Actual source code: dgefa4.c

  1: /*$Id: dgefa4.c,v 1.21 2001/06/22 19:50:38 buschelm Exp $*/
  2: /*
  3:        Inverts 4 by 4 matrix using partial pivoting.

  5:        Used by the sparse factorization routines in 
  6:      src/mat/impls/baij/seq and src/mat/impls/bdiag/seq

  8:        See also src/inline/ilu.h

 10:        This is a combination of the Linpack routines
 11:     dgefa() and dgedi() specialized for a size of 4.

 13: */
 14:  #include petsc.h

 16: int Kernel_A_gets_inverse_A_4(MatScalar *a)
 17: {
 18:     int        i__2,i__3,kp1,j,k,l,ll,i,ipvt[4],kb,k3;
 19:     int        k4,j3;
 20:     MatScalar  *aa,*ax,*ay,work[16],stmp;
 21:     MatReal    tmp,max;

 23: /*     gaussian elimination with partial pivoting */

 26:     /* Parameter adjustments */
 27:     a       -= 5;

 29:     for (k = 1; k <= 3; ++k) {
 30:         kp1 = k + 1;
 31:         k3  = 4*k;
 32:         k4  = k3 + k;
 33: /*        find l = pivot index */

 35:         i__2 = 4 - k;
 36:         aa = &a[k4];
 37:         max = PetscAbsScalar(aa[0]);
 38:         l = 1;
 39:         for (ll=1; ll<i__2; ll++) {
 40:           tmp = PetscAbsScalar(aa[ll]);
 41:           if (tmp > max) { max = tmp; l = ll+1;}
 42:         }
 43:         l       += k - 1;
 44:         ipvt[k-1] = l;

 46:         if (a[l + k3] == 0.) {
 47:           SETERRQ(k,"Zero pivot");
 48:         }

 50: /*           interchange if necessary */

 52:         if (l != k) {
 53:           stmp      = a[l + k3];
 54:           a[l + k3] = a[k4];
 55:           a[k4]     = stmp;
 56:         }

 58: /*           compute multipliers */

 60:         stmp = -1. / a[k4];
 61:         i__2 = 4 - k;
 62:         aa = &a[1 + k4];
 63:         for (ll=0; ll<i__2; ll++) {
 64:           aa[ll] *= stmp;
 65:         }

 67: /*           row elimination with column indexing */

 69:         ax = &a[k4+1];
 70:         for (j = kp1; j <= 4; ++j) {
 71:             j3   = 4*j;
 72:             stmp = a[l + j3];
 73:             if (l != k) {
 74:               a[l + j3] = a[k + j3];
 75:               a[k + j3] = stmp;
 76:             }

 78:             i__3 = 4 - k;
 79:             ay = &a[1+k+j3];
 80:             for (ll=0; ll<i__3; ll++) {
 81:               ay[ll] += stmp*ax[ll];
 82:             }
 83:         }
 84:     }
 85:     ipvt[3] = 4;
 86:     if (a[20] == 0.) {
 87:         SETERRQ(3,"Zero pivot,final row");
 88:     }

 90:     /*
 91:          Now form the inverse 
 92:     */

 94:    /*     compute inverse(u) */

 96:     for (k = 1; k <= 4; ++k) {
 97:         k3    = 4*k;
 98:         k4    = k3 + k;
 99:         a[k4] = 1.0 / a[k4];
100:         stmp  = -a[k4];
101:         i__2  = k - 1;
102:         aa    = &a[k3 + 1];
103:         for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
104:         kp1 = k + 1;
105:         if (4 < kp1) continue;
106:         ax = aa;
107:         for (j = kp1; j <= 4; ++j) {
108:             j3        = 4*j;
109:             stmp      = a[k + j3];
110:             a[k + j3] = 0.0;
111:             ay        = &a[j3 + 1];
112:             for (ll=0; ll<k; ll++) {
113:               ay[ll] += stmp*ax[ll];
114:             }
115:         }
116:     }

118:    /*    form inverse(u)*inverse(l) */

120:     for (kb = 1; kb <= 3; ++kb) {
121:         k   = 4 - kb;
122:         k3  = 4*k;
123:         kp1 = k + 1;
124:         aa  = a + k3;
125:         for (i = kp1; i <= 4; ++i) {
126:             work[i-1] = aa[i];
127:             aa[i]   = 0.0;
128:         }
129:         for (j = kp1; j <= 4; ++j) {
130:             stmp  = work[j-1];
131:             ax    = &a[4*j + 1];
132:             ay    = &a[k3 + 1];
133:             ay[0] += stmp*ax[0];
134:             ay[1] += stmp*ax[1];
135:             ay[2] += stmp*ax[2];
136:             ay[3] += stmp*ax[3];
137:         }
138:         l = ipvt[k-1];
139:         if (l != k) {
140:             ax = &a[k3 + 1];
141:             ay = &a[4*l + 1];
142:             stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
143:             stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
144:             stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
145:             stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
146:         }
147:     }
148:     return(0);
149: }

151: #if defined(PETSC_HAVE_SSE)
152: #include PETSC_HAVE_SSE

154: int Kernel_A_gets_inverse_A_4_SSE(float *a)
155: {
156:   /* 
157:      This routine is converted from Intel's Small Matrix Library.
158:      See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
159:      Order Number: 245043-001
160:      March 1999
161:      http://www.intel.com

163:      Inverse of a 4x4 matrix via Kramer's Rule:
164:      bool Invert4x4(SMLXMatrix &);
165:   */

168:   SSE_SCOPE_BEGIN;
169:     SSE_INLINE_BEGIN_1(a)

171: /* ----------------------------------------------- */

173:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
174:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_4,XMM0)

176:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
177:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_12,XMM5)

179:       SSE_COPY_PS(XMM3,XMM0)
180:       SSE_SHUFFLE(XMM3,XMM5,0x88)

182:       SSE_SHUFFLE(XMM5,XMM0,0xDD)

184:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_2,XMM0)
185:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM0)

187:       SSE_LOADL_PS(SSE_ARG_1,FLOAT_10,XMM6)
188:       SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM6)

190:       SSE_COPY_PS(XMM4,XMM0)
191:       SSE_SHUFFLE(XMM4,XMM6,0x88)

193:       SSE_SHUFFLE(XMM6,XMM0,0xDD)

195: /* ----------------------------------------------- */

197:       SSE_COPY_PS(XMM7,XMM4)
198:       SSE_MULT_PS(XMM7,XMM6)

200:       SSE_SHUFFLE(XMM7,XMM7,0xB1)

202:       SSE_COPY_PS(XMM0,XMM5)
203:       SSE_MULT_PS(XMM0,XMM7)

205:       SSE_COPY_PS(XMM2,XMM3)
206:       SSE_MULT_PS(XMM2,XMM7)

208:       SSE_SHUFFLE(XMM7,XMM7,0x4E)

210:       SSE_COPY_PS(XMM1,XMM5)
211:       SSE_MULT_PS(XMM1,XMM7)
212:       SSE_SUB_PS(XMM1,XMM0)

214:       SSE_MULT_PS(XMM7,XMM3)
215:       SSE_SUB_PS(XMM7,XMM2)

217:       SSE_SHUFFLE(XMM7,XMM7,0x4E)
218:       SSE_STORE_PS(SSE_ARG_1,FLOAT_4,XMM7)

220: /* ----------------------------------------------- */

222:       SSE_COPY_PS(XMM0,XMM5)
223:       SSE_MULT_PS(XMM0,XMM4)

225:       SSE_SHUFFLE(XMM0,XMM0,0xB1)

227:       SSE_COPY_PS(XMM2,XMM6)
228:       SSE_MULT_PS(XMM2,XMM0)
229:       SSE_ADD_PS(XMM2,XMM1)
230: 
231:       SSE_COPY_PS(XMM7,XMM3)
232:       SSE_MULT_PS(XMM7,XMM0)

234:       SSE_SHUFFLE(XMM0,XMM0,0x4E)

236:       SSE_COPY_PS(XMM1,XMM6)
237:       SSE_MULT_PS(XMM1,XMM0)
238:       SSE_SUB_PS(XMM2,XMM1)

240:       SSE_MULT_PS(XMM0,XMM3)
241:       SSE_SUB_PS(XMM0,XMM7)

243:       SSE_SHUFFLE(XMM0,XMM0,0x4E)
244:       SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM0)

246:       /* ----------------------------------------------- */

248:       SSE_COPY_PS(XMM7,XMM5)
249:       SSE_SHUFFLE(XMM7,XMM5,0x4E)
250:       SSE_MULT_PS(XMM7,XMM6)

252:       SSE_SHUFFLE(XMM7,XMM7,0xB1)

254:       SSE_SHUFFLE(XMM4,XMM4,0x4E)

256:       SSE_COPY_PS(XMM0,XMM4)
257:       SSE_MULT_PS(XMM0,XMM7)
258:       SSE_ADD_PS(XMM0,XMM2)

260:       SSE_COPY_PS(XMM2,XMM3)
261:       SSE_MULT_PS(XMM2,XMM7)

263:       SSE_SHUFFLE(XMM7,XMM7,0x4E)

265:       SSE_COPY_PS(XMM1,XMM4)
266:       SSE_MULT_PS(XMM1,XMM7)
267:       SSE_SUB_PS(XMM0,XMM1)
268:       SSE_STORE_PS(SSE_ARG_1,FLOAT_0,XMM0)

270:       SSE_MULT_PS(XMM7,XMM3)
271:       SSE_SUB_PS(XMM7,XMM2)

273:       SSE_SHUFFLE(XMM7,XMM7,0x4E)

275:       /* ----------------------------------------------- */

277:       SSE_COPY_PS(XMM1,XMM3)
278:       SSE_MULT_PS(XMM1,XMM5)

280:       SSE_SHUFFLE(XMM1,XMM1,0xB1)

282:       SSE_COPY_PS(XMM0,XMM6)
283:       SSE_MULT_PS(XMM0,XMM1)
284:       SSE_ADD_PS(XMM0,XMM7)
285: 
286:       SSE_COPY_PS(XMM2,XMM4)
287:       SSE_MULT_PS(XMM2,XMM1)
288:       SSE_SUB_PS_M(XMM2,SSE_ARG_1,FLOAT_12)

290:       SSE_SHUFFLE(XMM1,XMM1,0x4E)

292:       SSE_COPY_PS(XMM7,XMM6)
293:       SSE_MULT_PS(XMM7,XMM1)
294:       SSE_SUB_PS(XMM7,XMM0)

296:       SSE_MULT_PS(XMM1,XMM4)
297:       SSE_SUB_PS(XMM2,XMM1)
298:       SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM2)

300:       /* ----------------------------------------------- */

302:       SSE_COPY_PS(XMM1,XMM3)
303:       SSE_MULT_PS(XMM1,XMM6)

305:       SSE_SHUFFLE(XMM1,XMM1,0xB1)

307:       SSE_COPY_PS(XMM2,XMM4)
308:       SSE_MULT_PS(XMM2,XMM1)
309:       SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM0)
310:       SSE_SUB_PS(XMM0,XMM2)

312:       SSE_COPY_PS(XMM2,XMM5)
313:       SSE_MULT_PS(XMM2,XMM1)
314:       SSE_ADD_PS(XMM2,XMM7)

316:       SSE_SHUFFLE(XMM1,XMM1,0x4E)

318:       SSE_COPY_PS(XMM7,XMM4)
319:       SSE_MULT_PS(XMM7,XMM1)
320:       SSE_ADD_PS(XMM7,XMM0)

322:       SSE_MULT_PS(XMM1,XMM5)
323:       SSE_SUB_PS(XMM2,XMM1)

325:       /* ----------------------------------------------- */

327:       SSE_MULT_PS(XMM4,XMM3)

329:       SSE_SHUFFLE(XMM4,XMM4,0xB1)

331:       SSE_COPY_PS(XMM1,XMM6)
332:       SSE_MULT_PS(XMM1,XMM4)
333:       SSE_ADD_PS(XMM1,XMM7)

335:       SSE_COPY_PS(XMM0,XMM5)
336:       SSE_MULT_PS(XMM0,XMM4)
337:       SSE_LOAD_PS(SSE_ARG_1,FLOAT_12,XMM7)
338:       SSE_SUB_PS(XMM7,XMM0)

340:       SSE_SHUFFLE(XMM4,XMM4,0x4E)

342:       SSE_MULT_PS(XMM6,XMM4)
343:       SSE_SUB_PS(XMM1,XMM6)

345:       SSE_MULT_PS(XMM5,XMM4)
346:       SSE_ADD_PS(XMM5,XMM7)

348:       /* ----------------------------------------------- */

350:       SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
351:       SSE_MULT_PS(XMM3,XMM0)

353:       SSE_COPY_PS(XMM4,XMM3)
354:       SSE_SHUFFLE(XMM4,XMM3,0x4E)
355:       SSE_ADD_PS(XMM4,XMM3)

357:       SSE_COPY_PS(XMM6,XMM4)
358:       SSE_SHUFFLE(XMM6,XMM4,0xB1)
359:       SSE_ADD_SS(XMM6,XMM4)

361:       SSE_COPY_PS(XMM3,XMM6)
362:       SSE_RECIP_SS(XMM3,XMM6)
363:       SSE_COPY_SS(XMM4,XMM3)
364:       SSE_ADD_SS(XMM4,XMM3)
365:       SSE_MULT_SS(XMM3,XMM3)
366:       SSE_MULT_SS(XMM6,XMM3)
367:       SSE_SUB_SS(XMM4,XMM6)

369:       SSE_SHUFFLE(XMM4,XMM4,0x00)

371:       SSE_MULT_PS(XMM0,XMM4)
372:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM0)
373:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM0)

375:       SSE_MULT_PS(XMM1,XMM4)
376:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM1)
377:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM1)

379:       SSE_MULT_PS(XMM2,XMM4)
380:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM2)
381:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM2)

383:       SSE_MULT_PS(XMM4,XMM5)
384:       SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
385:       SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)

387:       /* ----------------------------------------------- */

389:       SSE_INLINE_END_1;
390:   SSE_SCOPE_END;

392:   return(0);
393: }

395: #endif