[i];
    v     = aa + bs2*ai[i];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* elimination */
    bjtmp = bj + bi[i];
    nzL   = bi[i+1] - bi[i];
    for(k=0;k < nzL;k++) {
      row = bjtmp[k];
      pc = rtmp + bs2*row;
      for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
      if (flg) {
        pv = b->a + bs2*bdiag[row];
        /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
        ierr = Kernel_A_gets_A_times_B_4(pc,pv,mwork);CHKERRQ(ierr);

        pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
        pv = b->a + bs2*(bdiag[row+1]+1);
        nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
        for (j=0; j<nz; j++) {
          /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
          /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
          v    = rtmp + bs2*pj[j];
          ierr = Kernel_A_gets_A_minus_B_times_C_4(v,pc,pv);CHKERRQ(ierr);
          pv  += bs2;
        }
        ierr = PetscLogFlops(128*nz+112);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
      }
    }

    /* finished row so stick it into b->a */
    /* L part */
    pv   = b->a + bs2*bi[i] ;
    pj   = b->j + bi[i] ;
    nz   = bi[i+1] - bi[i];
    for (j=0; j<nz; j++) {
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }

    /* Mark diagonal and invert diagonal for simplier triangular solves */
    pv   = b->a + bs2*bdiag[i];
    pj   = b->j + bdiag[i];
    ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
    ierr = Kernel_A_gets_inverse_A_4(pv,shift);CHKERRQ(ierr);

    /* U part */
    pv = b->a + bs2*(bdiag[i+1]+1);
    pj = b->j + bdiag[i+1]+1;
    nz = bdiag[i] - bdiag[i+1] - 1;
    for (j=0; j<nz; j++){
      ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_SSE)

#include PETSC_HAVE_SSE

/* SSE Version for when blocks are 4 by 4 Using natural ordering */
#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE(Mat B,Mat A,const MatFactorInfo *info)
{
  Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
  PetscErrorCode ierr;
  int i,j,n = a->mbs;
  int         *bj = b->j,*bjtmp,*pj;
  int         row;
  int         *ajtmpold,nz,*bi=b->i;
  int         *diag_offset = b->diag,*ai=a->i,*aj=a->j;
  MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
  MatScalar   *ba = b->a,*aa = a->a;
  int         nonzero=0;
/*    int            nonzero=0,colscale = 16; */
  PetscTruth  pivotinblocks = b->pivotinblocks;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  SSE_SCOPE_BEGIN;

  if ((unsigned long)aa%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer aa is not 16 byte aligned.  SSE will not work.");
  if ((unsigned long)ba%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer ba is not 16 byte aligned.  SSE will not work.");
  ierr = PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  if ((unsigned long)rtmp%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer rtmp is not 16 byte aligned.  SSE will not work.");
/*    if ((unsigned long)bj==(unsigned long)aj) { */
/*      colscale = 4; */
/*    } */
  for (i=0; i<n; i++) {
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    /* zero out the 4x4 block accumulators */
    /* zero out one register */
    XOR_PS(XMM7,XMM7);
    for  (j=0; j<nz; j++) {
      x = rtmp+16*bjtmp[j];
/*        x = rtmp+4*bjtmp[j]; */
      SSE_INLINE_BEGIN_1(x)
        /* Copy zero register to memory locations */
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
      SSE_INLINE_END_1;
    }
    /* load in initial (unfactored row) */
    nz       = ai[i+1] - ai[i];
    ajtmpold = aj + ai[i];
    v        = aa + 16*ai[i];
    for (j=0; j<nz; j++) {
      x = rtmp+16*ajtmpold[j];
/*        x = rtmp+colscale*ajtmpold[j]; */
      /* Copy v block into x block */
      SSE_INLINE_BEGIN_2(v,x)
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
      SSE_INLINE_END_2;

      v += 16;
    }
/*      row = (*bjtmp++)/4; */
    row = *bjtmp++;
    while (row < i) {
      pc  = rtmp + 16*row;
      SSE_INLINE_BEGIN_1(pc)
        /* Load block from lower triangle */
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

        /* Compare block to zero block */

        SSE_COPY_PS(XMM4,XMM7)
        SSE_CMPNEQ_PS(XMM4,XMM0)

        SSE_COPY_PS(XMM5,XMM7)
        SSE_CMPNEQ_PS(XMM5,XMM1)

        SSE_COPY_PS(XMM6,XMM7)
        SSE_CMPNEQ_PS(XMM6,XMM2)

        SSE_CMPNEQ_PS(XMM7,XMM3)

        /* Reduce the comparisons to one SSE register */
        SSE_OR_PS(XMM6,XMM7)
        SSE_OR_PS(XMM5,XMM4)
        SSE_OR_PS(XMM5,XMM6)
      SSE_INLINE_END_1;

      /* Reduce the one SSE register to an integer register for branching */
      /* Note: Since nonzero is an int, there is no INLINE block version of this call */
      MOVEMASK(nonzero,XMM5);

      /* If block is nonzero ... */
      if (nonzero) {
        pv = ba + 16*diag_offset[row];
        PREFETCH_L1(&pv[16]);
        pj = bj + diag_offset[row] + 1;

        /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
        /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
        /* but the diagonal was inverted already */
        /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

        SSE_INLINE_BEGIN_2(pv,pc)
          /* Column 0, product is accumulated in XMM4 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
          SSE_SHUFFLE(XMM4,XMM4,0x00)
          SSE_MULT_PS(XMM4,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
          SSE_SHUFFLE(XMM5,XMM5,0x00)
          SSE_MULT_PS(XMM5,XMM1)
          SSE_ADD_PS(XMM4,XMM5)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM2)
          SSE_ADD_PS(XMM4,XMM6)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM3)
          SSE_ADD_PS(XMM4,XMM7)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

          /* Column 1, product is accumulated in XMM5 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
          SSE_SHUFFLE(XMM5,XMM5,0x00)
          SSE_MULT_PS(XMM5,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM1)
          SSE_ADD_PS(XMM5,XMM6)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM2)
          SSE_ADD_PS(XMM5,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM3)
          SSE_ADD_PS(XMM5,XMM6)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

          SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

          /* Column 2, product is accumulated in XMM6 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM1)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM2)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM3)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

          /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
          /* Column 3, product is accumulated in XMM0 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM0,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM1,XMM7)
          SSE_ADD_PS(XMM0,XMM1)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
          SSE_SHUFFLE(XMM1,XMM1,0x00)
          SSE_MULT_PS(XMM1,XMM2)
          SSE_ADD_PS(XMM0,XMM1)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM3,XMM7)
          SSE_ADD_PS(XMM0,XMM3)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

          /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
          /* This is code to be maintained and read by humans afterall. */
          /* Copy Multiplier Col 3 into XMM3 */
          SSE_COPY_PS(XMM3,XMM0)
          /* Copy Multiplier Col 2 into XMM2 */
          SSE_COPY_PS(XMM2,XMM6)
          /* Copy Multiplier Col 1 into XMM1 */
          SSE_COPY_PS(XMM1,XMM5)
          /* Copy Multiplier Col 0 into XMM0 */
          SSE_COPY_PS(XMM0,XMM4)
        SSE_INLINE_END_2;

        /* Update the row: */
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 16;
        for (j=0; j<nz; j++) {
          PREFETCH_L1(&pv[16]);
          x = rtmp + 16*pj[j];
/*            x = rtmp + 4*pj[j]; */

          /* X:=X-M*PV, One column at a time */
          /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
          SSE_INLINE_BEGIN_2(x,pv)
            /* Load First Column of X*/
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM0)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM1)
            SSE_SUB_PS(XMM4,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM2)
            SSE_SUB_PS(XMM4,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM3)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

            /* Second Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM0)
            SSE_SUB_PS(XMM5,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM1)
            SSE_SUB_PS(XMM5,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
            SSE_SHUFFLE(XMM4,XMM4,0x00)
            SSE_MULT_PS(XMM4,XMM2)
            SSE_SUB_PS(XMM5,XMM4)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM3)
            SSE_SUB_PS(XMM5,XMM6)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

            SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

            /* Third Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM0)
            SSE_SUB_PS(XMM6,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
            SSE_SHUFFLE(XMM4,XMM4,0x00)
            SSE_MULT_PS(XMM4,XMM1)
            SSE_SUB_PS(XMM6,XMM4)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM2)
            SSE_SUB_PS(XMM6,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM3)
            SSE_SUB_PS(XMM6,XMM7)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

            /* Fourth Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM0)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM1)
            SSE_SUB_PS(XMM4,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM2)
            SSE_SUB_PS(XMM4,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM3)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
          SSE_INLINE_END_2;
          pv   += 16;
        }
        ierr = PetscLogFlops(128.0*nz+112.0);CHKERRQ(ierr);
      }
      row = *bjtmp++;
/*        row = (*bjtmp++)/4; */
    }
    /* finished row so stick it into b->a */
    pv = ba + 16*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];

    /* Copy x block back into pv block */
    for (j=0; j<nz; j++) {
      x  = rtmp+16*pj[j];
/*        x  = rtmp+4*pj[j]; */

      SSE_INLINE_BEGIN_2(x,pv)
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
      SSE_INLINE_END_2;
      pv += 16;
    }
    /* invert diagonal block */
    w = ba + 16*diag_offset[i];
    if (pivotinblocks) {
      ierr = Kernel_A_gets_inverse_A_4(w,shift);CHKERRQ(ierr);
    } else {
      ierr = Kernel_A_gets_inverse_A_4_nopivot(w);CHKERRQ(ierr);
    }
/*      ierr = Kernel_A_gets_inverse_A_4_SSE(w);CHKERRQ(ierr); */
    /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr);
  /* Flop Count from inverting diagonal blocks */
  SSE_SCOPE_END;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(Mat C)
{
  Mat            A=C;
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
  PetscErrorCode ierr;
  int i,j,n = a->mbs;
  unsigned short *bj = (unsigned short *)(b->j),*bjtmp,*pj;
  unsigned short *aj = (unsigned short *)(a->j),*ajtmp;
  unsigned int   row;
  int            nz,*bi=b->i;
  int            *diag_offset = b->diag,*ai=a->i;
  MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
  MatScalar      *ba = b->a,*aa = a->a;
  int            nonzero=0;
/*    int            nonzero=0,colscale = 16; */
  PetscTruth     pivotinblocks = b->pivotinblocks;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  SSE_SCOPE_BEGIN;

  if ((unsigned long)aa%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer aa is not 16 byte aligned.  SSE will not work.");
  if ((unsigned long)ba%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer ba is not 16 byte aligned.  SSE will not work.");
  ierr = PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  if ((unsigned long)rtmp%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer rtmp is not 16 byte aligned.  SSE will not work.");
/*    if ((unsigned long)bj==(unsigned long)aj) { */
/*      colscale = 4; */
/*    } */

  for (i=0; i<n; i++) {
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    /* zero out the 4x4 block accumulators */
    /* zero out one register */
    XOR_PS(XMM7,XMM7);
    for  (j=0; j<nz; j++) {
      x = rtmp+16*((unsigned int)bjtmp[j]);
/*        x = rtmp+4*bjtmp[j]; */
      SSE_INLINE_BEGIN_1(x)
        /* Copy zero register to memory locations */
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
      SSE_INLINE_END_1;
    }
    /* load in initial (unfactored row) */
    nz    = ai[i+1] - ai[i];
    ajtmp = aj + ai[i];
    v     = aa + 16*ai[i];
    for (j=0; j<nz; j++) {
      x = rtmp+16*((unsigned int)ajtmp[j]);
/*        x = rtmp+colscale*ajtmp[j]; */
      /* Copy v block into x block */
      SSE_INLINE_BEGIN_2(v,x)
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
      SSE_INLINE_END_2;

      v += 16;
    }
/*      row = (*bjtmp++)/4; */
    row = (unsigned int)(*bjtmp++);
    while (row < i) {
      pc  = rtmp + 16*row;
      SSE_INLINE_BEGIN_1(pc)
        /* Load block from lower triangle */
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

        /* Compare block to zero block */

        SSE_COPY_PS(XMM4,XMM7)
        SSE_CMPNEQ_PS(XMM4,XMM0)

        SSE_COPY_PS(XMM5,XMM7)
        SSE_CMPNEQ_PS(XMM5,XMM1)

        SSE_COPY_PS(XMM6,XMM7)
        SSE_CMPNEQ_PS(XMM6,XMM2)

        SSE_CMPNEQ_PS(XMM7,XMM3)

        /* Reduce the comparisons to one SSE register */
        SSE_OR_PS(XMM6,XMM7)
        SSE_OR_PS(XMM5,XMM4)
        SSE_OR_PS(XMM5,XMM6)
      SSE_INLINE_END_1;

      /* Reduce the one SSE register to an integer register for branching */
      /* Note: Since nonzero is an int, there is no INLINE block version of this call */
      MOVEMASK(nonzero,XMM5);

      /* If block is nonzero ... */
      if (nonzero) {
        pv = ba + 16*diag_offset[row];
        PREFETCH_L1(&pv[16]);
        pj = bj + diag_offset[row] + 1;

        /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
        /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
        /* but the diagonal was inverted already */
        /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

        SSE_INLINE_BEGIN_2(pv,pc)
          /* Column 0, product is accumulated in XMM4 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
          SSE_SHUFFLE(XMM4,XMM4,0x00)
          SSE_MULT_PS(XMM4,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
          SSE_SHUFFLE(XMM5,XMM5,0x00)
          SSE_MULT_PS(XMM5,XMM1)
          SSE_ADD_PS(XMM4,XMM5)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM2)
          SSE_ADD_PS(XMM4,XMM6)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM3)
          SSE_ADD_PS(XMM4,XMM7)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

          /* Column 1, product is accumulated in XMM5 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
          SSE_SHUFFLE(XMM5,XMM5,0x00)
          SSE_MULT_PS(XMM5,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM1)
          SSE_ADD_PS(XMM5,XMM6)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM2)
          SSE_ADD_PS(XMM5,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM3)
          SSE_ADD_PS(XMM5,XMM6)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

          SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

          /* Column 2, product is accumulated in XMM6 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM1)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM2)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM3)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

          /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
          /* Column 3, product is accumulated in XMM0 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM0,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM1,XMM7)
          SSE_ADD_PS(XMM0,XMM1)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
          SSE_SHUFFLE(XMM1,XMM1,0x00)
          SSE_MULT_PS(XMM1,XMM2)
          SSE_ADD_PS(XMM0,XMM1)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM3,XMM7)
          SSE_ADD_PS(XMM0,XMM3)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

          /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
          /* This is code to be maintained and read by humans afterall. */
          /* Copy Multiplier Col 3 into XMM3 */
          SSE_COPY_PS(XMM3,XMM0)
          /* Copy Multiplier Col 2 into XMM2 */
          SSE_COPY_PS(XMM2,XMM6)
          /* Copy Multiplier Col 1 into XMM1 */
          SSE_COPY_PS(XMM1,XMM5)
          /* Copy Multiplier Col 0 into XMM0 */
          SSE_COPY_PS(XMM0,XMM4)
        SSE_INLINE_END_2;

        /* Update the row: */
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 16;
        for (j=0; j<nz; j++) {
          PREFETCH_L1(&pv[16]);
          x = rtmp + 16*((unsigned int)pj[j]);
/*            x = rtmp + 4*pj[j]; */

          /* X:=X-M*PV, One column at a time */
          /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
          SSE_INLINE_BEGIN_2(x,pv)
            /* Load First Column of X*/
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM0)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM1)
            SSE_SUB_PS(XMM4,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM2)
            SSE_SUB_PS(XMM4,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM3)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

            /* Second Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM0)
            SSE_SUB_PS(XMM5,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM1)
            SSE_SUB_PS(XMM5,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
            SSE_SHUFFLE(XMM4,XMM4,0x00)
            SSE_MULT_PS(XMM4,XMM2)
            SSE_SUB_PS(XMM5,XMM4)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM3)
            SSE_SUB_PS(XMM5,XMM6)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

            SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

            /* Third Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM0)
            SSE_SUB_PS(XMM6,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
            SSE_SHUFFLE(XMM4,XMM4,0x00)
            SSE_MULT_PS(XMM4,XMM1)
            SSE_SUB_PS(XMM6,XMM4)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM2)
            SSE_SUB_PS(XMM6,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM3)
            SSE_SUB_PS(XMM6,XMM7)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

            /* Fourth Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM0)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM1)
            SSE_SUB_PS(XMM4,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM2)
            SSE_SUB_PS(XMM4,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM3)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
          SSE_INLINE_END_2;
          pv   += 16;
        }
        ierr = PetscLogFlops(128.0*nz+112.0);CHKERRQ(ierr);
      }
      row = (unsigned int)(*bjtmp++);
/*        row = (*bjtmp++)/4; */
/*        bjtmp++; */
    }
    /* finished row so stick it into b->a */
    pv = ba + 16*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];

    /* Copy x block back into pv block */
    for (j=0; j<nz; j++) {
      x  = rtmp+16*((unsigned int)pj[j]);
/*        x  = rtmp+4*pj[j]; */

      SSE_INLINE_BEGIN_2(x,pv)
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
      SSE_INLINE_END_2;
      pv += 16;
    }
    /* invert diagonal block */
    w = ba + 16*diag_offset[i];
    if (pivotinblocks) {
      ierr = Kernel_A_gets_inverse_A_4(w,shift);CHKERRQ(ierr);
    } else {
      ierr = Kernel_A_gets_inverse_A_4_nopivot(w);CHKERRQ(ierr);
    }
/*      ierr = Kernel_A_gets_inverse_A_4_SSE(w);CHKERRQ(ierr); */
    /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr);
  /* Flop Count from inverting diagonal blocks */
  SSE_SCOPE_END;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj"
PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat C,Mat A,const MatFactorInfo *info)
{
  Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
  PetscErrorCode ierr;
  int  i,j,n = a->mbs;
  unsigned short *bj = (unsigned short *)(b->j),*bjtmp,*pj;
  unsigned int   row;
  int            *ajtmpold,nz,*bi=b->i;
  int            *diag_offset = b->diag,*ai=a->i,*aj=a->j;
  MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
  MatScalar      *ba = b->a,*aa = a->a;
  int            nonzero=0;
/*    int            nonzero=0,colscale = 16; */
  PetscTruth     pivotinblocks = b->pivotinblocks;
  PetscReal      shift = info->shiftinblocks;

  PetscFunctionBegin;
  SSE_SCOPE_BEGIN;

  if ((unsigned long)aa%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer aa is not 16 byte aligned.  SSE will not work.");
  if ((unsigned long)ba%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer ba is not 16 byte aligned.  SSE will not work.");
  ierr = PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
  if ((unsigned long)rtmp%16!=0) SETERRQ(PETSC_ERR_ARG_BADPTR,"Pointer rtmp is not 16 byte aligned.  SSE will not work.");
/*    if ((unsigned long)bj==(unsigned long)aj) { */
/*      colscale = 4; */
/*    } */
  if ((unsigned long)bj==(unsigned long)aj) {
    return(MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(C));
  }

  for (i=0; i<n; i++) {
    nz    = bi[i+1] - bi[i];
    bjtmp = bj + bi[i];
    /* zero out the 4x4 block accumulators */
    /* zero out one register */
    XOR_PS(XMM7,XMM7);
    for  (j=0; j<nz; j++) {
      x = rtmp+16*((unsigned int)bjtmp[j]);
/*        x = rtmp+4*bjtmp[j]; */
      SSE_INLINE_BEGIN_1(x)
        /* Copy zero register to memory locations */
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
        SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
        SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
      SSE_INLINE_END_1;
    }
    /* load in initial (unfactored row) */
    nz       = ai[i+1] - ai[i];
    ajtmpold = aj + ai[i];
    v        = aa + 16*ai[i];
    for (j=0; j<nz; j++) {
      x = rtmp+16*ajtmpold[j];
/*        x = rtmp+colscale*ajtmpold[j]; */
      /* Copy v block into x block */
      SSE_INLINE_BEGIN_2(v,x)
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
      SSE_INLINE_END_2;

      v += 16;
    }
/*      row = (*bjtmp++)/4; */
    row = (unsigned int)(*bjtmp++);
    while (row < i) {
      pc  = rtmp + 16*row;
      SSE_INLINE_BEGIN_1(pc)
        /* Load block from lower triangle */
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

        /* Compare block to zero block */

        SSE_COPY_PS(XMM4,XMM7)
        SSE_CMPNEQ_PS(XMM4,XMM0)

        SSE_COPY_PS(XMM5,XMM7)
        SSE_CMPNEQ_PS(XMM5,XMM1)

        SSE_COPY_PS(XMM6,XMM7)
        SSE_CMPNEQ_PS(XMM6,XMM2)

        SSE_CMPNEQ_PS(XMM7,XMM3)

        /* Reduce the comparisons to one SSE register */
        SSE_OR_PS(XMM6,XMM7)
        SSE_OR_PS(XMM5,XMM4)
        SSE_OR_PS(XMM5,XMM6)
      SSE_INLINE_END_1;

      /* Reduce the one SSE register to an integer register for branching */
      /* Note: Since nonzero is an int, there is no INLINE block version of this call */
      MOVEMASK(nonzero,XMM5);

      /* If block is nonzero ... */
      if (nonzero) {
        pv = ba + 16*diag_offset[row];
        PREFETCH_L1(&pv[16]);
        pj = bj + diag_offset[row] + 1;

        /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
        /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
        /* but the diagonal was inverted already */
        /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

        SSE_INLINE_BEGIN_2(pv,pc)
          /* Column 0, product is accumulated in XMM4 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
          SSE_SHUFFLE(XMM4,XMM4,0x00)
          SSE_MULT_PS(XMM4,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
          SSE_SHUFFLE(XMM5,XMM5,0x00)
          SSE_MULT_PS(XMM5,XMM1)
          SSE_ADD_PS(XMM4,XMM5)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM2)
          SSE_ADD_PS(XMM4,XMM6)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM3)
          SSE_ADD_PS(XMM4,XMM7)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

          /* Column 1, product is accumulated in XMM5 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
          SSE_SHUFFLE(XMM5,XMM5,0x00)
          SSE_MULT_PS(XMM5,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM1)
          SSE_ADD_PS(XMM5,XMM6)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM2)
          SSE_ADD_PS(XMM5,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM3)
          SSE_ADD_PS(XMM5,XMM6)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

          SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

          /* Column 2, product is accumulated in XMM6 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
          SSE_SHUFFLE(XMM6,XMM6,0x00)
          SSE_MULT_PS(XMM6,XMM0)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM1)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM2)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM7,XMM3)
          SSE_ADD_PS(XMM6,XMM7)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

          /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
          /* Column 3, product is accumulated in XMM0 */
          SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM0,XMM7)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM1,XMM7)
          SSE_ADD_PS(XMM0,XMM1)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
          SSE_SHUFFLE(XMM1,XMM1,0x00)
          SSE_MULT_PS(XMM1,XMM2)
          SSE_ADD_PS(XMM0,XMM1)

          SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
          SSE_SHUFFLE(XMM7,XMM7,0x00)
          SSE_MULT_PS(XMM3,XMM7)
          SSE_ADD_PS(XMM0,XMM3)

          SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
          SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

          /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
          /* This is code to be maintained and read by humans afterall. */
          /* Copy Multiplier Col 3 into XMM3 */
          SSE_COPY_PS(XMM3,XMM0)
          /* Copy Multiplier Col 2 into XMM2 */
          SSE_COPY_PS(XMM2,XMM6)
          /* Copy Multiplier Col 1 into XMM1 */
          SSE_COPY_PS(XMM1,XMM5)
          /* Copy Multiplier Col 0 into XMM0 */
          SSE_COPY_PS(XMM0,XMM4)
        SSE_INLINE_END_2;

        /* Update the row: */
        nz = bi[row+1] - diag_offset[row] - 1;
        pv += 16;
        for (j=0; j<nz; j++) {
          PREFETCH_L1(&pv[16]);
          x = rtmp + 16*((unsigned int)pj[j]);
/*            x = rtmp + 4*pj[j]; */

          /* X:=X-M*PV, One column at a time */
          /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
          SSE_INLINE_BEGIN_2(x,pv)
            /* Load First Column of X*/
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM0)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM1)
            SSE_SUB_PS(XMM4,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM2)
            SSE_SUB_PS(XMM4,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM3)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

            /* Second Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM0)
            SSE_SUB_PS(XMM5,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM1)
            SSE_SUB_PS(XMM5,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
            SSE_SHUFFLE(XMM4,XMM4,0x00)
            SSE_MULT_PS(XMM4,XMM2)
            SSE_SUB_PS(XMM5,XMM4)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM3)
            SSE_SUB_PS(XMM5,XMM6)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

            SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

            /* Third Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM0)
            SSE_SUB_PS(XMM6,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
            SSE_SHUFFLE(XMM4,XMM4,0x00)
            SSE_MULT_PS(XMM4,XMM1)
            SSE_SUB_PS(XMM6,XMM4)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM2)
            SSE_SUB_PS(XMM6,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM3)
            SSE_SUB_PS(XMM6,XMM7)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

            /* Fourth Column */
            SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
            SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

            /* Matrix-Vector Product: */
            SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM0)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
            SSE_SHUFFLE(XMM6,XMM6,0x00)
            SSE_MULT_PS(XMM6,XMM1)
            SSE_SUB_PS(XMM4,XMM6)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
            SSE_SHUFFLE(XMM7,XMM7,0x00)
            SSE_MULT_PS(XMM7,XMM2)
            SSE_SUB_PS(XMM4,XMM7)

            SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
            SSE_SHUFFLE(XMM5,XMM5,0x00)
            SSE_MULT_PS(XMM5,XMM3)
            SSE_SUB_PS(XMM4,XMM5)

            SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
            SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
          SSE_INLINE_END_2;
          pv   += 16;
        }
        ierr = PetscLogFlops(128.0*nz+112.0);CHKERRQ(ierr);
      }
      row = (unsigned int)(*bjtmp++);
/*        row = (*bjtmp++)/4; */
/*        bjtmp++; */
    }
    /* finished row so stick it into b->a */
    pv = ba + 16*bi[i];
    pj = bj + bi[i];
    nz = bi[i+1] - bi[i];

    /* Copy x block back into pv block */
    for (j=0; j<nz; j++) {
      x  = rtmp+16*((unsigned int)pj[j]);
/*        x  = rtmp+4*pj[j]; */

      SSE_INLINE_BEGIN_2(x,pv)
        /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
        SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

        SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
        SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

        SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
        SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
      SSE_INLINE_END_2;
      pv += 16;
    }
    /* invert diagonal block */
    w = ba + 16*diag_offset[i];
    if (pivotinblocks) {
      ierr = Kernel_A_gets_inverse_A_4(w,shift);CHKERRQ(ierr);
    } else {
      ierr = Kernel_A_gets_inverse_A_4_nopivot(w);CHKERRQ(ierr);
    }
/*      ierr = Kernel_A_gets_inverse_A_4_SSE(w);CHKERRQ(ierr); */
    /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
  }

  ierr = PetscFree(rtmp);CHKERRQ(ierr);
  C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
  C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
  C->assembled = PETSC_TRUE;
  ierr = PetscLogFlops(1.3333*64*b->mbs);CHKERRQ(ierr);
  /* Flop Count from inverting diagonal blocks */
  SSE_SCOPE_END;
  PetscFunctionReturn(0);
}

#endif