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