Actual source code: baijfact11.c
petsc-3.7.1 2016-05-15
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      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;
     31:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

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

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

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

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

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

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

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

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

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

    125:           pv += 16;
    126:         }
    127:         PetscLogFlops(128.0*nz+112.0);
    128:       }
    129:       row = *ajtmp++;
    130:     }
    131:     /* finished row so stick it into b->a */
    132:     pv = ba + 16*bi[i];
    133:     pj = bj + bi[i];
    134:     nz = bi[i+1] - bi[i];
    135:     for (j=0; j<nz; j++) {
    136:       x      = rtmp+16*pj[j];
    137:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    138:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    139:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
    140:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
    141:       pv    += 16;
    142:     }
    143:     /* invert diagonal block */
    144:     w = ba + 16*diag_offset[i];
    145:     if (pivotinblocks) {
    146:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    147:       if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    148:     } else {
    149:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    150:     }
    151:   }

    153:   PetscFree(rtmp);
    154:   ISRestoreIndices(isicol,&ic);
    155:   ISRestoreIndices(isrow,&r);

    157:   C->ops->solve          = MatSolve_SeqBAIJ_4_inplace;
    158:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_inplace;
    159:   C->assembled           = PETSC_TRUE;

    161:   PetscLogFlops(1.333333333333*4*4*4*b->mbs); /* from inverting diagonal blocks */
    162:   return(0);
    163: }

    165: /* MatLUFactorNumeric_SeqBAIJ_4 -
    166:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    167:        PetscKernel_A_gets_A_times_B()
    168:        PetscKernel_A_gets_A_minus_B_times_C()
    169:        PetscKernel_A_gets_inverse_A()
    170: */

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

    190:   allowzeropivot = PetscNot(A->erroriffailure);
    191:   ISGetIndices(isrow,&r);
    192:   ISGetIndices(isicol,&ic);

    194:   if (info->shifttype == MAT_SHIFT_NONE) {
    195:     shift = 0;
    196:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    197:     shift = info->shiftamount;
    198:   }

    200:   /* generate work space needed by the factorization */
    201:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    202:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    204:   for (i=0; i<n; i++) {
    205:     /* zero rtmp */
    206:     /* L part */
    207:     nz    = bi[i+1] - bi[i];
    208:     bjtmp = bj + bi[i];
    209:     for  (j=0; j<nz; j++) {
    210:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    211:     }

    213:     /* U part */
    214:     nz    = bdiag[i]-bdiag[i+1];
    215:     bjtmp = bj + bdiag[i+1]+1;
    216:     for  (j=0; j<nz; j++) {
    217:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    218:     }

    220:     /* load in initial (unfactored row) */
    221:     nz    = ai[r[i]+1] - ai[r[i]];
    222:     ajtmp = aj + ai[r[i]];
    223:     v     = aa + bs2*ai[r[i]];
    224:     for (j=0; j<nz; j++) {
    225:       PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
    226:     }

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

    245:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
    246:         pv = b->a + bs2*(bdiag[row+1]+1);
    247:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
    248:         for (j=0; j<nz; j++) {
    249:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    250:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    251:           v    = rtmp + bs2*pj[j];
    252:           PetscKernel_A_gets_A_minus_B_times_C_4(v,pc,pv);
    253:           pv  += bs2;
    254:         }
    255:         PetscLogFlops(128*nz+112); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    256:       }
    257:     }

    259:     /* finished row so stick it into b->a */
    260:     /* L part */
    261:     pv = b->a + bs2*bi[i];
    262:     pj = b->j + bi[i];
    263:     nz = bi[i+1] - bi[i];
    264:     for (j=0; j<nz; j++) {
    265:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    266:     }

    268:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    269:     pv   = b->a + bs2*bdiag[i];
    270:     pj   = b->j + bdiag[i];
    271:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    272:     PetscKernel_A_gets_inverse_A_4(pv,shift,allowzeropivot,&zeropivotdetected);
    273:     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    275:     /* U part */
    276:     pv = b->a + bs2*(bdiag[i+1]+1);
    277:     pj = b->j + bdiag[i+1]+1;
    278:     nz = bdiag[i] - bdiag[i+1] - 1;
    279:     for (j=0; j<nz; j++) {
    280:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    281:     }
    282:   }

    284:   PetscFree2(rtmp,mwork);
    285:   ISRestoreIndices(isicol,&ic);
    286:   ISRestoreIndices(isrow,&r);

    288:   C->ops->solve          = MatSolve_SeqBAIJ_4;
    289:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
    290:   C->assembled           = PETSC_TRUE;

    292:   PetscLogFlops(1.333333333333*4*4*4*n); /* from inverting diagonal blocks */
    293:   return(0);
    294: }

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

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

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

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

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

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

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

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

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

    406:           pv += 16;
    407:         }
    408:         PetscLogFlops(128.0*nz+112.0);
    409:       }
    410:       row = *ajtmp++;
    411:     }
    412:     /* finished row so stick it into b->a */
    413:     pv = ba + 16*bi[i];
    414:     pj = bj + bi[i];
    415:     nz = bi[i+1] - bi[i];
    416:     for (j=0; j<nz; j++) {
    417:       x      = rtmp+16*pj[j];
    418:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
    419:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
    420:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
    421:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
    422:       pv    += 16;
    423:     }
    424:     /* invert diagonal block */
    425:     w = ba + 16*diag_offset[i];
    426:     if (pivotinblocks) {
    427:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    428:       if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    429:     } else {
    430:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    431:     }
    432:   }

    434:   PetscFree(rtmp);

    436:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_inplace;
    437:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace;
    438:   C->assembled           = PETSC_TRUE;

    440:   PetscLogFlops(1.333333333333*4*4*4*b->mbs); /* from inverting diagonal blocks */
    441:   return(0);
    442: }

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

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

    466:   /* generate work space needed by the factorization */
    467:   PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
    468:   PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));

    470:   if (info->shifttype == MAT_SHIFT_NONE) {
    471:     shift = 0;
    472:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    473:     shift = info->shiftamount;
    474:   }

    476:   for (i=0; i<n; i++) {
    477:     /* zero rtmp */
    478:     /* L part */
    479:     nz    = bi[i+1] - bi[i];
    480:     bjtmp = bj + bi[i];
    481:     for  (j=0; j<nz; j++) {
    482:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    483:     }

    485:     /* U part */
    486:     nz    = bdiag[i] - bdiag[i+1];
    487:     bjtmp = bj + bdiag[i+1]+1;
    488:     for  (j=0; j<nz; j++) {
    489:       PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
    490:     }

    492:     /* load in initial (unfactored row) */
    493:     nz    = ai[i+1] - ai[i];
    494:     ajtmp = aj + ai[i];
    495:     v     = aa + bs2*ai[i];
    496:     for (j=0; j<nz; j++) {
    497:       PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
    498:     }

    500:     /* elimination */
    501:     bjtmp = bj + bi[i];
    502:     nzL   = bi[i+1] - bi[i];
    503:     for (k=0; k < nzL; k++) {
    504:       row = bjtmp[k];
    505:       pc  = rtmp + bs2*row;
    506:       for (flg=0,j=0; j<bs2; j++) {
    507:         if (pc[j]!=0.0) {
    508:           flg = 1;
    509:           break;
    510:         }
    511:       }
    512:       if (flg) {
    513:         pv = b->a + bs2*bdiag[row];
    514:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    515:         PetscKernel_A_gets_A_times_B_4(pc,pv,mwork);

    517:         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
    518:         pv = b->a + bs2*(bdiag[row+1]+1);
    519:         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
    520:         for (j=0; j<nz; j++) {
    521:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    522:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    523:           v    = rtmp + bs2*pj[j];
    524:           PetscKernel_A_gets_A_minus_B_times_C_4(v,pc,pv);
    525:           pv  += bs2;
    526:         }
    527:         PetscLogFlops(128*nz+112); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    528:       }
    529:     }

    531:     /* finished row so stick it into b->a */
    532:     /* L part */
    533:     pv = b->a + bs2*bi[i];
    534:     pj = b->j + bi[i];
    535:     nz = bi[i+1] - bi[i];
    536:     for (j=0; j<nz; j++) {
    537:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    538:     }

    540:     /* Mark diagonal and invert diagonal for simplier triangular solves */
    541:     pv   = b->a + bs2*bdiag[i];
    542:     pj   = b->j + bdiag[i];
    543:     PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
    544:     PetscKernel_A_gets_inverse_A_4(pv,shift,allowzeropivot,&zeropivotdetected);
    545:     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    547:     /* U part */
    548:     pv = b->a + bs2*(bdiag[i+1]+1);
    549:     pj = b->j + bdiag[i+1]+1;
    550:     nz = bdiag[i] - bdiag[i+1] - 1;
    551:     for (j=0; j<nz; j++) {
    552:       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
    553:     }
    554:   }
    555:   PetscFree2(rtmp,mwork);

    557:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
    558:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
    559:   C->assembled           = PETSC_TRUE;

    561:   PetscLogFlops(1.333333333333*4*4*4*n); /* from inverting diagonal blocks */
    562:   return(0);
    563: }

    565: #if defined(PETSC_HAVE_SSE)

    567: #include PETSC_HAVE_SSE

    569: /* SSE Version for when blocks are 4 by 4 Using natural ordering */
    572: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE(Mat B,Mat A,const MatFactorInfo *info)
    573: {
    574:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    576:   int            i,j,n = a->mbs;
    577:   int            *bj = b->j,*bjtmp,*pj;
    578:   int            row;
    579:   int            *ajtmpold,nz,*bi=b->i;
    580:   int            *diag_offset = b->diag,*ai=a->i,*aj=a->j;
    581:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    582:   MatScalar      *ba    = b->a,*aa = a->a;
    583:   int            nonzero=0;
    584:   PetscBool      pivotinblocks = b->pivotinblocks;
    585:   PetscReal      shift         = info->shiftamount;
    586:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

    589:   allowzeropivot = PetscNot(A->erroriffailure);
    590:   SSE_SCOPE_BEGIN;

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

    634:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    635:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    637:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    638:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    640:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    641:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    643:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    644:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    646:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    647:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    649:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    650:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    652:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    653:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    654:       SSE_INLINE_END_2;

    656:       v += 16;
    657:     }
    658: /*      row = (*bjtmp++)/4; */
    659:     row = *bjtmp++;
    660:     while (row < i) {
    661:       pc = rtmp + 16*row;
    662:       SSE_INLINE_BEGIN_1(pc)
    663:       /* Load block from lower triangle */
    664:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    665:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    666:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    668:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    669:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    671:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    672:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    674:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    675:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    677:       /* Compare block to zero block */

    679:       SSE_COPY_PS(XMM4,XMM7)
    680:       SSE_CMPNEQ_PS(XMM4,XMM0)

    682:       SSE_COPY_PS(XMM5,XMM7)
    683:       SSE_CMPNEQ_PS(XMM5,XMM1)

    685:       SSE_COPY_PS(XMM6,XMM7)
    686:       SSE_CMPNEQ_PS(XMM6,XMM2)

    688:       SSE_CMPNEQ_PS(XMM7,XMM3)

    690:       /* Reduce the comparisons to one SSE register */
    691:       SSE_OR_PS(XMM6,XMM7)
    692:       SSE_OR_PS(XMM5,XMM4)
    693:       SSE_OR_PS(XMM5,XMM6)
    694:       SSE_INLINE_END_1;

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

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

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

    711:         SSE_INLINE_BEGIN_2(pv,pc)
    712:         /* Column 0, product is accumulated in XMM4 */
    713:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    714:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    715:         SSE_MULT_PS(XMM4,XMM0)

    717:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    718:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    719:         SSE_MULT_PS(XMM5,XMM1)
    720:         SSE_ADD_PS(XMM4,XMM5)

    722:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    723:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    724:         SSE_MULT_PS(XMM6,XMM2)
    725:         SSE_ADD_PS(XMM4,XMM6)

    727:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    728:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    729:         SSE_MULT_PS(XMM7,XMM3)
    730:         SSE_ADD_PS(XMM4,XMM7)

    732:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    733:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

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

    740:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    741:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    742:         SSE_MULT_PS(XMM6,XMM1)
    743:         SSE_ADD_PS(XMM5,XMM6)

    745:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    746:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    747:         SSE_MULT_PS(XMM7,XMM2)
    748:         SSE_ADD_PS(XMM5,XMM7)

    750:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    751:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    752:         SSE_MULT_PS(XMM6,XMM3)
    753:         SSE_ADD_PS(XMM5,XMM6)

    755:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    756:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    758:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

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

    765:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    766:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    767:         SSE_MULT_PS(XMM7,XMM1)
    768:         SSE_ADD_PS(XMM6,XMM7)

    770:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    771:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    772:         SSE_MULT_PS(XMM7,XMM2)
    773:         SSE_ADD_PS(XMM6,XMM7)

    775:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    776:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    777:         SSE_MULT_PS(XMM7,XMM3)
    778:         SSE_ADD_PS(XMM6,XMM7)

    780:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    781:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

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

    789:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    790:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    791:         SSE_MULT_PS(XMM1,XMM7)
    792:         SSE_ADD_PS(XMM0,XMM1)

    794:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    795:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    796:         SSE_MULT_PS(XMM1,XMM2)
    797:         SSE_ADD_PS(XMM0,XMM1)

    799:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    800:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    801:         SSE_MULT_PS(XMM3,XMM7)
    802:         SSE_ADD_PS(XMM0,XMM3)

    804:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    805:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    807:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    808:         /* This is code to be maintained and read by humans afterall. */
    809:         /* Copy Multiplier Col 3 into XMM3 */
    810:         SSE_COPY_PS(XMM3,XMM0)
    811:         /* Copy Multiplier Col 2 into XMM2 */
    812:         SSE_COPY_PS(XMM2,XMM6)
    813:         /* Copy Multiplier Col 1 into XMM1 */
    814:         SSE_COPY_PS(XMM1,XMM5)
    815:         /* Copy Multiplier Col 0 into XMM0 */
    816:         SSE_COPY_PS(XMM0,XMM4)
    817:         SSE_INLINE_END_2;

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

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

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

    840:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    841:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    842:           SSE_MULT_PS(XMM6,XMM1)
    843:           SSE_SUB_PS(XMM4,XMM6)

    845:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    846:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    847:           SSE_MULT_PS(XMM7,XMM2)
    848:           SSE_SUB_PS(XMM4,XMM7)

    850:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    851:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    852:           SSE_MULT_PS(XMM5,XMM3)
    853:           SSE_SUB_PS(XMM4,XMM5)

    855:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    856:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    858:           /* Second Column */
    859:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    860:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

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

    868:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    869:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    870:           SSE_MULT_PS(XMM7,XMM1)
    871:           SSE_SUB_PS(XMM5,XMM7)

    873:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    874:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    875:           SSE_MULT_PS(XMM4,XMM2)
    876:           SSE_SUB_PS(XMM5,XMM4)

    878:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    879:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    880:           SSE_MULT_PS(XMM6,XMM3)
    881:           SSE_SUB_PS(XMM5,XMM6)

    883:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    884:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    886:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    888:           /* Third Column */
    889:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    890:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

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

    898:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    899:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    900:           SSE_MULT_PS(XMM4,XMM1)
    901:           SSE_SUB_PS(XMM6,XMM4)

    903:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    904:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    905:           SSE_MULT_PS(XMM5,XMM2)
    906:           SSE_SUB_PS(XMM6,XMM5)

    908:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    909:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    910:           SSE_MULT_PS(XMM7,XMM3)
    911:           SSE_SUB_PS(XMM6,XMM7)

    913:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    914:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    916:           /* Fourth Column */
    917:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    918:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

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

    926:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    927:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    928:           SSE_MULT_PS(XMM6,XMM1)
    929:           SSE_SUB_PS(XMM4,XMM6)

    931:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    932:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    933:           SSE_MULT_PS(XMM7,XMM2)
    934:           SSE_SUB_PS(XMM4,XMM7)

    936:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    937:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    938:           SSE_MULT_PS(XMM5,XMM3)
    939:           SSE_SUB_PS(XMM4,XMM5)

    941:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    942:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    943:           SSE_INLINE_END_2;
    944:           pv += 16;
    945:         }
    946:         PetscLogFlops(128.0*nz+112.0);
    947:       }
    948:       row = *bjtmp++;
    949: /*        row = (*bjtmp++)/4; */
    950:     }
    951:     /* finished row so stick it into b->a */
    952:     pv = ba + 16*bi[i];
    953:     pj = bj + bi[i];
    954:     nz = bi[i+1] - bi[i];

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

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

    966:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    967:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    969:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    970:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    972:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    973:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    975:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    976:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    978:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    979:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    981:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    982:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    984:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    985:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    986:       SSE_INLINE_END_2;
    987:       pv += 16;
    988:     }
    989:     /* invert diagonal block */
    990:     w = ba + 16*diag_offset[i];
    991:     if (pivotinblocks) {
    992:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    993:       if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    994:     } else {
    995:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    996:     }
    997: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    998:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    999:   }

    1001:   PetscFree(rtmp);

    1003:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1004:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1005:   C->assembled           = PETSC_TRUE;

    1007:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1008:   /* Flop Count from inverting diagonal blocks */
    1009:   SSE_SCOPE_END;
    1010:   return(0);
    1011: }

    1015: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(Mat C)
    1016: {
    1017:   Mat            A  =C;
    1018:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    1020:   int            i,j,n = a->mbs;
    1021:   unsigned short *bj = (unsigned short*)(b->j),*bjtmp,*pj;
    1022:   unsigned short *aj = (unsigned short*)(a->j),*ajtmp;
    1023:   unsigned int   row;
    1024:   int            nz,*bi=b->i;
    1025:   int            *diag_offset = b->diag,*ai=a->i;
    1026:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    1027:   MatScalar      *ba    = b->a,*aa = a->a;
    1028:   int            nonzero=0;
    1029:   PetscBool      pivotinblocks = b->pivotinblocks;
    1030:   PetscReal      shift = info->shiftamount;
    1031:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

    1034:   allowzeropivot = PetscNot(A->erroriffailure);
    1035:   SSE_SCOPE_BEGIN;

    1037:   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.");
    1038:   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.");
    1039:   PetscMalloc1(16*(n+1),&rtmp);
    1040:   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.");
    1041: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1042: /*      colscale = 4; */
    1043: /*    } */

    1045:   for (i=0; i<n; i++) {
    1046:     nz    = bi[i+1] - bi[i];
    1047:     bjtmp = bj + bi[i];
    1048:     /* zero out the 4x4 block accumulators */
    1049:     /* zero out one register */
    1050:     XOR_PS(XMM7,XMM7);
    1051:     for  (j=0; j<nz; j++) {
    1052:       x = rtmp+16*((unsigned int)bjtmp[j]);
    1053: /*        x = rtmp+4*bjtmp[j]; */
    1054:       SSE_INLINE_BEGIN_1(x)
    1055:       /* Copy zero register to memory locations */
    1056:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1057:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    1058:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    1059:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    1060:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    1061:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    1062:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    1063:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1064:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    1065:       SSE_INLINE_END_1;
    1066:     }
    1067:     /* load in initial (unfactored row) */
    1068:     nz    = ai[i+1] - ai[i];
    1069:     ajtmp = aj + ai[i];
    1070:     v     = aa + 16*ai[i];
    1071:     for (j=0; j<nz; j++) {
    1072:       x = rtmp+16*((unsigned int)ajtmp[j]);
    1073: /*        x = rtmp+colscale*ajtmp[j]; */
    1074:       /* Copy v block into x block */
    1075:       SSE_INLINE_BEGIN_2(v,x)
    1076:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1077:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1078:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    1080:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    1081:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    1083:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    1084:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    1086:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    1087:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    1089:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    1090:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    1092:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    1093:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    1095:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    1096:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    1098:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1099:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1100:       SSE_INLINE_END_2;

    1102:       v += 16;
    1103:     }
    1104: /*      row = (*bjtmp++)/4; */
    1105:     row = (unsigned int)(*bjtmp++);
    1106:     while (row < i) {
    1107:       pc = rtmp + 16*row;
    1108:       SSE_INLINE_BEGIN_1(pc)
    1109:       /* Load block from lower triangle */
    1110:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1111:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1112:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    1114:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    1115:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    1117:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    1118:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    1120:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    1121:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    1123:       /* Compare block to zero block */

    1125:       SSE_COPY_PS(XMM4,XMM7)
    1126:       SSE_CMPNEQ_PS(XMM4,XMM0)

    1128:       SSE_COPY_PS(XMM5,XMM7)
    1129:       SSE_CMPNEQ_PS(XMM5,XMM1)

    1131:       SSE_COPY_PS(XMM6,XMM7)
    1132:       SSE_CMPNEQ_PS(XMM6,XMM2)

    1134:       SSE_CMPNEQ_PS(XMM7,XMM3)

    1136:       /* Reduce the comparisons to one SSE register */
    1137:       SSE_OR_PS(XMM6,XMM7)
    1138:       SSE_OR_PS(XMM5,XMM4)
    1139:       SSE_OR_PS(XMM5,XMM6)
    1140:       SSE_INLINE_END_1;

    1142:       /* Reduce the one SSE register to an integer register for branching */
    1143:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1144:       MOVEMASK(nonzero,XMM5);

    1146:       /* If block is nonzero ... */
    1147:       if (nonzero) {
    1148:         pv = ba + 16*diag_offset[row];
    1149:         PREFETCH_L1(&pv[16]);
    1150:         pj = bj + diag_offset[row] + 1;

    1152:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1153:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1154:         /* but the diagonal was inverted already */
    1155:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1157:         SSE_INLINE_BEGIN_2(pv,pc)
    1158:         /* Column 0, product is accumulated in XMM4 */
    1159:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    1160:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    1161:         SSE_MULT_PS(XMM4,XMM0)

    1163:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    1164:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1165:         SSE_MULT_PS(XMM5,XMM1)
    1166:         SSE_ADD_PS(XMM4,XMM5)

    1168:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    1169:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1170:         SSE_MULT_PS(XMM6,XMM2)
    1171:         SSE_ADD_PS(XMM4,XMM6)

    1173:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    1174:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1175:         SSE_MULT_PS(XMM7,XMM3)
    1176:         SSE_ADD_PS(XMM4,XMM7)

    1178:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    1179:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

    1181:         /* Column 1, product is accumulated in XMM5 */
    1182:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
    1183:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1184:         SSE_MULT_PS(XMM5,XMM0)

    1186:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    1187:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1188:         SSE_MULT_PS(XMM6,XMM1)
    1189:         SSE_ADD_PS(XMM5,XMM6)

    1191:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    1192:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1193:         SSE_MULT_PS(XMM7,XMM2)
    1194:         SSE_ADD_PS(XMM5,XMM7)

    1196:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    1197:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1198:         SSE_MULT_PS(XMM6,XMM3)
    1199:         SSE_ADD_PS(XMM5,XMM6)

    1201:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    1202:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    1204:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

    1206:         /* Column 2, product is accumulated in XMM6 */
    1207:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
    1208:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1209:         SSE_MULT_PS(XMM6,XMM0)

    1211:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    1212:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1213:         SSE_MULT_PS(XMM7,XMM1)
    1214:         SSE_ADD_PS(XMM6,XMM7)

    1216:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    1217:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1218:         SSE_MULT_PS(XMM7,XMM2)
    1219:         SSE_ADD_PS(XMM6,XMM7)

    1221:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    1222:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1223:         SSE_MULT_PS(XMM7,XMM3)
    1224:         SSE_ADD_PS(XMM6,XMM7)

    1226:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    1227:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1229:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1230:         /* Column 3, product is accumulated in XMM0 */
    1231:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
    1232:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1233:         SSE_MULT_PS(XMM0,XMM7)

    1235:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    1236:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1237:         SSE_MULT_PS(XMM1,XMM7)
    1238:         SSE_ADD_PS(XMM0,XMM1)

    1240:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    1241:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    1242:         SSE_MULT_PS(XMM1,XMM2)
    1243:         SSE_ADD_PS(XMM0,XMM1)

    1245:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    1246:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1247:         SSE_MULT_PS(XMM3,XMM7)
    1248:         SSE_ADD_PS(XMM0,XMM3)

    1250:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    1251:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    1253:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1254:         /* This is code to be maintained and read by humans afterall. */
    1255:         /* Copy Multiplier Col 3 into XMM3 */
    1256:         SSE_COPY_PS(XMM3,XMM0)
    1257:         /* Copy Multiplier Col 2 into XMM2 */
    1258:         SSE_COPY_PS(XMM2,XMM6)
    1259:         /* Copy Multiplier Col 1 into XMM1 */
    1260:         SSE_COPY_PS(XMM1,XMM5)
    1261:         /* Copy Multiplier Col 0 into XMM0 */
    1262:         SSE_COPY_PS(XMM0,XMM4)
    1263:         SSE_INLINE_END_2;

    1265:         /* Update the row: */
    1266:         nz  = bi[row+1] - diag_offset[row] - 1;
    1267:         pv += 16;
    1268:         for (j=0; j<nz; j++) {
    1269:           PREFETCH_L1(&pv[16]);
    1270:           x = rtmp + 16*((unsigned int)pj[j]);
    1271: /*            x = rtmp + 4*pj[j]; */

    1273:           /* X:=X-M*PV, One column at a time */
    1274:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1275:           SSE_INLINE_BEGIN_2(x,pv)
    1276:           /* Load First Column of X*/
    1277:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1278:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1280:           /* Matrix-Vector Product: */
    1281:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
    1282:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1283:           SSE_MULT_PS(XMM5,XMM0)
    1284:           SSE_SUB_PS(XMM4,XMM5)

    1286:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    1287:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1288:           SSE_MULT_PS(XMM6,XMM1)
    1289:           SSE_SUB_PS(XMM4,XMM6)

    1291:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    1292:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1293:           SSE_MULT_PS(XMM7,XMM2)
    1294:           SSE_SUB_PS(XMM4,XMM7)

    1296:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    1297:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1298:           SSE_MULT_PS(XMM5,XMM3)
    1299:           SSE_SUB_PS(XMM4,XMM5)

    1301:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1302:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1304:           /* Second Column */
    1305:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1306:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1308:           /* Matrix-Vector Product: */
    1309:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
    1310:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1311:           SSE_MULT_PS(XMM6,XMM0)
    1312:           SSE_SUB_PS(XMM5,XMM6)

    1314:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    1315:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1316:           SSE_MULT_PS(XMM7,XMM1)
    1317:           SSE_SUB_PS(XMM5,XMM7)

    1319:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    1320:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1321:           SSE_MULT_PS(XMM4,XMM2)
    1322:           SSE_SUB_PS(XMM5,XMM4)

    1324:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    1325:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1326:           SSE_MULT_PS(XMM6,XMM3)
    1327:           SSE_SUB_PS(XMM5,XMM6)

    1329:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1330:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1332:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    1334:           /* Third Column */
    1335:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1336:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1338:           /* Matrix-Vector Product: */
    1339:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
    1340:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1341:           SSE_MULT_PS(XMM7,XMM0)
    1342:           SSE_SUB_PS(XMM6,XMM7)

    1344:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    1345:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1346:           SSE_MULT_PS(XMM4,XMM1)
    1347:           SSE_SUB_PS(XMM6,XMM4)

    1349:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    1350:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1351:           SSE_MULT_PS(XMM5,XMM2)
    1352:           SSE_SUB_PS(XMM6,XMM5)

    1354:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    1355:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1356:           SSE_MULT_PS(XMM7,XMM3)
    1357:           SSE_SUB_PS(XMM6,XMM7)

    1359:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1360:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1362:           /* Fourth Column */
    1363:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1364:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    1366:           /* Matrix-Vector Product: */
    1367:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
    1368:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1369:           SSE_MULT_PS(XMM5,XMM0)
    1370:           SSE_SUB_PS(XMM4,XMM5)

    1372:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    1373:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1374:           SSE_MULT_PS(XMM6,XMM1)
    1375:           SSE_SUB_PS(XMM4,XMM6)

    1377:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    1378:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1379:           SSE_MULT_PS(XMM7,XMM2)
    1380:           SSE_SUB_PS(XMM4,XMM7)

    1382:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    1383:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1384:           SSE_MULT_PS(XMM5,XMM3)
    1385:           SSE_SUB_PS(XMM4,XMM5)

    1387:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1388:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    1389:           SSE_INLINE_END_2;
    1390:           pv += 16;
    1391:         }
    1392:         PetscLogFlops(128.0*nz+112.0);
    1393:       }
    1394:       row = (unsigned int)(*bjtmp++);
    1395: /*        row = (*bjtmp++)/4; */
    1396: /*        bjtmp++; */
    1397:     }
    1398:     /* finished row so stick it into b->a */
    1399:     pv = ba + 16*bi[i];
    1400:     pj = bj + bi[i];
    1401:     nz = bi[i+1] - bi[i];

    1403:     /* Copy x block back into pv block */
    1404:     for (j=0; j<nz; j++) {
    1405:       x = rtmp+16*((unsigned int)pj[j]);
    1406: /*        x  = rtmp+4*pj[j]; */

    1408:       SSE_INLINE_BEGIN_2(x,pv)
    1409:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1410:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
    1411:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

    1413:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    1414:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    1416:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    1417:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    1419:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    1420:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    1422:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    1423:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    1425:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    1426:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1428:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1429:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    1431:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1432:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1433:       SSE_INLINE_END_2;
    1434:       pv += 16;
    1435:     }
    1436:     /* invert diagonal block */
    1437:     w = ba + 16*diag_offset[i];
    1438:     if (pivotinblocks) {
    1439:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,&zeropivotdetected);
    1440:       if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1441:     } else {
    1442:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    1443:     }
    1444:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1445:   }

    1447:   PetscFree(rtmp);

    1449:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1450:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1451:   C->assembled           = PETSC_TRUE;

    1453:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1454:   /* Flop Count from inverting diagonal blocks */
    1455:   SSE_SCOPE_END;
    1456:   return(0);
    1457: }

    1461: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat C,Mat A,const MatFactorInfo *info)
    1462: {
    1463:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
    1465:   int            i,j,n = a->mbs;
    1466:   unsigned short *bj = (unsigned short*)(b->j),*bjtmp,*pj;
    1467:   unsigned int   row;
    1468:   int            *ajtmpold,nz,*bi=b->i;
    1469:   int            *diag_offset = b->diag,*ai=a->i,*aj=a->j;
    1470:   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
    1471:   MatScalar      *ba    = b->a,*aa = a->a;
    1472:   int            nonzero=0;
    1473:   PetscBool      pivotinblocks = b->pivotinblocks;
    1474:   PetscReal      shift = info->shiftamount;
    1475:   PetscBool      allowzeropivot,zeropivotdetected=PETSC_FALSE;

    1478:   allowzeropivot = PetscNot(A->erroriffailure);
    1479:   SSE_SCOPE_BEGIN;

    1481:   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.");
    1482:   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.");
    1483:   PetscMalloc1(16*(n+1),&rtmp);
    1484:   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.");
    1485: /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1486: /*      colscale = 4; */
    1487: /*    } */
    1488:   if ((unsigned long)bj==(unsigned long)aj) {
    1489:     return(MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(C));
    1490:   }

    1492:   for (i=0; i<n; i++) {
    1493:     nz    = bi[i+1] - bi[i];
    1494:     bjtmp = bj + bi[i];
    1495:     /* zero out the 4x4 block accumulators */
    1496:     /* zero out one register */
    1497:     XOR_PS(XMM7,XMM7);
    1498:     for  (j=0; j<nz; j++) {
    1499:       x = rtmp+16*((unsigned int)bjtmp[j]);
    1500: /*        x = rtmp+4*bjtmp[j]; */
    1501:       SSE_INLINE_BEGIN_1(x)
    1502:       /* Copy zero register to memory locations */
    1503:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1504:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
    1505:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
    1506:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
    1507:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
    1508:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
    1509:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
    1510:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1511:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
    1512:       SSE_INLINE_END_1;
    1513:     }
    1514:     /* load in initial (unfactored row) */
    1515:     nz       = ai[i+1] - ai[i];
    1516:     ajtmpold = aj + ai[i];
    1517:     v        = aa + 16*ai[i];
    1518:     for (j=0; j<nz; j++) {
    1519:       x = rtmp+16*ajtmpold[j];
    1520: /*        x = rtmp+colscale*ajtmpold[j]; */
    1521:       /* Copy v block into x block */
    1522:       SSE_INLINE_BEGIN_2(v,x)
    1523:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1524:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1525:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

    1527:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
    1528:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

    1530:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
    1531:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

    1533:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
    1534:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

    1536:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
    1537:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

    1539:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
    1540:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

    1542:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
    1543:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

    1545:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1546:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1547:       SSE_INLINE_END_2;

    1549:       v += 16;
    1550:     }
    1551: /*      row = (*bjtmp++)/4; */
    1552:     row = (unsigned int)(*bjtmp++);
    1553:     while (row < i) {
    1554:       pc = rtmp + 16*row;
    1555:       SSE_INLINE_BEGIN_1(pc)
    1556:       /* Load block from lower triangle */
    1557:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1558:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
    1559:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

    1561:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
    1562:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

    1564:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
    1565:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

    1567:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
    1568:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

    1570:       /* Compare block to zero block */

    1572:       SSE_COPY_PS(XMM4,XMM7)
    1573:       SSE_CMPNEQ_PS(XMM4,XMM0)

    1575:       SSE_COPY_PS(XMM5,XMM7)
    1576:       SSE_CMPNEQ_PS(XMM5,XMM1)

    1578:       SSE_COPY_PS(XMM6,XMM7)
    1579:       SSE_CMPNEQ_PS(XMM6,XMM2)

    1581:       SSE_CMPNEQ_PS(XMM7,XMM3)

    1583:       /* Reduce the comparisons to one SSE register */
    1584:       SSE_OR_PS(XMM6,XMM7)
    1585:       SSE_OR_PS(XMM5,XMM4)
    1586:       SSE_OR_PS(XMM5,XMM6)
    1587:       SSE_INLINE_END_1;

    1589:       /* Reduce the one SSE register to an integer register for branching */
    1590:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1591:       MOVEMASK(nonzero,XMM5);

    1593:       /* If block is nonzero ... */
    1594:       if (nonzero) {
    1595:         pv = ba + 16*diag_offset[row];
    1596:         PREFETCH_L1(&pv[16]);
    1597:         pj = bj + diag_offset[row] + 1;

    1599:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1600:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1601:         /* but the diagonal was inverted already */
    1602:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1604:         SSE_INLINE_BEGIN_2(pv,pc)
    1605:         /* Column 0, product is accumulated in XMM4 */
    1606:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
    1607:         SSE_SHUFFLE(XMM4,XMM4,0x00)
    1608:         SSE_MULT_PS(XMM4,XMM0)

    1610:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
    1611:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1612:         SSE_MULT_PS(XMM5,XMM1)
    1613:         SSE_ADD_PS(XMM4,XMM5)

    1615:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
    1616:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1617:         SSE_MULT_PS(XMM6,XMM2)
    1618:         SSE_ADD_PS(XMM4,XMM6)

    1620:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
    1621:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1622:         SSE_MULT_PS(XMM7,XMM3)
    1623:         SSE_ADD_PS(XMM4,XMM7)

    1625:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
    1626:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

    1628:         /* Column 1, product is accumulated in XMM5 */
    1629:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
    1630:         SSE_SHUFFLE(XMM5,XMM5,0x00)
    1631:         SSE_MULT_PS(XMM5,XMM0)

    1633:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
    1634:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1635:         SSE_MULT_PS(XMM6,XMM1)
    1636:         SSE_ADD_PS(XMM5,XMM6)

    1638:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
    1639:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1640:         SSE_MULT_PS(XMM7,XMM2)
    1641:         SSE_ADD_PS(XMM5,XMM7)

    1643:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
    1644:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1645:         SSE_MULT_PS(XMM6,XMM3)
    1646:         SSE_ADD_PS(XMM5,XMM6)

    1648:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
    1649:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

    1651:         SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

    1653:         /* Column 2, product is accumulated in XMM6 */
    1654:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
    1655:         SSE_SHUFFLE(XMM6,XMM6,0x00)
    1656:         SSE_MULT_PS(XMM6,XMM0)

    1658:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
    1659:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1660:         SSE_MULT_PS(XMM7,XMM1)
    1661:         SSE_ADD_PS(XMM6,XMM7)

    1663:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
    1664:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1665:         SSE_MULT_PS(XMM7,XMM2)
    1666:         SSE_ADD_PS(XMM6,XMM7)

    1668:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
    1669:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1670:         SSE_MULT_PS(XMM7,XMM3)
    1671:         SSE_ADD_PS(XMM6,XMM7)

    1673:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
    1674:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1676:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1677:         /* Column 3, product is accumulated in XMM0 */
    1678:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
    1679:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1680:         SSE_MULT_PS(XMM0,XMM7)

    1682:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
    1683:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1684:         SSE_MULT_PS(XMM1,XMM7)
    1685:         SSE_ADD_PS(XMM0,XMM1)

    1687:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
    1688:         SSE_SHUFFLE(XMM1,XMM1,0x00)
    1689:         SSE_MULT_PS(XMM1,XMM2)
    1690:         SSE_ADD_PS(XMM0,XMM1)

    1692:         SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
    1693:         SSE_SHUFFLE(XMM7,XMM7,0x00)
    1694:         SSE_MULT_PS(XMM3,XMM7)
    1695:         SSE_ADD_PS(XMM0,XMM3)

    1697:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
    1698:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

    1700:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1701:         /* This is code to be maintained and read by humans afterall. */
    1702:         /* Copy Multiplier Col 3 into XMM3 */
    1703:         SSE_COPY_PS(XMM3,XMM0)
    1704:         /* Copy Multiplier Col 2 into XMM2 */
    1705:         SSE_COPY_PS(XMM2,XMM6)
    1706:         /* Copy Multiplier Col 1 into XMM1 */
    1707:         SSE_COPY_PS(XMM1,XMM5)
    1708:         /* Copy Multiplier Col 0 into XMM0 */
    1709:         SSE_COPY_PS(XMM0,XMM4)
    1710:         SSE_INLINE_END_2;

    1712:         /* Update the row: */
    1713:         nz  = bi[row+1] - diag_offset[row] - 1;
    1714:         pv += 16;
    1715:         for (j=0; j<nz; j++) {
    1716:           PREFETCH_L1(&pv[16]);
    1717:           x = rtmp + 16*((unsigned int)pj[j]);
    1718: /*            x = rtmp + 4*pj[j]; */

    1720:           /* X:=X-M*PV, One column at a time */
    1721:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1722:           SSE_INLINE_BEGIN_2(x,pv)
    1723:           /* Load First Column of X*/
    1724:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1725:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1727:           /* Matrix-Vector Product: */
    1728:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
    1729:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1730:           SSE_MULT_PS(XMM5,XMM0)
    1731:           SSE_SUB_PS(XMM4,XMM5)

    1733:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
    1734:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1735:           SSE_MULT_PS(XMM6,XMM1)
    1736:           SSE_SUB_PS(XMM4,XMM6)

    1738:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
    1739:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1740:           SSE_MULT_PS(XMM7,XMM2)
    1741:           SSE_SUB_PS(XMM4,XMM7)

    1743:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
    1744:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1745:           SSE_MULT_PS(XMM5,XMM3)
    1746:           SSE_SUB_PS(XMM4,XMM5)

    1748:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
    1749:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

    1751:           /* Second Column */
    1752:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1753:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1755:           /* Matrix-Vector Product: */
    1756:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
    1757:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1758:           SSE_MULT_PS(XMM6,XMM0)
    1759:           SSE_SUB_PS(XMM5,XMM6)

    1761:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
    1762:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1763:           SSE_MULT_PS(XMM7,XMM1)
    1764:           SSE_SUB_PS(XMM5,XMM7)

    1766:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
    1767:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1768:           SSE_MULT_PS(XMM4,XMM2)
    1769:           SSE_SUB_PS(XMM5,XMM4)

    1771:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
    1772:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1773:           SSE_MULT_PS(XMM6,XMM3)
    1774:           SSE_SUB_PS(XMM5,XMM6)

    1776:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
    1777:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

    1779:           SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

    1781:           /* Third Column */
    1782:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1783:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1785:           /* Matrix-Vector Product: */
    1786:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
    1787:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1788:           SSE_MULT_PS(XMM7,XMM0)
    1789:           SSE_SUB_PS(XMM6,XMM7)

    1791:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
    1792:           SSE_SHUFFLE(XMM4,XMM4,0x00)
    1793:           SSE_MULT_PS(XMM4,XMM1)
    1794:           SSE_SUB_PS(XMM6,XMM4)

    1796:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
    1797:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1798:           SSE_MULT_PS(XMM5,XMM2)
    1799:           SSE_SUB_PS(XMM6,XMM5)

    1801:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
    1802:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1803:           SSE_MULT_PS(XMM7,XMM3)
    1804:           SSE_SUB_PS(XMM6,XMM7)

    1806:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
    1807:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)

    1809:           /* Fourth Column */
    1810:           SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1811:           SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

    1813:           /* Matrix-Vector Product: */
    1814:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
    1815:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1816:           SSE_MULT_PS(XMM5,XMM0)
    1817:           SSE_SUB_PS(XMM4,XMM5)

    1819:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
    1820:           SSE_SHUFFLE(XMM6,XMM6,0x00)
    1821:           SSE_MULT_PS(XMM6,XMM1)
    1822:           SSE_SUB_PS(XMM4,XMM6)

    1824:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
    1825:           SSE_SHUFFLE(XMM7,XMM7,0x00)
    1826:           SSE_MULT_PS(XMM7,XMM2)
    1827:           SSE_SUB_PS(XMM4,XMM7)

    1829:           SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
    1830:           SSE_SHUFFLE(XMM5,XMM5,0x00)
    1831:           SSE_MULT_PS(XMM5,XMM3)
    1832:           SSE_SUB_PS(XMM4,XMM5)

    1834:           SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
    1835:           SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
    1836:           SSE_INLINE_END_2;
    1837:           pv += 16;
    1838:         }
    1839:         PetscLogFlops(128.0*nz+112.0);
    1840:       }
    1841:       row = (unsigned int)(*bjtmp++);
    1842: /*        row = (*bjtmp++)/4; */
    1843: /*        bjtmp++; */
    1844:     }
    1845:     /* finished row so stick it into b->a */
    1846:     pv = ba + 16*bi[i];
    1847:     pj = bj + bi[i];
    1848:     nz = bi[i+1] - bi[i];

    1850:     /* Copy x block back into pv block */
    1851:     for (j=0; j<nz; j++) {
    1852:       x = rtmp+16*((unsigned int)pj[j]);
    1853: /*        x  = rtmp+4*pj[j]; */

    1855:       SSE_INLINE_BEGIN_2(x,pv)
    1856:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1857:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
    1858:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

    1860:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
    1861:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

    1863:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
    1864:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

    1866:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
    1867:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

    1869:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
    1870:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

    1872:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
    1873:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

    1875:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
    1876:       SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

    1878:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
    1879:       SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
    1880:       SSE_INLINE_END_2;
    1881:       pv += 16;
    1882:     }
    1883:     /* invert diagonal block */
    1884:     w = ba + 16*diag_offset[i];
    1885:     if (pivotinblocks) {
    1886:       PetscKernel_A_gets_inverse_A_4(w,shift,allowzeropivot,,&zeropivotdetected);
    1887:       if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1888:     } else {
    1889:       PetscKernel_A_gets_inverse_A_4_nopivot(w);
    1890:     }
    1891: /*      PetscKernel_A_gets_inverse_A_4_SSE(w); */
    1892:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1893:   }

    1895:   PetscFree(rtmp);

    1897:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1898:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1899:   C->assembled           = PETSC_TRUE;

    1901:   PetscLogFlops(1.333333333333*bs*bs2*b->mbs);
    1902:   /* Flop Count from inverting diagonal blocks */
    1903:   SSE_SCOPE_END;
    1904:   return(0);
    1905: }

    1907: #endif