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
18: int Kernel_A_gets_inverse_A_4(MatScalar *a)
19: {
20: int i__2,i__3,kp1,j,k,l,ll,i,ipvt[4],kb,k3;
21: int k4,j3;
22: MatScalar *aa,*ax,*ay,work[16],stmp;
23: MatReal tmp,max;
25: /* gaussian elimination with partial pivoting */
28: /* Parameter adjustments */
29: a -= 5;
31: for (k = 1; k <= 3; ++k) {
32: kp1 = k + 1;
33: k3 = 4*k;
34: k4 = k3 + k;
35: /* find l = pivot index */
37: i__2 = 4 - k;
38: aa = &a[k4];
39: max = PetscAbsScalar(aa[0]);
40: l = 1;
41: for (ll=1; ll<i__2; ll++) {
42: tmp = PetscAbsScalar(aa[ll]);
43: if (tmp > max) { max = tmp; l = ll+1;}
44: }
45: l += k - 1;
46: ipvt[k-1] = l;
48: if (a[l + k3] == 0.) {
49: SETERRQ(k,"Zero pivot");
50: }
52: /* interchange if necessary */
54: if (l != k) {
55: stmp = a[l + k3];
56: a[l + k3] = a[k4];
57: a[k4] = stmp;
58: }
60: /* compute multipliers */
62: stmp = -1. / a[k4];
63: i__2 = 4 - k;
64: aa = &a[1 + k4];
65: for (ll=0; ll<i__2; ll++) {
66: aa[ll] *= stmp;
67: }
69: /* row elimination with column indexing */
71: ax = &a[k4+1];
72: for (j = kp1; j <= 4; ++j) {
73: j3 = 4*j;
74: stmp = a[l + j3];
75: if (l != k) {
76: a[l + j3] = a[k + j3];
77: a[k + j3] = stmp;
78: }
80: i__3 = 4 - k;
81: ay = &a[1+k+j3];
82: for (ll=0; ll<i__3; ll++) {
83: ay[ll] += stmp*ax[ll];
84: }
85: }
86: }
87: ipvt[3] = 4;
88: if (a[20] == 0.) {
89: SETERRQ(3,"Zero pivot,final row");
90: }
92: /*
93: Now form the inverse
94: */
96: /* compute inverse(u) */
98: for (k = 1; k <= 4; ++k) {
99: k3 = 4*k;
100: k4 = k3 + k;
101: a[k4] = 1.0 / a[k4];
102: stmp = -a[k4];
103: i__2 = k - 1;
104: aa = &a[k3 + 1];
105: for (ll=0; ll<i__2; ll++) aa[ll] *= stmp;
106: kp1 = k + 1;
107: if (4 < kp1) continue;
108: ax = aa;
109: for (j = kp1; j <= 4; ++j) {
110: j3 = 4*j;
111: stmp = a[k + j3];
112: a[k + j3] = 0.0;
113: ay = &a[j3 + 1];
114: for (ll=0; ll<k; ll++) {
115: ay[ll] += stmp*ax[ll];
116: }
117: }
118: }
120: /* form inverse(u)*inverse(l) */
122: for (kb = 1; kb <= 3; ++kb) {
123: k = 4 - kb;
124: k3 = 4*k;
125: kp1 = k + 1;
126: aa = a + k3;
127: for (i = kp1; i <= 4; ++i) {
128: work[i-1] = aa[i];
129: aa[i] = 0.0;
130: }
131: for (j = kp1; j <= 4; ++j) {
132: stmp = work[j-1];
133: ax = &a[4*j + 1];
134: ay = &a[k3 + 1];
135: ay[0] += stmp*ax[0];
136: ay[1] += stmp*ax[1];
137: ay[2] += stmp*ax[2];
138: ay[3] += stmp*ax[3];
139: }
140: l = ipvt[k-1];
141: if (l != k) {
142: ax = &a[k3 + 1];
143: ay = &a[4*l + 1];
144: stmp = ax[0]; ax[0] = ay[0]; ay[0] = stmp;
145: stmp = ax[1]; ax[1] = ay[1]; ay[1] = stmp;
146: stmp = ax[2]; ax[2] = ay[2]; ay[2] = stmp;
147: stmp = ax[3]; ax[3] = ay[3]; ay[3] = stmp;
148: }
149: }
150: return(0);
151: }
153: #if defined(PETSC_HAVE_SSE)
154: #include PETSC_HAVE_SSE
158: int Kernel_A_gets_inverse_A_4_SSE(float *a)
159: {
160: /*
161: This routine is converted from Intel's Small Matrix Library.
162: See: Streaming SIMD Extensions -- Inverse of 4x4 Matrix
163: Order Number: 245043-001
164: March 1999
165: http://www.intel.com
167: Inverse of a 4x4 matrix via Kramer's Rule:
168: bool Invert4x4(SMLXMatrix &);
169: */
172: SSE_SCOPE_BEGIN;
173: SSE_INLINE_BEGIN_1(a)
175: /* ----------------------------------------------- */
177: SSE_LOADL_PS(SSE_ARG_1,FLOAT_0,XMM0)
178: SSE_LOADH_PS(SSE_ARG_1,FLOAT_4,XMM0)
180: SSE_LOADL_PS(SSE_ARG_1,FLOAT_8,XMM5)
181: SSE_LOADH_PS(SSE_ARG_1,FLOAT_12,XMM5)
183: SSE_COPY_PS(XMM3,XMM0)
184: SSE_SHUFFLE(XMM3,XMM5,0x88)
186: SSE_SHUFFLE(XMM5,XMM0,0xDD)
188: SSE_LOADL_PS(SSE_ARG_1,FLOAT_2,XMM0)
189: SSE_LOADH_PS(SSE_ARG_1,FLOAT_6,XMM0)
191: SSE_LOADL_PS(SSE_ARG_1,FLOAT_10,XMM6)
192: SSE_LOADH_PS(SSE_ARG_1,FLOAT_14,XMM6)
194: SSE_COPY_PS(XMM4,XMM0)
195: SSE_SHUFFLE(XMM4,XMM6,0x88)
197: SSE_SHUFFLE(XMM6,XMM0,0xDD)
199: /* ----------------------------------------------- */
201: SSE_COPY_PS(XMM7,XMM4)
202: SSE_MULT_PS(XMM7,XMM6)
204: SSE_SHUFFLE(XMM7,XMM7,0xB1)
206: SSE_COPY_PS(XMM0,XMM5)
207: SSE_MULT_PS(XMM0,XMM7)
209: SSE_COPY_PS(XMM2,XMM3)
210: SSE_MULT_PS(XMM2,XMM7)
212: SSE_SHUFFLE(XMM7,XMM7,0x4E)
214: SSE_COPY_PS(XMM1,XMM5)
215: SSE_MULT_PS(XMM1,XMM7)
216: SSE_SUB_PS(XMM1,XMM0)
218: SSE_MULT_PS(XMM7,XMM3)
219: SSE_SUB_PS(XMM7,XMM2)
221: SSE_SHUFFLE(XMM7,XMM7,0x4E)
222: SSE_STORE_PS(SSE_ARG_1,FLOAT_4,XMM7)
224: /* ----------------------------------------------- */
226: SSE_COPY_PS(XMM0,XMM5)
227: SSE_MULT_PS(XMM0,XMM4)
229: SSE_SHUFFLE(XMM0,XMM0,0xB1)
231: SSE_COPY_PS(XMM2,XMM6)
232: SSE_MULT_PS(XMM2,XMM0)
233: SSE_ADD_PS(XMM2,XMM1)
234:
235: SSE_COPY_PS(XMM7,XMM3)
236: SSE_MULT_PS(XMM7,XMM0)
238: SSE_SHUFFLE(XMM0,XMM0,0x4E)
240: SSE_COPY_PS(XMM1,XMM6)
241: SSE_MULT_PS(XMM1,XMM0)
242: SSE_SUB_PS(XMM2,XMM1)
244: SSE_MULT_PS(XMM0,XMM3)
245: SSE_SUB_PS(XMM0,XMM7)
247: SSE_SHUFFLE(XMM0,XMM0,0x4E)
248: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM0)
250: /* ----------------------------------------------- */
252: SSE_COPY_PS(XMM7,XMM5)
253: SSE_SHUFFLE(XMM7,XMM5,0x4E)
254: SSE_MULT_PS(XMM7,XMM6)
256: SSE_SHUFFLE(XMM7,XMM7,0xB1)
258: SSE_SHUFFLE(XMM4,XMM4,0x4E)
260: SSE_COPY_PS(XMM0,XMM4)
261: SSE_MULT_PS(XMM0,XMM7)
262: SSE_ADD_PS(XMM0,XMM2)
264: SSE_COPY_PS(XMM2,XMM3)
265: SSE_MULT_PS(XMM2,XMM7)
267: SSE_SHUFFLE(XMM7,XMM7,0x4E)
269: SSE_COPY_PS(XMM1,XMM4)
270: SSE_MULT_PS(XMM1,XMM7)
271: SSE_SUB_PS(XMM0,XMM1)
272: SSE_STORE_PS(SSE_ARG_1,FLOAT_0,XMM0)
274: SSE_MULT_PS(XMM7,XMM3)
275: SSE_SUB_PS(XMM7,XMM2)
277: SSE_SHUFFLE(XMM7,XMM7,0x4E)
279: /* ----------------------------------------------- */
281: SSE_COPY_PS(XMM1,XMM3)
282: SSE_MULT_PS(XMM1,XMM5)
284: SSE_SHUFFLE(XMM1,XMM1,0xB1)
286: SSE_COPY_PS(XMM0,XMM6)
287: SSE_MULT_PS(XMM0,XMM1)
288: SSE_ADD_PS(XMM0,XMM7)
289:
290: SSE_COPY_PS(XMM2,XMM4)
291: SSE_MULT_PS(XMM2,XMM1)
292: SSE_SUB_PS_M(XMM2,SSE_ARG_1,FLOAT_12)
294: SSE_SHUFFLE(XMM1,XMM1,0x4E)
296: SSE_COPY_PS(XMM7,XMM6)
297: SSE_MULT_PS(XMM7,XMM1)
298: SSE_SUB_PS(XMM7,XMM0)
300: SSE_MULT_PS(XMM1,XMM4)
301: SSE_SUB_PS(XMM2,XMM1)
302: SSE_STORE_PS(SSE_ARG_1,FLOAT_12,XMM2)
304: /* ----------------------------------------------- */
306: SSE_COPY_PS(XMM1,XMM3)
307: SSE_MULT_PS(XMM1,XMM6)
309: SSE_SHUFFLE(XMM1,XMM1,0xB1)
311: SSE_COPY_PS(XMM2,XMM4)
312: SSE_MULT_PS(XMM2,XMM1)
313: SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM0)
314: SSE_SUB_PS(XMM0,XMM2)
316: SSE_COPY_PS(XMM2,XMM5)
317: SSE_MULT_PS(XMM2,XMM1)
318: SSE_ADD_PS(XMM2,XMM7)
320: SSE_SHUFFLE(XMM1,XMM1,0x4E)
322: SSE_COPY_PS(XMM7,XMM4)
323: SSE_MULT_PS(XMM7,XMM1)
324: SSE_ADD_PS(XMM7,XMM0)
326: SSE_MULT_PS(XMM1,XMM5)
327: SSE_SUB_PS(XMM2,XMM1)
329: /* ----------------------------------------------- */
331: SSE_MULT_PS(XMM4,XMM3)
333: SSE_SHUFFLE(XMM4,XMM4,0xB1)
335: SSE_COPY_PS(XMM1,XMM6)
336: SSE_MULT_PS(XMM1,XMM4)
337: SSE_ADD_PS(XMM1,XMM7)
339: SSE_COPY_PS(XMM0,XMM5)
340: SSE_MULT_PS(XMM0,XMM4)
341: SSE_LOAD_PS(SSE_ARG_1,FLOAT_12,XMM7)
342: SSE_SUB_PS(XMM7,XMM0)
344: SSE_SHUFFLE(XMM4,XMM4,0x4E)
346: SSE_MULT_PS(XMM6,XMM4)
347: SSE_SUB_PS(XMM1,XMM6)
349: SSE_MULT_PS(XMM5,XMM4)
350: SSE_ADD_PS(XMM5,XMM7)
352: /* ----------------------------------------------- */
354: SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
355: SSE_MULT_PS(XMM3,XMM0)
357: SSE_COPY_PS(XMM4,XMM3)
358: SSE_SHUFFLE(XMM4,XMM3,0x4E)
359: SSE_ADD_PS(XMM4,XMM3)
361: SSE_COPY_PS(XMM6,XMM4)
362: SSE_SHUFFLE(XMM6,XMM4,0xB1)
363: SSE_ADD_SS(XMM6,XMM4)
365: SSE_COPY_PS(XMM3,XMM6)
366: SSE_RECIP_SS(XMM3,XMM6)
367: SSE_COPY_SS(XMM4,XMM3)
368: SSE_ADD_SS(XMM4,XMM3)
369: SSE_MULT_SS(XMM3,XMM3)
370: SSE_MULT_SS(XMM6,XMM3)
371: SSE_SUB_SS(XMM4,XMM6)
373: SSE_SHUFFLE(XMM4,XMM4,0x00)
375: SSE_MULT_PS(XMM0,XMM4)
376: SSE_STOREL_PS(SSE_ARG_1,FLOAT_0,XMM0)
377: SSE_STOREH_PS(SSE_ARG_1,FLOAT_2,XMM0)
379: SSE_MULT_PS(XMM1,XMM4)
380: SSE_STOREL_PS(SSE_ARG_1,FLOAT_4,XMM1)
381: SSE_STOREH_PS(SSE_ARG_1,FLOAT_6,XMM1)
383: SSE_MULT_PS(XMM2,XMM4)
384: SSE_STOREL_PS(SSE_ARG_1,FLOAT_8,XMM2)
385: SSE_STOREH_PS(SSE_ARG_1,FLOAT_10,XMM2)
387: SSE_MULT_PS(XMM4,XMM5)
388: SSE_STOREL_PS(SSE_ARG_1,FLOAT_12,XMM4)
389: SSE_STOREH_PS(SSE_ARG_1,FLOAT_14,XMM4)
391: /* ----------------------------------------------- */
393: SSE_INLINE_END_1;
394: SSE_SCOPE_END;
396: return(0);
397: }
399: #endif