Actual source code: baijfact12.c

  1: /*$Id: baijfact12.c,v 1.17 2001/08/31 16:22:11 bsmith Exp $*/
  2: /*
  3:     Factorization code for BAIJ format. 
  4: */
 5:  #include src/mat/impls/baij/seq/baij.h
 6:  #include src/vec/vecimpl.h
 7:  #include src/inline/ilu.h

  9: int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat A,Mat *B)
 10: {
 11: /*
 12:     Default Version for when blocks are 4 by 4 Using natural ordering
 13: */
 14:   Mat         C = *B;
 15:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
 16:   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
 17:   int         *ajtmpold,*ajtmp,nz,row;
 18:   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
 19:   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
 20:   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
 21:   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
 22:   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
 23:   MatScalar   m13,m14,m15,m16;
 24:   MatScalar   *ba = b->a,*aa = a->a;
 25:   PetscTruth  pivotinblocks = b->pivotinblocks;

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

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

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

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

 82:         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
 83:         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
 84:         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
 85:         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
 86:         nz = bi[row+1] - diag_offset[row] - 1;
 87:         pv += 16;
 88:         for (j=0; j<nz; j++) {
 89:           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
 90:           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
 91:           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
 92:           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
 93:           x    = rtmp + 16*pj[j];
 94:           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
 95:           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
 96:           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
 97:           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;

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

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

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

114:           pv   += 16;
115:         }
116:         PetscLogFlops(128*nz+112);
117:       }
118:       row = *ajtmp++;
119:     }
120:     /* finished row so stick it into b->a */
121:     pv = ba + 16*bi[i];
122:     pj = bj + bi[i];
123:     nz = bi[i+1] - bi[i];
124:     for (j=0; j<nz; j++) {
125:       x      = rtmp+16*pj[j];
126:       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
127:       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
128:       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
129:       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
130:       pv   += 16;
131:     }
132:     /* invert diagonal block */
133:     w = ba + 16*diag_offset[i];
134:     if (pivotinblocks) {
135:       Kernel_A_gets_inverse_A_4(w);
136:     } else {
137:       Kernel_A_gets_inverse_A_4_nopivot(w);
138:     }
139:   }

141:   PetscFree(rtmp);
142:   C->factor    = FACTOR_LU;
143:   C->assembled = PETSC_TRUE;
144:   PetscLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
145:   return(0);
146: }


149: #if defined(PETSC_HAVE_SSE)

151: #include PETSC_HAVE_SSE

153: /* SSE Version for when blocks are 4 by 4 Using natural ordering */
154: int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering_SSE(Mat A,Mat *B)
155: {
156:   Mat         C = *B;
157:   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
158:   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
159:   int         *ajtmpold,*ajtmp,nz,row;
160:   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
161:   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
162:   MatScalar   *ba = b->a,*aa = a->a;
163:   int nonzero=0;

166:   SSE_SCOPE_BEGIN;

168:   PetscMalloc(16*(n+1)*sizeof(MatScalar),&rtmp);
169:   for (i=0; i<n; i++) {
170:     nz    = bi[i+1] - bi[i];
171:     ajtmp = bj + bi[i];
172:     /* zero out the 4x4 block accumulators */
173:     /* zero out one register */
174:     XOR_PS(XMM7,XMM7);
175:     for  (j=0; j<nz; j++) {
176:       x = rtmp+16*ajtmp[j];
177:       SSE_INLINE_BEGIN_1(x)
178:         /* Copy zero register to memory locations */
179:         /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
180:         SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM7)
181:         SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM7)
182:         SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM7)
183:         SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM7)
184:         SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM7)
185:         SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM7)
186:         SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM7)
187:         SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM7)
188:       SSE_INLINE_END_1;
189:     }
190:     /* load in initial (unfactored row) */
191:     nz       = ai[i+1] - ai[i];
192:     ajtmpold = aj + ai[i];
193:     v        = aa + 16*ai[i];
194:     for (j=0; j<nz; j++) {
195:       x = rtmp+16*ajtmpold[j];
196:       /* Copy v block into x block */
197:       SSE_INLINE_BEGIN_2(v,x)
198:         /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
199:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
200:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM0)

202:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM1)
203:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM1)

205:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM2)
206:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM2)

208:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM3)
209:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM3)

211:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM4)
212:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM4)

214:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM5)
215:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM5)

217:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM6)
218:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM6)

220:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
221:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
222:       SSE_INLINE_END_2;

224:       v += 16;
225:     }
226:     row = *ajtmp++;
227:     while (row < i) {
228:       pc  = rtmp + 16*row;
229:       SSE_INLINE_BEGIN_1(pc)
230:         /* Load block from lower triangle */
231:         /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
232:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
233:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM0)

235:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM1)
236:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM1)

238:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM2)
239:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM2)

241:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM3)
242:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM3)

244:         /* Compare block to zero block */

246:         SSE_COPY_PS(XMM4,XMM7)
247:         SSE_CMPNEQ_PS(XMM4,XMM0)

249:         SSE_COPY_PS(XMM5,XMM7)
250:         SSE_CMPNEQ_PS(XMM5,XMM1)

252:         SSE_COPY_PS(XMM6,XMM7)
253:         SSE_CMPNEQ_PS(XMM6,XMM2)

255:         SSE_CMPNEQ_PS(XMM7,XMM3)

257:         /* Reduce the comparisons to one SSE register */
258:         SSE_OR_PS(XMM6,XMM7)
259:         SSE_OR_PS(XMM5,XMM4)
260:         SSE_OR_PS(XMM5,XMM6)
261:       SSE_INLINE_END_1;

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

267:       /* If block is nonzero ... */
268:       if (nonzero) {
269:         pv = ba + 16*diag_offset[row];
270:         PREFETCH_L1(&pv[16]);
271:         pj = bj + diag_offset[row] + 1;

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

278:         SSE_INLINE_BEGIN_2(pv,pc)
279:           /* Column 0, product is accumulated in XMM4 */
280:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_0,XMM4)
281:           SSE_SHUFFLE(XMM4,XMM4,0x00)
282:           SSE_MULT_PS(XMM4,XMM0)

284:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_1,XMM5)
285:           SSE_SHUFFLE(XMM5,XMM5,0x00)
286:           SSE_MULT_PS(XMM5,XMM1)
287:           SSE_ADD_PS(XMM4,XMM5)

289:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_2,XMM6)
290:           SSE_SHUFFLE(XMM6,XMM6,0x00)
291:           SSE_MULT_PS(XMM6,XMM2)
292:           SSE_ADD_PS(XMM4,XMM6)

294:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_3,XMM7)
295:           SSE_SHUFFLE(XMM7,XMM7,0x00)
296:           SSE_MULT_PS(XMM7,XMM3)
297:           SSE_ADD_PS(XMM4,XMM7)

299:           SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM4)
300:           SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM4)

302:           /* Column 1, product is accumulated in XMM5 */
303:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_4,XMM5)
304:           SSE_SHUFFLE(XMM5,XMM5,0x00)
305:           SSE_MULT_PS(XMM5,XMM0)

307:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_5,XMM6)
308:           SSE_SHUFFLE(XMM6,XMM6,0x00)
309:           SSE_MULT_PS(XMM6,XMM1)
310:           SSE_ADD_PS(XMM5,XMM6)

312:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_6,XMM7)
313:           SSE_SHUFFLE(XMM7,XMM7,0x00)
314:           SSE_MULT_PS(XMM7,XMM2)
315:           SSE_ADD_PS(XMM5,XMM7)

317:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_7,XMM6)
318:           SSE_SHUFFLE(XMM6,XMM6,0x00)
319:           SSE_MULT_PS(XMM6,XMM3)
320:           SSE_ADD_PS(XMM5,XMM6)

322:           SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM5)
323:           SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM5)

325:           SSE_PREFETCH_L1(SSE_ARG_1,FLOAT_24)

327:           /* Column 2, product is accumulated in XMM6 */
328:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_8,XMM6)
329:           SSE_SHUFFLE(XMM6,XMM6,0x00)
330:           SSE_MULT_PS(XMM6,XMM0)

332:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_9,XMM7)
333:           SSE_SHUFFLE(XMM7,XMM7,0x00)
334:           SSE_MULT_PS(XMM7,XMM1)
335:           SSE_ADD_PS(XMM6,XMM7)

337:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_10,XMM7)
338:           SSE_SHUFFLE(XMM7,XMM7,0x00)
339:           SSE_MULT_PS(XMM7,XMM2)
340:           SSE_ADD_PS(XMM6,XMM7)

342:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_11,XMM7)
343:           SSE_SHUFFLE(XMM7,XMM7,0x00)
344:           SSE_MULT_PS(XMM7,XMM3)
345:           SSE_ADD_PS(XMM6,XMM7)
346: 
347:           SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM6)
348:           SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

350:           /* Note: For the last column, we no longer need to preserve XMM0->XMM3 */
351:           /* Column 3, product is accumulated in XMM0 */
352:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_12,XMM7)
353:           SSE_SHUFFLE(XMM7,XMM7,0x00)
354:           SSE_MULT_PS(XMM0,XMM7)

356:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_13,XMM7)
357:           SSE_SHUFFLE(XMM7,XMM7,0x00)
358:           SSE_MULT_PS(XMM1,XMM7)
359:           SSE_ADD_PS(XMM0,XMM1)

361:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_14,XMM1)
362:           SSE_SHUFFLE(XMM1,XMM1,0x00)
363:           SSE_MULT_PS(XMM1,XMM2)
364:           SSE_ADD_PS(XMM0,XMM1)

366:           SSE_LOAD_SS(SSE_ARG_1,FLOAT_15,XMM7)
367:           SSE_SHUFFLE(XMM7,XMM7,0x00)
368:           SSE_MULT_PS(XMM3,XMM7)
369:           SSE_ADD_PS(XMM0,XMM3)

371:           SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM0)
372:           SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)

374:           /* Simplify Bookkeeping -- Completely Unnecessary Instructions */
375:           /* This is code to be maintained and read by humans afterall. */
376:           /* Copy Multiplier Col 3 into XMM3 */
377:           SSE_COPY_PS(XMM3,XMM0)
378:           /* Copy Multiplier Col 2 into XMM2 */
379:           SSE_COPY_PS(XMM2,XMM6)
380:           /* Copy Multiplier Col 1 into XMM1 */
381:           SSE_COPY_PS(XMM1,XMM5)
382:           /* Copy Multiplier Col 0 into XMM0 */
383:           SSE_COPY_PS(XMM0,XMM4)
384:         SSE_INLINE_END_2;

386:         /* Update the row: */
387:         nz = bi[row+1] - diag_offset[row] - 1;
388:         pv += 16;
389:         for (j=0; j<nz; j++) {
390:           PREFETCH_L1(&pv[16]);
391:           x = rtmp + 16*pj[j];

393:           /* X:=X-M*PV, One column at a time */
394:           /* Note: M is already loaded columnwise into registers XMM0-XMM3 */
395:           SSE_INLINE_BEGIN_2(x,pv)
396:             /* Load First Column of X*/
397:             SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM4)
398:             SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM4)

400:             /* Matrix-Vector Product: */
401:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_0,XMM5)
402:             SSE_SHUFFLE(XMM5,XMM5,0x00)
403:             SSE_MULT_PS(XMM5,XMM0)
404:             SSE_SUB_PS(XMM4,XMM5)

406:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_1,XMM6)
407:             SSE_SHUFFLE(XMM6,XMM6,0x00)
408:             SSE_MULT_PS(XMM6,XMM1)
409:             SSE_SUB_PS(XMM4,XMM6)

411:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_2,XMM7)
412:             SSE_SHUFFLE(XMM7,XMM7,0x00)
413:             SSE_MULT_PS(XMM7,XMM2)
414:             SSE_SUB_PS(XMM4,XMM7)

416:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_3,XMM5)
417:             SSE_SHUFFLE(XMM5,XMM5,0x00)
418:             SSE_MULT_PS(XMM5,XMM3)
419:             SSE_SUB_PS(XMM4,XMM5)

421:             SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM4)
422:             SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM4)

424:             /* Second Column */
425:             SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM5)
426:             SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM5)

428:             /* Matrix-Vector Product: */
429:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_4,XMM6)
430:             SSE_SHUFFLE(XMM6,XMM6,0x00)
431:             SSE_MULT_PS(XMM6,XMM0)
432:             SSE_SUB_PS(XMM5,XMM6)

434:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_5,XMM7)
435:             SSE_SHUFFLE(XMM7,XMM7,0x00)
436:             SSE_MULT_PS(XMM7,XMM1)
437:             SSE_SUB_PS(XMM5,XMM7)

439:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_6,XMM4)
440:             SSE_SHUFFLE(XMM4,XMM4,0x00)
441:             SSE_MULT_PS(XMM4,XMM2)
442:             SSE_SUB_PS(XMM5,XMM4)

444:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_7,XMM6)
445:             SSE_SHUFFLE(XMM6,XMM6,0x00)
446:             SSE_MULT_PS(XMM6,XMM3)
447:             SSE_SUB_PS(XMM5,XMM6)
448: 
449:             SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM5)
450:             SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM5)

452:             SSE_PREFETCH_L1(SSE_ARG_2,FLOAT_24)

454:             /* Third Column */
455:             SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM6)
456:             SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)

458:             /* Matrix-Vector Product: */
459:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_8,XMM7)
460:             SSE_SHUFFLE(XMM7,XMM7,0x00)
461:             SSE_MULT_PS(XMM7,XMM0)
462:             SSE_SUB_PS(XMM6,XMM7)

464:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_9,XMM4)
465:             SSE_SHUFFLE(XMM4,XMM4,0x00)
466:             SSE_MULT_PS(XMM4,XMM1)
467:             SSE_SUB_PS(XMM6,XMM4)

469:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_10,XMM5)
470:             SSE_SHUFFLE(XMM5,XMM5,0x00)
471:             SSE_MULT_PS(XMM5,XMM2)
472:             SSE_SUB_PS(XMM6,XMM5)

474:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_11,XMM7)
475:             SSE_SHUFFLE(XMM7,XMM7,0x00)
476:             SSE_MULT_PS(XMM7,XMM3)
477:             SSE_SUB_PS(XMM6,XMM7)
478: 
479:             SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM6)
480:             SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM6)
481: 
482:             /* Fourth Column */
483:             SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM4)
484:             SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM4)

486:             /* Matrix-Vector Product: */
487:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_12,XMM5)
488:             SSE_SHUFFLE(XMM5,XMM5,0x00)
489:             SSE_MULT_PS(XMM5,XMM0)
490:             SSE_SUB_PS(XMM4,XMM5)

492:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_13,XMM6)
493:             SSE_SHUFFLE(XMM6,XMM6,0x00)
494:             SSE_MULT_PS(XMM6,XMM1)
495:             SSE_SUB_PS(XMM4,XMM6)

497:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_14,XMM7)
498:             SSE_SHUFFLE(XMM7,XMM7,0x00)
499:             SSE_MULT_PS(XMM7,XMM2)
500:             SSE_SUB_PS(XMM4,XMM7)

502:             SSE_LOAD_SS(SSE_ARG_2,FLOAT_15,XMM5)
503:             SSE_SHUFFLE(XMM5,XMM5,0x00)
504:             SSE_MULT_PS(XMM5,XMM3)
505:             SSE_SUB_PS(XMM4,XMM5)
506: 
507:             SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
508:             SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
509:           SSE_INLINE_END_2;
510:           pv   += 16;
511:         }
512:         PetscLogFlops(128*nz+112);
513:       }
514:       row = *ajtmp++;
515:     }
516:     /* finished row so stick it into b->a */
517:     pv = ba + 16*bi[i];
518:     pj = bj + bi[i];
519:     nz = bi[i+1] - bi[i];

521:     /* Copy x block back into pv block */
522:     for (j=0; j<nz; j++) {
523:       x  = rtmp+16*pj[j];

525:       SSE_INLINE_BEGIN_2(x,pv)
526:         /* Note: on future SSE architectures, STORE might be more efficient than STOREL/H */
527:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM1)
528:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_0,XMM1)

530:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_2,XMM2)
531:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_2,XMM2)

533:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_4,XMM3)
534:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_4,XMM3)

536:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM4)
537:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_6,XMM4)

539:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
540:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_8,XMM5)

542:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_10,XMM6)
543:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_10,XMM6)

545:         SSE_LOADL_PS(SSE_ARG_1,FLOAT_12,XMM7)
546:         SSE_STOREL_PS(SSE_ARG_2,FLOAT_12,XMM7)

548:         SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM0)
549:         SSE_STOREH_PS(SSE_ARG_2,FLOAT_14,XMM0)
550:       SSE_INLINE_END_2;
551:       pv += 16;
552:     }
553:     /* invert diagonal block */
554:     w = ba + 16*diag_offset[i];
555:     Kernel_A_gets_inverse_A_4_SSE(w);
556:     /* Note: Using Kramer's rule, flop count below might be infairly high or low? */
557:   }

559:   PetscFree(rtmp);
560:   C->factor    = FACTOR_LU;
561:   C->assembled = PETSC_TRUE;
562:   PetscLogFlops(1.3333*64*b->mbs);
563:   /* Flop Count from inverting diagonal blocks */
564:   SSE_SCOPE_END;
565:   return(0);
566: }

568: #endif