Date: 2013-07-02T14:42:41+00:00

Actual source code: baijfact11.c
petsc-3.4.2 2013-07-02

      2: /*
      3:     Factorization code for BAIJ format.
      4: */
      5: #include <../src/mat/impls/baij/seq/baij.h>
      6: #include <petsc-private/kernels/blockinvert.h>

      8: /* ------------------------------------------------------------*/
      9: /*
     10:       Version for when blocks are 4 by 4
     11: */
     14: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_inplace(Mat C,Mat A,const MatFactorInfo *info)
     15: {
     16:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
     17:   IS             isrow = b->row,isicol = b->icol;
     19:   const PetscInt *r,*ic;
     20:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
     21:   PetscInt       *ajtmpold,*ajtmp,nz,row;
     22:   PetscInt       *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
     23:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
     24:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
     25:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
     26:   MatScalar      p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
     27:   MatScalar      m13,m14,m15,m16;
     28:   MatScalar      *ba           = b->a,*aa = a->a;
     29:   PetscBool      pivotinblocks = b->pivotinblocks;
     30:   PetscReal      shift         = info->shiftamount;

     33:   ISGetIndices(isrow,&r);
     34:   ISGetIndices(isicol,&ic);
     35:   PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);

     37:   for (i=0; i<n; i++) {
     38:     nz    = bi[i+1] - bi[i];
     39:     ajtmp = bj + bi[i];
     40:     for  (j=0; j<nz; j++) {
     41:       x     = rtmp+16*ajtmp[j];
     42:       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
     43:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
     44:     }
     45:     /* load in initial (unfactored row) */
     46:     idx      = r[i];
     47:     nz       = ai[idx+1] - ai[idx];
     48:     ajtmpold = aj + ai[idx];
     49:     v        = aa + 16*ai[idx];
     50:     for (j=0; j<nz; j++) {
     51:       x     = rtmp+16*ic[ajtmpold[j]];
     52:       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
     53:       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
     54:       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
     55:       x[14] = v[14]; x[15] = v[15];
     56:       v    += 16;
     57:     }
     58:     row = *ajtmp++;
     59:     while (row < i) {
     60:       pc  = rtmp + 16*row;
     61:       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
     62:       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
     63:       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
     64:       p15 = pc[14]; p16 = pc[15];
     65:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
     66:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
     67:           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
     68:           || p16 != 0.0) {
     69:         pv    = ba + 16*diag_offset[row];
     70:         pj    = bj + diag_offset[row] + 1;
     71:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
     72:         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
     73:         x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
     74:         x15   = pv[14]; x16 = pv[15];
     75:         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
     76:         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
     77:         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
     78:         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;

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

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

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

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

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

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

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

    123:           pv += 16;
    124:         }
    125:         PetscLogFlops(128.0*nz+112.0);
    126:       }
    127:       row = *ajtmp++;
    128:     }
    129:     /* finished row so stick it into b->a */
    130:     pv = ba + 16*bi[i];
    131:     pj = bj + bi[i];
    132:     nz = bi[i+1] - bi[i];
    133:     for (j=0; j<nz; j++) {
    134:       x      = rtmp+16*pj[j];
    135:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    136:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    137:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
    138:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
    139:       pv    += 16;
    140:     }
    141:     /* invert diagonal block */
    142:     w = ba + 16*diag_offset[i];
    143:     if (pivotinblocks) {
    144:       PetscKernel_A_gets_inverse_A_4(w,shift);
    145:     } else {
    146:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    147:     }
    148:   }

    150:   PetscFree(rtmp);
    151:   ISRestoreIndices(isicol,&ic);
    152:   ISRestoreIndices(isrow,&r);

    154:   C->ops->solve          = MatSolve_SeqBAIJ_4_inplace;
    155:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_inplace;
    156:   C->assembled           = PETSC_TRUE;

    158:   PetscLogFlops(1.333333333333*4*4*4*b->mbs); /* from inverting diagonal blocks */
    159:   return(0);
    160: }

    162: /* MatLUFactorNumeric_SeqBAIJ_4 -
    163:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    164:        PetscKernel_A_gets_A_times_B()
    165:        PetscKernel_A_gets_A_minus_B_times_C()
    166:        PetscKernel_A_gets_inverse_A()
    167: */

    171: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4(Mat B,Mat A,const MatFactorInfo *info)
    172: {
    173:   Mat            C     = B;
    174:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    175:   IS             isrow = b->row,isicol = b->icol;
    177:   const PetscInt *r,*ic;
    178:   PetscInt       i,j,k,nz,nzL,row;
    179:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    180:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
    181:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    182:   PetscInt       flg;
    183:   PetscReal      shift;

    186:   ISGetIndices(isrow,&r);
    187:   ISGetIndices(isicol,&ic);

    189:   if (info->shifttype == MAT_SHIFT_NONE) {
    190:     shift = 0;
    191:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    192:     shift = info->shiftamount;
    193:   }

    195:   /* generate work space needed by the factorization */
    196:   PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
    197:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    199:   for (i=0; i<n; i++) {
    200:     /* zero rtmp */
    201:     /* L part */
    202:     nz    = bi[i+1] - bi[i];
    203:     bjtmp = bj + bi[i];
    204:     for  (j=0; j<nz; j++) {
    205:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    206:     }

    208:     /* U part */
    209:     nz    = bdiag[i]-bdiag[i+1];
    210:     bjtmp = bj + bdiag[i+1]+1;
    211:     for  (j=0; j<nz; j++) {
    212:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    213:     }

    215:     /* load in initial (unfactored row) */
    216:     nz    = ai[r[i]+1] - ai[r[i]];
    217:     ajtmp = aj + ai[r[i]];
    218:     v     = aa + bs2*ai[r[i]];
    219:     for (j=0; j<nz; j++) {
    220:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
    221:     }

    223:     /* elimination */
    224:     bjtmp = bj + bi[i];
    225:     nzL   = bi[i+1] - bi[i];
    226:     for (k=0; k < nzL; k++) {
    227:       row = bjtmp[k];
    228:       pc  = rtmp + bs2*row;
    229:       for (flg=0,j=0; j<bs2; j++) {
    230:         if (pc[j]!=0.0) {
    231:           flg = 1;
    232:           break;
    233:         }
    234:       }
    235:       if (flg) {
    236:         pv = b->a + bs2*bdiag[row];
    237:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    238:         PetscKernel_A_gets_A_times_B_4(pc,pv,mwork);

    240:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
    241:         pv = b->a + bs2*(bdiag[row+1]+1);
    242:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
    243:         for (j=0; j<nz; j++) {
    244:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    245:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    246:           v    = rtmp + bs2*pj[j];
    247:           PetscKernel_A_gets_A_minus_B_times_C_4(v,pc,pv);
    248:           pv  += bs2;
    249:         }
    250:         PetscLogFlops(128*nz+112); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    251:       }
    252:     }

    254:     /* finished row so stick it into b->a */
    255:     /* L part */
    256:     pv = b->a + bs2*bi[i];
    257:     pj = b->j + bi[i];
    258:     nz = bi[i+1] - bi[i];
    259:     for (j=0; j<nz; j++) {
    260:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    261:     }

    263:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    264:     pv   = b->a + bs2*bdiag[i];
    265:     pj   = b->j + bdiag[i];
    266:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    267:     PetscKernel_A_gets_inverse_A_4(pv,shift);

    269:     /* U part */
    270:     pv = b->a + bs2*(bdiag[i+1]+1);
    271:     pj = b->j + bdiag[i+1]+1;
    272:     nz = bdiag[i] - bdiag[i+1] - 1;
    273:     for (j=0; j<nz; j++) {
    274:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    275:     }
    276:   }

    278:   PetscFree2(rtmp,mwork);
    279:   ISRestoreIndices(isicol,&ic);
    280:   ISRestoreIndices(isrow,&r);

    282:   C->ops->solve          = MatSolve_SeqBAIJ_4;
    283:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
    284:   C->assembled           = PETSC_TRUE;

    286:   PetscLogFlops(1.333333333333*4*4*4*n); /* from inverting diagonal blocks */
    287:   return(0);
    288: }

    292: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
    293: {
    294: /*
    295:     Default Version for when blocks are 4 by 4 Using natural ordering
    296: */
    297:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    299:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
    300:   PetscInt       *ajtmpold,*ajtmp,nz,row;
    301:   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
    302:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    303:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
    304:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
    305:   MatScalar      p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
    306:   MatScalar      m13,m14,m15,m16;
    307:   MatScalar      *ba           = b->a,*aa = a->a;
    308:   PetscBool      pivotinblocks = b->pivotinblocks;
    309:   PetscReal      shift         = info->shiftamount;

    312:   PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);

    314:   for (i=0; i<n; i++) {
    315:     nz    = bi[i+1] - bi[i];
    316:     ajtmp = bj + bi[i];
    317:     for  (j=0; j<nz; j++) {
    318:       x     = rtmp+16*ajtmp[j];
    319:       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
    320:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
    321:     }
    322:     /* load in initial (unfactored row) */
    323:     nz       = ai[i+1] - ai[i];
    324:     ajtmpold = aj + ai[i];
    325:     v        = aa + 16*ai[i];
    326:     for (j=0; j<nz; j++) {
    327:       x     = rtmp+16*ajtmpold[j];
    328:       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
    329:       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
    330:       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
    331:       x[14] = v[14]; x[15] = v[15];
    332:       v    += 16;
    333:     }
    334:     row = *ajtmp++;
    335:     while (row < i) {
    336:       pc  = rtmp + 16*row;
    337:       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
    338:       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
    339:       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
    340:       p15 = pc[14]; p16 = pc[15];
    341:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
    342:           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
    343:           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
    344:           || p16 != 0.0) {
    345:         pv    = ba + 16*diag_offset[row];
    346:         pj    = bj + diag_offset[row] + 1;
    347:         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
    348:         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
    349:         x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
    350:         x15   = pv[14]; x16 = pv[15];
    351:         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
    352:         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
    353:         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
    354:         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;

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

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

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

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

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

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

    398:           pv += 16;
    399:         }
    400:         PetscLogFlops(128.0*nz+112.0);
    401:       }
    402:       row = *ajtmp++;
    403:     }
    404:     /* finished row so stick it into b->a */
    405:     pv = ba + 16*bi[i];
    406:     pj = bj + bi[i];
    407:     nz = bi[i+1] - bi[i];
    408:     for (j=0; j<nz; j++) {
    409:       x      = rtmp+16*pj[j];
    410:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    411:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    412:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
    413:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
    414:       pv    += 16;
    415:     }
    416:     /* invert diagonal block */
    417:     w = ba + 16*diag_offset[i];
    418:     if (pivotinblocks) {
    419:       PetscKernel_A_gets_inverse_A_4(w,shift);
    420:     } else {
    421:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    422:     }
    423:   }

    425:   PetscFree(rtmp);

    427:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_inplace;
    428:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace;
    429:   C->assembled           = PETSC_TRUE;

    431:   PetscLogFlops(1.333333333333*4*4*4*b->mbs); /* from inverting diagonal blocks */
    432:   return(0);
    433: }

    435: /*
    436:   MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering -
    437:     copied from MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace()
    438: */
    441: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
    442: {
    443:   Mat            C =B;
    444:   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
    446:   PetscInt       i,j,k,nz,nzL,row;
    447:   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
    448:   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
    449:   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
    450:   PetscInt       flg;
    451:   PetscReal      shift;

    454:   /* generate work space needed by the factorization */
    455:   PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);
    456:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    458:   if (info->shifttype == MAT_SHIFT_NONE) {
    459:     shift = 0;
    460:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    461:     shift = info->shiftamount;
    462:   }

    464:   for (i=0; i<n; i++) {
    465:     /* zero rtmp */
    466:     /* L part */
    467:     nz    = bi[i+1] - bi[i];
    468:     bjtmp = bj + bi[i];
    469:     for  (j=0; j<nz; j++) {
    470:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    471:     }

    473:     /* U part */
    474:     nz    = bdiag[i] - bdiag[i+1];
    475:     bjtmp = bj + bdiag[i+1]+1;
    476:     for  (j=0; j<nz; j++) {
    477:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    478:     }

    480:     /* load in initial (unfactored row) */
    481:     nz    = ai[i+1] - ai[i];
    482:     ajtmp = aj + ai[i];
    483:     v     = aa + bs2*ai[i];
    484:     for (j=0; j<nz; j++) {
    485:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
    486:     }

    488:     /* elimination */
    489:     bjtmp = bj + bi[i];
    490:     nzL   = bi[i+1] - bi[i];
    491:     for (k=0; k < nzL; k++) {
    492:       row = bjtmp[k];
    493:       pc  = rtmp + bs2*row;
    494:       for (flg=0,j=0; j<bs2; j++) {
    495:         if (pc[j]!=0.0) {
    496:           flg = 1;
    497:           break;
    498:         }
    499:       }
    500:       if (flg) {
    501:         pv = b->a + bs2*bdiag[row];
    502:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    503:         PetscKernel_A_gets_A_times_B_4(pc,pv,mwork);

    505:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
    506:         pv = b->a + bs2*(bdiag[row+1]+1);
    507:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
    508:         for (j=0; j<nz; j++) {
    509:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    510:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    511:           v    = rtmp + bs2*pj[j];
    512:           PetscKernel_A_gets_A_minus_B_times_C_4(v,pc,pv);
    513:           pv  += bs2;
    514:         }
    515:         PetscLogFlops(128*nz+112); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    516:       }
    517:     }

    519:     /* finished row so stick it into b->a */
    520:     /* L part */
    521:     pv = b->a + bs2*bi[i];
    522:     pj = b->j + bi[i];
    523:     nz = bi[i+1] - bi[i];
    524:     for (j=0; j<nz; j++) {
    525:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    526:     }

    528:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    529:     pv   = b->a + bs2*bdiag[i];
    530:     pj   = b->j + bdiag[i];
    531:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    532:     PetscKernel_A_gets_inverse_A_4(pv,shift);

    534:     /* U part */
    535:     pv = b->a + bs2*(bdiag[i+1]+1);
    536:     pj = b->j + bdiag[i+1]+1;
    537:     nz = bdiag[i] - bdiag[i+1] - 1;
    538:     for (j=0; j<nz; j++) {
    539:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    540:     }
    541:   }
    542:   PetscFree2(rtmp,mwork);

    544:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
    545:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
    546:   C->assembled           = PETSC_TRUE;

    548:   PetscLogFlops(1.333333333333*4*4*4*n); /* from inverting diagonal blocks */
    549:   return(0);
    550: }

    552: #if defined(PETSC_HAVE_SSE)

    554: #include PETSC_HAVE_SSE

    556: /* SSE Version for when blocks are 4 by 4 Using natural ordering */
    559: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE(Mat B,Mat A,const MatFactorInfo *info)
    560: {
    561:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    563:   int            i,j,n = a->mbs;
    564:   int            *bj = b->j,*bjtmp,*pj;
    565:   int            row;
    566:   int            *ajtmpold,nz,*bi=b->i;
    567:   int            *diag_offset = b->diag,*ai=a->i,*aj=a->j;
    568:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    569:   MatScalar      *ba    = b->a,*aa = a->a;
    570:   int            nonzero=0;
    571: /*    int            nonzero=0,colscale = 16; */
    572:   PetscBool pivotinblocks = b->pivotinblocks;
    573:   PetscReal shift         = info->shiftamount;

    576:   SSE_SCOPE_BEGIN;

    578:   if ((unsigned long)aa%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer aa is not 16 byte aligned.  SSE will not work.");
    579:   if ((unsigned long)ba%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer ba is not 16 byte aligned.  SSE will not work.");
    580:   PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);
    581:   if ((unsigned long)rtmp%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer rtmp is not 16 byte aligned.  SSE will not work.");
    582: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    583: /*      colscale = 4; */
    584: /*    } */
    585:   for (i=0; i<n; i++) {
    586:     nz    = bi[i+1] - bi[i];
    587:     bjtmp = bj + bi[i];
    588:     /* zero out the 4x4 block accumulators */
    589:     /* zero out one register */
    590:     XOR_PS(XMM7,XMM7);
    591:     for  (j=0; j<nz; j++) {
    592:       x = rtmp+16*bjtmp[j];
    593: /*        x = rtmp+4*bjtmp[j]; */
    594:       SSE_INLINE_BEGIN_1(x)
    595:       /* Copy zero register to memory locations */
    596:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    597:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    598:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    599:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    600:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    601:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    602:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    603:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    604:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    605:       SSE_INLINE_END_1;
    606:     }
    607:     /* load in initial (unfactored row) */
    608:     nz       = ai[i+1] - ai[i];
    609:     ajtmpold = aj + ai[i];
    610:     v        = aa + 16*ai[i];
    611:     for (j=0; j<nz; j++) {
    612:       x = rtmp+16*ajtmpold[j];
    613: /*        x = rtmp+colscale*ajtmpold[j]; */
    614:       /* Copy v block into x block */
    615:       SSE_INLINE_BEGIN_2(v,x)
    616:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    617:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    618:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    620:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    621:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    623:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    624:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    626:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    627:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    629:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    630:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    632:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    633:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    635:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    636:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    638:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    639:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    640:       SSE_INLINE_END_2;

    642:       v += 16;
    643:     }
    644: /*      row = (*bjtmp++)/4; */
    645:     row = *bjtmp++;
    646:     while (row < i) {
    647:       pc = rtmp + 16*row;
    648:       SSE_INLINE_BEGIN_1(pc)
    649:       /* Load block from lower triangle */
    650:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    651:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    652:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    654:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    655:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    657:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    658:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    660:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    661:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    663:       /* Compare block to zero block */

    665:       SSE_COPY_PS(XMM4,XMM7)
    666:       SSE_CMPNEQ_PS(XMM4,XMM0)

    668:       SSE_COPY_PS(XMM5,XMM7)
    669:       SSE_CMPNEQ_PS(XMM5,XMM1)

    671:       SSE_COPY_PS(XMM6,XMM7)
    672:       SSE_CMPNEQ_PS(XMM6,XMM2)

    674:       SSE_CMPNEQ_PS(XMM7,XMM3)

    676:       /* Reduce the comparisons to one SSE register */
    677:       SSE_OR_PS(XMM6,XMM7)
    678:       SSE_OR_PS(XMM5,XMM4)
    679:       SSE_OR_PS(XMM5,XMM6)
    680:       SSE_INLINE_END_1;

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

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

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

    697:         SSE_INLINE_BEGIN_2(pv,pc)
    698:         /* Column 0, product is accumulated in XMM4 */
    699:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    700:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    701:         SSE_MULT_PS(XMM4,XMM0)

    703:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    704:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    705:         SSE_MULT_PS(XMM5,XMM1)
    706:         SSE_ADD_PS(XMM4,XMM5)

    708:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    709:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    710:         SSE_MULT_PS(XMM6,XMM2)
    711:         SSE_ADD_PS(XMM4,XMM6)

    713:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    714:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    715:         SSE_MULT_PS(XMM7,XMM3)
    716:         SSE_ADD_PS(XMM4,XMM7)

    718:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    719:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

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

    726:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    727:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    728:         SSE_MULT_PS(XMM6,XMM1)
    729:         SSE_ADD_PS(XMM5,XMM6)

    731:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    732:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    733:         SSE_MULT_PS(XMM7,XMM2)
    734:         SSE_ADD_PS(XMM5,XMM7)

    736:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    737:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    738:         SSE_MULT_PS(XMM6,XMM3)
    739:         SSE_ADD_PS(XMM5,XMM6)

    741:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    742:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    744:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

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

    751:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    752:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    753:         SSE_MULT_PS(XMM7,XMM1)
    754:         SSE_ADD_PS(XMM6,XMM7)

    756:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    757:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    758:         SSE_MULT_PS(XMM7,XMM2)
    759:         SSE_ADD_PS(XMM6,XMM7)

    761:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    762:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    763:         SSE_MULT_PS(XMM7,XMM3)
    764:         SSE_ADD_PS(XMM6,XMM7)

    766:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    767:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

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

    775:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    776:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    777:         SSE_MULT_PS(XMM1,XMM7)
    778:         SSE_ADD_PS(XMM0,XMM1)

    780:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    781:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    782:         SSE_MULT_PS(XMM1,XMM2)
    783:         SSE_ADD_PS(XMM0,XMM1)

    785:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    786:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    787:         SSE_MULT_PS(XMM3,XMM7)
    788:         SSE_ADD_PS(XMM0,XMM3)

    790:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    791:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    793:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    794:         /* This is code to be maintained and read by humans afterall. */
    795:         /* Copy Multiplier Col 3 into XMM3 */
    796:         SSE_COPY_PS(XMM3,XMM0)
    797:         /* Copy Multiplier Col 2 into XMM2 */
    798:         SSE_COPY_PS(XMM2,XMM6)
    799:         /* Copy Multiplier Col 1 into XMM1 */
    800:         SSE_COPY_PS(XMM1,XMM5)
    801:         /* Copy Multiplier Col 0 into XMM0 */
    802:         SSE_COPY_PS(XMM0,XMM4)
    803:         SSE_INLINE_END_2;

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

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

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

    826:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    827:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    828:           SSE_MULT_PS(XMM6,XMM1)
    829:           SSE_SUB_PS(XMM4,XMM6)

    831:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    832:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    833:           SSE_MULT_PS(XMM7,XMM2)
    834:           SSE_SUB_PS(XMM4,XMM7)

    836:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    837:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    838:           SSE_MULT_PS(XMM5,XMM3)
    839:           SSE_SUB_PS(XMM4,XMM5)

    841:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    842:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    844:           /* Second Column */
    845:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    846:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

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

    854:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    855:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    856:           SSE_MULT_PS(XMM7,XMM1)
    857:           SSE_SUB_PS(XMM5,XMM7)

    859:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    860:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    861:           SSE_MULT_PS(XMM4,XMM2)
    862:           SSE_SUB_PS(XMM5,XMM4)

    864:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    865:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    866:           SSE_MULT_PS(XMM6,XMM3)
    867:           SSE_SUB_PS(XMM5,XMM6)

    869:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    870:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    872:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    874:           /* Third Column */
    875:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    876:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

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

    884:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    885:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    886:           SSE_MULT_PS(XMM4,XMM1)
    887:           SSE_SUB_PS(XMM6,XMM4)

    889:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    890:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    891:           SSE_MULT_PS(XMM5,XMM2)
    892:           SSE_SUB_PS(XMM6,XMM5)

    894:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    895:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    896:           SSE_MULT_PS(XMM7,XMM3)
    897:           SSE_SUB_PS(XMM6,XMM7)

    899:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    900:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    902:           /* Fourth Column */
    903:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    904:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

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

    912:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    913:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    914:           SSE_MULT_PS(XMM6,XMM1)
    915:           SSE_SUB_PS(XMM4,XMM6)

    917:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    918:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    919:           SSE_MULT_PS(XMM7,XMM2)
    920:           SSE_SUB_PS(XMM4,XMM7)

    922:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    923:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    924:           SSE_MULT_PS(XMM5,XMM3)
    925:           SSE_SUB_PS(XMM4,XMM5)

    927:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    928:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    929:           SSE_INLINE_END_2;
    930:           pv += 16;
    931:         }
    932:         PetscLogFlops(128.0*nz+112.0);
    933:       }
    934:       row = *bjtmp++;
    935: /*        row = (*bjtmp++)/4; */
    936:     }
    937:     /* finished row so stick it into b->a */
    938:     pv = ba + 16*bi[i];
    939:     pj = bj + bi[i];
    940:     nz = bi[i+1] - bi[i];

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

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

    952:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    953:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    955:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    956:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    958:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    959:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    961:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    962:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    964:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    965:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    967:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    968:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    970:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    971:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    972:       SSE_INLINE_END_2;
    973:       pv += 16;
    974:     }
    975:     /* invert diagonal block */
    976:     w = ba + 16*diag_offset[i];
    977:     if (pivotinblocks) {
    978:       PetscKernel_A_gets_inverse_A_4(w,shift);
    979:     } else {
    980:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    981:     }
    982: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    983:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    984:   }

    986:   PetscFree(rtmp);

    988:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    989:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    990:   C->assembled           = PETSC_TRUE;

    992:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    993:   /* Flop Count from inverting diagonal blocks */
    994:   SSE_SCOPE_END;
    995:   return(0);
    996: }

    1000: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(Mat C)
    1001: {
    1002:   Mat            A  =C;
    1003:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    1005:   int            i,j,n = a->mbs;
    1006:   unsigned short *bj = (unsigned short*)(b->j),*bjtmp,*pj;
    1007:   unsigned short *aj = (unsigned short*)(a->j),*ajtmp;
    1008:   unsigned int   row;
    1009:   int            nz,*bi=b->i;
    1010:   int            *diag_offset = b->diag,*ai=a->i;
    1011:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    1012:   MatScalar      *ba    = b->a,*aa = a->a;
    1013:   int            nonzero=0;
    1014: /*    int            nonzero=0,colscale = 16; */
    1015:   PetscBool pivotinblocks = b->pivotinblocks;
    1016:   PetscReal shift         = info->shiftamount;

    1019:   SSE_SCOPE_BEGIN;

    1021:   if ((unsigned long)aa%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer aa is not 16 byte aligned.  SSE will not work.");
    1022:   if ((unsigned long)ba%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer ba is not 16 byte aligned.  SSE will not work.");
    1023:   PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);
    1024:   if ((unsigned long)rtmp%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer rtmp is not 16 byte aligned.  SSE will not work.");
    1025: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1026: /*      colscale = 4; */
    1027: /*    } */

    1029:   for (i=0; i<n; i++) {
    1030:     nz    = bi[i+1] - bi[i];
    1031:     bjtmp = bj + bi[i];
    1032:     /* zero out the 4x4 block accumulators */
    1033:     /* zero out one register */
    1034:     XOR_PS(XMM7,XMM7);
    1035:     for  (j=0; j<nz; j++) {
    1036:       x = rtmp+16*((unsigned int)bjtmp[j]);
    1037: /*        x = rtmp+4*bjtmp[j]; */
    1038:       SSE_INLINE_BEGIN_1(x)
    1039:       /* Copy zero register to memory locations */
    1040:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1041:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    1042:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    1043:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    1044:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    1045:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    1046:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    1047:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1048:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    1049:       SSE_INLINE_END_1;
    1050:     }
    1051:     /* load in initial (unfactored row) */
    1052:     nz    = ai[i+1] - ai[i];
    1053:     ajtmp = aj + ai[i];
    1054:     v     = aa + 16*ai[i];
    1055:     for (j=0; j<nz; j++) {
    1056:       x = rtmp+16*((unsigned int)ajtmp[j]);
    1057: /*        x = rtmp+colscale*ajtmp[j]; */
    1058:       /* Copy v block into x block */
    1059:       SSE_INLINE_BEGIN_2(v,x)
    1060:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1061:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1062:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    1064:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    1065:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    1067:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    1068:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    1070:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    1071:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    1073:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    1074:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    1076:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    1077:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    1079:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    1080:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    1082:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1083:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1084:       SSE_INLINE_END_2;

    1086:       v += 16;
    1087:     }
    1088: /*      row = (*bjtmp++)/4; */
    1089:     row = (unsigned int)(*bjtmp++);
    1090:     while (row < i) {
    1091:       pc = rtmp + 16*row;
    1092:       SSE_INLINE_BEGIN_1(pc)
    1093:       /* Load block from lower triangle */
    1094:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1095:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1096:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    1098:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    1099:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    1101:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    1102:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    1104:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    1105:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    1107:       /* Compare block to zero block */

    1109:       SSE_COPY_PS(XMM4,XMM7)
    1110:       SSE_CMPNEQ_PS(XMM4,XMM0)

    1112:       SSE_COPY_PS(XMM5,XMM7)
    1113:       SSE_CMPNEQ_PS(XMM5,XMM1)

    1115:       SSE_COPY_PS(XMM6,XMM7)
    1116:       SSE_CMPNEQ_PS(XMM6,XMM2)

    1118:       SSE_CMPNEQ_PS(XMM7,XMM3)

    1120:       /* Reduce the comparisons to one SSE register */
    1121:       SSE_OR_PS(XMM6,XMM7)
    1122:       SSE_OR_PS(XMM5,XMM4)
    1123:       SSE_OR_PS(XMM5,XMM6)
    1124:       SSE_INLINE_END_1;

    1126:       /* Reduce the one SSE register to an integer register for branching */
    1127:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1128:       MOVEMASK(nonzero,XMM5);

    1130:       /* If block is nonzero ... */
    1131:       if (nonzero) {
    1132:         pv = ba + 16*diag_offset[row];
    1133:         PREFETCH_L1(&pv[16]);
    1134:         pj = bj + diag_offset[row] + 1;

    1136:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1137:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1138:         /* but the diagonal was inverted already */
    1139:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1141:         SSE_INLINE_BEGIN_2(pv,pc)
    1142:         /* Column 0, product is accumulated in XMM4 */
    1143:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    1144:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    1145:         SSE_MULT_PS(XMM4,XMM0)

    1147:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    1148:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1149:         SSE_MULT_PS(XMM5,XMM1)
    1150:         SSE_ADD_PS(XMM4,XMM5)

    1152:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    1153:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1154:         SSE_MULT_PS(XMM6,XMM2)
    1155:         SSE_ADD_PS(XMM4,XMM6)

    1157:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    1158:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1159:         SSE_MULT_PS(XMM7,XMM3)
    1160:         SSE_ADD_PS(XMM4,XMM7)

    1162:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    1163:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

    1165:         /* Column 1, product is accumulated in XMM5 */
    1166:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
    1167:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1168:         SSE_MULT_PS(XMM5,XMM0)

    1170:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    1171:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1172:         SSE_MULT_PS(XMM6,XMM1)
    1173:         SSE_ADD_PS(XMM5,XMM6)

    1175:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    1176:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1177:         SSE_MULT_PS(XMM7,XMM2)
    1178:         SSE_ADD_PS(XMM5,XMM7)

    1180:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    1181:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1182:         SSE_MULT_PS(XMM6,XMM3)
    1183:         SSE_ADD_PS(XMM5,XMM6)

    1185:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    1186:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    1188:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

    1190:         /* Column 2, product is accumulated in XMM6 */
    1191:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
    1192:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1193:         SSE_MULT_PS(XMM6,XMM0)

    1195:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    1196:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1197:         SSE_MULT_PS(XMM7,XMM1)
    1198:         SSE_ADD_PS(XMM6,XMM7)

    1200:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    1201:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1202:         SSE_MULT_PS(XMM7,XMM2)
    1203:         SSE_ADD_PS(XMM6,XMM7)

    1205:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    1206:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1207:         SSE_MULT_PS(XMM7,XMM3)
    1208:         SSE_ADD_PS(XMM6,XMM7)

    1210:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    1211:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1213:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1214:         /* Column 3, product is accumulated in XMM0 */
    1215:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
    1216:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1217:         SSE_MULT_PS(XMM0,XMM7)

    1219:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    1220:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1221:         SSE_MULT_PS(XMM1,XMM7)
    1222:         SSE_ADD_PS(XMM0,XMM1)

    1224:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    1225:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    1226:         SSE_MULT_PS(XMM1,XMM2)
    1227:         SSE_ADD_PS(XMM0,XMM1)

    1229:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    1230:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1231:         SSE_MULT_PS(XMM3,XMM7)
    1232:         SSE_ADD_PS(XMM0,XMM3)

    1234:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    1235:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    1237:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1238:         /* This is code to be maintained and read by humans afterall. */
    1239:         /* Copy Multiplier Col 3 into XMM3 */
    1240:         SSE_COPY_PS(XMM3,XMM0)
    1241:         /* Copy Multiplier Col 2 into XMM2 */
    1242:         SSE_COPY_PS(XMM2,XMM6)
    1243:         /* Copy Multiplier Col 1 into XMM1 */
    1244:         SSE_COPY_PS(XMM1,XMM5)
    1245:         /* Copy Multiplier Col 0 into XMM0 */
    1246:         SSE_COPY_PS(XMM0,XMM4)
    1247:         SSE_INLINE_END_2;

    1249:         /* Update the row: */
    1250:         nz  = bi[row+1] - diag_offset[row] - 1;
    1251:         pv += 16;
    1252:         for (j=0; j<nz; j++) {
    1253:           PREFETCH_L1(&pv[16]);
    1254:           x = rtmp + 16*((unsigned int)pj[j]);
    1255: /*            x = rtmp + 4*pj[j]; */

    1257:           /* X:=X-M*PV, One column at a time */
    1258:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1259:           SSE_INLINE_BEGIN_2(x,pv)
    1260:           /* Load First Column of X*/
    1261:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1262:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1264:           /* Matrix-Vector Product: */
    1265:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
    1266:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1267:           SSE_MULT_PS(XMM5,XMM0)
    1268:           SSE_SUB_PS(XMM4,XMM5)

    1270:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    1271:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1272:           SSE_MULT_PS(XMM6,XMM1)
    1273:           SSE_SUB_PS(XMM4,XMM6)

    1275:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    1276:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1277:           SSE_MULT_PS(XMM7,XMM2)
    1278:           SSE_SUB_PS(XMM4,XMM7)

    1280:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    1281:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1282:           SSE_MULT_PS(XMM5,XMM3)
    1283:           SSE_SUB_PS(XMM4,XMM5)

    1285:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1286:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1288:           /* Second Column */
    1289:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1290:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1292:           /* Matrix-Vector Product: */
    1293:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
    1294:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1295:           SSE_MULT_PS(XMM6,XMM0)
    1296:           SSE_SUB_PS(XMM5,XMM6)

    1298:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    1299:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1300:           SSE_MULT_PS(XMM7,XMM1)
    1301:           SSE_SUB_PS(XMM5,XMM7)

    1303:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    1304:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1305:           SSE_MULT_PS(XMM4,XMM2)
    1306:           SSE_SUB_PS(XMM5,XMM4)

    1308:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    1309:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1310:           SSE_MULT_PS(XMM6,XMM3)
    1311:           SSE_SUB_PS(XMM5,XMM6)

    1313:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1314:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1316:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    1318:           /* Third Column */
    1319:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1320:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1322:           /* Matrix-Vector Product: */
    1323:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
    1324:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1325:           SSE_MULT_PS(XMM7,XMM0)
    1326:           SSE_SUB_PS(XMM6,XMM7)

    1328:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    1329:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1330:           SSE_MULT_PS(XMM4,XMM1)
    1331:           SSE_SUB_PS(XMM6,XMM4)

    1333:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    1334:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1335:           SSE_MULT_PS(XMM5,XMM2)
    1336:           SSE_SUB_PS(XMM6,XMM5)

    1338:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    1339:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1340:           SSE_MULT_PS(XMM7,XMM3)
    1341:           SSE_SUB_PS(XMM6,XMM7)

    1343:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1344:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1346:           /* Fourth Column */
    1347:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1348:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    1350:           /* Matrix-Vector Product: */
    1351:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
    1352:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1353:           SSE_MULT_PS(XMM5,XMM0)
    1354:           SSE_SUB_PS(XMM4,XMM5)

    1356:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    1357:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1358:           SSE_MULT_PS(XMM6,XMM1)
    1359:           SSE_SUB_PS(XMM4,XMM6)

    1361:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    1362:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1363:           SSE_MULT_PS(XMM7,XMM2)
    1364:           SSE_SUB_PS(XMM4,XMM7)

    1366:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    1367:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1368:           SSE_MULT_PS(XMM5,XMM3)
    1369:           SSE_SUB_PS(XMM4,XMM5)

    1371:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1372:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    1373:           SSE_INLINE_END_2;
    1374:           pv += 16;
    1375:         }
    1376:         PetscLogFlops(128.0*nz+112.0);
    1377:       }
    1378:       row = (unsigned int)(*bjtmp++);
    1379: /*        row = (*bjtmp++)/4; */
    1380: /*        bjtmp++; */
    1381:     }
    1382:     /* finished row so stick it into b->a */
    1383:     pv = ba + 16*bi[i];
    1384:     pj = bj + bi[i];
    1385:     nz = bi[i+1] - bi[i];

    1387:     /* Copy x block back into pv block */
    1388:     for (j=0; j<nz; j++) {
    1389:       x = rtmp+16*((unsigned int)pj[j]);
    1390: /*        x  = rtmp+4*pj[j]; */

    1392:       SSE_INLINE_BEGIN_2(x,pv)
    1393:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1394:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
    1395:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

    1397:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    1398:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    1400:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    1401:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    1403:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    1404:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    1406:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    1407:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    1409:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    1410:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1412:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1413:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    1415:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1416:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1417:       SSE_INLINE_END_2;
    1418:       pv += 16;
    1419:     }
    1420:     /* invert diagonal block */
    1421:     w = ba + 16*diag_offset[i];
    1422:     if (pivotinblocks) {
    1423:       PetscKernel_A_gets_inverse_A_4(w,shift);
    1424:     } else {
    1425:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    1426:     }
    1427: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    1428:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1429:   }

    1431:   PetscFree(rtmp);

    1433:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1434:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1435:   C->assembled           = PETSC_TRUE;

    1437:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1438:   /* Flop Count from inverting diagonal blocks */
    1439:   SSE_SCOPE_END;
    1440:   return(0);
    1441: }

    1445: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat C,Mat A,const MatFactorInfo *info)
    1446: {
    1447:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    1449:   int            i,j,n = a->mbs;
    1450:   unsigned short *bj = (unsigned short*)(b->j),*bjtmp,*pj;
    1451:   unsigned int   row;
    1452:   int            *ajtmpold,nz,*bi=b->i;
    1453:   int            *diag_offset = b->diag,*ai=a->i,*aj=a->j;
    1454:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    1455:   MatScalar      *ba    = b->a,*aa = a->a;
    1456:   int            nonzero=0;
    1457: /*    int            nonzero=0,colscale = 16; */
    1458:   PetscBool pivotinblocks = b->pivotinblocks;
    1459:   PetscReal shift         = info->shiftamount;

    1462:   SSE_SCOPE_BEGIN;

    1464:   if ((unsigned long)aa%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer aa is not 16 byte aligned.  SSE will not work.");
    1465:   if ((unsigned long)ba%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer ba is not 16 byte aligned.  SSE will not work.");
    1466:   PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);
    1467:   if ((unsigned long)rtmp%16!=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_BADPTR,"Pointer rtmp is not 16 byte aligned.  SSE will not work.");
    1468: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1469: /*      colscale = 4; */
    1470: /*    } */
    1471:   if ((unsigned long)bj==(unsigned long)aj) {
    1472:     return(MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(C));
    1473:   }

    1475:   for (i=0; i<n; i++) {
    1476:     nz    = bi[i+1] - bi[i];
    1477:     bjtmp = bj + bi[i];
    1478:     /* zero out the 4x4 block accumulators */
    1479:     /* zero out one register */
    1480:     XOR_PS(XMM7,XMM7);
    1481:     for  (j=0; j<nz; j++) {
    1482:       x = rtmp+16*((unsigned int)bjtmp[j]);
    1483: /*        x = rtmp+4*bjtmp[j]; */
    1484:       SSE_INLINE_BEGIN_1(x)
    1485:       /* Copy zero register to memory locations */
    1486:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1487:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    1488:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    1489:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    1490:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    1491:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    1492:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    1493:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1494:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    1495:       SSE_INLINE_END_1;
    1496:     }
    1497:     /* load in initial (unfactored row) */
    1498:     nz       = ai[i+1] - ai[i];
    1499:     ajtmpold = aj + ai[i];
    1500:     v        = aa + 16*ai[i];
    1501:     for (j=0; j<nz; j++) {
    1502:       x = rtmp+16*ajtmpold[j];
    1503: /*        x = rtmp+colscale*ajtmpold[j]; */
    1504:       /* Copy v block into x block */
    1505:       SSE_INLINE_BEGIN_2(v,x)
    1506:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1507:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1508:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    1510:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    1511:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    1513:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    1514:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    1516:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    1517:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    1519:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    1520:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    1522:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    1523:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    1525:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    1526:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    1528:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1529:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1530:       SSE_INLINE_END_2;

    1532:       v += 16;
    1533:     }
    1534: /*      row = (*bjtmp++)/4; */
    1535:     row = (unsigned int)(*bjtmp++);
    1536:     while (row < i) {
    1537:       pc = rtmp + 16*row;
    1538:       SSE_INLINE_BEGIN_1(pc)
    1539:       /* Load block from lower triangle */
    1540:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1541:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1542:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    1544:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    1545:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    1547:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    1548:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    1550:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    1551:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    1553:       /* Compare block to zero block */

    1555:       SSE_COPY_PS(XMM4,XMM7)
    1556:       SSE_CMPNEQ_PS(XMM4,XMM0)

    1558:       SSE_COPY_PS(XMM5,XMM7)
    1559:       SSE_CMPNEQ_PS(XMM5,XMM1)

    1561:       SSE_COPY_PS(XMM6,XMM7)
    1562:       SSE_CMPNEQ_PS(XMM6,XMM2)

    1564:       SSE_CMPNEQ_PS(XMM7,XMM3)

    1566:       /* Reduce the comparisons to one SSE register */
    1567:       SSE_OR_PS(XMM6,XMM7)
    1568:       SSE_OR_PS(XMM5,XMM4)
    1569:       SSE_OR_PS(XMM5,XMM6)
    1570:       SSE_INLINE_END_1;

    1572:       /* Reduce the one SSE register to an integer register for branching */
    1573:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1574:       MOVEMASK(nonzero,XMM5);

    1576:       /* If block is nonzero ... */
    1577:       if (nonzero) {
    1578:         pv = ba + 16*diag_offset[row];
    1579:         PREFETCH_L1(&pv[16]);
    1580:         pj = bj + diag_offset[row] + 1;

    1582:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1583:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1584:         /* but the diagonal was inverted already */
    1585:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1587:         SSE_INLINE_BEGIN_2(pv,pc)
    1588:         /* Column 0, product is accumulated in XMM4 */
    1589:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    1590:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    1591:         SSE_MULT_PS(XMM4,XMM0)

    1593:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    1594:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1595:         SSE_MULT_PS(XMM5,XMM1)
    1596:         SSE_ADD_PS(XMM4,XMM5)

    1598:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    1599:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1600:         SSE_MULT_PS(XMM6,XMM2)
    1601:         SSE_ADD_PS(XMM4,XMM6)

    1603:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    1604:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1605:         SSE_MULT_PS(XMM7,XMM3)
    1606:         SSE_ADD_PS(XMM4,XMM7)

    1608:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    1609:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

    1611:         /* Column 1, product is accumulated in XMM5 */
    1612:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
    1613:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1614:         SSE_MULT_PS(XMM5,XMM0)

    1616:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    1617:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1618:         SSE_MULT_PS(XMM6,XMM1)
    1619:         SSE_ADD_PS(XMM5,XMM6)

    1621:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    1622:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1623:         SSE_MULT_PS(XMM7,XMM2)
    1624:         SSE_ADD_PS(XMM5,XMM7)

    1626:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    1627:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1628:         SSE_MULT_PS(XMM6,XMM3)
    1629:         SSE_ADD_PS(XMM5,XMM6)

    1631:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    1632:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    1634:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

    1636:         /* Column 2, product is accumulated in XMM6 */
    1637:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
    1638:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1639:         SSE_MULT_PS(XMM6,XMM0)

    1641:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    1642:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1643:         SSE_MULT_PS(XMM7,XMM1)
    1644:         SSE_ADD_PS(XMM6,XMM7)

    1646:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    1647:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1648:         SSE_MULT_PS(XMM7,XMM2)
    1649:         SSE_ADD_PS(XMM6,XMM7)

    1651:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    1652:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1653:         SSE_MULT_PS(XMM7,XMM3)
    1654:         SSE_ADD_PS(XMM6,XMM7)

    1656:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    1657:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1659:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1660:         /* Column 3, product is accumulated in XMM0 */
    1661:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
    1662:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1663:         SSE_MULT_PS(XMM0,XMM7)

    1665:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    1666:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1667:         SSE_MULT_PS(XMM1,XMM7)
    1668:         SSE_ADD_PS(XMM0,XMM1)

    1670:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    1671:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    1672:         SSE_MULT_PS(XMM1,XMM2)
    1673:         SSE_ADD_PS(XMM0,XMM1)

    1675:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    1676:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1677:         SSE_MULT_PS(XMM3,XMM7)
    1678:         SSE_ADD_PS(XMM0,XMM3)

    1680:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    1681:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    1683:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1684:         /* This is code to be maintained and read by humans afterall. */
    1685:         /* Copy Multiplier Col 3 into XMM3 */
    1686:         SSE_COPY_PS(XMM3,XMM0)
    1687:         /* Copy Multiplier Col 2 into XMM2 */
    1688:         SSE_COPY_PS(XMM2,XMM6)
    1689:         /* Copy Multiplier Col 1 into XMM1 */
    1690:         SSE_COPY_PS(XMM1,XMM5)
    1691:         /* Copy Multiplier Col 0 into XMM0 */
    1692:         SSE_COPY_PS(XMM0,XMM4)
    1693:         SSE_INLINE_END_2;

    1695:         /* Update the row: */
    1696:         nz  = bi[row+1] - diag_offset[row] - 1;
    1697:         pv += 16;
    1698:         for (j=0; j<nz; j++) {
    1699:           PREFETCH_L1(&pv[16]);
    1700:           x = rtmp + 16*((unsigned int)pj[j]);
    1701: /*            x = rtmp + 4*pj[j]; */

    1703:           /* X:=X-M*PV, One column at a time */
    1704:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1705:           SSE_INLINE_BEGIN_2(x,pv)
    1706:           /* Load First Column of X*/
    1707:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1708:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1710:           /* Matrix-Vector Product: */
    1711:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
    1712:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1713:           SSE_MULT_PS(XMM5,XMM0)
    1714:           SSE_SUB_PS(XMM4,XMM5)

    1716:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    1717:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1718:           SSE_MULT_PS(XMM6,XMM1)
    1719:           SSE_SUB_PS(XMM4,XMM6)

    1721:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    1722:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1723:           SSE_MULT_PS(XMM7,XMM2)
    1724:           SSE_SUB_PS(XMM4,XMM7)

    1726:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    1727:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1728:           SSE_MULT_PS(XMM5,XMM3)
    1729:           SSE_SUB_PS(XMM4,XMM5)

    1731:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1732:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1734:           /* Second Column */
    1735:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1736:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1738:           /* Matrix-Vector Product: */
    1739:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
    1740:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1741:           SSE_MULT_PS(XMM6,XMM0)
    1742:           SSE_SUB_PS(XMM5,XMM6)

    1744:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    1745:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1746:           SSE_MULT_PS(XMM7,XMM1)
    1747:           SSE_SUB_PS(XMM5,XMM7)

    1749:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    1750:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1751:           SSE_MULT_PS(XMM4,XMM2)
    1752:           SSE_SUB_PS(XMM5,XMM4)

    1754:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    1755:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1756:           SSE_MULT_PS(XMM6,XMM3)
    1757:           SSE_SUB_PS(XMM5,XMM6)

    1759:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1760:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1762:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    1764:           /* Third Column */
    1765:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1766:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1768:           /* Matrix-Vector Product: */
    1769:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
    1770:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1771:           SSE_MULT_PS(XMM7,XMM0)
    1772:           SSE_SUB_PS(XMM6,XMM7)

    1774:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    1775:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1776:           SSE_MULT_PS(XMM4,XMM1)
    1777:           SSE_SUB_PS(XMM6,XMM4)

    1779:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    1780:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1781:           SSE_MULT_PS(XMM5,XMM2)
    1782:           SSE_SUB_PS(XMM6,XMM5)

    1784:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    1785:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1786:           SSE_MULT_PS(XMM7,XMM3)
    1787:           SSE_SUB_PS(XMM6,XMM7)

    1789:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1790:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1792:           /* Fourth Column */
    1793:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1794:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    1796:           /* Matrix-Vector Product: */
    1797:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
    1798:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1799:           SSE_MULT_PS(XMM5,XMM0)
    1800:           SSE_SUB_PS(XMM4,XMM5)

    1802:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    1803:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1804:           SSE_MULT_PS(XMM6,XMM1)
    1805:           SSE_SUB_PS(XMM4,XMM6)

    1807:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    1808:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1809:           SSE_MULT_PS(XMM7,XMM2)
    1810:           SSE_SUB_PS(XMM4,XMM7)

    1812:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    1813:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1814:           SSE_MULT_PS(XMM5,XMM3)
    1815:           SSE_SUB_PS(XMM4,XMM5)

    1817:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1818:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    1819:           SSE_INLINE_END_2;
    1820:           pv += 16;
    1821:         }
    1822:         PetscLogFlops(128.0*nz+112.0);
    1823:       }
    1824:       row = (unsigned int)(*bjtmp++);
    1825: /*        row = (*bjtmp++)/4; */
    1826: /*        bjtmp++; */
    1827:     }
    1828:     /* finished row so stick it into b->a */
    1829:     pv = ba + 16*bi[i];
    1830:     pj = bj + bi[i];
    1831:     nz = bi[i+1] - bi[i];

    1833:     /* Copy x block back into pv block */
    1834:     for (j=0; j<nz; j++) {
    1835:       x = rtmp+16*((unsigned int)pj[j]);
    1836: /*        x  = rtmp+4*pj[j]; */

    1838:       SSE_INLINE_BEGIN_2(x,pv)
    1839:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1840:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
    1841:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

    1843:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    1844:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    1846:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    1847:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    1849:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    1850:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    1852:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    1853:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    1855:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    1856:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1858:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1859:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    1861:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1862:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1863:       SSE_INLINE_END_2;
    1864:       pv += 16;
    1865:     }
    1866:     /* invert diagonal block */
    1867:     w = ba + 16*diag_offset[i];
    1868:     if (pivotinblocks) {
    1869:       PetscKernel_A_gets_inverse_A_4(w,shift);
    1870:     } else {
    1871:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    1872:     }
    1873: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    1874:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1875:   }

    1877:   PetscFree(rtmp);

    1879:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1880:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1881:   C->assembled           = PETSC_TRUE;

    1883:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1884:   /* Flop Count from inverting diagonal blocks */
    1885:   SSE_SCOPE_END;
    1886:   return(0);
    1887: }

    1889: #endif