Date: 2022-03-04T17:37:49+00:00

Actual source code: baijfact11.c

      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: */
     12: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_inplace(Mat C,Mat A,const MatFactorInfo *info)
     13: {
     14:   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
     15:   IS             isrow = b->row,isicol = b->icol;
     17:   const PetscInt *r,*ic;
     18:   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
     19:   PetscInt       *ajtmpold,*ajtmp,nz,row;
     20:   PetscInt       *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
     21:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
     22:   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
     23:   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
     24:   MatScalar      p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
     25:   MatScalar      m13,m14,m15,m16;
     26:   MatScalar      *ba           = b->a,*aa = a->a;
     27:   PetscBool      pivotinblocks = b->pivotinblocks;
     28:   PetscReal      shift         = info->shiftamount;
     29:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

     32:   ISGetIndices(isrow,&r);
     33:   ISGetIndices(isicol,&ic);
     34:   PetscMalloc1(16*(n+1),&rtmp);
     35:   allowzeropivot = PetscNot(A->erroriffailure);

     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,allowzeropivot,&zeropivotdetected);
    145:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    146:     } else {
    147:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    148:     }
    149:   }

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

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

    159:   PetscLogFlops(1.333333333333*4*4*4*b->mbs); /* from inverting diagonal blocks */
    160:   return(0);
    161: }

    163: /* MatLUFactorNumeric_SeqBAIJ_4 -
    164:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    165:        PetscKernel_A_gets_A_times_B()
    166:        PetscKernel_A_gets_A_minus_B_times_C()
    167:        PetscKernel_A_gets_inverse_A()
    168: */

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

    186:   allowzeropivot = PetscNot(A->erroriffailure);
    187:   ISGetIndices(isrow,&r);
    188:   ISGetIndices(isicol,&ic);

    190:   if (info->shifttype == MAT_SHIFT_NONE) {
    191:     shift = 0;
    192:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    193:     shift = info->shiftamount;
    194:   }

    196:   /* generate work space needed by the factorization */
    197:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    198:   PetscArrayzero(rtmp,bs2*n);

    200:   for (i=0; i<n; i++) {
    201:     /* zero rtmp */
    202:     /* L part */
    203:     nz    = bi[i+1] - bi[i];
    204:     bjtmp = bj + bi[i];
    205:     for  (j=0; j<nz; j++) {
    206:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    207:     }

    209:     /* U part */
    210:     nz    = bdiag[i]-bdiag[i+1];
    211:     bjtmp = bj + bdiag[i+1]+1;
    212:     for  (j=0; j<nz; j++) {
    213:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    214:     }

    216:     /* load in initial (unfactored row) */
    217:     nz    = ai[r[i]+1] - ai[r[i]];
    218:     ajtmp = aj + ai[r[i]];
    219:     v     = aa + bs2*ai[r[i]];
    220:     for (j=0; j<nz; j++) {
    221:       PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2);
    222:     }

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

    241:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    242:         pv = b->a + bs2*(bdiag[row+1]+1);
    243:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
    244:         for (j=0; j<nz; j++) {
    245:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    246:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    247:           v    = rtmp + bs2*pj[j];
    248:           PetscKernel_A_gets_A_minus_B_times_C_4(v,pc,pv);
    249:           pv  += bs2;
    250:         }
    251:         PetscLogFlops(128.0*nz+112); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    252:       }
    253:     }

    255:     /* finished row so stick it into b->a */
    256:     /* L part */
    257:     pv = b->a + bs2*bi[i];
    258:     pj = b->j + bi[i];
    259:     nz = bi[i+1] - bi[i];
    260:     for (j=0; j<nz; j++) {
    261:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    262:     }

    264:     /* Mark diagonal and invert diagonal for simpler triangular solves */
    265:     pv   = b->a + bs2*bdiag[i];
    266:     pj   = b->j + bdiag[i];
    267:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
    268:     PetscKernel_A_gets_inverse_A_4(pv,shift,allowzeropivot,&zeropivotdetected);
    269:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    271:     /* U part */
    272:     pv = b->a + bs2*(bdiag[i+1]+1);
    273:     pj = b->j + bdiag[i+1]+1;
    274:     nz = bdiag[i] - bdiag[i+1] - 1;
    275:     for (j=0; j<nz; j++) {
    276:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    277:     }
    278:   }

    280:   PetscFree2(rtmp,mwork);
    281:   ISRestoreIndices(isicol,&ic);
    282:   ISRestoreIndices(isrow,&r);

    284:   C->ops->solve          = MatSolve_SeqBAIJ_4;
    285:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
    286:   C->assembled           = PETSC_TRUE;

    288:   PetscLogFlops(1.333333333333*4*4*4*n); /* from inverting diagonal blocks */
    289:   return(0);
    290: }

    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;
    310:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

    313:   allowzeropivot = PetscNot(A->erroriffailure);
    314:   PetscMalloc1(16*(n+1),&rtmp);

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

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

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

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

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

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

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

    400:           pv += 16;
    401:         }
    402:         PetscLogFlops(128.0*nz+112.0);
    403:       }
    404:       row = *ajtmp++;
    405:     }
    406:     /* finished row so stick it into b->a */
    407:     pv = ba + 16*bi[i];
    408:     pj = bj + bi[i];
    409:     nz = bi[i+1] - bi[i];
    410:     for (j=0; j<nz; j++) {
    411:       x      = rtmp+16*pj[j];
    412:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    413:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    414:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
    415:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
    416:       pv    += 16;
    417:     }
    418:     /* invert diagonal block */
    419:     w = ba + 16*diag_offset[i];
    420:     if (pivotinblocks) {
    421:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    422:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    423:     } else {
    424:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    425:     }
    426:   }

    428:   PetscFree(rtmp);

    430:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_inplace;
    431:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace;
    432:   C->assembled           = PETSC_TRUE;

    434:   PetscLogFlops(1.333333333333*4*4*4*b->mbs); /* from inverting diagonal blocks */
    435:   return(0);
    436: }

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

    456:   allowzeropivot = PetscNot(A->erroriffailure);

    458:   /* generate work space needed by the factorization */
    459:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    460:   PetscArrayzero(rtmp,bs2*n);

    462:   if (info->shifttype == MAT_SHIFT_NONE) {
    463:     shift = 0;
    464:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    465:     shift = info->shiftamount;
    466:   }

    468:   for (i=0; i<n; i++) {
    469:     /* zero rtmp */
    470:     /* L part */
    471:     nz    = bi[i+1] - bi[i];
    472:     bjtmp = bj + bi[i];
    473:     for  (j=0; j<nz; j++) {
    474:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    475:     }

    477:     /* U part */
    478:     nz    = bdiag[i] - bdiag[i+1];
    479:     bjtmp = bj + bdiag[i+1]+1;
    480:     for  (j=0; j<nz; j++) {
    481:       PetscArrayzero(rtmp+bs2*bjtmp[j],bs2);
    482:     }

    484:     /* load in initial (unfactored row) */
    485:     nz    = ai[i+1] - ai[i];
    486:     ajtmp = aj + ai[i];
    487:     v     = aa + bs2*ai[i];
    488:     for (j=0; j<nz; j++) {
    489:       PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2);
    490:     }

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

    509:         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
    510:         pv = b->a + bs2*(bdiag[row+1]+1);
    511:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
    512:         for (j=0; j<nz; j++) {
    513:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    514:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    515:           v    = rtmp + bs2*pj[j];
    516:           PetscKernel_A_gets_A_minus_B_times_C_4(v,pc,pv);
    517:           pv  += bs2;
    518:         }
    519:         PetscLogFlops(128.0*nz+112); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    520:       }
    521:     }

    523:     /* finished row so stick it into b->a */
    524:     /* L part */
    525:     pv = b->a + bs2*bi[i];
    526:     pj = b->j + bi[i];
    527:     nz = bi[i+1] - bi[i];
    528:     for (j=0; j<nz; j++) {
    529:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    530:     }

    532:     /* Mark diagonal and invert diagonal for simpler triangular solves */
    533:     pv   = b->a + bs2*bdiag[i];
    534:     pj   = b->j + bdiag[i];
    535:     PetscArraycpy(pv,rtmp+bs2*pj[0],bs2);
    536:     PetscKernel_A_gets_inverse_A_4(pv,shift,allowzeropivot,&zeropivotdetected);
    537:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    539:     /* U part */
    540:     pv = b->a + bs2*(bdiag[i+1]+1);
    541:     pj = b->j + bdiag[i+1]+1;
    542:     nz = bdiag[i] - bdiag[i+1] - 1;
    543:     for (j=0; j<nz; j++) {
    544:       PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2);
    545:     }
    546:   }
    547:   PetscFree2(rtmp,mwork);

    549:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
    550:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
    551:   C->assembled           = PETSC_TRUE;

    553:   PetscLogFlops(1.333333333333*4*4*4*n); /* from inverting diagonal blocks */
    554:   return(0);
    555: }

    557: #if defined(PETSC_HAVE_SSE)

    559: #include PETSC_HAVE_SSE

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

    579:   allowzeropivot = PetscNot(A->erroriffailure);
    580:   SSE_SCOPE_BEGIN;

    582:   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.");
    583:   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.");
    584:   PetscMalloc1(16*(n+1),&rtmp);
    585:   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.");
    586: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    587: /*      colscale = 4; */
    588: /*    } */
    589:   for (i=0; i<n; i++) {
    590:     nz    = bi[i+1] - bi[i];
    591:     bjtmp = bj + bi[i];
    592:     /* zero out the 4x4 block accumulators */
    593:     /* zero out one register */
    594:     XOR_PS(XMM7,XMM7);
    595:     for  (j=0; j<nz; j++) {
    596:       x = rtmp+16*bjtmp[j];
    597: /*        x = rtmp+4*bjtmp[j]; */
    598:       SSE_INLINE_BEGIN_1(x)
    599:       /* Copy zero register to memory locations */
    600:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    601:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    602:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    603:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    604:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    605:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    606:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    607:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    608:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    609:       SSE_INLINE_END_1;
    610:     }
    611:     /* load in initial (unfactored row) */
    612:     nz       = ai[i+1] - ai[i];
    613:     ajtmpold = aj + ai[i];
    614:     v        = aa + 16*ai[i];
    615:     for (j=0; j<nz; j++) {
    616:       x = rtmp+16*ajtmpold[j];
    617: /*        x = rtmp+colscale*ajtmpold[j]; */
    618:       /* Copy v block into x block */
    619:       SSE_INLINE_BEGIN_2(v,x)
    620:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    621:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    622:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    624:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    625:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    627:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    628:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    630:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    631:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    633:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    634:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    636:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    637:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    639:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    640:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    642:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    643:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    644:       SSE_INLINE_END_2;

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

    658:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    659:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    661:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    662:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    664:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    665:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    667:       /* Compare block to zero block */

    669:       SSE_COPY_PS(XMM4,XMM7)
    670:       SSE_CMPNEQ_PS(XMM4,XMM0)

    672:       SSE_COPY_PS(XMM5,XMM7)
    673:       SSE_CMPNEQ_PS(XMM5,XMM1)

    675:       SSE_COPY_PS(XMM6,XMM7)
    676:       SSE_CMPNEQ_PS(XMM6,XMM2)

    678:       SSE_CMPNEQ_PS(XMM7,XMM3)

    680:       /* Reduce the comparisons to one SSE register */
    681:       SSE_OR_PS(XMM6,XMM7)
    682:       SSE_OR_PS(XMM5,XMM4)
    683:       SSE_OR_PS(XMM5,XMM6)
    684:       SSE_INLINE_END_1;

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

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

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

    701:         SSE_INLINE_BEGIN_2(pv,pc)
    702:         /* Column 0, product is accumulated in XMM4 */
    703:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    704:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    705:         SSE_MULT_PS(XMM4,XMM0)

    707:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    708:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    709:         SSE_MULT_PS(XMM5,XMM1)
    710:         SSE_ADD_PS(XMM4,XMM5)

    712:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    713:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    714:         SSE_MULT_PS(XMM6,XMM2)
    715:         SSE_ADD_PS(XMM4,XMM6)

    717:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    718:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    719:         SSE_MULT_PS(XMM7,XMM3)
    720:         SSE_ADD_PS(XMM4,XMM7)

    722:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    723:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

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

    730:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    731:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    732:         SSE_MULT_PS(XMM6,XMM1)
    733:         SSE_ADD_PS(XMM5,XMM6)

    735:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    736:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    737:         SSE_MULT_PS(XMM7,XMM2)
    738:         SSE_ADD_PS(XMM5,XMM7)

    740:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    741:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    742:         SSE_MULT_PS(XMM6,XMM3)
    743:         SSE_ADD_PS(XMM5,XMM6)

    745:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    746:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    748:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

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

    755:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    756:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    757:         SSE_MULT_PS(XMM7,XMM1)
    758:         SSE_ADD_PS(XMM6,XMM7)

    760:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    761:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    762:         SSE_MULT_PS(XMM7,XMM2)
    763:         SSE_ADD_PS(XMM6,XMM7)

    765:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    766:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    767:         SSE_MULT_PS(XMM7,XMM3)
    768:         SSE_ADD_PS(XMM6,XMM7)

    770:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    771:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

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

    779:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    780:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    781:         SSE_MULT_PS(XMM1,XMM7)
    782:         SSE_ADD_PS(XMM0,XMM1)

    784:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    785:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    786:         SSE_MULT_PS(XMM1,XMM2)
    787:         SSE_ADD_PS(XMM0,XMM1)

    789:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    790:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    791:         SSE_MULT_PS(XMM3,XMM7)
    792:         SSE_ADD_PS(XMM0,XMM3)

    794:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    795:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

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

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

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

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

    830:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    831:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    832:           SSE_MULT_PS(XMM6,XMM1)
    833:           SSE_SUB_PS(XMM4,XMM6)

    835:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    836:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    837:           SSE_MULT_PS(XMM7,XMM2)
    838:           SSE_SUB_PS(XMM4,XMM7)

    840:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    841:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    842:           SSE_MULT_PS(XMM5,XMM3)
    843:           SSE_SUB_PS(XMM4,XMM5)

    845:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    846:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    848:           /* Second Column */
    849:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    850:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

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

    858:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    859:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    860:           SSE_MULT_PS(XMM7,XMM1)
    861:           SSE_SUB_PS(XMM5,XMM7)

    863:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    864:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    865:           SSE_MULT_PS(XMM4,XMM2)
    866:           SSE_SUB_PS(XMM5,XMM4)

    868:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    869:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    870:           SSE_MULT_PS(XMM6,XMM3)
    871:           SSE_SUB_PS(XMM5,XMM6)

    873:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    874:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    876:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    878:           /* Third Column */
    879:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    880:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

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

    888:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    889:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    890:           SSE_MULT_PS(XMM4,XMM1)
    891:           SSE_SUB_PS(XMM6,XMM4)

    893:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    894:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    895:           SSE_MULT_PS(XMM5,XMM2)
    896:           SSE_SUB_PS(XMM6,XMM5)

    898:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    899:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    900:           SSE_MULT_PS(XMM7,XMM3)
    901:           SSE_SUB_PS(XMM6,XMM7)

    903:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    904:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    906:           /* Fourth Column */
    907:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    908:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

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

    916:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    917:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    918:           SSE_MULT_PS(XMM6,XMM1)
    919:           SSE_SUB_PS(XMM4,XMM6)

    921:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    922:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    923:           SSE_MULT_PS(XMM7,XMM2)
    924:           SSE_SUB_PS(XMM4,XMM7)

    926:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    927:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    928:           SSE_MULT_PS(XMM5,XMM3)
    929:           SSE_SUB_PS(XMM4,XMM5)

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

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

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

    956:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    957:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    959:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    960:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    962:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    963:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    965:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    966:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    968:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    969:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    971:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    972:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    974:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    975:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    976:       SSE_INLINE_END_2;
    977:       pv += 16;
    978:     }
    979:     /* invert diagonal block */
    980:     w = ba + 16*diag_offset[i];
    981:     if (pivotinblocks) {
    982:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    983:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    984:     } else {
    985:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    986:     }
    987: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    988:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    989:   }

    991:   PetscFree(rtmp);

    993:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    994:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    995:   C->assembled           = PETSC_TRUE;

    997:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    998:   /* Flop Count from inverting diagonal blocks */
    999:   SSE_SCOPE_END;
    1000:   return(0);
    1001: }

    1003: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(Mat C)
    1004: {
    1005:   Mat            A  =C;
    1006:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    1008:   int            i,j,n = a->mbs;
    1009:   unsigned short *bj = (unsigned short*)(b->j),*bjtmp,*pj;
    1010:   unsigned short *aj = (unsigned short*)(a->j),*ajtmp;
    1011:   unsigned int   row;
    1012:   int            nz,*bi=b->i;
    1013:   int            *diag_offset = b->diag,*ai=a->i;
    1014:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    1015:   MatScalar      *ba    = b->a,*aa = a->a;
    1016:   int            nonzero=0;
    1017:   PetscBool      pivotinblocks = b->pivotinblocks;
    1018:   PetscReal      shift = info->shiftamount;
    1019:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

    1022:   allowzeropivot = PetscNot(A->erroriffailure);
    1023:   SSE_SCOPE_BEGIN;

    1025:   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.");
    1026:   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.");
    1027:   PetscMalloc1(16*(n+1),&rtmp);
    1028:   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.");
    1029: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1030: /*      colscale = 4; */
    1031: /*    } */

    1033:   for (i=0; i<n; i++) {
    1034:     nz    = bi[i+1] - bi[i];
    1035:     bjtmp = bj + bi[i];
    1036:     /* zero out the 4x4 block accumulators */
    1037:     /* zero out one register */
    1038:     XOR_PS(XMM7,XMM7);
    1039:     for  (j=0; j<nz; j++) {
    1040:       x = rtmp+16*((unsigned int)bjtmp[j]);
    1041: /*        x = rtmp+4*bjtmp[j]; */
    1042:       SSE_INLINE_BEGIN_1(x)
    1043:       /* Copy zero register to memory locations */
    1044:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1045:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    1046:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    1047:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    1048:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    1049:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    1050:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    1051:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1052:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    1053:       SSE_INLINE_END_1;
    1054:     }
    1055:     /* load in initial (unfactored row) */
    1056:     nz    = ai[i+1] - ai[i];
    1057:     ajtmp = aj + ai[i];
    1058:     v     = aa + 16*ai[i];
    1059:     for (j=0; j<nz; j++) {
    1060:       x = rtmp+16*((unsigned int)ajtmp[j]);
    1061: /*        x = rtmp+colscale*ajtmp[j]; */
    1062:       /* Copy v block into x block */
    1063:       SSE_INLINE_BEGIN_2(v,x)
    1064:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1065:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1066:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    1068:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    1069:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    1071:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    1072:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    1074:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    1075:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    1077:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    1078:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    1080:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    1081:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    1083:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    1084:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    1086:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1087:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1088:       SSE_INLINE_END_2;

    1090:       v += 16;
    1091:     }
    1092: /*      row = (*bjtmp++)/4; */
    1093:     row = (unsigned int)(*bjtmp++);
    1094:     while (row < i) {
    1095:       pc = rtmp + 16*row;
    1096:       SSE_INLINE_BEGIN_1(pc)
    1097:       /* Load block from lower triangle */
    1098:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1099:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1100:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    1102:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    1103:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    1105:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    1106:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    1108:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    1109:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    1111:       /* Compare block to zero block */

    1113:       SSE_COPY_PS(XMM4,XMM7)
    1114:       SSE_CMPNEQ_PS(XMM4,XMM0)

    1116:       SSE_COPY_PS(XMM5,XMM7)
    1117:       SSE_CMPNEQ_PS(XMM5,XMM1)

    1119:       SSE_COPY_PS(XMM6,XMM7)
    1120:       SSE_CMPNEQ_PS(XMM6,XMM2)

    1122:       SSE_CMPNEQ_PS(XMM7,XMM3)

    1124:       /* Reduce the comparisons to one SSE register */
    1125:       SSE_OR_PS(XMM6,XMM7)
    1126:       SSE_OR_PS(XMM5,XMM4)
    1127:       SSE_OR_PS(XMM5,XMM6)
    1128:       SSE_INLINE_END_1;

    1130:       /* Reduce the one SSE register to an integer register for branching */
    1131:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1132:       MOVEMASK(nonzero,XMM5);

    1134:       /* If block is nonzero ... */
    1135:       if (nonzero) {
    1136:         pv = ba + 16*diag_offset[row];
    1137:         PREFETCH_L1(&pv[16]);
    1138:         pj = bj + diag_offset[row] + 1;

    1140:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1141:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1142:         /* but the diagonal was inverted already */
    1143:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1145:         SSE_INLINE_BEGIN_2(pv,pc)
    1146:         /* Column 0, product is accumulated in XMM4 */
    1147:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    1148:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    1149:         SSE_MULT_PS(XMM4,XMM0)

    1151:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    1152:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1153:         SSE_MULT_PS(XMM5,XMM1)
    1154:         SSE_ADD_PS(XMM4,XMM5)

    1156:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    1157:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1158:         SSE_MULT_PS(XMM6,XMM2)
    1159:         SSE_ADD_PS(XMM4,XMM6)

    1161:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    1162:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1163:         SSE_MULT_PS(XMM7,XMM3)
    1164:         SSE_ADD_PS(XMM4,XMM7)

    1166:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    1167:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

    1169:         /* Column 1, product is accumulated in XMM5 */
    1170:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
    1171:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1172:         SSE_MULT_PS(XMM5,XMM0)

    1174:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    1175:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1176:         SSE_MULT_PS(XMM6,XMM1)
    1177:         SSE_ADD_PS(XMM5,XMM6)

    1179:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    1180:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1181:         SSE_MULT_PS(XMM7,XMM2)
    1182:         SSE_ADD_PS(XMM5,XMM7)

    1184:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    1185:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1186:         SSE_MULT_PS(XMM6,XMM3)
    1187:         SSE_ADD_PS(XMM5,XMM6)

    1189:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    1190:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    1192:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

    1194:         /* Column 2, product is accumulated in XMM6 */
    1195:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
    1196:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1197:         SSE_MULT_PS(XMM6,XMM0)

    1199:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    1200:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1201:         SSE_MULT_PS(XMM7,XMM1)
    1202:         SSE_ADD_PS(XMM6,XMM7)

    1204:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    1205:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1206:         SSE_MULT_PS(XMM7,XMM2)
    1207:         SSE_ADD_PS(XMM6,XMM7)

    1209:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    1210:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1211:         SSE_MULT_PS(XMM7,XMM3)
    1212:         SSE_ADD_PS(XMM6,XMM7)

    1214:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    1215:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1217:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1218:         /* Column 3, product is accumulated in XMM0 */
    1219:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
    1220:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1221:         SSE_MULT_PS(XMM0,XMM7)

    1223:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    1224:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1225:         SSE_MULT_PS(XMM1,XMM7)
    1226:         SSE_ADD_PS(XMM0,XMM1)

    1228:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    1229:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    1230:         SSE_MULT_PS(XMM1,XMM2)
    1231:         SSE_ADD_PS(XMM0,XMM1)

    1233:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    1234:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1235:         SSE_MULT_PS(XMM3,XMM7)
    1236:         SSE_ADD_PS(XMM0,XMM3)

    1238:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    1239:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    1241:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1242:         /* This is code to be maintained and read by humans afterall. */
    1243:         /* Copy Multiplier Col 3 into XMM3 */
    1244:         SSE_COPY_PS(XMM3,XMM0)
    1245:         /* Copy Multiplier Col 2 into XMM2 */
    1246:         SSE_COPY_PS(XMM2,XMM6)
    1247:         /* Copy Multiplier Col 1 into XMM1 */
    1248:         SSE_COPY_PS(XMM1,XMM5)
    1249:         /* Copy Multiplier Col 0 into XMM0 */
    1250:         SSE_COPY_PS(XMM0,XMM4)
    1251:         SSE_INLINE_END_2;

    1253:         /* Update the row: */
    1254:         nz  = bi[row+1] - diag_offset[row] - 1;
    1255:         pv += 16;
    1256:         for (j=0; j<nz; j++) {
    1257:           PREFETCH_L1(&pv[16]);
    1258:           x = rtmp + 16*((unsigned int)pj[j]);
    1259: /*            x = rtmp + 4*pj[j]; */

    1261:           /* X:=X-M*PV, One column at a time */
    1262:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1263:           SSE_INLINE_BEGIN_2(x,pv)
    1264:           /* Load First Column of X*/
    1265:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1266:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1268:           /* Matrix-Vector Product: */
    1269:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
    1270:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1271:           SSE_MULT_PS(XMM5,XMM0)
    1272:           SSE_SUB_PS(XMM4,XMM5)

    1274:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    1275:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1276:           SSE_MULT_PS(XMM6,XMM1)
    1277:           SSE_SUB_PS(XMM4,XMM6)

    1279:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    1280:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1281:           SSE_MULT_PS(XMM7,XMM2)
    1282:           SSE_SUB_PS(XMM4,XMM7)

    1284:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    1285:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1286:           SSE_MULT_PS(XMM5,XMM3)
    1287:           SSE_SUB_PS(XMM4,XMM5)

    1289:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1290:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1292:           /* Second Column */
    1293:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1294:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1296:           /* Matrix-Vector Product: */
    1297:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
    1298:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1299:           SSE_MULT_PS(XMM6,XMM0)
    1300:           SSE_SUB_PS(XMM5,XMM6)

    1302:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    1303:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1304:           SSE_MULT_PS(XMM7,XMM1)
    1305:           SSE_SUB_PS(XMM5,XMM7)

    1307:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    1308:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1309:           SSE_MULT_PS(XMM4,XMM2)
    1310:           SSE_SUB_PS(XMM5,XMM4)

    1312:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    1313:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1314:           SSE_MULT_PS(XMM6,XMM3)
    1315:           SSE_SUB_PS(XMM5,XMM6)

    1317:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1318:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1320:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    1322:           /* Third Column */
    1323:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1324:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1326:           /* Matrix-Vector Product: */
    1327:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
    1328:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1329:           SSE_MULT_PS(XMM7,XMM0)
    1330:           SSE_SUB_PS(XMM6,XMM7)

    1332:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    1333:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1334:           SSE_MULT_PS(XMM4,XMM1)
    1335:           SSE_SUB_PS(XMM6,XMM4)

    1337:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    1338:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1339:           SSE_MULT_PS(XMM5,XMM2)
    1340:           SSE_SUB_PS(XMM6,XMM5)

    1342:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    1343:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1344:           SSE_MULT_PS(XMM7,XMM3)
    1345:           SSE_SUB_PS(XMM6,XMM7)

    1347:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1348:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1350:           /* Fourth Column */
    1351:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1352:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    1354:           /* Matrix-Vector Product: */
    1355:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
    1356:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1357:           SSE_MULT_PS(XMM5,XMM0)
    1358:           SSE_SUB_PS(XMM4,XMM5)

    1360:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    1361:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1362:           SSE_MULT_PS(XMM6,XMM1)
    1363:           SSE_SUB_PS(XMM4,XMM6)

    1365:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    1366:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1367:           SSE_MULT_PS(XMM7,XMM2)
    1368:           SSE_SUB_PS(XMM4,XMM7)

    1370:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    1371:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1372:           SSE_MULT_PS(XMM5,XMM3)
    1373:           SSE_SUB_PS(XMM4,XMM5)

    1375:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1376:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    1377:           SSE_INLINE_END_2;
    1378:           pv += 16;
    1379:         }
    1380:         PetscLogFlops(128.0*nz+112.0);
    1381:       }
    1382:       row = (unsigned int)(*bjtmp++);
    1383: /*        row = (*bjtmp++)/4; */
    1384: /*        bjtmp++; */
    1385:     }
    1386:     /* finished row so stick it into b->a */
    1387:     pv = ba + 16*bi[i];
    1388:     pj = bj + bi[i];
    1389:     nz = bi[i+1] - bi[i];

    1391:     /* Copy x block back into pv block */
    1392:     for (j=0; j<nz; j++) {
    1393:       x = rtmp+16*((unsigned int)pj[j]);
    1394: /*        x  = rtmp+4*pj[j]; */

    1396:       SSE_INLINE_BEGIN_2(x,pv)
    1397:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1398:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
    1399:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

    1401:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    1402:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    1404:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    1405:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    1407:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    1408:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    1410:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    1411:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    1413:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    1414:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1416:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1417:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    1419:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1420:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1421:       SSE_INLINE_END_2;
    1422:       pv += 16;
    1423:     }
    1424:     /* invert diagonal block */
    1425:     w = ba + 16*diag_offset[i];
    1426:     if (pivotinblocks) {
    1427:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    1428:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1429:     } else {
    1430:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    1431:     }
    1432:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1433:   }

    1435:   PetscFree(rtmp);

    1437:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1438:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1439:   C->assembled           = PETSC_TRUE;

    1441:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1442:   /* Flop Count from inverting diagonal blocks */
    1443:   SSE_SCOPE_END;
    1444:   return(0);
    1445: }

    1447: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat C,Mat A,const MatFactorInfo *info)
    1448: {
    1449:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    1451:   int            i,j,n = a->mbs;
    1452:   unsigned short *bj = (unsigned short*)(b->j),*bjtmp,*pj;
    1453:   unsigned int   row;
    1454:   int            *ajtmpold,nz,*bi=b->i;
    1455:   int            *diag_offset = b->diag,*ai=a->i,*aj=a->j;
    1456:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    1457:   MatScalar      *ba    = b->a,*aa = a->a;
    1458:   int            nonzero=0;
    1459:   PetscBool      pivotinblocks = b->pivotinblocks;
    1460:   PetscReal      shift = info->shiftamount;
    1461:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

    1464:   allowzeropivot = PetscNot(A->erroriffailure);
    1465:   SSE_SCOPE_BEGIN;

    1467:   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.");
    1468:   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.");
    1469:   PetscMalloc1(16*(n+1),&rtmp);
    1470:   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.");
    1471: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1472: /*      colscale = 4; */
    1473: /*    } */
    1474:   if ((unsigned long)bj==(unsigned long)aj) {
    1475:     return(MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(C));
    1476:   }

    1478:   for (i=0; i<n; i++) {
    1479:     nz    = bi[i+1] - bi[i];
    1480:     bjtmp = bj + bi[i];
    1481:     /* zero out the 4x4 block accumulators */
    1482:     /* zero out one register */
    1483:     XOR_PS(XMM7,XMM7);
    1484:     for  (j=0; j<nz; j++) {
    1485:       x = rtmp+16*((unsigned int)bjtmp[j]);
    1486: /*        x = rtmp+4*bjtmp[j]; */
    1487:       SSE_INLINE_BEGIN_1(x)
    1488:       /* Copy zero register to memory locations */
    1489:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1490:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    1491:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    1492:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    1493:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    1494:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    1495:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    1496:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1497:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    1498:       SSE_INLINE_END_1;
    1499:     }
    1500:     /* load in initial (unfactored row) */
    1501:     nz       = ai[i+1] - ai[i];
    1502:     ajtmpold = aj + ai[i];
    1503:     v        = aa + 16*ai[i];
    1504:     for (j=0; j<nz; j++) {
    1505:       x = rtmp+16*ajtmpold[j];
    1506: /*        x = rtmp+colscale*ajtmpold[j]; */
    1507:       /* Copy v block into x block */
    1508:       SSE_INLINE_BEGIN_2(v,x)
    1509:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1510:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1511:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    1513:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    1514:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    1516:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    1517:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    1519:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    1520:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    1522:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    1523:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    1525:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    1526:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    1528:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    1529:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    1531:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1532:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1533:       SSE_INLINE_END_2;

    1535:       v += 16;
    1536:     }
    1537: /*      row = (*bjtmp++)/4; */
    1538:     row = (unsigned int)(*bjtmp++);
    1539:     while (row < i) {
    1540:       pc = rtmp + 16*row;
    1541:       SSE_INLINE_BEGIN_1(pc)
    1542:       /* Load block from lower triangle */
    1543:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1544:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1545:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    1547:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    1548:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    1550:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    1551:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    1553:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    1554:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    1556:       /* Compare block to zero block */

    1558:       SSE_COPY_PS(XMM4,XMM7)
    1559:       SSE_CMPNEQ_PS(XMM4,XMM0)

    1561:       SSE_COPY_PS(XMM5,XMM7)
    1562:       SSE_CMPNEQ_PS(XMM5,XMM1)

    1564:       SSE_COPY_PS(XMM6,XMM7)
    1565:       SSE_CMPNEQ_PS(XMM6,XMM2)

    1567:       SSE_CMPNEQ_PS(XMM7,XMM3)

    1569:       /* Reduce the comparisons to one SSE register */
    1570:       SSE_OR_PS(XMM6,XMM7)
    1571:       SSE_OR_PS(XMM5,XMM4)
    1572:       SSE_OR_PS(XMM5,XMM6)
    1573:       SSE_INLINE_END_1;

    1575:       /* Reduce the one SSE register to an integer register for branching */
    1576:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1577:       MOVEMASK(nonzero,XMM5);

    1579:       /* If block is nonzero ... */
    1580:       if (nonzero) {
    1581:         pv = ba + 16*diag_offset[row];
    1582:         PREFETCH_L1(&pv[16]);
    1583:         pj = bj + diag_offset[row] + 1;

    1585:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1586:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1587:         /* but the diagonal was inverted already */
    1588:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1590:         SSE_INLINE_BEGIN_2(pv,pc)
    1591:         /* Column 0, product is accumulated in XMM4 */
    1592:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    1593:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    1594:         SSE_MULT_PS(XMM4,XMM0)

    1596:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    1597:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1598:         SSE_MULT_PS(XMM5,XMM1)
    1599:         SSE_ADD_PS(XMM4,XMM5)

    1601:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    1602:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1603:         SSE_MULT_PS(XMM6,XMM2)
    1604:         SSE_ADD_PS(XMM4,XMM6)

    1606:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    1607:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1608:         SSE_MULT_PS(XMM7,XMM3)
    1609:         SSE_ADD_PS(XMM4,XMM7)

    1611:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    1612:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

    1614:         /* Column 1, product is accumulated in XMM5 */
    1615:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
    1616:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1617:         SSE_MULT_PS(XMM5,XMM0)

    1619:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    1620:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1621:         SSE_MULT_PS(XMM6,XMM1)
    1622:         SSE_ADD_PS(XMM5,XMM6)

    1624:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    1625:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1626:         SSE_MULT_PS(XMM7,XMM2)
    1627:         SSE_ADD_PS(XMM5,XMM7)

    1629:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    1630:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1631:         SSE_MULT_PS(XMM6,XMM3)
    1632:         SSE_ADD_PS(XMM5,XMM6)

    1634:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    1635:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    1637:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

    1639:         /* Column 2, product is accumulated in XMM6 */
    1640:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
    1641:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1642:         SSE_MULT_PS(XMM6,XMM0)

    1644:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    1645:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1646:         SSE_MULT_PS(XMM7,XMM1)
    1647:         SSE_ADD_PS(XMM6,XMM7)

    1649:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    1650:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1651:         SSE_MULT_PS(XMM7,XMM2)
    1652:         SSE_ADD_PS(XMM6,XMM7)

    1654:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    1655:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1656:         SSE_MULT_PS(XMM7,XMM3)
    1657:         SSE_ADD_PS(XMM6,XMM7)

    1659:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    1660:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1662:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1663:         /* Column 3, product is accumulated in XMM0 */
    1664:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
    1665:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1666:         SSE_MULT_PS(XMM0,XMM7)

    1668:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    1669:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1670:         SSE_MULT_PS(XMM1,XMM7)
    1671:         SSE_ADD_PS(XMM0,XMM1)

    1673:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    1674:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    1675:         SSE_MULT_PS(XMM1,XMM2)
    1676:         SSE_ADD_PS(XMM0,XMM1)

    1678:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    1679:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1680:         SSE_MULT_PS(XMM3,XMM7)
    1681:         SSE_ADD_PS(XMM0,XMM3)

    1683:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    1684:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    1686:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1687:         /* This is code to be maintained and read by humans afterall. */
    1688:         /* Copy Multiplier Col 3 into XMM3 */
    1689:         SSE_COPY_PS(XMM3,XMM0)
    1690:         /* Copy Multiplier Col 2 into XMM2 */
    1691:         SSE_COPY_PS(XMM2,XMM6)
    1692:         /* Copy Multiplier Col 1 into XMM1 */
    1693:         SSE_COPY_PS(XMM1,XMM5)
    1694:         /* Copy Multiplier Col 0 into XMM0 */
    1695:         SSE_COPY_PS(XMM0,XMM4)
    1696:         SSE_INLINE_END_2;

    1698:         /* Update the row: */
    1699:         nz  = bi[row+1] - diag_offset[row] - 1;
    1700:         pv += 16;
    1701:         for (j=0; j<nz; j++) {
    1702:           PREFETCH_L1(&pv[16]);
    1703:           x = rtmp + 16*((unsigned int)pj[j]);
    1704: /*            x = rtmp + 4*pj[j]; */

    1706:           /* X:=X-M*PV, One column at a time */
    1707:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1708:           SSE_INLINE_BEGIN_2(x,pv)
    1709:           /* Load First Column of X*/
    1710:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1711:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1713:           /* Matrix-Vector Product: */
    1714:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
    1715:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1716:           SSE_MULT_PS(XMM5,XMM0)
    1717:           SSE_SUB_PS(XMM4,XMM5)

    1719:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    1720:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1721:           SSE_MULT_PS(XMM6,XMM1)
    1722:           SSE_SUB_PS(XMM4,XMM6)

    1724:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    1725:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1726:           SSE_MULT_PS(XMM7,XMM2)
    1727:           SSE_SUB_PS(XMM4,XMM7)

    1729:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    1730:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1731:           SSE_MULT_PS(XMM5,XMM3)
    1732:           SSE_SUB_PS(XMM4,XMM5)

    1734:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1735:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1737:           /* Second Column */
    1738:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1739:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1741:           /* Matrix-Vector Product: */
    1742:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
    1743:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1744:           SSE_MULT_PS(XMM6,XMM0)
    1745:           SSE_SUB_PS(XMM5,XMM6)

    1747:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    1748:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1749:           SSE_MULT_PS(XMM7,XMM1)
    1750:           SSE_SUB_PS(XMM5,XMM7)

    1752:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    1753:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1754:           SSE_MULT_PS(XMM4,XMM2)
    1755:           SSE_SUB_PS(XMM5,XMM4)

    1757:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    1758:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1759:           SSE_MULT_PS(XMM6,XMM3)
    1760:           SSE_SUB_PS(XMM5,XMM6)

    1762:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1763:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1765:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    1767:           /* Third Column */
    1768:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1769:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1771:           /* Matrix-Vector Product: */
    1772:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
    1773:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1774:           SSE_MULT_PS(XMM7,XMM0)
    1775:           SSE_SUB_PS(XMM6,XMM7)

    1777:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    1778:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1779:           SSE_MULT_PS(XMM4,XMM1)
    1780:           SSE_SUB_PS(XMM6,XMM4)

    1782:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    1783:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1784:           SSE_MULT_PS(XMM5,XMM2)
    1785:           SSE_SUB_PS(XMM6,XMM5)

    1787:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    1788:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1789:           SSE_MULT_PS(XMM7,XMM3)
    1790:           SSE_SUB_PS(XMM6,XMM7)

    1792:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1793:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1795:           /* Fourth Column */
    1796:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1797:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    1799:           /* Matrix-Vector Product: */
    1800:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
    1801:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1802:           SSE_MULT_PS(XMM5,XMM0)
    1803:           SSE_SUB_PS(XMM4,XMM5)

    1805:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    1806:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1807:           SSE_MULT_PS(XMM6,XMM1)
    1808:           SSE_SUB_PS(XMM4,XMM6)

    1810:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    1811:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1812:           SSE_MULT_PS(XMM7,XMM2)
    1813:           SSE_SUB_PS(XMM4,XMM7)

    1815:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    1816:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1817:           SSE_MULT_PS(XMM5,XMM3)
    1818:           SSE_SUB_PS(XMM4,XMM5)

    1820:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1821:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    1822:           SSE_INLINE_END_2;
    1823:           pv += 16;
    1824:         }
    1825:         PetscLogFlops(128.0*nz+112.0);
    1826:       }
    1827:       row = (unsigned int)(*bjtmp++);
    1828: /*        row = (*bjtmp++)/4; */
    1829: /*        bjtmp++; */
    1830:     }
    1831:     /* finished row so stick it into b->a */
    1832:     pv = ba + 16*bi[i];
    1833:     pj = bj + bi[i];
    1834:     nz = bi[i+1] - bi[i];

    1836:     /* Copy x block back into pv block */
    1837:     for (j=0; j<nz; j++) {
    1838:       x = rtmp+16*((unsigned int)pj[j]);
    1839: /*        x  = rtmp+4*pj[j]; */

    1841:       SSE_INLINE_BEGIN_2(x,pv)
    1842:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1843:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
    1844:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

    1846:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    1847:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    1849:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    1850:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    1852:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    1853:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    1855:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    1856:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    1858:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    1859:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1861:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1862:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    1864:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1865:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1866:       SSE_INLINE_END_2;
    1867:       pv += 16;
    1868:     }
    1869:     /* invert diagonal block */
    1870:     w = ba + 16*diag_offset[i];
    1871:     if (pivotinblocks) {
    1872:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,,&zeropivotdetected);
    1873:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1874:     } else {
    1875:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    1876:     }
    1877: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    1878:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1879:   }

    1881:   PetscFree(rtmp);

    1883:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1884:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1885:   C->assembled           = PETSC_TRUE;

    1887:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1888:   /* Flop Count from inverting diagonal blocks */
    1889:   SSE_SCOPE_END;
    1890:   return(0);
    1891: }

    1893: #endif