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Singular_Value_Decomposition_Main_Kernel_Body.hpp

Singular_Value_Decomposition_Main_Kernel_Body.hpp 112 KB
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  1. //#####################################################################
    2. 

  2. // Copyright (c) 2010-2011, Eftychios Sifakis.
    3. 

  3. //
    4. 

  4. // Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
    5. 

  5. //   * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
    6. 

  6. //   * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or
    7. 

  7. //     other materials provided with the distribution.
    8. 

  8. //
    9. 

  9. // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
    10. 

  10. // BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
    11. 

  11. // SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
    12. 

  12. // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
    13. 

  13. // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
    14. 

  14. // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
    15. 

  15. //#####################################################################
    16. 

  16. 

  17. #ifdef __INTEL_COMPILER
    18. 

  18. #pragma warning( disable : 592 )
    19. 

  19. #endif
    20. 

  20. 

  21. // #define USE_ACCURATE_RSQRT_IN_JACOBI_CONJUGATION
    22. 

  22. // #define PERFORM_STRICT_QUATERNION_RENORMALIZATION
    23. 

  23. 

  24. { // Begin block : Scope of qV (if not maintained)
    25. 

  25. 

  26. #ifndef COMPUTE_V_AS_QUATERNION
    27. 

  27.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvs;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vqvs;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vqvs;) 
    28. 

  28.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvx;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvx;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvx;)
    29. 

  29.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvy;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvy;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvy;)
    30. 

  30.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvz;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvz;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvz;)
    31. 

  31. #endif
    32. 

  32. 

  33. { // Begin block : Symmetric eigenanalysis
    34. 

  34. 

  35.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss11;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs11;)
    36. 

  36.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss21;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs21;)
    37. 

  37.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss31;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs31;)
    38. 

  38.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss22;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs22;)
    39. 

  39.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss32;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs32;)
    40. 

  40.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss33;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs33;)
    41. 

  41. 

  42.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vqvs=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vqvs=Vone;)
    43. 

  43.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_xor_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_xor_ps(Vqvvx,Vqvvx);)
    44. 

  44.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_xor_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_xor_ps(Vqvvy,Vqvvy);)
    45. 

  45.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_xor_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_xor_ps(Vqvvz,Vqvvz);)
    46. 

  46. 

  47.     //###########################################################
    48. 

  48.     // Compute normal equations matrix
    49. 

  49.     //###########################################################
    50. 

  50. 

  51.     ENABLE_SCALAR_IMPLEMENTATION(Ss11.f=Sa11.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs11=_mm_mul_ps(Va11,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Vs11=_mm256_mul_ps(Va11,Va11);)
    52. 

  52.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa21.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va21,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va21,Va21);)
    53. 

  53.     ENABLE_SCALAR_IMPLEMENTATION(Ss11.f=Stmp1.f+Ss11.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs11=_mm_add_ps(Vtmp1,Vs11);)                                   ENABLE_AVX_IMPLEMENTATION(Vs11=_mm256_add_ps(Vtmp1,Vs11);)
    54. 

  54.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa31.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va31,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va31,Va31);)
    55. 

  55.     ENABLE_SCALAR_IMPLEMENTATION(Ss11.f=Stmp1.f+Ss11.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs11=_mm_add_ps(Vtmp1,Vs11);)                                   ENABLE_AVX_IMPLEMENTATION(Vs11=_mm256_add_ps(Vtmp1,Vs11);)
    56. 

  56. 

  57.     ENABLE_SCALAR_IMPLEMENTATION(Ss21.f=Sa12.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs21=_mm_mul_ps(Va12,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Vs21=_mm256_mul_ps(Va12,Va11);)
    58. 

  58.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa22.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va22,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va22,Va21);)
    59. 

  59.     ENABLE_SCALAR_IMPLEMENTATION(Ss21.f=Stmp1.f+Ss21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs21=_mm_add_ps(Vtmp1,Vs21);)                                   ENABLE_AVX_IMPLEMENTATION(Vs21=_mm256_add_ps(Vtmp1,Vs21);)
    60. 

  60.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa32.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va32,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va32,Va31);)
    61. 

  61.     ENABLE_SCALAR_IMPLEMENTATION(Ss21.f=Stmp1.f+Ss21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs21=_mm_add_ps(Vtmp1,Vs21);)                                   ENABLE_AVX_IMPLEMENTATION(Vs21=_mm256_add_ps(Vtmp1,Vs21);)
    62. 

  62. 

  63.     ENABLE_SCALAR_IMPLEMENTATION(Ss31.f=Sa13.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs31=_mm_mul_ps(Va13,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Vs31=_mm256_mul_ps(Va13,Va11);)
    64. 

  64.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa23.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va23,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va23,Va21);)
    65. 

  65.     ENABLE_SCALAR_IMPLEMENTATION(Ss31.f=Stmp1.f+Ss31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs31=_mm_add_ps(Vtmp1,Vs31);)                                   ENABLE_AVX_IMPLEMENTATION(Vs31=_mm256_add_ps(Vtmp1,Vs31);)
    66. 

  66.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa33.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va33,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va33,Va31);)
    67. 

  67.     ENABLE_SCALAR_IMPLEMENTATION(Ss31.f=Stmp1.f+Ss31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs31=_mm_add_ps(Vtmp1,Vs31);)                                   ENABLE_AVX_IMPLEMENTATION(Vs31=_mm256_add_ps(Vtmp1,Vs31);)
    68. 

  68. 

  69.     ENABLE_SCALAR_IMPLEMENTATION(Ss22.f=Sa12.f*Sa12.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs22=_mm_mul_ps(Va12,Va12);)                                    ENABLE_AVX_IMPLEMENTATION(Vs22=_mm256_mul_ps(Va12,Va12);)
    70. 

  70.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa22.f*Sa22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va22,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va22,Va22);)
    71. 

  71.     ENABLE_SCALAR_IMPLEMENTATION(Ss22.f=Stmp1.f+Ss22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs22=_mm_add_ps(Vtmp1,Vs22);)                                   ENABLE_AVX_IMPLEMENTATION(Vs22=_mm256_add_ps(Vtmp1,Vs22);)
    72. 

  72.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa32.f*Sa32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va32,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va32,Va32);)
    73. 

  73.     ENABLE_SCALAR_IMPLEMENTATION(Ss22.f=Stmp1.f+Ss22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs22=_mm_add_ps(Vtmp1,Vs22);)                                   ENABLE_AVX_IMPLEMENTATION(Vs22=_mm256_add_ps(Vtmp1,Vs22);)
    74. 

  74. 

  75.     ENABLE_SCALAR_IMPLEMENTATION(Ss32.f=Sa13.f*Sa12.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs32=_mm_mul_ps(Va13,Va12);)                                    ENABLE_AVX_IMPLEMENTATION(Vs32=_mm256_mul_ps(Va13,Va12);)
    76. 

  76.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa23.f*Sa22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va23,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va23,Va22);)
    77. 

  77.     ENABLE_SCALAR_IMPLEMENTATION(Ss32.f=Stmp1.f+Ss32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs32=_mm_add_ps(Vtmp1,Vs32);)                                   ENABLE_AVX_IMPLEMENTATION(Vs32=_mm256_add_ps(Vtmp1,Vs32);)
    78. 

  78.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa33.f*Sa32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va33,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va33,Va32);)
    79. 

  79.     ENABLE_SCALAR_IMPLEMENTATION(Ss32.f=Stmp1.f+Ss32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs32=_mm_add_ps(Vtmp1,Vs32);)                                   ENABLE_AVX_IMPLEMENTATION(Vs32=_mm256_add_ps(Vtmp1,Vs32);)
    80. 

  80. 

  81.     ENABLE_SCALAR_IMPLEMENTATION(Ss33.f=Sa13.f*Sa13.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs33=_mm_mul_ps(Va13,Va13);)                                    ENABLE_AVX_IMPLEMENTATION(Vs33=_mm256_mul_ps(Va13,Va13);)
    82. 

  82.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa23.f*Sa23.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va23,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va23,Va23);)
    83. 

  83.     ENABLE_SCALAR_IMPLEMENTATION(Ss33.f=Stmp1.f+Ss33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs33=_mm_add_ps(Vtmp1,Vs33);)                                   ENABLE_AVX_IMPLEMENTATION(Vs33=_mm256_add_ps(Vtmp1,Vs33);)
    84. 

  84.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa33.f*Sa33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va33,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va33,Va33);)
    85. 

  85.     ENABLE_SCALAR_IMPLEMENTATION(Ss33.f=Stmp1.f+Ss33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs33=_mm_add_ps(Vtmp1,Vs33);)                                   ENABLE_AVX_IMPLEMENTATION(Vs33=_mm256_add_ps(Vtmp1,Vs33);)
    86. 

  86.     
    87. 

  87.     //###########################################################
    88. 

  88.     // Solve symmetric eigenproblem using Jacobi iteration
    89. 

  89.     //###########################################################
    90. 

  90. 

  91.     for(int sweep=1;sweep<=4;sweep++){
    92. 

  92. 

  93.         // First Jacobi conjugation
    94. 

  94. 

  95. #define SS11 Ss11
    96. 

  96. #define SS21 Ss21
    97. 

  97. #define SS31 Ss31
    98. 

  98. #define SS22 Ss22
    99. 

  99. #define SS32 Ss32
    100. 

  100. #define SS33 Ss33
    101. 

  101. #define SQVVX Sqvvx
    102. 

  102. #define SQVVY Sqvvy
    103. 

  103. #define SQVVZ Sqvvz
    104. 

  104. #define STMP1 Stmp1
    105. 

  105. #define STMP2 Stmp2
    106. 

  106. #define STMP3 Stmp3
    107. 

  107. 

  108. #define VS11 Vs11
    109. 

  109. #define VS21 Vs21
    110. 

  110. #define VS31 Vs31
    111. 

  111. #define VS22 Vs22
    112. 

  112. #define VS32 Vs32
    113. 

  113. #define VS33 Vs33
    114. 

  114. #define VQVVX Vqvvx
    115. 

  115. #define VQVVY Vqvvy
    116. 

  116. #define VQVVZ Vqvvz
    117. 

  117. #define VTMP1 Vtmp1
    118. 

  118. #define VTMP2 Vtmp2
    119. 

  119. #define VTMP3 Vtmp3
    120. 

  120. 

  121. #include "Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp"
    122. 

  122. 

  123. #undef SS11
    124. 

  124. #undef SS21
    125. 

  125. #undef SS31
    126. 

  126. #undef SS22
    127. 

  127. #undef SS32
    128. 

  128. #undef SS33
    129. 

  129. #undef SQVVX
    130. 

  130. #undef SQVVY
    131. 

  131. #undef SQVVZ
    132. 

  132. #undef STMP1
    133. 

  133. #undef STMP2
    134. 

  134. #undef STMP3
    135. 

  135. 

  136. #undef VS11
    137. 

  137. #undef VS21
    138. 

  138. #undef VS31
    139. 

  139. #undef VS22
    140. 

  140. #undef VS32
    141. 

  141. #undef VS33
    142. 

  142. #undef VQVVX
    143. 

  143. #undef VQVVY
    144. 

  144. #undef VQVVZ
    145. 

  145. #undef VTMP1
    146. 

  146. #undef VTMP2
    147. 

  147. #undef VTMP3
    148. 

  148. 

  149.         // Second Jacobi conjugation
    150. 

  150. 

  151. #define SS11 Ss22
    152. 

  152. #define SS21 Ss32
    153. 

  153. #define SS31 Ss21
    154. 

  154. #define SS22 Ss33
    155. 

  155. #define SS32 Ss31
    156. 

  156. #define SS33 Ss11
    157. 

  157. #define SQVVX Sqvvy
    158. 

  158. #define SQVVY Sqvvz
    159. 

  159. #define SQVVZ Sqvvx
    160. 

  160. #define STMP1 Stmp2
    161. 

  161. #define STMP2 Stmp3
    162. 

  162. #define STMP3 Stmp1
    163. 

  163. 

  164. #define VS11 Vs22
    165. 

  165. #define VS21 Vs32
    166. 

  166. #define VS31 Vs21
    167. 

  167. #define VS22 Vs33
    168. 

  168. #define VS32 Vs31
    169. 

  169. #define VS33 Vs11
    170. 

  170. #define VQVVX Vqvvy
    171. 

  171. #define VQVVY Vqvvz
    172. 

  172. #define VQVVZ Vqvvx
    173. 

  173. #define VTMP1 Vtmp2
    174. 

  174. #define VTMP2 Vtmp3
    175. 

  175. #define VTMP3 Vtmp1
    176. 

  176. 

  177. #include "Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp"
    178. 

  178. 

  179. #undef SS11
    180. 

  180. #undef SS21
    181. 

  181. #undef SS31
    182. 

  182. #undef SS22
    183. 

  183. #undef SS32
    184. 

  184. #undef SS33
    185. 

  185. #undef SQVVX
    186. 

  186. #undef SQVVY
    187. 

  187. #undef SQVVZ
    188. 

  188. #undef STMP1
    189. 

  189. #undef STMP2
    190. 

  190. #undef STMP3
    191. 

  191. 

  192. #undef VS11
    193. 

  193. #undef VS21
    194. 

  194. #undef VS31
    195. 

  195. #undef VS22
    196. 

  196. #undef VS32
    197. 

  197. #undef VS33
    198. 

  198. #undef VQVVX
    199. 

  199. #undef VQVVY
    200. 

  200. #undef VQVVZ
    201. 

  201. #undef VTMP1
    202. 

  202. #undef VTMP2
    203. 

  203. #undef VTMP3
    204. 

  204. 

  205.         // Third Jacobi conjugation
    206. 

  206. 

  207. #define SS11 Ss33
    208. 

  208. #define SS21 Ss31
    209. 

  209. #define SS31 Ss32
    210. 

  210. #define SS22 Ss11
    211. 

  211. #define SS32 Ss21
    212. 

  212. #define SS33 Ss22
    213. 

  213. #define SQVVX Sqvvz
    214. 

  214. #define SQVVY Sqvvx
    215. 

  215. #define SQVVZ Sqvvy
    216. 

  216. #define STMP1 Stmp3
    217. 

  217. #define STMP2 Stmp1
    218. 

  218. #define STMP3 Stmp2
    219. 

  219. 

  220. #define VS11 Vs33
    221. 

  221. #define VS21 Vs31
    222. 

  222. #define VS31 Vs32
    223. 

  223. #define VS22 Vs11
    224. 

  224. #define VS32 Vs21
    225. 

  225. #define VS33 Vs22
    226. 

  226. #define VQVVX Vqvvz
    227. 

  227. #define VQVVY Vqvvx
    228. 

  228. #define VQVVZ Vqvvy
    229. 

  229. #define VTMP1 Vtmp3
    230. 

  230. #define VTMP2 Vtmp1
    231. 

  231. #define VTMP3 Vtmp2
    232. 

  232. 

  233. #include "Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp"
    234. 

  234. 

  235. #undef SS11
    236. 

  236. #undef SS21
    237. 

  237. #undef SS31
    238. 

  238. #undef SS22
    239. 

  239. #undef SS32
    240. 

  240. #undef SS33
    241. 

  241. #undef SQVVX
    242. 

  242. #undef SQVVY
    243. 

  243. #undef SQVVZ
    244. 

  244. #undef STMP1
    245. 

  245. #undef STMP2
    246. 

  246. #undef STMP3
    247. 

  247. 

  248. #undef VS11
    249. 

  249. #undef VS21
    250. 

  250. #undef VS31
    251. 

  251. #undef VS22
    252. 

  252. #undef VS32
    253. 

  253. #undef VS33
    254. 

  254. #undef VQVVX
    255. 

  255. #undef VQVVY
    256. 

  256. #undef VQVVZ
    257. 

  257. #undef VTMP1
    258. 

  258. #undef VTMP2
    259. 

  259. #undef VTMP3
    260. 

  260.     }
    261. 

  261. 

  262. #ifdef PRINT_DEBUGGING_OUTPUT
    263. 

  263. #ifdef USE_SCALAR_IMPLEMENTATION
    264. 

  264.     std::cout<<"Scalar S ="<<std::endl;
    265. 

  265.     std::cout<<std::setw(12)<<Ss11.f<<std::endl;
    266. 

  266.     std::cout<<std::setw(12)<<Ss21.f<<"  "<<std::setw(12)<<Ss22.f<<std::endl;
    267. 

  267.     std::cout<<std::setw(12)<<Ss31.f<<"  "<<std::setw(12)<<Ss32.f<<"  "<<std::setw(12)<<Ss33.f<<std::endl;
    268. 

  268. #endif
    269. 

  269. #ifdef USE_SSE_IMPLEMENTATION
    270. 

  270.     _mm_storeu_ps(buf,Vs11);S11=buf[0];
    271. 

  271.     _mm_storeu_ps(buf,Vs21);S21=buf[0];
    272. 

  272.     _mm_storeu_ps(buf,Vs31);S31=buf[0];
    273. 

  273.     _mm_storeu_ps(buf,Vs22);S22=buf[0];
    274. 

  274.     _mm_storeu_ps(buf,Vs32);S32=buf[0];
    275. 

  275.     _mm_storeu_ps(buf,Vs33);S33=buf[0];
    276. 

  276.     std::cout<<"Vector S ="<<std::endl;
    277. 

  277.     std::cout<<std::setw(12)<<S11<<std::endl;
    278. 

  278.     std::cout<<std::setw(12)<<S21<<"  "<<std::setw(12)<<S22<<std::endl;
    279. 

  279.     std::cout<<std::setw(12)<<S31<<"  "<<std::setw(12)<<S32<<"  "<<std::setw(12)<<S33<<std::endl;
    280. 

  280. #endif
    281. 

  281. #ifdef USE_AVX_IMPLEMENTATION
    282. 

  282.     _mm256_storeu_ps(buf,Vs11);S11=buf[0];
    283. 

  283.     _mm256_storeu_ps(buf,Vs21);S21=buf[0];
    284. 

  284.     _mm256_storeu_ps(buf,Vs31);S31=buf[0];
    285. 

  285.     _mm256_storeu_ps(buf,Vs22);S22=buf[0];
    286. 

  286.     _mm256_storeu_ps(buf,Vs32);S32=buf[0];
    287. 

  287.     _mm256_storeu_ps(buf,Vs33);S33=buf[0];
    288. 

  288.     std::cout<<"Vector S ="<<std::endl;
    289. 

  289.     std::cout<<std::setw(12)<<S11<<std::endl;
    290. 

  290.     std::cout<<std::setw(12)<<S21<<"  "<<std::setw(12)<<S22<<std::endl;
    291. 

  291.     std::cout<<std::setw(12)<<S31<<"  "<<std::setw(12)<<S32<<"  "<<std::setw(12)<<S33<<std::endl;
    292. 

  292. #endif
    293. 

  293. #endif
    294. 

  294. 

  295. } // End block : Symmetric eigenanalysis
    296. 

  296. 

  297.     //###########################################################
    298. 

  298.     // Normalize quaternion for matrix V
    299. 

  299.     //###########################################################
    300. 

  300. 

  301. #if !defined(USE_ACCURATE_RSQRT_IN_JACOBI_CONJUGATION) || defined(PERFORM_STRICT_QUATERNION_RENORMALIZATION)
    302. 

  302. 

  303.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvs.f*Sqvs.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvs,Vqvs);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvs,Vqvs);)
    304. 

  304.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvx,Vqvvx);)
    305. 

  305.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    306. 

  306.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvy.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvy,Vqvvy);)
    307. 

  307.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    308. 

  308.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvz.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvz,Vqvvz);)
    309. 

  309.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    310. 

  310. 

  311.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=rsqrt(Stmp2.f);)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_rsqrt_ps(Vtmp2);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_rsqrt_ps(Vtmp2);)
    312. 

  312.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp1.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp1,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp1,Vone_half);)
    313. 

  313.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp4);)
    314. 

  314.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp3);)
    315. 

  315.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp2.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp2,Vtmp3);)
    316. 

  316.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    317. 

  317.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f-Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_sub_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_sub_ps(Vtmp1,Vtmp3);)
    318. 

  318. 

  319.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp1);)
    320. 

  320.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vqvvx,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vqvvx,Vtmp1);)
    321. 

  321.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vqvvy,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vqvvy,Vtmp1);)
    322. 

  322.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vqvvz,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vqvvz,Vtmp1);)
    323. 

  323. 

  324. #ifdef PRINT_DEBUGGING_OUTPUT
    325. 

  325. #ifdef USE_SCALAR_IMPLEMENTATION
    326. 

  326.     std::cout<<"Scalar qV ="<<std::endl;
    327. 

  327.     std::cout<<std::setw(12)<<Sqvs.f<<"  "<<std::setw(12)<<Sqvvx.f<<"  "<<std::setw(12)<<Sqvvy.f<<"  "<<std::setw(12)<<Sqvvz.f<<std::endl;
    328. 

  328. #endif
    329. 

  329. #ifdef USE_SSE_IMPLEMENTATION
    330. 

  330.     _mm_storeu_ps(buf,Vqvs);QVS=buf[0];
    331. 

  331.     _mm_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    332. 

  332.     _mm_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    333. 

  333.     _mm_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    334. 

  334.     std::cout<<"Vector qV ="<<std::endl;
    335. 

  335.     std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
    336. 

  336. #endif
    337. 

  337. #ifdef USE_AVX_IMPLEMENTATION
    338. 

  338.     _mm256_storeu_ps(buf,Vqvs);QVS=buf[0];
    339. 

  339.     _mm256_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    340. 

  340.     _mm256_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    341. 

  341.     _mm256_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    342. 

  342.     std::cout<<"Vector qV ="<<std::endl;
    343. 

  343.     std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
    344. 

  344. #endif
    345. 

  345. #endif
    346. 

  346. 

  347. #endif
    348. 

  348. 

  349. { // Begin block : Conjugation with V
    350. 

  350. 

  351.     //###########################################################
    352. 

  352.     // Transform quaternion to matrix V
    353. 

  353.     //###########################################################
    354. 

  354. 

  355. #ifndef COMPUTE_V_AS_MATRIX
    356. 

  356.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv11;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv11;)
    357. 

  357.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv21;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv21;)
    358. 

  358.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv31;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv31;)
    359. 

  359.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv12;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv12;)
    360. 

  360.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv22;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv22;)
    361. 

  361.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv32;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv32;)
    362. 

  362.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv13;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv13;)
    363. 

  363.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv23;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv23;)
    364. 

  364.     ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv33;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv33;)
    365. 

  365. #endif
    366. 

  366. 

  367.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvx,Vqvvx);)
    368. 

  368.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvvy.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvvy,Vqvvy);)
    369. 

  369.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sqvvz.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vqvvz,Vqvvz);)
    370. 

  370.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sqvs.f*Sqvs.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_mul_ps(Vqvs,Vqvs);)                                    ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_mul_ps(Vqvs,Vqvs);)
    371. 

  371.     ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv11.f-Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_sub_ps(Vv11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_sub_ps(Vv11,Vtmp1);)
    372. 

  372.     ENABLE_SCALAR_IMPLEMENTATION(Sv33.f=Sv22.f-Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_sub_ps(Vv22,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_sub_ps(Vv22,Vtmp2);)
    373. 

  373.     ENABLE_SCALAR_IMPLEMENTATION(Sv33.f=Sv33.f+Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_add_ps(Vv33,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_add_ps(Vv33,Vtmp3);)
    374. 

  374.     ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv22.f+Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_add_ps(Vv22,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_add_ps(Vv22,Vtmp2);)
    375. 

  375.     ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv22.f-Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_sub_ps(Vv22,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_sub_ps(Vv22,Vtmp3);)
    376. 

  376.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_add_ps(Vv11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_add_ps(Vv11,Vtmp1);)
    377. 

  377.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f-Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_sub_ps(Vv11,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_sub_ps(Vv11,Vtmp2);)
    378. 

  378.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f-Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_sub_ps(Vv11,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_sub_ps(Vv11,Vtmp3);)
    379. 

  379.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f+Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vqvvx,Vqvvx);)
    380. 

  380.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvvy.f+Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vqvvy,Vqvvy);)
    381. 

  381.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sqvvz.f+Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vqvvz,Vqvvz);)
    382. 

  382.     ENABLE_SCALAR_IMPLEMENTATION(Sv32.f=Sqvs.f*Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_mul_ps(Vqvs,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_mul_ps(Vqvs,Vtmp1);)
    383. 

  383.     ENABLE_SCALAR_IMPLEMENTATION(Sv13.f=Sqvs.f*Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_mul_ps(Vqvs,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_mul_ps(Vqvs,Vtmp2);)
    384. 

  384.     ENABLE_SCALAR_IMPLEMENTATION(Sv21.f=Sqvs.f*Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_mul_ps(Vqvs,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_mul_ps(Vqvs,Vtmp3);)
    385. 

  385.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvy.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvy,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvy,Vtmp1);)
    386. 

  386.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvvz.f*Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvvz,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvvz,Vtmp2);)
    387. 

  387.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sqvvx.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vqvvx,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vqvvx,Vtmp3);)
    388. 

  388.     ENABLE_SCALAR_IMPLEMENTATION(Sv12.f=Stmp1.f-Sv21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_sub_ps(Vtmp1,Vv21);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_sub_ps(Vtmp1,Vv21);)
    389. 

  389.     ENABLE_SCALAR_IMPLEMENTATION(Sv23.f=Stmp2.f-Sv32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_sub_ps(Vtmp2,Vv32);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_sub_ps(Vtmp2,Vv32);)
    390. 

  390.     ENABLE_SCALAR_IMPLEMENTATION(Sv31.f=Stmp3.f-Sv13.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_sub_ps(Vtmp3,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_sub_ps(Vtmp3,Vv13);)
    391. 

  391.     ENABLE_SCALAR_IMPLEMENTATION(Sv21.f=Stmp1.f+Sv21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_add_ps(Vtmp1,Vv21);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_add_ps(Vtmp1,Vv21);)
    392. 

  392.     ENABLE_SCALAR_IMPLEMENTATION(Sv32.f=Stmp2.f+Sv32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_add_ps(Vtmp2,Vv32);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_add_ps(Vtmp2,Vv32);)
    393. 

  393.     ENABLE_SCALAR_IMPLEMENTATION(Sv13.f=Stmp3.f+Sv13.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_add_ps(Vtmp3,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_add_ps(Vtmp3,Vv13);)
    394. 

  394. 

  395. #ifdef COMPUTE_V_AS_MATRIX
    396. 

  396. #ifdef PRINT_DEBUGGING_OUTPUT
    397. 

  397. #ifdef USE_SCALAR_IMPLEMENTATION
    398. 

  398.     std::cout<<"Scalar V ="<<std::endl;
    399. 

  399.     std::cout<<std::setw(12)<<Sv11.f<<"  "<<std::setw(12)<<Sv12.f<<"  "<<std::setw(12)<<Sv13.f<<std::endl;
    400. 

  400.     std::cout<<std::setw(12)<<Sv21.f<<"  "<<std::setw(12)<<Sv22.f<<"  "<<std::setw(12)<<Sv23.f<<std::endl;
    401. 

  401.     std::cout<<std::setw(12)<<Sv31.f<<"  "<<std::setw(12)<<Sv32.f<<"  "<<std::setw(12)<<Sv33.f<<std::endl;
    402. 

  402. #endif
    403. 

  403. #ifdef USE_SSE_IMPLEMENTATION
    404. 

  404.     _mm_storeu_ps(buf,Vv11);V11=buf[0];
    405. 

  405.     _mm_storeu_ps(buf,Vv21);V21=buf[0];
    406. 

  406.     _mm_storeu_ps(buf,Vv31);V31=buf[0];
    407. 

  407.     _mm_storeu_ps(buf,Vv12);V12=buf[0];
    408. 

  408.     _mm_storeu_ps(buf,Vv22);V22=buf[0];
    409. 

  409.     _mm_storeu_ps(buf,Vv32);V32=buf[0];
    410. 

  410.     _mm_storeu_ps(buf,Vv13);V13=buf[0];
    411. 

  411.     _mm_storeu_ps(buf,Vv23);V23=buf[0];
    412. 

  412.     _mm_storeu_ps(buf,Vv33);V33=buf[0];
    413. 

  413.     std::cout<<"Vector V ="<<std::endl;
    414. 

  414.     std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    415. 

  415.     std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    416. 

  416.     std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
    417. 

  417. #endif
    418. 

  418. #ifdef USE_AVX_IMPLEMENTATION
    419. 

  419.     _mm256_storeu_ps(buf,Vv11);V11=buf[0];
    420. 

  420.     _mm256_storeu_ps(buf,Vv21);V21=buf[0];
    421. 

  421.     _mm256_storeu_ps(buf,Vv31);V31=buf[0];
    422. 

  422.     _mm256_storeu_ps(buf,Vv12);V12=buf[0];
    423. 

  423.     _mm256_storeu_ps(buf,Vv22);V22=buf[0];
    424. 

  424.     _mm256_storeu_ps(buf,Vv32);V32=buf[0];
    425. 

  425.     _mm256_storeu_ps(buf,Vv13);V13=buf[0];
    426. 

  426.     _mm256_storeu_ps(buf,Vv23);V23=buf[0];
    427. 

  427.     _mm256_storeu_ps(buf,Vv33);V33=buf[0];
    428. 

  428.     std::cout<<"Vector V ="<<std::endl;
    429. 

  429.     std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    430. 

  430.     std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    431. 

  431.     std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
    432. 

  432. #endif
    433. 

  433. #endif
    434. 

  434. #endif
    435. 

  435. 

  436.     //###########################################################
    437. 

  437.     // Multiply (from the right) with V
    438. 

  438.     //###########################################################
    439. 

  439. 

  440.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa12.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp2=Va12;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp2=Va12;)
    441. 

  441.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa13.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp3=Va13;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp3=Va13;)
    442. 

  442.     ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sv12.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va12=_mm_mul_ps(Vv12,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_mul_ps(Vv12,Va11);)
    443. 

  443.     ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sv13.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va13=_mm_mul_ps(Vv13,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_mul_ps(Vv13,Va11);)
    444. 

  444.     ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sv11.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va11=_mm_mul_ps(Vv11,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_mul_ps(Vv11,Va11);)
    445. 

  445.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv21.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv21,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv21,Vtmp2);)
    446. 

  446.     ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sa11.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va11=_mm_add_ps(Va11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_add_ps(Va11,Vtmp1);)
    447. 

  447.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv31.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv31,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv31,Vtmp3);)
    448. 

  448.     ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sa11.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va11=_mm_add_ps(Va11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_add_ps(Va11,Vtmp1);)
    449. 

  449.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv22.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv22,Vtmp2);)
    450. 

  450.     ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sa12.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va12=_mm_add_ps(Va12,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_add_ps(Va12,Vtmp1);)
    451. 

  451.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv32.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv32,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv32,Vtmp3);)
    452. 

  452.     ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sa12.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va12=_mm_add_ps(Va12,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_add_ps(Va12,Vtmp1);)
    453. 

  453.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv23.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv23,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv23,Vtmp2);)
    454. 

  454.     ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sa13.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va13=_mm_add_ps(Va13,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_add_ps(Va13,Vtmp1);)
    455. 

  455.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv33.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv33,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv33,Vtmp3);)
    456. 

  456.     ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sa13.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va13=_mm_add_ps(Va13,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_add_ps(Va13,Vtmp1);)
    457. 

  457. 

  458.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa22.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp2=Va22;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp2=Va22;)
    459. 

  459.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa23.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp3=Va23;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp3=Va23;)
    460. 

  460.     ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sv12.f*Sa21.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va22=_mm_mul_ps(Vv12,Va21);)                                    ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_mul_ps(Vv12,Va21);)
    461. 

  461.     ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sv13.f*Sa21.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va23=_mm_mul_ps(Vv13,Va21);)                                    ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_mul_ps(Vv13,Va21);)
    462. 

  462.     ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sv11.f*Sa21.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va21=_mm_mul_ps(Vv11,Va21);)                                    ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_mul_ps(Vv11,Va21);)
    463. 

  463.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv21.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv21,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv21,Vtmp2);)
    464. 

  464.     ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sa21.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va21=_mm_add_ps(Va21,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_add_ps(Va21,Vtmp1);)
    465. 

  465.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv31.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv31,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv31,Vtmp3);)
    466. 

  466.     ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sa21.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va21=_mm_add_ps(Va21,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_add_ps(Va21,Vtmp1);)
    467. 

  467.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv22.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv22,Vtmp2);)
    468. 

  468.     ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sa22.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va22=_mm_add_ps(Va22,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_add_ps(Va22,Vtmp1);)
    469. 

  469.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv32.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv32,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv32,Vtmp3);)
    470. 

  470.     ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sa22.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va22=_mm_add_ps(Va22,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_add_ps(Va22,Vtmp1);)
    471. 

  471.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv23.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv23,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv23,Vtmp2);)
    472. 

  472.     ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sa23.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va23=_mm_add_ps(Va23,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_add_ps(Va23,Vtmp1);)
    473. 

  473.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv33.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv33,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv33,Vtmp3);)
    474. 

  474.     ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sa23.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va23=_mm_add_ps(Va23,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_add_ps(Va23,Vtmp1);)
    475. 

  475. 

  476.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa32.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp2=Va32;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp2=Va32;)
    477. 

  477.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa33.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp3=Va33;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp3=Va33;)
    478. 

  478.     ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sv12.f*Sa31.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va32=_mm_mul_ps(Vv12,Va31);)                                    ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_mul_ps(Vv12,Va31);)
    479. 

  479.     ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sv13.f*Sa31.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va33=_mm_mul_ps(Vv13,Va31);)                                    ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_mul_ps(Vv13,Va31);)
    480. 

  480.     ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sv11.f*Sa31.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va31=_mm_mul_ps(Vv11,Va31);)                                    ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_mul_ps(Vv11,Va31);)
    481. 

  481.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv21.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv21,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv21,Vtmp2);)
    482. 

  482.     ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sa31.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va31=_mm_add_ps(Va31,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_add_ps(Va31,Vtmp1);)
    483. 

  483.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv31.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv31,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv31,Vtmp3);)
    484. 

  484.     ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sa31.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va31=_mm_add_ps(Va31,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_add_ps(Va31,Vtmp1);)
    485. 

  485.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv22.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv22,Vtmp2);)
    486. 

  486.     ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sa32.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va32=_mm_add_ps(Va32,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_add_ps(Va32,Vtmp1);)
    487. 

  487.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv32.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv32,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv32,Vtmp3);)
    488. 

  488.     ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sa32.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va32=_mm_add_ps(Va32,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_add_ps(Va32,Vtmp1);)
    489. 

  489.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv23.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv23,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv23,Vtmp2);)
    490. 

  490.     ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sa33.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va33=_mm_add_ps(Va33,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_add_ps(Va33,Vtmp1);)
    491. 

  491.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv33.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv33,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv33,Vtmp3);)
    492. 

  492.     ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sa33.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va33=_mm_add_ps(Va33,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_add_ps(Va33,Vtmp1);)
    493. 

  493. 

  494. #ifdef PRINT_DEBUGGING_OUTPUT
    495. 

  495. #ifdef USE_SCALAR_IMPLEMENTATION
    496. 

  496.     std::cout<<"Scalar A (after multiplying with V) ="<<std::endl;
    497. 

  497.     std::cout<<std::setw(12)<<Sa11.f<<"  "<<std::setw(12)<<Sa12.f<<"  "<<std::setw(12)<<Sa13.f<<std::endl;
    498. 

  498.     std::cout<<std::setw(12)<<Sa21.f<<"  "<<std::setw(12)<<Sa22.f<<"  "<<std::setw(12)<<Sa23.f<<std::endl;
    499. 

  499.     std::cout<<std::setw(12)<<Sa31.f<<"  "<<std::setw(12)<<Sa32.f<<"  "<<std::setw(12)<<Sa33.f<<std::endl;
    500. 

  500. #endif
    501. 

  501. #ifdef USE_SSE_IMPLEMENTATION
    502. 

  502.     _mm_storeu_ps(buf,Va11);A11=buf[0];
    503. 

  503.     _mm_storeu_ps(buf,Va21);A21=buf[0];
    504. 

  504.     _mm_storeu_ps(buf,Va31);A31=buf[0];
    505. 

  505.     _mm_storeu_ps(buf,Va12);A12=buf[0];
    506. 

  506.     _mm_storeu_ps(buf,Va22);A22=buf[0];
    507. 

  507.     _mm_storeu_ps(buf,Va32);A32=buf[0];
    508. 

  508.     _mm_storeu_ps(buf,Va13);A13=buf[0];
    509. 

  509.     _mm_storeu_ps(buf,Va23);A23=buf[0];
    510. 

  510.     _mm_storeu_ps(buf,Va33);A33=buf[0];
    511. 

  511.     std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    512. 

  512.     std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    513. 

  513.     std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    514. 

  514.     std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
    515. 

  515. #endif
    516. 

  516. #ifdef USE_AVX_IMPLEMENTATION
    517. 

  517.     _mm256_storeu_ps(buf,Va11);A11=buf[0];
    518. 

  518.     _mm256_storeu_ps(buf,Va21);A21=buf[0];
    519. 

  519.     _mm256_storeu_ps(buf,Va31);A31=buf[0];
    520. 

  520.     _mm256_storeu_ps(buf,Va12);A12=buf[0];
    521. 

  521.     _mm256_storeu_ps(buf,Va22);A22=buf[0];
    522. 

  522.     _mm256_storeu_ps(buf,Va32);A32=buf[0];
    523. 

  523.     _mm256_storeu_ps(buf,Va13);A13=buf[0];
    524. 

  524.     _mm256_storeu_ps(buf,Va23);A23=buf[0];
    525. 

  525.     _mm256_storeu_ps(buf,Va33);A33=buf[0];
    526. 

  526.     std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    527. 

  527.     std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    528. 

  528.     std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    529. 

  529.     std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
    530. 

  530. #endif
    531. 

  531. #endif
    532. 

  532. 

  533. } // End block : Conjugation with V
    534. 

  534. 

  535. } // End block : Scope of qV (if not maintained)
    536. 

  536. 

  537.     //###########################################################
    538. 

  538.     // Permute columns such that the singular values are sorted
    539. 

  539.     //###########################################################
    540. 

  540. 

  541.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa11.f*Sa11.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va11,Va11);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va11,Va11);)
    542. 

  542.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa21.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va21,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va21,Va21);)
    543. 

  543.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    544. 

  544.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa31.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va31,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va31,Va31);)
    545. 

  545.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    546. 

  546. 

  547.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa12.f*Sa12.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Va12,Va12);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Va12,Va12);)
    548. 

  548.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa22.f*Sa22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va22,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va22,Va22);)
    549. 

  549.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp2.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp2,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp2,Vtmp4);)
    550. 

  550.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa32.f*Sa32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va32,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va32,Va32);)
    551. 

  551.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp2.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp2,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp2,Vtmp4);)
    552. 

  552. 

  553.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa13.f*Sa13.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Va13,Va13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Va13,Va13);)
    554. 

  554.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa23.f*Sa23.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va23,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va23,Va23);)
    555. 

  555.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp3.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vtmp3,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vtmp3,Vtmp4);)
    556. 

  556.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa33.f*Sa33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va33,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va33,Va33);)
    557. 

  557.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp3.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vtmp3,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vtmp3,Vtmp4);)
    558. 

  558. 

  559.     // Swap columns 1-2 if necessary
    560. 

  560. 

  561.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.ui=(Stmp1.f<Stmp2.f)?0xffffffff:0;)                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_cmplt_ps(Vtmp1,Vtmp2);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmp_ps(Vtmp1,Vtmp2, _CMP_LT_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmplt_ps(Vtmp1,Vtmp2);)
    562. 

  562.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa11.ui^Sa12.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va11,Va12);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va11,Va12);)
    563. 

  563.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    564. 

  564.     ENABLE_SCALAR_IMPLEMENTATION(Sa11.ui=Sa11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va11=_mm_xor_ps(Va11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_xor_ps(Va11,Vtmp5);)
    565. 

  565.     ENABLE_SCALAR_IMPLEMENTATION(Sa12.ui=Sa12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va12=_mm_xor_ps(Va12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_xor_ps(Va12,Vtmp5);)
    566. 

  566. 

  567.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa21.ui^Sa22.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va21,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va21,Va22);)
    568. 

  568.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    569. 

  569.     ENABLE_SCALAR_IMPLEMENTATION(Sa21.ui=Sa21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va21=_mm_xor_ps(Va21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_xor_ps(Va21,Vtmp5);)
    570. 

  570.     ENABLE_SCALAR_IMPLEMENTATION(Sa22.ui=Sa22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va22=_mm_xor_ps(Va22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_xor_ps(Va22,Vtmp5);)
    571. 

  571. 

  572.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa31.ui^Sa32.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va31,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va31,Va32);)
    573. 

  573.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    574. 

  574.     ENABLE_SCALAR_IMPLEMENTATION(Sa31.ui=Sa31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va31=_mm_xor_ps(Va31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_xor_ps(Va31,Vtmp5);)
    575. 

  575.     ENABLE_SCALAR_IMPLEMENTATION(Sa32.ui=Sa32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va32=_mm_xor_ps(Va32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_xor_ps(Va32,Vtmp5);)
    576. 

  576. 

  577. #ifdef COMPUTE_V_AS_MATRIX
    578. 

  578.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv11.ui^Sv12.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv11,Vv12);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv11,Vv12);)
    579. 

  579.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    580. 

  580.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.ui=Sv11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_xor_ps(Vv11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_xor_ps(Vv11,Vtmp5);)
    581. 

  581.     ENABLE_SCALAR_IMPLEMENTATION(Sv12.ui=Sv12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_xor_ps(Vv12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_xor_ps(Vv12,Vtmp5);)
    582. 

  582. 

  583.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv21.ui^Sv22.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv21,Vv22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv21,Vv22);)
    584. 

  584.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    585. 

  585.     ENABLE_SCALAR_IMPLEMENTATION(Sv21.ui=Sv21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_xor_ps(Vv21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_xor_ps(Vv21,Vtmp5);)
    586. 

  586.     ENABLE_SCALAR_IMPLEMENTATION(Sv22.ui=Sv22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_xor_ps(Vv22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_xor_ps(Vv22,Vtmp5);)
    587. 

  587. 

  588.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv31.ui^Sv32.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv31,Vv32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv31,Vv32);)
    589. 

  589.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    590. 

  590.     ENABLE_SCALAR_IMPLEMENTATION(Sv31.ui=Sv31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_xor_ps(Vv31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_xor_ps(Vv31,Vtmp5);)
    591. 

  591.     ENABLE_SCALAR_IMPLEMENTATION(Sv32.ui=Sv32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_xor_ps(Vv32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_xor_ps(Vv32,Vtmp5);)
    592. 

  592. #endif
    593. 

  593. 

  594.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp1.ui^Stmp2.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp1,Vtmp2);)
    595. 

  595.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    596. 

  596.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=Stmp1.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_xor_ps(Vtmp1,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_xor_ps(Vtmp1,Vtmp5);)
    597. 

  597.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=Stmp2.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_xor_ps(Vtmp2,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_xor_ps(Vtmp2,Vtmp5);)
    598. 

  598. 

  599.     // If columns 1-2 have been swapped, negate 2nd column of A and V so that V is still a rotation
    600. 

  600. 

  601.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=-2.;)                                            ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_set1_ps(-2.);)                                        ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_set1_ps(-2.);)
    602. 

  602.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    603. 

  603.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=1.;)                                             ENABLE_SSE_IMPLEMENTATION(Vtmp4=Vone;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=Vone;)
    604. 

  604.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Stmp5.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vtmp5);)
    605. 

  605. 

  606.     ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sa12.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va12=_mm_mul_ps(Va12,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_mul_ps(Va12,Vtmp4);)
    607. 

  607.     ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sa22.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va22=_mm_mul_ps(Va22,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_mul_ps(Va22,Vtmp4);)
    608. 

  608.     ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sa32.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va32=_mm_mul_ps(Va32,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_mul_ps(Va32,Vtmp4);)
    609. 

  609. 

  610. #ifdef COMPUTE_V_AS_MATRIX
    611. 

  611.     ENABLE_SCALAR_IMPLEMENTATION(Sv12.f=Sv12.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_mul_ps(Vv12,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_mul_ps(Vv12,Vtmp4);)
    612. 

  612.     ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv22.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_mul_ps(Vv22,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_mul_ps(Vv22,Vtmp4);)
    613. 

  613.     ENABLE_SCALAR_IMPLEMENTATION(Sv32.f=Sv32.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_mul_ps(Vv32,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_mul_ps(Vv32,Vtmp4);)
    614. 

  614. #endif
    615. 

  615. 

  616.     // If columns 1-2 have been swapped, also update quaternion representation of V (the quaternion may become un-normalized after this)
    617. 

  617. 

  618. #ifdef COMPUTE_V_AS_QUATERNION
    619. 

  619.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp4,Vone_half);)
    620. 

  620.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vone_half);)
    621. 

  621. 

  622.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvz);)
    623. 

  623.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvs);)
    624. 

  624.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp4);)
    625. 

  625.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f-Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_sub_ps(Vqvvz,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_sub_ps(Vqvvz,Vqvs);)
    626. 

  626.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Stmp5.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vqvs=Vtmp5;)                                                    ENABLE_AVX_IMPLEMENTATION(Vqvs=Vtmp5;)
    627. 

  627. 

  628.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvx);)
    629. 

  629.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvvy);)
    630. 

  630.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vqvvy,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vqvvy,Vtmp4);)
    631. 

  631.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f-Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_sub_ps(Vqvvx,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_sub_ps(Vqvvx,Vqvvy);)
    632. 

  632.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Stmp5.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvvy=Vtmp5;)                                                   ENABLE_AVX_IMPLEMENTATION(Vqvvy=Vtmp5;)
    633. 

  633. #endif
    634. 

  634. 

  635.     // Swap columns 1-3 if necessary
    636. 

  636. 

  637.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.ui=(Stmp1.f<Stmp3.f)?0xffffffff:0;)                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_cmplt_ps(Vtmp1,Vtmp3);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmp_ps(Vtmp1,Vtmp3, _CMP_LT_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmplt_ps(Vtmp1,Vtmp3);)
    638. 

  638.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa11.ui^Sa13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va11,Va13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va11,Va13);)
    639. 

  639.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    640. 

  640.     ENABLE_SCALAR_IMPLEMENTATION(Sa11.ui=Sa11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va11=_mm_xor_ps(Va11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_xor_ps(Va11,Vtmp5);)
    641. 

  641.     ENABLE_SCALAR_IMPLEMENTATION(Sa13.ui=Sa13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va13=_mm_xor_ps(Va13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_xor_ps(Va13,Vtmp5);)
    642. 

  642. 

  643.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa21.ui^Sa23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va21,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va21,Va23);)
    644. 

  644.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    645. 

  645.     ENABLE_SCALAR_IMPLEMENTATION(Sa21.ui=Sa21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va21=_mm_xor_ps(Va21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_xor_ps(Va21,Vtmp5);)
    646. 

  646.     ENABLE_SCALAR_IMPLEMENTATION(Sa23.ui=Sa23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va23=_mm_xor_ps(Va23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_xor_ps(Va23,Vtmp5);)
    647. 

  647. 

  648.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa31.ui^Sa33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va31,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va31,Va33);)
    649. 

  649.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    650. 

  650.     ENABLE_SCALAR_IMPLEMENTATION(Sa31.ui=Sa31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va31=_mm_xor_ps(Va31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_xor_ps(Va31,Vtmp5);)
    651. 

  651.     ENABLE_SCALAR_IMPLEMENTATION(Sa33.ui=Sa33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va33=_mm_xor_ps(Va33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_xor_ps(Va33,Vtmp5);)
    652. 

  652. 

  653. #ifdef COMPUTE_V_AS_MATRIX
    654. 

  654.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv11.ui^Sv13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv11,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv11,Vv13);)
    655. 

  655.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    656. 

  656.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.ui=Sv11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_xor_ps(Vv11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_xor_ps(Vv11,Vtmp5);)
    657. 

  657.     ENABLE_SCALAR_IMPLEMENTATION(Sv13.ui=Sv13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_xor_ps(Vv13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_xor_ps(Vv13,Vtmp5);)
    658. 

  658. 

  659.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv21.ui^Sv23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv21,Vv23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv21,Vv23);)
    660. 

  660.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    661. 

  661.     ENABLE_SCALAR_IMPLEMENTATION(Sv21.ui=Sv21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_xor_ps(Vv21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_xor_ps(Vv21,Vtmp5);)
    662. 

  662.     ENABLE_SCALAR_IMPLEMENTATION(Sv23.ui=Sv23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_xor_ps(Vv23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_xor_ps(Vv23,Vtmp5);)
    663. 

  663. 

  664.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv31.ui^Sv33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv31,Vv33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv31,Vv33);)
    665. 

  665.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    666. 

  666.     ENABLE_SCALAR_IMPLEMENTATION(Sv31.ui=Sv31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_xor_ps(Vv31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_xor_ps(Vv31,Vtmp5);)
    667. 

  667.     ENABLE_SCALAR_IMPLEMENTATION(Sv33.ui=Sv33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_xor_ps(Vv33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_xor_ps(Vv33,Vtmp5);)
    668. 

  668. #endif
    669. 

  669. 

  670.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp1.ui^Stmp3.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp1,Vtmp3);)
    671. 

  671.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    672. 

  672.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=Stmp1.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_xor_ps(Vtmp1,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_xor_ps(Vtmp1,Vtmp5);)
    673. 

  673.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.ui=Stmp3.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_xor_ps(Vtmp3,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_xor_ps(Vtmp3,Vtmp5);)
    674. 

  674. 

  675.     // If columns 1-3 have been swapped, negate 1st column of A and V so that V is still a rotation
    676. 

  676. 

  677.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=-2.;)                                            ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_set1_ps(-2.);)                                        ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_set1_ps(-2.);)
    678. 

  678.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    679. 

  679.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=1.;)                                             ENABLE_SSE_IMPLEMENTATION(Vtmp4=Vone;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=Vone;)
    680. 

  680.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Stmp5.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vtmp5);)
    681. 

  681. 

  682.     ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sa11.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va11=_mm_mul_ps(Va11,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_mul_ps(Va11,Vtmp4);)
    683. 

  683.     ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sa21.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va21=_mm_mul_ps(Va21,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_mul_ps(Va21,Vtmp4);)
    684. 

  684.     ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sa31.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va31=_mm_mul_ps(Va31,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_mul_ps(Va31,Vtmp4);)
    685. 

  685. 

  686. #ifdef COMPUTE_V_AS_MATRIX
    687. 

  687.     ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_mul_ps(Vv11,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_mul_ps(Vv11,Vtmp4);)
    688. 

  688.     ENABLE_SCALAR_IMPLEMENTATION(Sv21.f=Sv21.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_mul_ps(Vv21,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_mul_ps(Vv21,Vtmp4);)
    689. 

  689.     ENABLE_SCALAR_IMPLEMENTATION(Sv31.f=Sv31.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_mul_ps(Vv31,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_mul_ps(Vv31,Vtmp4);)
    690. 

  690. #endif
    691. 

  691. 

  692.     // If columns 1-3 have been swapped, also update quaternion representation of V (the quaternion may become un-normalized after this)
    693. 

  693. 

  694. #ifdef COMPUTE_V_AS_QUATERNION
    695. 

  695.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp4,Vone_half);)
    696. 

  696.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vone_half);)
    697. 

  697. 

  698.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvy);)
    699. 

  699.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvs);)
    700. 

  700.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp4);)
    701. 

  701.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f-Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_sub_ps(Vqvvy,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_sub_ps(Vqvvy,Vqvs);)
    702. 

  702.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Stmp5.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vqvs=Vtmp5;)                                                    ENABLE_AVX_IMPLEMENTATION(Vqvs=Vtmp5;)
    703. 

  703. 

  704.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvz);)
    705. 

  705.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvvx);)
    706. 

  706.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vqvvx,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vqvvx,Vtmp4);)
    707. 

  707.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f-Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_sub_ps(Vqvvz,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_sub_ps(Vqvvz,Vqvvx);)
    708. 

  708.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Stmp5.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvvx=Vtmp5;)                                                   ENABLE_AVX_IMPLEMENTATION(Vqvvx=Vtmp5;)
    709. 

  709. #endif
    710. 

  710. 

  711.     // Swap columns 2-3 if necessary
    712. 

  712. 

  713.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.ui=(Stmp2.f<Stmp3.f)?0xffffffff:0;)                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_cmplt_ps(Vtmp2,Vtmp3);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmp_ps(Vtmp2,Vtmp3, _CMP_LT_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmplt_ps(Vtmp2,Vtmp3);)
    714. 

  714.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa12.ui^Sa13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va12,Va13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va12,Va13);)
    715. 

  715.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    716. 

  716.     ENABLE_SCALAR_IMPLEMENTATION(Sa12.ui=Sa12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va12=_mm_xor_ps(Va12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_xor_ps(Va12,Vtmp5);)
    717. 

  717.     ENABLE_SCALAR_IMPLEMENTATION(Sa13.ui=Sa13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va13=_mm_xor_ps(Va13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_xor_ps(Va13,Vtmp5);)
    718. 

  718. 

  719.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa22.ui^Sa23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va22,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va22,Va23);)
    720. 

  720.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    721. 

  721.     ENABLE_SCALAR_IMPLEMENTATION(Sa22.ui=Sa22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va22=_mm_xor_ps(Va22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_xor_ps(Va22,Vtmp5);)
    722. 

  722.     ENABLE_SCALAR_IMPLEMENTATION(Sa23.ui=Sa23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va23=_mm_xor_ps(Va23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_xor_ps(Va23,Vtmp5);)
    723. 

  723. 

  724.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa32.ui^Sa33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va32,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va32,Va33);)
    725. 

  725.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    726. 

  726.     ENABLE_SCALAR_IMPLEMENTATION(Sa32.ui=Sa32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va32=_mm_xor_ps(Va32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_xor_ps(Va32,Vtmp5);)
    727. 

  727.     ENABLE_SCALAR_IMPLEMENTATION(Sa33.ui=Sa33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va33=_mm_xor_ps(Va33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_xor_ps(Va33,Vtmp5);)
    728. 

  728. 

  729. #ifdef COMPUTE_V_AS_MATRIX
    730. 

  730.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv12.ui^Sv13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv12,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv12,Vv13);)
    731. 

  731.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    732. 

  732.     ENABLE_SCALAR_IMPLEMENTATION(Sv12.ui=Sv12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_xor_ps(Vv12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_xor_ps(Vv12,Vtmp5);)
    733. 

  733.     ENABLE_SCALAR_IMPLEMENTATION(Sv13.ui=Sv13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_xor_ps(Vv13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_xor_ps(Vv13,Vtmp5);)
    734. 

  734. 

  735.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv22.ui^Sv23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv22,Vv23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv22,Vv23);)
    736. 

  736.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    737. 

  737.     ENABLE_SCALAR_IMPLEMENTATION(Sv22.ui=Sv22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_xor_ps(Vv22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_xor_ps(Vv22,Vtmp5);)
    738. 

  738.     ENABLE_SCALAR_IMPLEMENTATION(Sv23.ui=Sv23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_xor_ps(Vv23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_xor_ps(Vv23,Vtmp5);)
    739. 

  739. 

  740.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv32.ui^Sv33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv32,Vv33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv32,Vv33);)
    741. 

  741.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    742. 

  742.     ENABLE_SCALAR_IMPLEMENTATION(Sv32.ui=Sv32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_xor_ps(Vv32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_xor_ps(Vv32,Vtmp5);)
    743. 

  743.     ENABLE_SCALAR_IMPLEMENTATION(Sv33.ui=Sv33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_xor_ps(Vv33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_xor_ps(Vv33,Vtmp5);)
    744. 

  744. #endif
    745. 

  745. 

  746.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp2.ui^Stmp3.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp2,Vtmp3);)
    747. 

  747.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    748. 

  748.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=Stmp2.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_xor_ps(Vtmp2,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_xor_ps(Vtmp2,Vtmp5);)
    749. 

  749.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.ui=Stmp3.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_xor_ps(Vtmp3,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_xor_ps(Vtmp3,Vtmp5);)
    750. 

  750. 

  751.     // If columns 2-3 have been swapped, negate 3rd column of A and V so that V is still a rotation
    752. 

  752. 

  753.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=-2.;)                                            ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_set1_ps(-2.);)                                        ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_set1_ps(-2.);)
    754. 

  754.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    755. 

  755.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=1.;)                                             ENABLE_SSE_IMPLEMENTATION(Vtmp4=Vone;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=Vone;)
    756. 

  756.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Stmp5.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vtmp5);)
    757. 

  757. 

  758.     ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sa13.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va13=_mm_mul_ps(Va13,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_mul_ps(Va13,Vtmp4);)
    759. 

  759.     ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sa23.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va23=_mm_mul_ps(Va23,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_mul_ps(Va23,Vtmp4);)
    760. 

  760.     ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sa33.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va33=_mm_mul_ps(Va33,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_mul_ps(Va33,Vtmp4);)
    761. 

  761. 

  762. #ifdef COMPUTE_V_AS_MATRIX
    763. 

  763.     ENABLE_SCALAR_IMPLEMENTATION(Sv13.f=Sv13.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_mul_ps(Vv13,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_mul_ps(Vv13,Vtmp4);)
    764. 

  764.     ENABLE_SCALAR_IMPLEMENTATION(Sv23.f=Sv23.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_mul_ps(Vv23,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_mul_ps(Vv23,Vtmp4);)
    765. 

  765.     ENABLE_SCALAR_IMPLEMENTATION(Sv33.f=Sv33.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_mul_ps(Vv33,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_mul_ps(Vv33,Vtmp4);)
    766. 

  766. #endif
    767. 

  767. 

  768.     // If columns 2-3 have been swapped, also update quaternion representation of V (the quaternion may become un-normalized after this)
    769. 

  769. 

  770. #ifdef COMPUTE_V_AS_QUATERNION
    771. 

  771.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp4,Vone_half);)
    772. 

  772.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vone_half);)
    773. 

  773. 

  774.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvx);)
    775. 

  775.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvs);)
    776. 

  776.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp4);)
    777. 

  777.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f-Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_sub_ps(Vqvvx,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_sub_ps(Vqvvx,Vqvs);)
    778. 

  778.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Stmp5.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vqvs=Vtmp5;)                                                    ENABLE_AVX_IMPLEMENTATION(Vqvs=Vtmp5;)
    779. 

  779. 

  780.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvy);)
    781. 

  781.     ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvvz);)
    782. 

  782.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vqvvz,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vqvvz,Vtmp4);)
    783. 

  783.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f-Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_sub_ps(Vqvvy,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_sub_ps(Vqvvy,Vqvvz);)
    784. 

  784.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Stmp5.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvvz=Vtmp5;)                                                   ENABLE_AVX_IMPLEMENTATION(Vqvvz=Vtmp5;)
    785. 

  785. #endif
    786. 

  786. 

  787. #ifdef COMPUTE_V_AS_MATRIX
    788. 

  788. #ifdef PRINT_DEBUGGING_OUTPUT
    789. 

  789. #ifdef USE_SCALAR_IMPLEMENTATION
    790. 

  790.     std::cout<<"Scalar V ="<<std::endl;
    791. 

  791.     std::cout<<std::setw(12)<<Sv11.f<<"  "<<std::setw(12)<<Sv12.f<<"  "<<std::setw(12)<<Sv13.f<<std::endl;
    792. 

  792.     std::cout<<std::setw(12)<<Sv21.f<<"  "<<std::setw(12)<<Sv22.f<<"  "<<std::setw(12)<<Sv23.f<<std::endl;
    793. 

  793.     std::cout<<std::setw(12)<<Sv31.f<<"  "<<std::setw(12)<<Sv32.f<<"  "<<std::setw(12)<<Sv33.f<<std::endl;
    794. 

  794. #endif
    795. 

  795. #ifdef USE_SSE_IMPLEMENTATION
    796. 

  796.     _mm_storeu_ps(buf,Vv11);V11=buf[0];
    797. 

  797.     _mm_storeu_ps(buf,Vv21);V21=buf[0];
    798. 

  798.     _mm_storeu_ps(buf,Vv31);V31=buf[0];
    799. 

  799.     _mm_storeu_ps(buf,Vv12);V12=buf[0];
    800. 

  800.     _mm_storeu_ps(buf,Vv22);V22=buf[0];
    801. 

  801.     _mm_storeu_ps(buf,Vv32);V32=buf[0];
    802. 

  802.     _mm_storeu_ps(buf,Vv13);V13=buf[0];
    803. 

  803.     _mm_storeu_ps(buf,Vv23);V23=buf[0];
    804. 

  804.     _mm_storeu_ps(buf,Vv33);V33=buf[0];
    805. 

  805.     std::cout<<"Vector V ="<<std::endl;
    806. 

  806.     std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    807. 

  807.     std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    808. 

  808.     std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
    809. 

  809. #endif
    810. 

  810. #ifdef USE_AVX_IMPLEMENTATION
    811. 

  811.     _mm256_storeu_ps(buf,Vv11);V11=buf[0];
    812. 

  812.     _mm256_storeu_ps(buf,Vv21);V21=buf[0];
    813. 

  813.     _mm256_storeu_ps(buf,Vv31);V31=buf[0];
    814. 

  814.     _mm256_storeu_ps(buf,Vv12);V12=buf[0];
    815. 

  815.     _mm256_storeu_ps(buf,Vv22);V22=buf[0];
    816. 

  816.     _mm256_storeu_ps(buf,Vv32);V32=buf[0];
    817. 

  817.     _mm256_storeu_ps(buf,Vv13);V13=buf[0];
    818. 

  818.     _mm256_storeu_ps(buf,Vv23);V23=buf[0];
    819. 

  819.     _mm256_storeu_ps(buf,Vv33);V33=buf[0];
    820. 

  820.     std::cout<<"Vector V ="<<std::endl;
    821. 

  821.     std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    822. 

  822.     std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    823. 

  823.     std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
    824. 

  824. #endif
    825. 

  825. #endif
    826. 

  826. #endif
    827. 

  827. 

  828. #ifdef PRINT_DEBUGGING_OUTPUT
    829. 

  829. #ifdef USE_SCALAR_IMPLEMENTATION
    830. 

  830.     std::cout<<"Scalar A (after multiplying with V) ="<<std::endl;
    831. 

  831.     std::cout<<std::setw(12)<<Sa11.f<<"  "<<std::setw(12)<<Sa12.f<<"  "<<std::setw(12)<<Sa13.f<<std::endl;
    832. 

  832.     std::cout<<std::setw(12)<<Sa21.f<<"  "<<std::setw(12)<<Sa22.f<<"  "<<std::setw(12)<<Sa23.f<<std::endl;
    833. 

  833.     std::cout<<std::setw(12)<<Sa31.f<<"  "<<std::setw(12)<<Sa32.f<<"  "<<std::setw(12)<<Sa33.f<<std::endl;
    834. 

  834. #endif
    835. 

  835. #ifdef USE_SSE_IMPLEMENTATION
    836. 

  836.     _mm_storeu_ps(buf,Va11);A11=buf[0];
    837. 

  837.     _mm_storeu_ps(buf,Va21);A21=buf[0];
    838. 

  838.     _mm_storeu_ps(buf,Va31);A31=buf[0];
    839. 

  839.     _mm_storeu_ps(buf,Va12);A12=buf[0];
    840. 

  840.     _mm_storeu_ps(buf,Va22);A22=buf[0];
    841. 

  841.     _mm_storeu_ps(buf,Va32);A32=buf[0];
    842. 

  842.     _mm_storeu_ps(buf,Va13);A13=buf[0];
    843. 

  843.     _mm_storeu_ps(buf,Va23);A23=buf[0];
    844. 

  844.     _mm_storeu_ps(buf,Va33);A33=buf[0];
    845. 

  845.     std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    846. 

  846.     std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    847. 

  847.     std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    848. 

  848.     std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
    849. 

  849. #endif
    850. 

  850. #ifdef USE_AVX_IMPLEMENTATION
    851. 

  851.     _mm256_storeu_ps(buf,Va11);A11=buf[0];
    852. 

  852.     _mm256_storeu_ps(buf,Va21);A21=buf[0];
    853. 

  853.     _mm256_storeu_ps(buf,Va31);A31=buf[0];
    854. 

  854.     _mm256_storeu_ps(buf,Va12);A12=buf[0];
    855. 

  855.     _mm256_storeu_ps(buf,Va22);A22=buf[0];
    856. 

  856.     _mm256_storeu_ps(buf,Va32);A32=buf[0];
    857. 

  857.     _mm256_storeu_ps(buf,Va13);A13=buf[0];
    858. 

  858.     _mm256_storeu_ps(buf,Va23);A23=buf[0];
    859. 

  859.     _mm256_storeu_ps(buf,Va33);A33=buf[0];
    860. 

  860.     std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    861. 

  861.     std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    862. 

  862.     std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    863. 

  863.     std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
    864. 

  864. #endif
    865. 

  865. #endif
    866. 

  866. 

  867.     //###########################################################
    868. 

  868.     // Re-normalize quaternion for matrix V
    869. 

  869.     //###########################################################
    870. 

  870. 

  871. #ifdef COMPUTE_V_AS_QUATERNION
    872. 

  872.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvs.f*Sqvs.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvs,Vqvs);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvs,Vqvs);)
    873. 

  873.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvx,Vqvvx);)
    874. 

  874.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    875. 

  875.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvy.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvy,Vqvvy);)
    876. 

  876.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    877. 

  877.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvz.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvz,Vqvvz);)
    878. 

  878.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    879. 

  879.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=rsqrt(Stmp2.f);)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_rsqrt_ps(Vtmp2);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_rsqrt_ps(Vtmp2);)
    880. 

  880. 

  881. #ifdef PERFORM_STRICT_QUATERNION_RENORMALIZATION
    882. 

  882.     ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp1.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp1,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp1,Vone_half);)
    883. 

  883.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp4);)
    884. 

  884.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp3);)
    885. 

  885.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp2.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp2,Vtmp3);)
    886. 

  886.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    887. 

  887.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f-Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_sub_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_sub_ps(Vtmp1,Vtmp3);)
    888. 

  888. #endif
    889. 

  889. 

  890.     ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp1);)
    891. 

  891.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vqvvx,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vqvvx,Vtmp1);)
    892. 

  892.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vqvvy,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vqvvy,Vtmp1);)
    893. 

  893.     ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vqvvz,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vqvvz,Vtmp1);)
    894. 

  894. 

  895. #ifdef PRINT_DEBUGGING_OUTPUT
    896. 

  896. #ifdef USE_SCALAR_IMPLEMENTATION
    897. 

  897.     std::cout<<"Scalar qV ="<<std::endl;
    898. 

  898.     std::cout<<std::setw(12)<<Sqvs.f<<"  "<<std::setw(12)<<Sqvvx.f<<"  "<<std::setw(12)<<Sqvvy.f<<"  "<<std::setw(12)<<Sqvvz.f<<std::endl;
    899. 

  899. #endif
    900. 

  900. #ifdef USE_SSE_IMPLEMENTATION
    901. 

  901.     _mm_storeu_ps(buf,Vqvs);QVS=buf[0];
    902. 

  902.     _mm_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    903. 

  903.     _mm_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    904. 

  904.     _mm_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    905. 

  905.     std::cout<<"Vector qV ="<<std::endl;
    906. 

  906.     std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
    907. 

  907. #endif
    908. 

  908. #ifdef USE_AVX_IMPLEMENTATION
    909. 

  909.     _mm256_storeu_ps(buf,Vqvs);QVS=buf[0];
    910. 

  910.     _mm256_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    911. 

  911.     _mm256_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    912. 

  912.     _mm256_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    913. 

  913.     std::cout<<"Vector qV ="<<std::endl;
    914. 

  914.     std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
    915. 

  915. #endif
    916. 

  916. #endif
    917. 

  917. #endif
    918. 

  918. 

  919.     //###########################################################
    920. 

  920.     // Construct QR factorization of A*V (=U*D) using Givens rotations
    921. 

  921.     //###########################################################
    922. 

  922. 

  923. #ifdef COMPUTE_U_AS_MATRIX
    924. 

  924.     ENABLE_SCALAR_IMPLEMENTATION(Su11.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu11=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vu11=Vone;)
    925. 

  925.     ENABLE_SCALAR_IMPLEMENTATION(Su21.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu21=_mm_xor_ps(Vu21,Vu21);)                                    ENABLE_AVX_IMPLEMENTATION(Vu21=_mm256_xor_ps(Vu21,Vu21);)
    926. 

  926.     ENABLE_SCALAR_IMPLEMENTATION(Su31.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu31=_mm_xor_ps(Vu31,Vu31);)                                    ENABLE_AVX_IMPLEMENTATION(Vu31=_mm256_xor_ps(Vu31,Vu31);)
    927. 

  927.     ENABLE_SCALAR_IMPLEMENTATION(Su12.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu12=_mm_xor_ps(Vu12,Vu12);)                                    ENABLE_AVX_IMPLEMENTATION(Vu12=_mm256_xor_ps(Vu12,Vu12);)
    928. 

  928.     ENABLE_SCALAR_IMPLEMENTATION(Su22.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu22=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vu22=Vone;)
    929. 

  929.     ENABLE_SCALAR_IMPLEMENTATION(Su32.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu32=_mm_xor_ps(Vu32,Vu32);)                                    ENABLE_AVX_IMPLEMENTATION(Vu32=_mm256_xor_ps(Vu32,Vu32);)
    930. 

  930.     ENABLE_SCALAR_IMPLEMENTATION(Su13.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu13=_mm_xor_ps(Vu13,Vu13);)                                    ENABLE_AVX_IMPLEMENTATION(Vu13=_mm256_xor_ps(Vu13,Vu13);)
    931. 

  931.     ENABLE_SCALAR_IMPLEMENTATION(Su23.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu23=_mm_xor_ps(Vu23,Vu23);)                                    ENABLE_AVX_IMPLEMENTATION(Vu23=_mm256_xor_ps(Vu23,Vu23);)
    932. 

  932.     ENABLE_SCALAR_IMPLEMENTATION(Su33.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu33=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vu33=Vone;)
    933. 

  933. #endif
    934. 

  934. 

  935. #ifdef COMPUTE_U_AS_QUATERNION
    936. 

  936.     ENABLE_SCALAR_IMPLEMENTATION(Squs.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vqus=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vqus=Vone;)
    937. 

  937.     ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_xor_ps(Vquvx,Vquvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_xor_ps(Vquvx,Vquvx);)
    938. 

  938.     ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_xor_ps(Vquvy,Vquvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_xor_ps(Vquvy,Vquvy);)
    939. 

  939.     ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_xor_ps(Vquvz,Vquvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_xor_ps(Vquvz,Vquvz);)
    940. 

  940. #endif
    941. 

  941. 

  942.     // First Givens rotation
    943. 

  943. 

  944. #define SAPIVOT Sa11
    945. 

  945. #define SANPIVOT Sa21
    946. 

  946. #define SA11 Sa11
    947. 

  947. #define SA21 Sa21
    948. 

  948. #define SA12 Sa12
    949. 

  949. #define SA22 Sa22
    950. 

  950. #define SA13 Sa13
    951. 

  951. #define SA23 Sa23
    952. 

  952. #define SU11 Su11
    953. 

  953. #define SU12 Su12
    954. 

  954. #define SU21 Su21
    955. 

  955. #define SU22 Su22
    956. 

  956. #define SU31 Su31
    957. 

  957. #define SU32 Su32
    958. 

  958. 

  959. #define VAPIVOT Va11
    960. 

  960. #define VANPIVOT Va21
    961. 

  961. #define VA11 Va11
    962. 

  962. #define VA21 Va21
    963. 

  963. #define VA12 Va12
    964. 

  964. #define VA22 Va22
    965. 

  965. #define VA13 Va13
    966. 

  966. #define VA23 Va23
    967. 

  967. #define VU11 Vu11
    968. 

  968. #define VU12 Vu12
    969. 

  969. #define VU21 Vu21
    970. 

  970. #define VU22 Vu22
    971. 

  971. #define VU31 Vu31
    972. 

  972. #define VU32 Vu32
    973. 

  973. 

  974. #include "Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp"
    975. 

  975.     
    976. 

  976. #undef SAPIVOT
    977. 

  977. #undef SANPIVOT
    978. 

  978. #undef SA11
    979. 

  979. #undef SA21
    980. 

  980. #undef SA12
    981. 

  981. #undef SA22
    982. 

  982. #undef SA13
    983. 

  983. #undef SA23
    984. 

  984. #undef SU11
    985. 

  985. #undef SU12
    986. 

  986. #undef SU21
    987. 

  987. #undef SU22
    988. 

  988. #undef SU31
    989. 

  989. #undef SU32
    990. 

  990. 

  991. #undef VAPIVOT
    992. 

  992. #undef VANPIVOT
    993. 

  993. #undef VA11
    994. 

  994. #undef VA21
    995. 

  995. #undef VA12
    996. 

  996. #undef VA22
    997. 

  997. #undef VA13
    998. 

  998. #undef VA23
    999. 

  999. #undef VU11
    1000. 

  1000. #undef VU12
    1001. 

  1001. #undef VU21
    1002. 

  1002. #undef VU22
    1003. 

  1003. #undef VU31
    1004. 

  1004. #undef VU32
    1005. 

  1005. 

  1006.     // Update quaternion representation of U
    1007. 

  1007. 

  1008. #ifdef COMPUTE_U_AS_QUATERNION
    1009. 

  1009.     ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Sch.f;)                                           ENABLE_SSE_IMPLEMENTATION(Vqus=Vch;)                                                      ENABLE_AVX_IMPLEMENTATION(Vqus=Vch;)
    1010. 

  1010.     ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_xor_ps(Vquvx,Vquvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_xor_ps(Vquvx,Vquvx);)
    1011. 

  1011.     ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_xor_ps(Vquvy,Vquvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_xor_ps(Vquvy,Vquvy);)
    1012. 

  1012.     ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Ssh.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vquvz=Vsh;)                                                     ENABLE_AVX_IMPLEMENTATION(Vquvz=Vsh;)
    1013. 

  1013. #endif
    1014. 

  1014. 

  1015.     // Second Givens rotation
    1016. 

  1016. 

  1017. #define SAPIVOT Sa11
    1018. 

  1018. #define SANPIVOT Sa31
    1019. 

  1019. #define SA11 Sa11
    1020. 

  1020. #define SA21 Sa31
    1021. 

  1021. #define SA12 Sa12
    1022. 

  1022. #define SA22 Sa32
    1023. 

  1023. #define SA13 Sa13
    1024. 

  1024. #define SA23 Sa33
    1025. 

  1025. #define SU11 Su11
    1026. 

  1026. #define SU12 Su13
    1027. 

  1027. #define SU21 Su21
    1028. 

  1028. #define SU22 Su23
    1029. 

  1029. #define SU31 Su31
    1030. 

  1030. #define SU32 Su33
    1031. 

  1031. 

  1032. #define VAPIVOT Va11
    1033. 

  1033. #define VANPIVOT Va31
    1034. 

  1034. #define VA11 Va11
    1035. 

  1035. #define VA21 Va31
    1036. 

  1036. #define VA12 Va12
    1037. 

  1037. #define VA22 Va32
    1038. 

  1038. #define VA13 Va13
    1039. 

  1039. #define VA23 Va33
    1040. 

  1040. #define VU11 Vu11
    1041. 

  1041. #define VU12 Vu13
    1042. 

  1042. #define VU21 Vu21
    1043. 

  1043. #define VU22 Vu23
    1044. 

  1044. #define VU31 Vu31
    1045. 

  1045. #define VU32 Vu33
    1046. 

  1046. 

  1047. #include "Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp"
    1048. 

  1048.     
    1049. 

  1049. #undef SAPIVOT
    1050. 

  1050. #undef SANPIVOT
    1051. 

  1051. #undef SA11
    1052. 

  1052. #undef SA21
    1053. 

  1053. #undef SA12
    1054. 

  1054. #undef SA22
    1055. 

  1055. #undef SA13
    1056. 

  1056. #undef SA23
    1057. 

  1057. #undef SU11
    1058. 

  1058. #undef SU12
    1059. 

  1059. #undef SU21
    1060. 

  1060. #undef SU22
    1061. 

  1061. #undef SU31
    1062. 

  1062. #undef SU32
    1063. 

  1063. 

  1064. #undef VAPIVOT
    1065. 

  1065. #undef VANPIVOT
    1066. 

  1066. #undef VA11
    1067. 

  1067. #undef VA21
    1068. 

  1068. #undef VA12
    1069. 

  1069. #undef VA22
    1070. 

  1070. #undef VA13
    1071. 

  1071. #undef VA23
    1072. 

  1072. #undef VU11
    1073. 

  1073. #undef VU12
    1074. 

  1074. #undef VU21
    1075. 

  1075. #undef VU22
    1076. 

  1076. #undef VU31
    1077. 

  1077. #undef VU32
    1078. 

  1078. 

  1079.     // Update quaternion representation of U
    1080. 

  1080. 

  1081. #ifdef COMPUTE_U_AS_QUATERNION
    1082. 

  1082.     ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=Ssh.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_mul_ps(Vsh,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_mul_ps(Vsh,Vquvz);)
    1083. 

  1083.     ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Ssh.f*Squs.f;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vsh,Vqus);)                                      ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vsh,Vqus);)
    1084. 

  1084.     ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=Squvy.f-Ssh.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_sub_ps(Vquvy,Vsh);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_sub_ps(Vquvy,Vsh);)
    1085. 

  1085.     ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Sch.f*Squs.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vqus=_mm_mul_ps(Vch,Vqus);)                                     ENABLE_AVX_IMPLEMENTATION(Vqus=_mm256_mul_ps(Vch,Vqus);)
    1086. 

  1086.     ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Sch.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_mul_ps(Vch,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_mul_ps(Vch,Vquvz);)
    1087. 

  1087. #endif
    1088. 

  1088. 

  1089.     // Third Givens rotation
    1090. 

  1090. 

  1091. #define SAPIVOT Sa22
    1092. 

  1092. #define SANPIVOT Sa32
    1093. 

  1093. #define SA11 Sa21
    1094. 

  1094. #define SA21 Sa31
    1095. 

  1095. #define SA12 Sa22
    1096. 

  1096. #define SA22 Sa32
    1097. 

  1097. #define SA13 Sa23
    1098. 

  1098. #define SA23 Sa33
    1099. 

  1099. #define SU11 Su12
    1100. 

  1100. #define SU12 Su13
    1101. 

  1101. #define SU21 Su22
    1102. 

  1102. #define SU22 Su23
    1103. 

  1103. #define SU31 Su32
    1104. 

  1104. #define SU32 Su33
    1105. 

  1105. 

  1106. #define VAPIVOT Va22
    1107. 

  1107. #define VANPIVOT Va32
    1108. 

  1108. #define VA11 Va21
    1109. 

  1109. #define VA21 Va31
    1110. 

  1110. #define VA12 Va22
    1111. 

  1111. #define VA22 Va32
    1112. 

  1112. #define VA13 Va23
    1113. 

  1113. #define VA23 Va33
    1114. 

  1114. #define VU11 Vu12
    1115. 

  1115. #define VU12 Vu13
    1116. 

  1116. #define VU21 Vu22
    1117. 

  1117. #define VU22 Vu23
    1118. 

  1118. #define VU31 Vu32
    1119. 

  1119. #define VU32 Vu33
    1120. 

  1120. 

  1121. #include "Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp"
    1122. 

  1122.     
    1123. 

  1123. #undef SAPIVOT
    1124. 

  1124. #undef SANPIVOT
    1125. 

  1125. #undef SA11
    1126. 

  1126. #undef SA21
    1127. 

  1127. #undef SA12
    1128. 

  1128. #undef SA22
    1129. 

  1129. #undef SA13
    1130. 

  1130. #undef SA23
    1131. 

  1131. #undef SU11
    1132. 

  1132. #undef SU12
    1133. 

  1133. #undef SU21
    1134. 

  1134. #undef SU22
    1135. 

  1135. #undef SU31
    1136. 

  1136. #undef SU32
    1137. 

  1137. 

  1138. #undef VAPIVOT
    1139. 

  1139. #undef VANPIVOT
    1140. 

  1140. #undef VA11
    1141. 

  1141. #undef VA21
    1142. 

  1142. #undef VA12
    1143. 

  1143. #undef VA22
    1144. 

  1144. #undef VA13
    1145. 

  1145. #undef VA23
    1146. 

  1146. #undef VU11
    1147. 

  1147. #undef VU12
    1148. 

  1148. #undef VU21
    1149. 

  1149. #undef VU22
    1150. 

  1150. #undef VU31
    1151. 

  1151. #undef VU32
    1152. 

  1152. 

  1153.     // Update quaternion representation of U
    1154. 

  1154. 

  1155. #ifdef COMPUTE_U_AS_QUATERNION
    1156. 

  1156.     ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ssh.f*Squvx.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vsh,Vquvx);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vsh,Vquvx);)
    1157. 

  1157.     ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ssh.f*Squvy.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vsh,Vquvy);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vsh,Vquvy);)
    1158. 

  1158.     ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Ssh.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vsh,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vsh,Vquvz);)
    1159. 

  1159.     ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Ssh.f*Squs.f;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vsh,Vqus);)                                      ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vsh,Vqus);)
    1160. 

  1160.     ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Sch.f*Squs.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vqus=_mm_mul_ps(Vch,Vqus);)                                     ENABLE_AVX_IMPLEMENTATION(Vqus=_mm256_mul_ps(Vch,Vqus);)
    1161. 

  1161.     ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=Sch.f*Squvx.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_mul_ps(Vch,Vquvx);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_mul_ps(Vch,Vquvx);)
    1162. 

  1162.     ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=Sch.f*Squvy.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_mul_ps(Vch,Vquvy);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_mul_ps(Vch,Vquvy);)
    1163. 

  1163.     ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Sch.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_mul_ps(Vch,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_mul_ps(Vch,Vquvz);)
    1164. 

  1164.     ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=Squvx.f+Ssh.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_add_ps(Vquvx,Vsh);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_add_ps(Vquvx,Vsh);)
    1165. 

  1165.     ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Squs.f-Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqus=_mm_sub_ps(Vqus,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vqus=_mm256_sub_ps(Vqus,Vtmp1);)
    1166. 

  1166.     ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=Squvy.f+Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_add_ps(Vquvy,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_add_ps(Vquvy,Vtmp3);)
    1167. 

  1167.     ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Squvz.f-Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_sub_ps(Vquvz,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_sub_ps(Vquvz,Vtmp2);)
    1168. 

  1168. #endif
    1169. 

  1169. 

  1170. #ifdef COMPUTE_U_AS_MATRIX
    1171. 

  1171. #ifdef PRINT_DEBUGGING_OUTPUT
    1172. 

  1172. #ifdef USE_SCALAR_IMPLEMENTATION
    1173. 

  1173.     std::cout<<"Scalar U ="<<std::endl;
    1174. 

  1174.     std::cout<<std::setw(12)<<Su11.f<<"  "<<std::setw(12)<<Su12.f<<"  "<<std::setw(12)<<Su13.f<<std::endl;
    1175. 

  1175.     std::cout<<std::setw(12)<<Su21.f<<"  "<<std::setw(12)<<Su22.f<<"  "<<std::setw(12)<<Su23.f<<std::endl;
    1176. 

  1176.     std::cout<<std::setw(12)<<Su31.f<<"  "<<std::setw(12)<<Su32.f<<"  "<<std::setw(12)<<Su33.f<<std::endl;
    1177. 

  1177. #endif
    1178. 

  1178. #ifdef USE_SSE_IMPLEMENTATION
    1179. 

  1179.     _mm_storeu_ps(buf,Vu11);U11=buf[0];
    1180. 

  1180.     _mm_storeu_ps(buf,Vu21);U21=buf[0];
    1181. 

  1181.     _mm_storeu_ps(buf,Vu31);U31=buf[0];
    1182. 

  1182.     _mm_storeu_ps(buf,Vu12);U12=buf[0];
    1183. 

  1183.     _mm_storeu_ps(buf,Vu22);U22=buf[0];
    1184. 

  1184.     _mm_storeu_ps(buf,Vu32);U32=buf[0];
    1185. 

  1185.     _mm_storeu_ps(buf,Vu13);U13=buf[0];
    1186. 

  1186.     _mm_storeu_ps(buf,Vu23);U23=buf[0];
    1187. 

  1187.     _mm_storeu_ps(buf,Vu33);U33=buf[0];
    1188. 

  1188.     std::cout<<"Vector U ="<<std::endl;
    1189. 

  1189.     std::cout<<std::setw(12)<<U11<<"  "<<std::setw(12)<<U12<<"  "<<std::setw(12)<<U13<<std::endl;
    1190. 

  1190.     std::cout<<std::setw(12)<<U21<<"  "<<std::setw(12)<<U22<<"  "<<std::setw(12)<<U23<<std::endl;
    1191. 

  1191.     std::cout<<std::setw(12)<<U31<<"  "<<std::setw(12)<<U32<<"  "<<std::setw(12)<<U33<<std::endl;
    1192. 

  1192. #endif
    1193. 

  1193. #ifdef USE_AVX_IMPLEMENTATION
    1194. 

  1194.     _mm256_storeu_ps(buf,Vu11);U11=buf[0];
    1195. 

  1195.     _mm256_storeu_ps(buf,Vu21);U21=buf[0];
    1196. 

  1196.     _mm256_storeu_ps(buf,Vu31);U31=buf[0];
    1197. 

  1197.     _mm256_storeu_ps(buf,Vu12);U12=buf[0];
    1198. 

  1198.     _mm256_storeu_ps(buf,Vu22);U22=buf[0];
    1199. 

  1199.     _mm256_storeu_ps(buf,Vu32);U32=buf[0];
    1200. 

  1200.     _mm256_storeu_ps(buf,Vu13);U13=buf[0];
    1201. 

  1201.     _mm256_storeu_ps(buf,Vu23);U23=buf[0];
    1202. 

  1202.     _mm256_storeu_ps(buf,Vu33);U33=buf[0];
    1203. 

  1203.     std::cout<<"Vector U ="<<std::endl;
    1204. 

  1204.     std::cout<<std::setw(12)<<U11<<"  "<<std::setw(12)<<U12<<"  "<<std::setw(12)<<U13<<std::endl;
    1205. 

  1205.     std::cout<<std::setw(12)<<U21<<"  "<<std::setw(12)<<U22<<"  "<<std::setw(12)<<U23<<std::endl;
    1206. 

  1206.     std::cout<<std::setw(12)<<U31<<"  "<<std::setw(12)<<U32<<"  "<<std::setw(12)<<U33<<std::endl;
    1207. 

  1207. #endif
    1208. 

  1208. #endif
    1209. 

  1209. #endif
    1210. 

  1210. 

  1211. #ifdef PRINT_DEBUGGING_OUTPUT
    1212. 

  1212. #ifdef USE_SCALAR_IMPLEMENTATION
    1213. 

  1213.     std::cout<<"Scalar A (after multiplying with U-transpose and V) ="<<std::endl;
    1214. 

  1214.     std::cout<<std::setw(12)<<Sa11.f<<"  "<<std::setw(12)<<Sa12.f<<"  "<<std::setw(12)<<Sa13.f<<std::endl;
    1215. 

  1215.     std::cout<<std::setw(12)<<Sa21.f<<"  "<<std::setw(12)<<Sa22.f<<"  "<<std::setw(12)<<Sa23.f<<std::endl;
    1216. 

  1216.     std::cout<<std::setw(12)<<Sa31.f<<"  "<<std::setw(12)<<Sa32.f<<"  "<<std::setw(12)<<Sa33.f<<std::endl;
    1217. 

  1217. #endif
    1218. 

  1218. #ifdef USE_SSE_IMPLEMENTATION
    1219. 

  1219.     _mm_storeu_ps(buf,Va11);A11=buf[0];
    1220. 

  1220.     _mm_storeu_ps(buf,Va21);A21=buf[0];
    1221. 

  1221.     _mm_storeu_ps(buf,Va31);A31=buf[0];
    1222. 

  1222.     _mm_storeu_ps(buf,Va12);A12=buf[0];
    1223. 

  1223.     _mm_storeu_ps(buf,Va22);A22=buf[0];
    1224. 

  1224.     _mm_storeu_ps(buf,Va32);A32=buf[0];
    1225. 

  1225.     _mm_storeu_ps(buf,Va13);A13=buf[0];
    1226. 

  1226.     _mm_storeu_ps(buf,Va23);A23=buf[0];
    1227. 

  1227.     _mm_storeu_ps(buf,Va33);A33=buf[0];
    1228. 

  1228.     std::cout<<"Vector A (after multiplying with U-transpose and V) ="<<std::endl;
    1229. 

  1229.     std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    1230. 

  1230.     std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    1231. 

  1231.     std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
    1232. 

  1232. #endif
    1233. 

  1233. #ifdef USE_AVX_IMPLEMENTATION
    1234. 

  1234.     _mm256_storeu_ps(buf,Va11);A11=buf[0];
    1235. 

  1235.     _mm256_storeu_ps(buf,Va21);A21=buf[0];
    1236. 

  1236.     _mm256_storeu_ps(buf,Va31);A31=buf[0];
    1237. 

  1237.     _mm256_storeu_ps(buf,Va12);A12=buf[0];
    1238. 

  1238.     _mm256_storeu_ps(buf,Va22);A22=buf[0];
    1239. 

  1239.     _mm256_storeu_ps(buf,Va32);A32=buf[0];
    1240. 

  1240.     _mm256_storeu_ps(buf,Va13);A13=buf[0];
    1241. 

  1241.     _mm256_storeu_ps(buf,Va23);A23=buf[0];
    1242. 

  1242.     _mm256_storeu_ps(buf,Va33);A33=buf[0];
    1243. 

  1243.     std::cout<<"Vector A (after multiplying with U-transpose and V) ="<<std::endl;
    1244. 

  1244.     std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    1245. 

  1245.     std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    1246. 

  1246.     std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
    1247. 

  1247. #endif
    1248. 

  1248. #endif
    1249. 

  1249. 

  1250. #ifdef COMPUTE_U_AS_QUATERNION
    1251. 

  1251. #ifdef PRINT_DEBUGGING_OUTPUT
    1252. 

  1252. #ifdef USE_SCALAR_IMPLEMENTATION
    1253. 

  1253.     std::cout<<"Scalar qU ="<<std::endl;
    1254. 

  1254.     std::cout<<std::setw(12)<<Squs.f<<"  "<<std::setw(12)<<Squvx.f<<"  "<<std::setw(12)<<Squvy.f<<"  "<<std::setw(12)<<Squvz.f<<std::endl;
    1255. 

  1255. #endif
    1256. 

  1256. #ifdef USE_SSE_IMPLEMENTATION
    1257. 

  1257.     _mm_storeu_ps(buf,Vqus);QUS=buf[0];
    1258. 

  1258.     _mm_storeu_ps(buf,Vquvx);QUVX=buf[0];
    1259. 

  1259.     _mm_storeu_ps(buf,Vquvy);QUVY=buf[0];
    1260. 

  1260.     _mm_storeu_ps(buf,Vquvz);QUVZ=buf[0];
    1261. 

  1261.     std::cout<<"Vector qU ="<<std::endl;
    1262. 

  1262.     std::cout<<std::setw(12)<<QUS<<"  "<<std::setw(12)<<QUVX<<"  "<<std::setw(12)<<QUVY<<"  "<<std::setw(12)<<QUVZ<<std::endl;
    1263. 

  1263. #endif
    1264. 

  1264. #ifdef USE_AVX_IMPLEMENTATION
    1265. 

  1265.     _mm256_storeu_ps(buf,Vqus);QUS=buf[0];
    1266. 

  1266.     _mm256_storeu_ps(buf,Vquvx);QUVX=buf[0];
    1267. 

  1267.     _mm256_storeu_ps(buf,Vquvy);QUVY=buf[0];
    1268. 

  1268.     _mm256_storeu_ps(buf,Vquvz);QUVZ=buf[0];
    1269. 

  1269.     std::cout<<"Vector qU ="<<std::endl;
    1270. 

  1270.     std::cout<<std::setw(12)<<QUS<<"  "<<std::setw(12)<<QUVX<<"  "<<std::setw(12)<<QUVY<<"  "<<std::setw(12)<<QUVZ<<std::endl;
    1271. 

  1271. #endif
    1272. 

  1272. #endif
    1273. 

  1273. #endif
    1274. 

  1274. 

  1275. #ifdef __INTEL_COMPILER
    1276. 

  1276. #pragma warning( default : 592 )
    1277. 

  1277. #endif
    1278.