1 /*$Id: dgefa4.c,v 1.18 2001/04/07 15:42:33 bsmith Exp buschelm $*/ 2 /* 3 Inverts 4 by 4 matrix using partial pivoting. 4 5 Used by the sparse factorization routines in 6 src/mat/impls/baij/seq and src/mat/impls/bdiag/seq 7 8 See also src/inline/ilu.h 9 10 This is a combination of the Linpack routines 11 dgefa() and dgedi() specialized for a size of 4. 12 13 */ 14 #include "petsc.h" 15 16 #undef __FUNCT__ 17 #define __FUNCT__ "Kernel_A_gets_inverse_A_4" 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; 24 25 /* gaussian elimination with partial pivoting */ 26 27 PetscFunctionBegin; 28 /* Parameter adjustments */ 29 a -= 5; 30 31 for (k = 1; k <= 3; ++k) { 32 kp1 = k + 1; 33 k3 = 4*k; 34 k4 = k3 + k; 35 /* find l = pivot index */ 36 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; 47 48 if (a[l + k3] == 0.) { 49 SETERRQ(k,"Zero pivot"); 50 } 51 52 /* interchange if necessary */ 53 54 if (l != k) { 55 stmp = a[l + k3]; 56 a[l + k3] = a[k4]; 57 a[k4] = stmp; 58 } 59 60 /* compute multipliers */ 61 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 } 68 69 /* row elimination with column indexing */ 70 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 } 79 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 } 91 92 /* 93 Now form the inverse 94 */ 95 96 /* compute inverse(u) */ 97 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 } 119 120 /* form inverse(u)*inverse(l) */ 121 122 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 PetscFunctionReturn(0); 151 } 152 153 #if defined(PETSC_HAVE_ICL_SSE) 154 #include "xmmintrin.h" 155 156 #undef __FUNCT__ 157 #define __FUNCT__ "Kernel_A_gets_inverse_A_4_ICL_SSE" 158 int Kernel_A_gets_inverse_A_4_ICL_SSE(float *a) 159 { 160 /* 161 This routine is taken 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 166 167 Note: Intel's SML uses row-wise storage for these small matrices, 168 and PETSc uses column-wise storage. However since inv(A')=(inv(A))' 169 the same code can be used here. 170 171 Inverse of a 4x4 matrix via Kramer's Rule: 172 bool Invert4x4(SMLXMatrix &); 173 */ 174 __m128 minor0, minor1, minor2, minor3; 175 __m128 row0, row1, row2, row3; 176 __m128 det, tmp1; 177 178 PetscFunctionBegin; 179 tmp1 = _mm_loadh_pi(_mm_loadl_pi(tmp1, (__m64*)(a)), (__m64*)(a+ 4)); 180 row1 = _mm_loadh_pi(_mm_loadl_pi(row1, (__m64*)(a+8)), (__m64*)(a+12)); 181 row0 = _mm_shuffle_ps(tmp1, row1, 0x88); 182 row1 = _mm_shuffle_ps(row1, tmp1, 0xDD); 183 tmp1 = _mm_loadh_pi(_mm_loadl_pi(tmp1, (__m64*)(a+ 2)), (__m64*)(a+ 6)); 184 row3 = _mm_loadh_pi(_mm_loadl_pi(row3, (__m64*)(a+10)), (__m64*)(a+14)); 185 row2 = _mm_shuffle_ps(tmp1, row3, 0x88); 186 row3 = _mm_shuffle_ps(row3, tmp1, 0xDD); 187 /* ----------------------------------------------- */ 188 tmp1 = _mm_mul_ps(row2, row3); 189 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); 190 minor0 = _mm_mul_ps(row1, tmp1); 191 minor1 = _mm_mul_ps(row0, tmp1); 192 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); 193 minor0 = _mm_sub_ps(_mm_mul_ps(row1, tmp1), minor0); 194 minor1 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor1); 195 minor1 = _mm_shuffle_ps(minor1, minor1, 0x4E); 196 /* ----------------------------------------------- */ 197 tmp1 = _mm_mul_ps(row1, row2); 198 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); 199 minor0 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor0); 200 minor3 = _mm_mul_ps(row0, tmp1); 201 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); 202 minor0 = _mm_sub_ps(minor0, _mm_mul_ps(row3, tmp1)); 203 minor3 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor3); 204 minor3 = _mm_shuffle_ps(minor3, minor3, 0x4E); 205 /* ----------------------------------------------- */ 206 tmp1 = _mm_mul_ps(_mm_shuffle_ps(row1, row1, 0x4E), row3); 207 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); 208 row2 = _mm_shuffle_ps(row2, row2, 0x4E); 209 minor0 = _mm_add_ps(_mm_mul_ps(row2, tmp1), minor0); 210 minor2 = _mm_mul_ps(row0, tmp1); 211 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); 212 minor0 = _mm_sub_ps(minor0, _mm_mul_ps(row2, tmp1)); 213 minor2 = _mm_sub_ps(_mm_mul_ps(row0, tmp1), minor2); 214 minor2 = _mm_shuffle_ps(minor2, minor2, 0x4E); 215 /* ----------------------------------------------- */ 216 tmp1 = _mm_mul_ps(row0, row1); 217 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); 218 minor2 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor2); 219 minor3 = _mm_sub_ps(_mm_mul_ps(row2, tmp1), minor3); 220 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); 221 minor2 = _mm_sub_ps(_mm_mul_ps(row3, tmp1), minor2); 222 minor3 = _mm_sub_ps(minor3, _mm_mul_ps(row2, tmp1)); 223 /* ----------------------------------------------- */ 224 tmp1 = _mm_mul_ps(row0, row3); 225 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); 226 minor1 = _mm_sub_ps(minor1, _mm_mul_ps(row2, tmp1)); 227 minor2 = _mm_add_ps(_mm_mul_ps(row1, tmp1), minor2); 228 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); 229 minor1 = _mm_add_ps(_mm_mul_ps(row2, tmp1), minor1); 230 minor2 = _mm_sub_ps(minor2, _mm_mul_ps(row1, tmp1)); 231 /* ----------------------------------------------- */ 232 tmp1 = _mm_mul_ps(row0, row2); 233 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0xB1); 234 minor1 = _mm_add_ps(_mm_mul_ps(row3, tmp1), minor1); 235 minor3 = _mm_sub_ps(minor3, _mm_mul_ps(row1, tmp1)); 236 tmp1 = _mm_shuffle_ps(tmp1, tmp1, 0x4E); 237 minor1 = _mm_sub_ps(minor1, _mm_mul_ps(row3, tmp1)); 238 minor3 = _mm_add_ps(_mm_mul_ps(row1, tmp1), minor3); 239 /* ----------------------------------------------- */ 240 det = _mm_mul_ps(row0, minor0); 241 det = _mm_add_ps(_mm_shuffle_ps(det, det, 0x4E), det); 242 det = _mm_add_ss(_mm_shuffle_ps(det, det, 0xB1), det); 243 tmp1 = _mm_rcp_ss(det); 244 det = _mm_sub_ss(_mm_add_ss(tmp1, tmp1), _mm_mul_ss(det, _mm_mul_ss(tmp1, tmp1))); 245 det = _mm_shuffle_ps(det, det, 0x00); 246 minor0 = _mm_mul_ps(det, minor0); 247 _mm_storel_pi((__m64*)(a), minor0); 248 _mm_storeh_pi((__m64*)(a+2), minor0); 249 minor1 = _mm_mul_ps(det, minor1); 250 _mm_storel_pi((__m64*)(a+4), minor1); 251 _mm_storeh_pi((__m64*)(a+6), minor1); 252 minor2 = _mm_mul_ps(det, minor2); 253 _mm_storel_pi((__m64*)(a+ 8), minor2); 254 _mm_storeh_pi((__m64*)(a+10), minor2); 255 minor3 = _mm_mul_ps(det, minor3); 256 _mm_storel_pi((__m64*)(a+12), minor3); 257 _mm_storeh_pi((__m64*)(a+14), minor3); 258 PetscFunctionReturn(0); 259 } 260 261 #endif 262 263 264