Date: 2025-03-28T21:11:00+00:00

Actual source code: baijfact11.c

      1: /*
      2:     Factorization code for BAIJ format.
      3: */
      4: #include <../src/mat/impls/baij/seq/baij.h>
      5: #include <petsc/private/kernels/blockinvert.h>

      7: /*
      8:       Version for when blocks are 4 by 4
      9: */
     10: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_inplace(Mat C, Mat A, const MatFactorInfo *info)
     11: {
     12:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
     13:   IS              isrow = b->row, isicol = b->icol;
     14:   const PetscInt *r, *ic;
     15:   PetscInt        i, j, n = a->mbs, *bi = b->i, *bj = b->j;
     16:   PetscInt       *ajtmpold, *ajtmp, nz, row;
     17:   PetscInt       *diag_offset = b->diag, idx, *ai = a->i, *aj = a->j, *pj;
     18:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
     19:   MatScalar       p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
     20:   MatScalar       p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
     21:   MatScalar       p10, p11, p12, p13, p14, p15, p16, m10, m11, m12;
     22:   MatScalar       m13, m14, m15, m16;
     23:   MatScalar      *ba = b->a, *aa = a->a;
     24:   PetscBool       pivotinblocks = b->pivotinblocks;
     25:   PetscReal       shift         = info->shiftamount;
     26:   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;

     28:   PetscFunctionBegin;
     29:   PetscCall(ISGetIndices(isrow, &r));
     30:   PetscCall(ISGetIndices(isicol, &ic));
     31:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));
     32:   allowzeropivot = PetscNot(A->erroriffailure);

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

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

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

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

    125:         nz = bi[row + 1] - diag_offset[row] - 1;
    126:         pv += 16;
    127:         for (j = 0; j < nz; j++) {
    128:           x1  = pv[0];
    129:           x2  = pv[1];
    130:           x3  = pv[2];
    131:           x4  = pv[3];
    132:           x5  = pv[4];
    133:           x6  = pv[5];
    134:           x7  = pv[6];
    135:           x8  = pv[7];
    136:           x9  = pv[8];
    137:           x10 = pv[9];
    138:           x11 = pv[10];
    139:           x12 = pv[11];
    140:           x13 = pv[12];
    141:           x14 = pv[13];
    142:           x15 = pv[14];
    143:           x16 = pv[15];
    144:           x   = rtmp + 16 * pj[j];
    145:           x[0] -= m1 * x1 + m5 * x2 + m9 * x3 + m13 * x4;
    146:           x[1] -= m2 * x1 + m6 * x2 + m10 * x3 + m14 * x4;
    147:           x[2] -= m3 * x1 + m7 * x2 + m11 * x3 + m15 * x4;
    148:           x[3] -= m4 * x1 + m8 * x2 + m12 * x3 + m16 * x4;

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

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

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

    165:           pv += 16;
    166:         }
    167:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    168:       }
    169:       row = *ajtmp++;
    170:     }
    171:     /* finished row so stick it into b->a */
    172:     pv = ba + 16 * bi[i];
    173:     pj = bj + bi[i];
    174:     nz = bi[i + 1] - bi[i];
    175:     for (j = 0; j < nz; j++) {
    176:       x      = rtmp + 16 * pj[j];
    177:       pv[0]  = x[0];
    178:       pv[1]  = x[1];
    179:       pv[2]  = x[2];
    180:       pv[3]  = x[3];
    181:       pv[4]  = x[4];
    182:       pv[5]  = x[5];
    183:       pv[6]  = x[6];
    184:       pv[7]  = x[7];
    185:       pv[8]  = x[8];
    186:       pv[9]  = x[9];
    187:       pv[10] = x[10];
    188:       pv[11] = x[11];
    189:       pv[12] = x[12];
    190:       pv[13] = x[13];
    191:       pv[14] = x[14];
    192:       pv[15] = x[15];
    193:       pv += 16;
    194:     }
    195:     /* invert diagonal block */
    196:     w = ba + 16 * diag_offset[i];
    197:     if (pivotinblocks) {
    198:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
    199:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    200:     } else {
    201:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    202:     }
    203:   }

    205:   PetscCall(PetscFree(rtmp));
    206:   PetscCall(ISRestoreIndices(isicol, &ic));
    207:   PetscCall(ISRestoreIndices(isrow, &r));

    209:   C->ops->solve          = MatSolve_SeqBAIJ_4_inplace;
    210:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_inplace;
    211:   C->assembled           = PETSC_TRUE;

    213:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * b->mbs)); /* from inverting diagonal blocks */
    214:   PetscFunctionReturn(PETSC_SUCCESS);
    215: }

    217: /* MatLUFactorNumeric_SeqBAIJ_4 -
    218:      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
    219:        PetscKernel_A_gets_A_times_B()
    220:        PetscKernel_A_gets_A_minus_B_times_C()
    221:        PetscKernel_A_gets_inverse_A()
    222: */

    224: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4(Mat B, Mat A, const MatFactorInfo *info)
    225: {
    226:   Mat             C = B;
    227:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    228:   IS              isrow = b->row, isicol = b->icol;
    229:   const PetscInt *r, *ic;
    230:   PetscInt        i, j, k, nz, nzL, row;
    231:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
    232:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
    233:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
    234:   PetscInt        flg;
    235:   PetscReal       shift;
    236:   PetscBool       allowzeropivot, zeropivotdetected;

    238:   PetscFunctionBegin;
    239:   allowzeropivot = PetscNot(A->erroriffailure);
    240:   PetscCall(ISGetIndices(isrow, &r));
    241:   PetscCall(ISGetIndices(isicol, &ic));

    243:   if (info->shifttype == (PetscReal)MAT_SHIFT_NONE) {
    244:     shift = 0;
    245:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    246:     shift = info->shiftamount;
    247:   }

    249:   /* generate work space needed by the factorization */
    250:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
    251:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

    253:   for (i = 0; i < n; i++) {
    254:     /* zero rtmp */
    255:     /* L part */
    256:     nz    = bi[i + 1] - bi[i];
    257:     bjtmp = bj + bi[i];
    258:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    260:     /* U part */
    261:     nz    = bdiag[i] - bdiag[i + 1];
    262:     bjtmp = bj + bdiag[i + 1] + 1;
    263:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    265:     /* load in initial (unfactored row) */
    266:     nz    = ai[r[i] + 1] - ai[r[i]];
    267:     ajtmp = aj + ai[r[i]];
    268:     v     = aa + bs2 * ai[r[i]];
    269:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ic[ajtmp[j]], v + bs2 * j, bs2));

    271:     /* elimination */
    272:     bjtmp = bj + bi[i];
    273:     nzL   = bi[i + 1] - bi[i];
    274:     for (k = 0; k < nzL; k++) {
    275:       row = bjtmp[k];
    276:       pc  = rtmp + bs2 * row;
    277:       for (flg = 0, j = 0; j < bs2; j++) {
    278:         if (pc[j] != 0.0) {
    279:           flg = 1;
    280:           break;
    281:         }
    282:       }
    283:       if (flg) {
    284:         pv = b->a + bs2 * bdiag[row];
    285:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    286:         PetscCall(PetscKernel_A_gets_A_times_B_4(pc, pv, mwork));

    288:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
    289:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
    290:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
    291:         for (j = 0; j < nz; j++) {
    292:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    293:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    294:           v = rtmp + bs2 * pj[j];
    295:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_4(v, pc, pv));
    296:           pv += bs2;
    297:         }
    298:         PetscCall(PetscLogFlops(128.0 * nz + 112)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    299:       }
    300:     }

    302:     /* finished row so stick it into b->a */
    303:     /* L part */
    304:     pv = b->a + bs2 * bi[i];
    305:     pj = b->j + bi[i];
    306:     nz = bi[i + 1] - bi[i];
    307:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    309:     /* Mark diagonal and invert diagonal for simpler triangular solves */
    310:     pv = b->a + bs2 * bdiag[i];
    311:     pj = b->j + bdiag[i];
    312:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    313:     PetscCall(PetscKernel_A_gets_inverse_A_4(pv, shift, allowzeropivot, &zeropivotdetected));
    314:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    316:     /* U part */
    317:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
    318:     pj = b->j + bdiag[i + 1] + 1;
    319:     nz = bdiag[i] - bdiag[i + 1] - 1;
    320:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
    321:   }

    323:   PetscCall(PetscFree2(rtmp, mwork));
    324:   PetscCall(ISRestoreIndices(isicol, &ic));
    325:   PetscCall(ISRestoreIndices(isrow, &r));

    327:   C->ops->solve          = MatSolve_SeqBAIJ_4;
    328:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4;
    329:   C->assembled           = PETSC_TRUE;

    331:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * n)); /* from inverting diagonal blocks */
    332:   PetscFunctionReturn(PETSC_SUCCESS);
    333: }

    335: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_inplace(Mat C, Mat A, const MatFactorInfo *info)
    336: {
    337:   /*
    338:     Default Version for when blocks are 4 by 4 Using natural ordering
    339: */
    340:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    341:   PetscInt     i, j, n = a->mbs, *bi = b->i, *bj = b->j;
    342:   PetscInt    *ajtmpold, *ajtmp, nz, row;
    343:   PetscInt    *diag_offset = b->diag, *ai = a->i, *aj = a->j, *pj;
    344:   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
    345:   MatScalar    p1, p2, p3, p4, m1, m2, m3, m4, m5, m6, m7, m8, m9, x1, x2, x3, x4;
    346:   MatScalar    p5, p6, p7, p8, p9, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16;
    347:   MatScalar    p10, p11, p12, p13, p14, p15, p16, m10, m11, m12;
    348:   MatScalar    m13, m14, m15, m16;
    349:   MatScalar   *ba = b->a, *aa = a->a;
    350:   PetscBool    pivotinblocks = b->pivotinblocks;
    351:   PetscReal    shift         = info->shiftamount;
    352:   PetscBool    allowzeropivot, zeropivotdetected = PETSC_FALSE;

    354:   PetscFunctionBegin;
    355:   allowzeropivot = PetscNot(A->erroriffailure);
    356:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));

    358:   for (i = 0; i < n; i++) {
    359:     nz    = bi[i + 1] - bi[i];
    360:     ajtmp = bj + bi[i];
    361:     for (j = 0; j < nz; j++) {
    362:       x    = rtmp + 16 * ajtmp[j];
    363:       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
    364:       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
    365:     }
    366:     /* load in initial (unfactored row) */
    367:     nz       = ai[i + 1] - ai[i];
    368:     ajtmpold = aj + ai[i];
    369:     v        = aa + 16 * ai[i];
    370:     for (j = 0; j < nz; j++) {
    371:       x     = rtmp + 16 * ajtmpold[j];
    372:       x[0]  = v[0];
    373:       x[1]  = v[1];
    374:       x[2]  = v[2];
    375:       x[3]  = v[3];
    376:       x[4]  = v[4];
    377:       x[5]  = v[5];
    378:       x[6]  = v[6];
    379:       x[7]  = v[7];
    380:       x[8]  = v[8];
    381:       x[9]  = v[9];
    382:       x[10] = v[10];
    383:       x[11] = v[11];
    384:       x[12] = v[12];
    385:       x[13] = v[13];
    386:       x[14] = v[14];
    387:       x[15] = v[15];
    388:       v += 16;
    389:     }
    390:     row = *ajtmp++;
    391:     while (row < i) {
    392:       pc  = rtmp + 16 * row;
    393:       p1  = pc[0];
    394:       p2  = pc[1];
    395:       p3  = pc[2];
    396:       p4  = pc[3];
    397:       p5  = pc[4];
    398:       p6  = pc[5];
    399:       p7  = pc[6];
    400:       p8  = pc[7];
    401:       p9  = pc[8];
    402:       p10 = pc[9];
    403:       p11 = pc[10];
    404:       p12 = pc[11];
    405:       p13 = pc[12];
    406:       p14 = pc[13];
    407:       p15 = pc[14];
    408:       p16 = pc[15];
    409:       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 || p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0) {
    410:         pv    = ba + 16 * diag_offset[row];
    411:         pj    = bj + diag_offset[row] + 1;
    412:         x1    = pv[0];
    413:         x2    = pv[1];
    414:         x3    = pv[2];
    415:         x4    = pv[3];
    416:         x5    = pv[4];
    417:         x6    = pv[5];
    418:         x7    = pv[6];
    419:         x8    = pv[7];
    420:         x9    = pv[8];
    421:         x10   = pv[9];
    422:         x11   = pv[10];
    423:         x12   = pv[11];
    424:         x13   = pv[12];
    425:         x14   = pv[13];
    426:         x15   = pv[14];
    427:         x16   = pv[15];
    428:         pc[0] = m1 = p1 * x1 + p5 * x2 + p9 * x3 + p13 * x4;
    429:         pc[1] = m2 = p2 * x1 + p6 * x2 + p10 * x3 + p14 * x4;
    430:         pc[2] = m3 = p3 * x1 + p7 * x2 + p11 * x3 + p15 * x4;
    431:         pc[3] = m4 = p4 * x1 + p8 * x2 + p12 * x3 + p16 * x4;

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

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

    443:         pc[12] = m13 = p1 * x13 + p5 * x14 + p9 * x15 + p13 * x16;
    444:         pc[13] = m14 = p2 * x13 + p6 * x14 + p10 * x15 + p14 * x16;
    445:         pc[14] = m15 = p3 * x13 + p7 * x14 + p11 * x15 + p15 * x16;
    446:         pc[15] = m16 = p4 * x13 + p8 * x14 + p12 * x15 + p16 * x16;
    447:         nz           = bi[row + 1] - diag_offset[row] - 1;
    448:         pv += 16;
    449:         for (j = 0; j < nz; j++) {
    450:           x1  = pv[0];
    451:           x2  = pv[1];
    452:           x3  = pv[2];
    453:           x4  = pv[3];
    454:           x5  = pv[4];
    455:           x6  = pv[5];
    456:           x7  = pv[6];
    457:           x8  = pv[7];
    458:           x9  = pv[8];
    459:           x10 = pv[9];
    460:           x11 = pv[10];
    461:           x12 = pv[11];
    462:           x13 = pv[12];
    463:           x14 = pv[13];
    464:           x15 = pv[14];
    465:           x16 = pv[15];
    466:           x   = rtmp + 16 * pj[j];
    467:           x[0] -= m1 * x1 + m5 * x2 + m9 * x3 + m13 * x4;
    468:           x[1] -= m2 * x1 + m6 * x2 + m10 * x3 + m14 * x4;
    469:           x[2] -= m3 * x1 + m7 * x2 + m11 * x3 + m15 * x4;
    470:           x[3] -= m4 * x1 + m8 * x2 + m12 * x3 + m16 * x4;

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

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

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

    487:           pv += 16;
    488:         }
    489:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    490:       }
    491:       row = *ajtmp++;
    492:     }
    493:     /* finished row so stick it into b->a */
    494:     pv = ba + 16 * bi[i];
    495:     pj = bj + bi[i];
    496:     nz = bi[i + 1] - bi[i];
    497:     for (j = 0; j < nz; j++) {
    498:       x      = rtmp + 16 * pj[j];
    499:       pv[0]  = x[0];
    500:       pv[1]  = x[1];
    501:       pv[2]  = x[2];
    502:       pv[3]  = x[3];
    503:       pv[4]  = x[4];
    504:       pv[5]  = x[5];
    505:       pv[6]  = x[6];
    506:       pv[7]  = x[7];
    507:       pv[8]  = x[8];
    508:       pv[9]  = x[9];
    509:       pv[10] = x[10];
    510:       pv[11] = x[11];
    511:       pv[12] = x[12];
    512:       pv[13] = x[13];
    513:       pv[14] = x[14];
    514:       pv[15] = x[15];
    515:       pv += 16;
    516:     }
    517:     /* invert diagonal block */
    518:     w = ba + 16 * diag_offset[i];
    519:     if (pivotinblocks) {
    520:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
    521:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    522:     } else {
    523:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    524:     }
    525:   }

    527:   PetscCall(PetscFree(rtmp));

    529:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_inplace;
    530:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace;
    531:   C->assembled           = PETSC_TRUE;

    533:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * b->mbs)); /* from inverting diagonal blocks */
    534:   PetscFunctionReturn(PETSC_SUCCESS);
    535: }

    537: /*
    538:   MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering -
    539:     copied from MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_inplace()
    540: */
    541: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat B, Mat A, const MatFactorInfo *info)
    542: {
    543:   Mat             C = B;
    544:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    545:   PetscInt        i, j, k, nz, nzL, row;
    546:   const PetscInt  n = a->mbs, *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j;
    547:   const PetscInt *ajtmp, *bjtmp, *bdiag = b->diag, *pj, bs2 = a->bs2;
    548:   MatScalar      *rtmp, *pc, *mwork, *v, *pv, *aa = a->a;
    549:   PetscInt        flg;
    550:   PetscReal       shift;
    551:   PetscBool       allowzeropivot, zeropivotdetected;

    553:   PetscFunctionBegin;
    554:   allowzeropivot = PetscNot(A->erroriffailure);

    556:   /* generate work space needed by the factorization */
    557:   PetscCall(PetscMalloc2(bs2 * n, &rtmp, bs2, &mwork));
    558:   PetscCall(PetscArrayzero(rtmp, bs2 * n));

    560:   if (info->shifttype == (PetscReal)MAT_SHIFT_NONE) {
    561:     shift = 0;
    562:   } else { /* info->shifttype == MAT_SHIFT_INBLOCKS */
    563:     shift = info->shiftamount;
    564:   }

    566:   for (i = 0; i < n; i++) {
    567:     /* zero rtmp */
    568:     /* L part */
    569:     nz    = bi[i + 1] - bi[i];
    570:     bjtmp = bj + bi[i];
    571:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    573:     /* U part */
    574:     nz    = bdiag[i] - bdiag[i + 1];
    575:     bjtmp = bj + bdiag[i + 1] + 1;
    576:     for (j = 0; j < nz; j++) PetscCall(PetscArrayzero(rtmp + bs2 * bjtmp[j], bs2));

    578:     /* load in initial (unfactored row) */
    579:     nz    = ai[i + 1] - ai[i];
    580:     ajtmp = aj + ai[i];
    581:     v     = aa + bs2 * ai[i];
    582:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(rtmp + bs2 * ajtmp[j], v + bs2 * j, bs2));

    584:     /* elimination */
    585:     bjtmp = bj + bi[i];
    586:     nzL   = bi[i + 1] - bi[i];
    587:     for (k = 0; k < nzL; k++) {
    588:       row = bjtmp[k];
    589:       pc  = rtmp + bs2 * row;
    590:       for (flg = 0, j = 0; j < bs2; j++) {
    591:         if (pc[j] != 0.0) {
    592:           flg = 1;
    593:           break;
    594:         }
    595:       }
    596:       if (flg) {
    597:         pv = b->a + bs2 * bdiag[row];
    598:         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
    599:         PetscCall(PetscKernel_A_gets_A_times_B_4(pc, pv, mwork));

    601:         pj = b->j + bdiag[row + 1] + 1; /* beginning of U(row,:) */
    602:         pv = b->a + bs2 * (bdiag[row + 1] + 1);
    603:         nz = bdiag[row] - bdiag[row + 1] - 1; /* num of entries inU(row,:), excluding diag */
    604:         for (j = 0; j < nz; j++) {
    605:           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
    606:           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
    607:           v = rtmp + bs2 * pj[j];
    608:           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_4(v, pc, pv));
    609:           pv += bs2;
    610:         }
    611:         PetscCall(PetscLogFlops(128.0 * nz + 112)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
    612:       }
    613:     }

    615:     /* finished row so stick it into b->a */
    616:     /* L part */
    617:     pv = b->a + bs2 * bi[i];
    618:     pj = b->j + bi[i];
    619:     nz = bi[i + 1] - bi[i];
    620:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));

    622:     /* Mark diagonal and invert diagonal for simpler triangular solves */
    623:     pv = b->a + bs2 * bdiag[i];
    624:     pj = b->j + bdiag[i];
    625:     PetscCall(PetscArraycpy(pv, rtmp + bs2 * pj[0], bs2));
    626:     PetscCall(PetscKernel_A_gets_inverse_A_4(pv, shift, allowzeropivot, &zeropivotdetected));
    627:     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;

    629:     /* U part */
    630:     pv = b->a + bs2 * (bdiag[i + 1] + 1);
    631:     pj = b->j + bdiag[i + 1] + 1;
    632:     nz = bdiag[i] - bdiag[i + 1] - 1;
    633:     for (j = 0; j < nz; j++) PetscCall(PetscArraycpy(pv + bs2 * j, rtmp + bs2 * pj[j], bs2));
    634:   }
    635:   PetscCall(PetscFree2(rtmp, mwork));

    637:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering;
    638:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering;
    639:   C->assembled           = PETSC_TRUE;

    641:   PetscCall(PetscLogFlops(1.333333333333 * 4 * 4 * 4 * n)); /* from inverting diagonal blocks */
    642:   PetscFunctionReturn(PETSC_SUCCESS);
    643: }

    645: #if defined(PETSC_HAVE_SSE)

    647:   #include PETSC_HAVE_SSE

    649: /* SSE Version for when blocks are 4 by 4 Using natural ordering */
    650: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE(Mat B, Mat A, const MatFactorInfo *info)
    651: {
    652:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    653:   int          i, j, n = a->mbs;
    654:   int         *bj = b->j, *bjtmp, *pj;
    655:   int          row;
    656:   int         *ajtmpold, nz, *bi = b->i;
    657:   int         *diag_offset = b->diag, *ai = a->i, *aj = a->j;
    658:   MatScalar   *pv, *v, *rtmp, *pc, *w, *x;
    659:   MatScalar   *ba = b->a, *aa = a->a;
    660:   int          nonzero       = 0;
    661:   PetscBool    pivotinblocks = b->pivotinblocks;
    662:   PetscReal    shift         = info->shiftamount;
    663:   PetscBool    allowzeropivot, zeropivotdetected = PETSC_FALSE;

    665:   PetscFunctionBegin;
    666:   allowzeropivot = PetscNot(A->erroriffailure);
    667:   SSE_SCOPE_BEGIN;

    669:   PetscCheck((unsigned long)aa % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer aa is not 16 byte aligned.  SSE will not work.");
    670:   PetscCheck((unsigned long)ba % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer ba is not 16 byte aligned.  SSE will not work.");
    671:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));
    672:   PetscCheck((unsigned long)rtmp % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer rtmp is not 16 byte aligned.  SSE will not work.");
    673:   /*    if ((unsigned long)bj==(unsigned long)aj) { */
    674:   /*      colscale = 4; */
    675:   /*    } */
    676:   for (i = 0; i < n; i++) {
    677:     nz    = bi[i + 1] - bi[i];
    678:     bjtmp = bj + bi[i];
    679:     /* zero out the 4x4 block accumulators */
    680:     /* zero out one register */
    681:     XOR_PS(XMM7, XMM7);
    682:     for (j = 0; j < nz; j++) {
    683:       x = rtmp + 16 * bjtmp[j];
    684:       /*        x = rtmp+4*bjtmp[j]; */
    685:       SSE_INLINE_BEGIN_1(x)
    686:       /* Copy zero register to memory locations */
    687:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    688:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_0, XMM7)
    689:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM7)
    690:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM7)
    691:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM7)
    692:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM7)
    693:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM7)
    694:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM7)
    695:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM7)
    696:       SSE_INLINE_END_1;
    697:     }
    698:     /* load in initial (unfactored row) */
    699:     nz       = ai[i + 1] - ai[i];
    700:     ajtmpold = aj + ai[i];
    701:     v        = aa + 16 * ai[i];
    702:     for (j = 0; j < nz; j++) {
    703:       x = rtmp + 16 * ajtmpold[j];
    704:       /*        x = rtmp+colscale*ajtmpold[j]; */
    705:       /* Copy v block into x block */
    706:       SSE_INLINE_BEGIN_2(v, x)
    707:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    708:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
    709:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM0)

    711:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM1)
    712:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM1)

    714:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM2)
    715:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM2)

    717:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM3)
    718:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM3)

    720:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM4)
    721:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM4)

    723:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM5)
    724:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM5)

    726:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM6)
    727:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM6)

    729:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM0)
    730:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)
    731:       SSE_INLINE_END_2;

    733:       v += 16;
    734:     }
    735:     /*      row = (*bjtmp++)/4; */
    736:     row = *bjtmp++;
    737:     while (row < i) {
    738:       pc = rtmp + 16 * row;
    739:       SSE_INLINE_BEGIN_1(pc)
    740:       /* Load block from lower triangle */
    741:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    742:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
    743:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM0)

    745:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM1)
    746:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM1)

    748:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM2)
    749:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM2)

    751:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM3)
    752:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM3)

    754:       /* Compare block to zero block */

    756:       SSE_COPY_PS(XMM4, XMM7)
    757:       SSE_CMPNEQ_PS(XMM4, XMM0)

    759:       SSE_COPY_PS(XMM5, XMM7)
    760:       SSE_CMPNEQ_PS(XMM5, XMM1)

    762:       SSE_COPY_PS(XMM6, XMM7)
    763:       SSE_CMPNEQ_PS(XMM6, XMM2)

    765:       SSE_CMPNEQ_PS(XMM7, XMM3)

    767:       /* Reduce the comparisons to one SSE register */
    768:       SSE_OR_PS(XMM6, XMM7)
    769:       SSE_OR_PS(XMM5, XMM4)
    770:       SSE_OR_PS(XMM5, XMM6)
    771:       SSE_INLINE_END_1;

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

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

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

    788:         SSE_INLINE_BEGIN_2(pv, pc)
    789:         /* Column 0, product is accumulated in XMM4 */
    790:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_0, XMM4)
    791:         SSE_SHUFFLE(XMM4, XMM4, 0x00)
    792:         SSE_MULT_PS(XMM4, XMM0)

    794:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_1, XMM5)
    795:         SSE_SHUFFLE(XMM5, XMM5, 0x00)
    796:         SSE_MULT_PS(XMM5, XMM1)
    797:         SSE_ADD_PS(XMM4, XMM5)

    799:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_2, XMM6)
    800:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    801:         SSE_MULT_PS(XMM6, XMM2)
    802:         SSE_ADD_PS(XMM4, XMM6)

    804:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_3, XMM7)
    805:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    806:         SSE_MULT_PS(XMM7, XMM3)
    807:         SSE_ADD_PS(XMM4, XMM7)

    809:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM4)
    810:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM4)

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

    817:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_5, XMM6)
    818:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    819:         SSE_MULT_PS(XMM6, XMM1)
    820:         SSE_ADD_PS(XMM5, XMM6)

    822:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_6, XMM7)
    823:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    824:         SSE_MULT_PS(XMM7, XMM2)
    825:         SSE_ADD_PS(XMM5, XMM7)

    827:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_7, XMM6)
    828:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    829:         SSE_MULT_PS(XMM6, XMM3)
    830:         SSE_ADD_PS(XMM5, XMM6)

    832:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM5)
    833:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM5)

    835:         SSE_PREFETCH_L1(SSE_ARG_1, FLOAT_24)

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

    842:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_9, XMM7)
    843:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    844:         SSE_MULT_PS(XMM7, XMM1)
    845:         SSE_ADD_PS(XMM6, XMM7)

    847:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_10, XMM7)
    848:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    849:         SSE_MULT_PS(XMM7, XMM2)
    850:         SSE_ADD_PS(XMM6, XMM7)

    852:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_11, XMM7)
    853:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    854:         SSE_MULT_PS(XMM7, XMM3)
    855:         SSE_ADD_PS(XMM6, XMM7)

    857:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM6)
    858:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM6)

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

    866:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_13, XMM7)
    867:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    868:         SSE_MULT_PS(XMM1, XMM7)
    869:         SSE_ADD_PS(XMM0, XMM1)

    871:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_14, XMM1)
    872:         SSE_SHUFFLE(XMM1, XMM1, 0x00)
    873:         SSE_MULT_PS(XMM1, XMM2)
    874:         SSE_ADD_PS(XMM0, XMM1)

    876:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_15, XMM7)
    877:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    878:         SSE_MULT_PS(XMM3, XMM7)
    879:         SSE_ADD_PS(XMM0, XMM3)

    881:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM0)
    882:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)

    884:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    885:         /* This is code to be maintained and read by humans after all. */
    886:         /* Copy Multiplier Col 3 into XMM3 */
    887:         SSE_COPY_PS(XMM3, XMM0)
    888:         /* Copy Multiplier Col 2 into XMM2 */
    889:         SSE_COPY_PS(XMM2, XMM6)
    890:         /* Copy Multiplier Col 1 into XMM1 */
    891:         SSE_COPY_PS(XMM1, XMM5)
    892:         /* Copy Multiplier Col 0 into XMM0 */
    893:         SSE_COPY_PS(XMM0, XMM4)
    894:         SSE_INLINE_END_2;

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

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

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

    917:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_1, XMM6)
    918:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    919:           SSE_MULT_PS(XMM6, XMM1)
    920:           SSE_SUB_PS(XMM4, XMM6)

    922:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_2, XMM7)
    923:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    924:           SSE_MULT_PS(XMM7, XMM2)
    925:           SSE_SUB_PS(XMM4, XMM7)

    927:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_3, XMM5)
    928:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    929:           SSE_MULT_PS(XMM5, XMM3)
    930:           SSE_SUB_PS(XMM4, XMM5)

    932:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_0, XMM4)
    933:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM4)

    935:           /* Second Column */
    936:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM5)
    937:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM5)

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

    945:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_5, XMM7)
    946:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    947:           SSE_MULT_PS(XMM7, XMM1)
    948:           SSE_SUB_PS(XMM5, XMM7)

    950:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_6, XMM4)
    951:           SSE_SHUFFLE(XMM4, XMM4, 0x00)
    952:           SSE_MULT_PS(XMM4, XMM2)
    953:           SSE_SUB_PS(XMM5, XMM4)

    955:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_7, XMM6)
    956:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    957:           SSE_MULT_PS(XMM6, XMM3)
    958:           SSE_SUB_PS(XMM5, XMM6)

    960:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM5)
    961:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM5)

    963:           SSE_PREFETCH_L1(SSE_ARG_2, FLOAT_24)

    965:           /* Third Column */
    966:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM6)
    967:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM6)

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

    975:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_9, XMM4)
    976:           SSE_SHUFFLE(XMM4, XMM4, 0x00)
    977:           SSE_MULT_PS(XMM4, XMM1)
    978:           SSE_SUB_PS(XMM6, XMM4)

    980:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_10, XMM5)
    981:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    982:           SSE_MULT_PS(XMM5, XMM2)
    983:           SSE_SUB_PS(XMM6, XMM5)

    985:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_11, XMM7)
    986:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    987:           SSE_MULT_PS(XMM7, XMM3)
    988:           SSE_SUB_PS(XMM6, XMM7)

    990:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM6)
    991:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM6)

    993:           /* Fourth Column */
    994:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM4)
    995:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM4)

    997:           /* Matrix-Vector Product: */
    998:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_12, XMM5)
    999:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1000:           SSE_MULT_PS(XMM5, XMM0)
    1001:           SSE_SUB_PS(XMM4, XMM5)

    1003:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_13, XMM6)
    1004:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1005:           SSE_MULT_PS(XMM6, XMM1)
    1006:           SSE_SUB_PS(XMM4, XMM6)

    1008:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_14, XMM7)
    1009:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1010:           SSE_MULT_PS(XMM7, XMM2)
    1011:           SSE_SUB_PS(XMM4, XMM7)

    1013:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_15, XMM5)
    1014:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1015:           SSE_MULT_PS(XMM5, XMM3)
    1016:           SSE_SUB_PS(XMM4, XMM5)

    1018:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM4)
    1019:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM4)
    1020:           SSE_INLINE_END_2;
    1021:           pv += 16;
    1022:         }
    1023:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    1024:       }
    1025:       row = *bjtmp++;
    1026:       /*        row = (*bjtmp++)/4; */
    1027:     }
    1028:     /* finished row so stick it into b->a */
    1029:     pv = ba + 16 * bi[i];
    1030:     pj = bj + bi[i];
    1031:     nz = bi[i + 1] - bi[i];

    1033:     /* Copy x block back into pv block */
    1034:     for (j = 0; j < nz; j++) {
    1035:       x = rtmp + 16 * pj[j];
    1036:       /*        x  = rtmp+4*pj[j]; */

    1038:       SSE_INLINE_BEGIN_2(x, pv)
    1039:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1040:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM1)
    1041:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM1)

    1043:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM2)
    1044:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM2)

    1046:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM3)
    1047:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM3)

    1049:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM4)
    1050:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM4)

    1052:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM5)
    1053:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM5)

    1055:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM6)
    1056:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM6)

    1058:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM7)
    1059:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM7)

    1061:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM0)
    1062:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)
    1063:       SSE_INLINE_END_2;
    1064:       pv += 16;
    1065:     }
    1066:     /* invert diagonal block */
    1067:     w = ba + 16 * diag_offset[i];
    1068:     if (pivotinblocks) {
    1069:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
    1070:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1071:     } else {
    1072:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    1073:     }
    1074:     /*      PetscCall(PetscKernel_A_gets_inverse_A_4_SSE(w)); */
    1075:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1076:   }

    1078:   PetscCall(PetscFree(rtmp));

    1080:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1081:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1082:   C->assembled           = PETSC_TRUE;

    1084:   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs));
    1085:   /* Flop Count from inverting diagonal blocks */
    1086:   SSE_SCOPE_END;
    1087:   PetscFunctionReturn(PETSC_SUCCESS);
    1088: }

    1090: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(Mat C)
    1091: {
    1092:   Mat             A = C;
    1093:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    1094:   int             i, j, n = a->mbs;
    1095:   unsigned short *bj = (unsigned short *)b->j, *bjtmp, *pj;
    1096:   unsigned short *aj = (unsigned short *)a->j, *ajtmp;
    1097:   unsigned int    row;
    1098:   int             nz, *bi = b->i;
    1099:   int            *diag_offset = b->diag, *ai = a->i;
    1100:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
    1101:   MatScalar      *ba = b->a, *aa = a->a;
    1102:   int             nonzero       = 0;
    1103:   PetscBool       pivotinblocks = b->pivotinblocks;
    1104:   PetscReal       shift         = info->shiftamount;
    1105:   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;

    1107:   PetscFunctionBegin;
    1108:   allowzeropivot = PetscNot(A->erroriffailure);
    1109:   SSE_SCOPE_BEGIN;

    1111:   PetscCheck((unsigned long)aa % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer aa is not 16 byte aligned.  SSE will not work.");
    1112:   PetscCheck((unsigned long)ba % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer ba is not 16 byte aligned.  SSE will not work.");
    1113:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));
    1114:   PetscCheck((unsigned long)rtmp % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer rtmp is not 16 byte aligned.  SSE will not work.");
    1115:   /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1116:   /*      colscale = 4; */
    1117:   /*    } */

    1119:   for (i = 0; i < n; i++) {
    1120:     nz    = bi[i + 1] - bi[i];
    1121:     bjtmp = bj + bi[i];
    1122:     /* zero out the 4x4 block accumulators */
    1123:     /* zero out one register */
    1124:     XOR_PS(XMM7, XMM7);
    1125:     for (j = 0; j < nz; j++) {
    1126:       x = rtmp + 16 * ((unsigned int)bjtmp[j]);
    1127:       /*        x = rtmp+4*bjtmp[j]; */
    1128:       SSE_INLINE_BEGIN_1(x)
    1129:       /* Copy zero register to memory locations */
    1130:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1131:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_0, XMM7)
    1132:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM7)
    1133:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM7)
    1134:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM7)
    1135:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM7)
    1136:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM7)
    1137:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM7)
    1138:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM7)
    1139:       SSE_INLINE_END_1;
    1140:     }
    1141:     /* load in initial (unfactored row) */
    1142:     nz    = ai[i + 1] - ai[i];
    1143:     ajtmp = aj + ai[i];
    1144:     v     = aa + 16 * ai[i];
    1145:     for (j = 0; j < nz; j++) {
    1146:       x = rtmp + 16 * ((unsigned int)ajtmp[j]);
    1147:       /*        x = rtmp+colscale*ajtmp[j]; */
    1148:       /* Copy v block into x block */
    1149:       SSE_INLINE_BEGIN_2(v, x)
    1150:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1151:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
    1152:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM0)

    1154:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM1)
    1155:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM1)

    1157:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM2)
    1158:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM2)

    1160:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM3)
    1161:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM3)

    1163:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM4)
    1164:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM4)

    1166:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM5)
    1167:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM5)

    1169:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM6)
    1170:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM6)

    1172:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM0)
    1173:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)
    1174:       SSE_INLINE_END_2;

    1176:       v += 16;
    1177:     }
    1178:     /*      row = (*bjtmp++)/4; */
    1179:     row = (unsigned int)(*bjtmp++);
    1180:     while (row < i) {
    1181:       pc = rtmp + 16 * row;
    1182:       SSE_INLINE_BEGIN_1(pc)
    1183:       /* Load block from lower triangle */
    1184:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1185:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
    1186:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM0)

    1188:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM1)
    1189:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM1)

    1191:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM2)
    1192:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM2)

    1194:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM3)
    1195:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM3)

    1197:       /* Compare block to zero block */

    1199:       SSE_COPY_PS(XMM4, XMM7)
    1200:       SSE_CMPNEQ_PS(XMM4, XMM0)

    1202:       SSE_COPY_PS(XMM5, XMM7)
    1203:       SSE_CMPNEQ_PS(XMM5, XMM1)

    1205:       SSE_COPY_PS(XMM6, XMM7)
    1206:       SSE_CMPNEQ_PS(XMM6, XMM2)

    1208:       SSE_CMPNEQ_PS(XMM7, XMM3)

    1210:       /* Reduce the comparisons to one SSE register */
    1211:       SSE_OR_PS(XMM6, XMM7)
    1212:       SSE_OR_PS(XMM5, XMM4)
    1213:       SSE_OR_PS(XMM5, XMM6)
    1214:       SSE_INLINE_END_1;

    1216:       /* Reduce the one SSE register to an integer register for branching */
    1217:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1218:       MOVEMASK(nonzero, XMM5);

    1220:       /* If block is nonzero ... */
    1221:       if (nonzero) {
    1222:         pv = ba + 16 * diag_offset[row];
    1223:         PREFETCH_L1(&pv[16]);
    1224:         pj = bj + diag_offset[row] + 1;

    1226:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1227:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1228:         /* but the diagonal was inverted already */
    1229:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1231:         SSE_INLINE_BEGIN_2(pv, pc)
    1232:         /* Column 0, product is accumulated in XMM4 */
    1233:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_0, XMM4)
    1234:         SSE_SHUFFLE(XMM4, XMM4, 0x00)
    1235:         SSE_MULT_PS(XMM4, XMM0)

    1237:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_1, XMM5)
    1238:         SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1239:         SSE_MULT_PS(XMM5, XMM1)
    1240:         SSE_ADD_PS(XMM4, XMM5)

    1242:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_2, XMM6)
    1243:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1244:         SSE_MULT_PS(XMM6, XMM2)
    1245:         SSE_ADD_PS(XMM4, XMM6)

    1247:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_3, XMM7)
    1248:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1249:         SSE_MULT_PS(XMM7, XMM3)
    1250:         SSE_ADD_PS(XMM4, XMM7)

    1252:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM4)
    1253:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM4)

    1255:         /* Column 1, product is accumulated in XMM5 */
    1256:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_4, XMM5)
    1257:         SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1258:         SSE_MULT_PS(XMM5, XMM0)

    1260:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_5, XMM6)
    1261:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1262:         SSE_MULT_PS(XMM6, XMM1)
    1263:         SSE_ADD_PS(XMM5, XMM6)

    1265:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_6, XMM7)
    1266:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1267:         SSE_MULT_PS(XMM7, XMM2)
    1268:         SSE_ADD_PS(XMM5, XMM7)

    1270:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_7, XMM6)
    1271:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1272:         SSE_MULT_PS(XMM6, XMM3)
    1273:         SSE_ADD_PS(XMM5, XMM6)

    1275:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM5)
    1276:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM5)

    1278:         SSE_PREFETCH_L1(SSE_ARG_1, FLOAT_24)

    1280:         /* Column 2, product is accumulated in XMM6 */
    1281:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_8, XMM6)
    1282:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1283:         SSE_MULT_PS(XMM6, XMM0)

    1285:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_9, XMM7)
    1286:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1287:         SSE_MULT_PS(XMM7, XMM1)
    1288:         SSE_ADD_PS(XMM6, XMM7)

    1290:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_10, XMM7)
    1291:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1292:         SSE_MULT_PS(XMM7, XMM2)
    1293:         SSE_ADD_PS(XMM6, XMM7)

    1295:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_11, XMM7)
    1296:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1297:         SSE_MULT_PS(XMM7, XMM3)
    1298:         SSE_ADD_PS(XMM6, XMM7)

    1300:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM6)
    1301:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM6)

    1303:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1304:         /* Column 3, product is accumulated in XMM0 */
    1305:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_12, XMM7)
    1306:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1307:         SSE_MULT_PS(XMM0, XMM7)

    1309:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_13, XMM7)
    1310:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1311:         SSE_MULT_PS(XMM1, XMM7)
    1312:         SSE_ADD_PS(XMM0, XMM1)

    1314:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_14, XMM1)
    1315:         SSE_SHUFFLE(XMM1, XMM1, 0x00)
    1316:         SSE_MULT_PS(XMM1, XMM2)
    1317:         SSE_ADD_PS(XMM0, XMM1)

    1319:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_15, XMM7)
    1320:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1321:         SSE_MULT_PS(XMM3, XMM7)
    1322:         SSE_ADD_PS(XMM0, XMM3)

    1324:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM0)
    1325:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)

    1327:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1328:         /* This is code to be maintained and read by humans after all. */
    1329:         /* Copy Multiplier Col 3 into XMM3 */
    1330:         SSE_COPY_PS(XMM3, XMM0)
    1331:         /* Copy Multiplier Col 2 into XMM2 */
    1332:         SSE_COPY_PS(XMM2, XMM6)
    1333:         /* Copy Multiplier Col 1 into XMM1 */
    1334:         SSE_COPY_PS(XMM1, XMM5)
    1335:         /* Copy Multiplier Col 0 into XMM0 */
    1336:         SSE_COPY_PS(XMM0, XMM4)
    1337:         SSE_INLINE_END_2;

    1339:         /* Update the row: */
    1340:         nz = bi[row + 1] - diag_offset[row] - 1;
    1341:         pv += 16;
    1342:         for (j = 0; j < nz; j++) {
    1343:           PREFETCH_L1(&pv[16]);
    1344:           x = rtmp + 16 * ((unsigned int)pj[j]);
    1345:           /*            x = rtmp + 4*pj[j]; */

    1347:           /* X:=X-M*PV, One column at a time */
    1348:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1349:           SSE_INLINE_BEGIN_2(x, pv)
    1350:           /* Load First Column of X*/
    1351:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM4)
    1352:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM4)

    1354:           /* Matrix-Vector Product: */
    1355:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_0, 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_1, 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_2, 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_3, 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_0, XMM4)
    1376:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM4)

    1378:           /* Second Column */
    1379:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM5)
    1380:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM5)

    1382:           /* Matrix-Vector Product: */
    1383:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_4, XMM6)
    1384:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1385:           SSE_MULT_PS(XMM6, XMM0)
    1386:           SSE_SUB_PS(XMM5, XMM6)

    1388:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_5, XMM7)
    1389:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1390:           SSE_MULT_PS(XMM7, XMM1)
    1391:           SSE_SUB_PS(XMM5, XMM7)

    1393:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_6, XMM4)
    1394:           SSE_SHUFFLE(XMM4, XMM4, 0x00)
    1395:           SSE_MULT_PS(XMM4, XMM2)
    1396:           SSE_SUB_PS(XMM5, XMM4)

    1398:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_7, XMM6)
    1399:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1400:           SSE_MULT_PS(XMM6, XMM3)
    1401:           SSE_SUB_PS(XMM5, XMM6)

    1403:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM5)
    1404:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM5)

    1406:           SSE_PREFETCH_L1(SSE_ARG_2, FLOAT_24)

    1408:           /* Third Column */
    1409:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM6)
    1410:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM6)

    1412:           /* Matrix-Vector Product: */
    1413:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_8, XMM7)
    1414:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1415:           SSE_MULT_PS(XMM7, XMM0)
    1416:           SSE_SUB_PS(XMM6, XMM7)

    1418:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_9, XMM4)
    1419:           SSE_SHUFFLE(XMM4, XMM4, 0x00)
    1420:           SSE_MULT_PS(XMM4, XMM1)
    1421:           SSE_SUB_PS(XMM6, XMM4)

    1423:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_10, XMM5)
    1424:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1425:           SSE_MULT_PS(XMM5, XMM2)
    1426:           SSE_SUB_PS(XMM6, XMM5)

    1428:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_11, XMM7)
    1429:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1430:           SSE_MULT_PS(XMM7, XMM3)
    1431:           SSE_SUB_PS(XMM6, XMM7)

    1433:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM6)
    1434:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM6)

    1436:           /* Fourth Column */
    1437:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM4)
    1438:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM4)

    1440:           /* Matrix-Vector Product: */
    1441:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_12, XMM5)
    1442:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1443:           SSE_MULT_PS(XMM5, XMM0)
    1444:           SSE_SUB_PS(XMM4, XMM5)

    1446:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_13, XMM6)
    1447:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1448:           SSE_MULT_PS(XMM6, XMM1)
    1449:           SSE_SUB_PS(XMM4, XMM6)

    1451:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_14, XMM7)
    1452:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1453:           SSE_MULT_PS(XMM7, XMM2)
    1454:           SSE_SUB_PS(XMM4, XMM7)

    1456:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_15, XMM5)
    1457:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1458:           SSE_MULT_PS(XMM5, XMM3)
    1459:           SSE_SUB_PS(XMM4, XMM5)

    1461:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM4)
    1462:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM4)
    1463:           SSE_INLINE_END_2;
    1464:           pv += 16;
    1465:         }
    1466:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    1467:       }
    1468:       row = (unsigned int)(*bjtmp++);
    1469:       /*        row = (*bjtmp++)/4; */
    1470:       /*        bjtmp++; */
    1471:     }
    1472:     /* finished row so stick it into b->a */
    1473:     pv = ba + 16 * bi[i];
    1474:     pj = bj + bi[i];
    1475:     nz = bi[i + 1] - bi[i];

    1477:     /* Copy x block back into pv block */
    1478:     for (j = 0; j < nz; j++) {
    1479:       x = rtmp + 16 * ((unsigned int)pj[j]);
    1480:       /*        x  = rtmp+4*pj[j]; */

    1482:       SSE_INLINE_BEGIN_2(x, pv)
    1483:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1484:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM1)
    1485:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM1)

    1487:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM2)
    1488:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM2)

    1490:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM3)
    1491:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM3)

    1493:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM4)
    1494:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM4)

    1496:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM5)
    1497:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM5)

    1499:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM6)
    1500:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM6)

    1502:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM7)
    1503:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM7)

    1505:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM0)
    1506:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)
    1507:       SSE_INLINE_END_2;
    1508:       pv += 16;
    1509:     }
    1510:     /* invert diagonal block */
    1511:     w = ba + 16 * diag_offset[i];
    1512:     if (pivotinblocks) {
    1513:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, &zeropivotdetected));
    1514:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1515:     } else {
    1516:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    1517:     }
    1518:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1519:   }

    1521:   PetscCall(PetscFree(rtmp));

    1523:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1524:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1525:   C->assembled           = PETSC_TRUE;

    1527:   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs));
    1528:   /* Flop Count from inverting diagonal blocks */
    1529:   SSE_SCOPE_END;
    1530:   PetscFunctionReturn(PETSC_SUCCESS);
    1531: }

    1533: PetscErrorCode MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat C, Mat A, const MatFactorInfo *info)
    1534: {
    1535:   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data, *b = (Mat_SeqBAIJ *)C->data;
    1536:   int             i, j, n = a->mbs;
    1537:   unsigned short *bj = (unsigned short *)b->j, *bjtmp, *pj;
    1538:   unsigned int    row;
    1539:   int            *ajtmpold, nz, *bi = b->i;
    1540:   int            *diag_offset = b->diag, *ai = a->i, *aj = a->j;
    1541:   MatScalar      *pv, *v, *rtmp, *pc, *w, *x;
    1542:   MatScalar      *ba = b->a, *aa = a->a;
    1543:   int             nonzero       = 0;
    1544:   PetscBool       pivotinblocks = b->pivotinblocks;
    1545:   PetscReal       shift         = info->shiftamount;
    1546:   PetscBool       allowzeropivot, zeropivotdetected = PETSC_FALSE;

    1548:   PetscFunctionBegin;
    1549:   allowzeropivot = PetscNot(A->erroriffailure);
    1550:   SSE_SCOPE_BEGIN;

    1552:   PetscCheck((unsigned long)aa % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer aa is not 16 byte aligned.  SSE will not work.");
    1553:   PetscCheck((unsigned long)ba % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer ba is not 16 byte aligned.  SSE will not work.");
    1554:   PetscCall(PetscMalloc1(16 * (n + 1), &rtmp));
    1555:   PetscCheck((unsigned long)rtmp % 16 == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_BADPTR, "Pointer rtmp is not 16 byte aligned.  SSE will not work.");
    1556:   /*    if ((unsigned long)bj==(unsigned long)aj) { */
    1557:   /*      colscale = 4; */
    1558:   /*    } */
    1559:   if ((unsigned long)bj == (unsigned long)aj) return MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE_usj_Inplace(C);

    1561:   for (i = 0; i < n; i++) {
    1562:     nz    = bi[i + 1] - bi[i];
    1563:     bjtmp = bj + bi[i];
    1564:     /* zero out the 4x4 block accumulators */
    1565:     /* zero out one register */
    1566:     XOR_PS(XMM7, XMM7);
    1567:     for (j = 0; j < nz; j++) {
    1568:       x = rtmp + 16 * ((unsigned int)bjtmp[j]);
    1569:       /*        x = rtmp+4*bjtmp[j]; */
    1570:       SSE_INLINE_BEGIN_1(x)
    1571:       /* Copy zero register to memory locations */
    1572:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1573:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_0, XMM7)
    1574:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM7)
    1575:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM7)
    1576:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM7)
    1577:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM7)
    1578:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM7)
    1579:       SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM7)
    1580:       SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM7)
    1581:       SSE_INLINE_END_1;
    1582:     }
    1583:     /* load in initial (unfactored row) */
    1584:     nz       = ai[i + 1] - ai[i];
    1585:     ajtmpold = aj + ai[i];
    1586:     v        = aa + 16 * ai[i];
    1587:     for (j = 0; j < nz; j++) {
    1588:       x = rtmp + 16 * ajtmpold[j];
    1589:       /*        x = rtmp+colscale*ajtmpold[j]; */
    1590:       /* Copy v block into x block */
    1591:       SSE_INLINE_BEGIN_2(v, x)
    1592:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1593:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
    1594:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM0)

    1596:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM1)
    1597:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM1)

    1599:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM2)
    1600:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM2)

    1602:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM3)
    1603:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM3)

    1605:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM4)
    1606:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM4)

    1608:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM5)
    1609:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM5)

    1611:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM6)
    1612:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM6)

    1614:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM0)
    1615:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)
    1616:       SSE_INLINE_END_2;

    1618:       v += 16;
    1619:     }
    1620:     /*      row = (*bjtmp++)/4; */
    1621:     row = (unsigned int)(*bjtmp++);
    1622:     while (row < i) {
    1623:       pc = rtmp + 16 * row;
    1624:       SSE_INLINE_BEGIN_1(pc)
    1625:       /* Load block from lower triangle */
    1626:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1627:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM0)
    1628:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM0)

    1630:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM1)
    1631:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM1)

    1633:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM2)
    1634:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM2)

    1636:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM3)
    1637:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM3)

    1639:       /* Compare block to zero block */

    1641:       SSE_COPY_PS(XMM4, XMM7)
    1642:       SSE_CMPNEQ_PS(XMM4, XMM0)

    1644:       SSE_COPY_PS(XMM5, XMM7)
    1645:       SSE_CMPNEQ_PS(XMM5, XMM1)

    1647:       SSE_COPY_PS(XMM6, XMM7)
    1648:       SSE_CMPNEQ_PS(XMM6, XMM2)

    1650:       SSE_CMPNEQ_PS(XMM7, XMM3)

    1652:       /* Reduce the comparisons to one SSE register */
    1653:       SSE_OR_PS(XMM6, XMM7)
    1654:       SSE_OR_PS(XMM5, XMM4)
    1655:       SSE_OR_PS(XMM5, XMM6)
    1656:       SSE_INLINE_END_1;

    1658:       /* Reduce the one SSE register to an integer register for branching */
    1659:       /* Note: Since nonzero is an int, there is no INLINE block version of this call */
    1660:       MOVEMASK(nonzero, XMM5);

    1662:       /* If block is nonzero ... */
    1663:       if (nonzero) {
    1664:         pv = ba + 16 * diag_offset[row];
    1665:         PREFETCH_L1(&pv[16]);
    1666:         pj = bj + diag_offset[row] + 1;

    1668:         /* Form Multiplier, one column at a time (Matrix-Matrix Product) */
    1669:         /* L_ij^(k+1) = L_ij^(k)*inv(L_jj^(k)) */
    1670:         /* but the diagonal was inverted already */
    1671:         /* and, L_ij^(k) is already loaded into registers XMM0-XMM3 columnwise */

    1673:         SSE_INLINE_BEGIN_2(pv, pc)
    1674:         /* Column 0, product is accumulated in XMM4 */
    1675:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_0, XMM4)
    1676:         SSE_SHUFFLE(XMM4, XMM4, 0x00)
    1677:         SSE_MULT_PS(XMM4, XMM0)

    1679:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_1, XMM5)
    1680:         SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1681:         SSE_MULT_PS(XMM5, XMM1)
    1682:         SSE_ADD_PS(XMM4, XMM5)

    1684:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_2, XMM6)
    1685:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1686:         SSE_MULT_PS(XMM6, XMM2)
    1687:         SSE_ADD_PS(XMM4, XMM6)

    1689:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_3, XMM7)
    1690:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1691:         SSE_MULT_PS(XMM7, XMM3)
    1692:         SSE_ADD_PS(XMM4, XMM7)

    1694:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM4)
    1695:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM4)

    1697:         /* Column 1, product is accumulated in XMM5 */
    1698:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_4, XMM5)
    1699:         SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1700:         SSE_MULT_PS(XMM5, XMM0)

    1702:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_5, XMM6)
    1703:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1704:         SSE_MULT_PS(XMM6, XMM1)
    1705:         SSE_ADD_PS(XMM5, XMM6)

    1707:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_6, XMM7)
    1708:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1709:         SSE_MULT_PS(XMM7, XMM2)
    1710:         SSE_ADD_PS(XMM5, XMM7)

    1712:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_7, XMM6)
    1713:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1714:         SSE_MULT_PS(XMM6, XMM3)
    1715:         SSE_ADD_PS(XMM5, XMM6)

    1717:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM5)
    1718:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM5)

    1720:         SSE_PREFETCH_L1(SSE_ARG_1, FLOAT_24)

    1722:         /* Column 2, product is accumulated in XMM6 */
    1723:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_8, XMM6)
    1724:         SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1725:         SSE_MULT_PS(XMM6, XMM0)

    1727:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_9, XMM7)
    1728:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1729:         SSE_MULT_PS(XMM7, XMM1)
    1730:         SSE_ADD_PS(XMM6, XMM7)

    1732:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_10, XMM7)
    1733:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1734:         SSE_MULT_PS(XMM7, XMM2)
    1735:         SSE_ADD_PS(XMM6, XMM7)

    1737:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_11, XMM7)
    1738:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1739:         SSE_MULT_PS(XMM7, XMM3)
    1740:         SSE_ADD_PS(XMM6, XMM7)

    1742:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM6)
    1743:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM6)

    1745:         /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
    1746:         /* Column 3, product is accumulated in XMM0 */
    1747:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_12, XMM7)
    1748:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1749:         SSE_MULT_PS(XMM0, XMM7)

    1751:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_13, XMM7)
    1752:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1753:         SSE_MULT_PS(XMM1, XMM7)
    1754:         SSE_ADD_PS(XMM0, XMM1)

    1756:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_14, XMM1)
    1757:         SSE_SHUFFLE(XMM1, XMM1, 0x00)
    1758:         SSE_MULT_PS(XMM1, XMM2)
    1759:         SSE_ADD_PS(XMM0, XMM1)

    1761:         SSE_LOAD_SS(SSE_ARG_1, FLOAT_15, XMM7)
    1762:         SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1763:         SSE_MULT_PS(XMM3, XMM7)
    1764:         SSE_ADD_PS(XMM0, XMM3)

    1766:         SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM0)
    1767:         SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)

    1769:         /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
    1770:         /* This is code to be maintained and read by humans after all. */
    1771:         /* Copy Multiplier Col 3 into XMM3 */
    1772:         SSE_COPY_PS(XMM3, XMM0)
    1773:         /* Copy Multiplier Col 2 into XMM2 */
    1774:         SSE_COPY_PS(XMM2, XMM6)
    1775:         /* Copy Multiplier Col 1 into XMM1 */
    1776:         SSE_COPY_PS(XMM1, XMM5)
    1777:         /* Copy Multiplier Col 0 into XMM0 */
    1778:         SSE_COPY_PS(XMM0, XMM4)
    1779:         SSE_INLINE_END_2;

    1781:         /* Update the row: */
    1782:         nz = bi[row + 1] - diag_offset[row] - 1;
    1783:         pv += 16;
    1784:         for (j = 0; j < nz; j++) {
    1785:           PREFETCH_L1(&pv[16]);
    1786:           x = rtmp + 16 * ((unsigned int)pj[j]);
    1787:           /*            x = rtmp + 4*pj[j]; */

    1789:           /* X:=X-M*PV, One column at a time */
    1790:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
    1791:           SSE_INLINE_BEGIN_2(x, pv)
    1792:           /* Load First Column of X*/
    1793:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM4)
    1794:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM4)

    1796:           /* Matrix-Vector Product: */
    1797:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_0, XMM5)
    1798:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1799:           SSE_MULT_PS(XMM5, XMM0)
    1800:           SSE_SUB_PS(XMM4, XMM5)

    1802:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_1, XMM6)
    1803:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1804:           SSE_MULT_PS(XMM6, XMM1)
    1805:           SSE_SUB_PS(XMM4, XMM6)

    1807:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_2, XMM7)
    1808:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1809:           SSE_MULT_PS(XMM7, XMM2)
    1810:           SSE_SUB_PS(XMM4, XMM7)

    1812:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_3, XMM5)
    1813:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1814:           SSE_MULT_PS(XMM5, XMM3)
    1815:           SSE_SUB_PS(XMM4, XMM5)

    1817:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_0, XMM4)
    1818:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_2, XMM4)

    1820:           /* Second Column */
    1821:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM5)
    1822:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM5)

    1824:           /* Matrix-Vector Product: */
    1825:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_4, XMM6)
    1826:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1827:           SSE_MULT_PS(XMM6, XMM0)
    1828:           SSE_SUB_PS(XMM5, XMM6)

    1830:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_5, XMM7)
    1831:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1832:           SSE_MULT_PS(XMM7, XMM1)
    1833:           SSE_SUB_PS(XMM5, XMM7)

    1835:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_6, XMM4)
    1836:           SSE_SHUFFLE(XMM4, XMM4, 0x00)
    1837:           SSE_MULT_PS(XMM4, XMM2)
    1838:           SSE_SUB_PS(XMM5, XMM4)

    1840:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_7, XMM6)
    1841:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1842:           SSE_MULT_PS(XMM6, XMM3)
    1843:           SSE_SUB_PS(XMM5, XMM6)

    1845:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_4, XMM5)
    1846:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_6, XMM5)

    1848:           SSE_PREFETCH_L1(SSE_ARG_2, FLOAT_24)

    1850:           /* Third Column */
    1851:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM6)
    1852:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM6)

    1854:           /* Matrix-Vector Product: */
    1855:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_8, XMM7)
    1856:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1857:           SSE_MULT_PS(XMM7, XMM0)
    1858:           SSE_SUB_PS(XMM6, XMM7)

    1860:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_9, XMM4)
    1861:           SSE_SHUFFLE(XMM4, XMM4, 0x00)
    1862:           SSE_MULT_PS(XMM4, XMM1)
    1863:           SSE_SUB_PS(XMM6, XMM4)

    1865:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_10, XMM5)
    1866:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1867:           SSE_MULT_PS(XMM5, XMM2)
    1868:           SSE_SUB_PS(XMM6, XMM5)

    1870:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_11, XMM7)
    1871:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1872:           SSE_MULT_PS(XMM7, XMM3)
    1873:           SSE_SUB_PS(XMM6, XMM7)

    1875:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_8, XMM6)
    1876:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_10, XMM6)

    1878:           /* Fourth Column */
    1879:           SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM4)
    1880:           SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM4)

    1882:           /* Matrix-Vector Product: */
    1883:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_12, XMM5)
    1884:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1885:           SSE_MULT_PS(XMM5, XMM0)
    1886:           SSE_SUB_PS(XMM4, XMM5)

    1888:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_13, XMM6)
    1889:           SSE_SHUFFLE(XMM6, XMM6, 0x00)
    1890:           SSE_MULT_PS(XMM6, XMM1)
    1891:           SSE_SUB_PS(XMM4, XMM6)

    1893:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_14, XMM7)
    1894:           SSE_SHUFFLE(XMM7, XMM7, 0x00)
    1895:           SSE_MULT_PS(XMM7, XMM2)
    1896:           SSE_SUB_PS(XMM4, XMM7)

    1898:           SSE_LOAD_SS(SSE_ARG_2, FLOAT_15, XMM5)
    1899:           SSE_SHUFFLE(XMM5, XMM5, 0x00)
    1900:           SSE_MULT_PS(XMM5, XMM3)
    1901:           SSE_SUB_PS(XMM4, XMM5)

    1903:           SSE_STOREL_PS(SSE_ARG_1, FLOAT_12, XMM4)
    1904:           SSE_STOREH_PS(SSE_ARG_1, FLOAT_14, XMM4)
    1905:           SSE_INLINE_END_2;
    1906:           pv += 16;
    1907:         }
    1908:         PetscCall(PetscLogFlops(128.0 * nz + 112.0));
    1909:       }
    1910:       row = (unsigned int)(*bjtmp++);
    1911:       /*        row = (*bjtmp++)/4; */
    1912:       /*        bjtmp++; */
    1913:     }
    1914:     /* finished row so stick it into b->a */
    1915:     pv = ba + 16 * bi[i];
    1916:     pj = bj + bi[i];
    1917:     nz = bi[i + 1] - bi[i];

    1919:     /* Copy x block back into pv block */
    1920:     for (j = 0; j < nz; j++) {
    1921:       x = rtmp + 16 * ((unsigned int)pj[j]);
    1922:       /*        x  = rtmp+4*pj[j]; */

    1924:       SSE_INLINE_BEGIN_2(x, pv)
    1925:       /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
    1926:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_0, XMM1)
    1927:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_0, XMM1)

    1929:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_2, XMM2)
    1930:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_2, XMM2)

    1932:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_4, XMM3)
    1933:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_4, XMM3)

    1935:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_6, XMM4)
    1936:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_6, XMM4)

    1938:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_8, XMM5)
    1939:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_8, XMM5)

    1941:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_10, XMM6)
    1942:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_10, XMM6)

    1944:       SSE_LOADL_PS(SSE_ARG_1, FLOAT_12, XMM7)
    1945:       SSE_STOREL_PS(SSE_ARG_2, FLOAT_12, XMM7)

    1947:       SSE_LOADH_PS(SSE_ARG_1, FLOAT_14, XMM0)
    1948:       SSE_STOREH_PS(SSE_ARG_2, FLOAT_14, XMM0)
    1949:       SSE_INLINE_END_2;
    1950:       pv += 16;
    1951:     }
    1952:     /* invert diagonal block */
    1953:     w = ba + 16 * diag_offset[i];
    1954:     if (pivotinblocks) {
    1955:       PetscCall(PetscKernel_A_gets_inverse_A_4(w, shift, allowzeropivot, , &zeropivotdetected));
    1956:       if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    1957:     } else {
    1958:       PetscCall(PetscKernel_A_gets_inverse_A_4_nopivot(w));
    1959:     }
    1960:     /*      PetscCall(PetscKernel_A_gets_inverse_A_4_SSE(w)); */
    1961:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
    1962:   }

    1964:   PetscCall(PetscFree(rtmp));

    1966:   C->ops->solve          = MatSolve_SeqBAIJ_4_NaturalOrdering_SSE;
    1967:   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_SSE;
    1968:   C->assembled           = PETSC_TRUE;

    1970:   PetscCall(PetscLogFlops(1.333333333333 * bs * bs2 * b->mbs));
    1971:   /* Flop Count from inverting diagonal blocks */
    1972:   SSE_SCOPE_END;
    1973:   PetscFunctionReturn(PETSC_SUCCESS);
    1974: }

    1976: #endif