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Singular_Value_Decomposition_Kernel_Declarations.hpp

Singular_Value_Decomposition_Kernel_Declarations.hpp 16 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. //###########################################################
    18. 

  18. // Local variable declarations
    19. 

  19. //###########################################################
    20. 

  20. 

  21. #ifdef PRINT_DEBUGGING_OUTPUT
    22. 

  22. 

  23. #ifdef USE_SSE_IMPLEMENTATION
    24. 

  24.     float buf[4];
    25. 

  25.     float A11,A21,A31,A12,A22,A32,A13,A23,A33;
    26. 

  26.     float S11,S21,S31,S22,S32,S33;
    27. 

  27. #ifdef COMPUTE_V_AS_QUATERNION
    28. 

  28.     float QVS,QVVX,QVVY,QVVZ;
    29. 

  29. #endif
    30. 

  30. #ifdef COMPUTE_V_AS_MATRIX
    31. 

  31.     float V11,V21,V31,V12,V22,V32,V13,V23,V33;
    32. 

  32. #endif
    33. 

  33. #ifdef COMPUTE_U_AS_QUATERNION
    34. 

  34.     float QUS,QUVX,QUVY,QUVZ;
    35. 

  35. #endif
    36. 

  36. #ifdef COMPUTE_U_AS_MATRIX
    37. 

  37.     float U11,U21,U31,U12,U22,U32,U13,U23,U33;
    38. 

  38. #endif
    39. 

  39. #endif
    40. 

  40. 

  41. #ifdef USE_AVX_IMPLEMENTATION
    42. 

  42.     float buf[8];
    43. 

  43.     float A11,A21,A31,A12,A22,A32,A13,A23,A33;
    44. 

  44.     float S11,S21,S31,S22,S32,S33;
    45. 

  45. #ifdef COMPUTE_V_AS_QUATERNION
    46. 

  46.     float QVS,QVVX,QVVY,QVVZ;
    47. 

  47. #endif
    48. 

  48. #ifdef COMPUTE_V_AS_MATRIX
    49. 

  49.     float V11,V21,V31,V12,V22,V32,V13,V23,V33;
    50. 

  50. #endif
    51. 

  51. #ifdef COMPUTE_U_AS_QUATERNION
    52. 

  52.     float QUS,QUVX,QUVY,QUVZ;
    53. 

  53. #endif
    54. 

  54. #ifdef COMPUTE_U_AS_MATRIX
    55. 

  55.     float U11,U21,U31,U12,U22,U32,U13,U23,U33;
    56. 

  56. #endif
    57. 

  57. #endif
    58. 

  58. 

  59. #endif
    60. 

  60. 

  61. const float Four_Gamma_Squared=sqrt(8.)+3.;
    62. 

  62. const float Sine_Pi_Over_Eight=.5*sqrt(2.-sqrt(2.));
    63. 

  63. const float Cosine_Pi_Over_Eight=.5*sqrt(2.+sqrt(2.));
    64. 

  64. 

  65. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sfour_gamma_squared;)       ENABLE_SSE_IMPLEMENTATION(__m128 Vfour_gamma_squared;)                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vfour_gamma_squared;)
    66. 

  66. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ssine_pi_over_eight;)       ENABLE_SSE_IMPLEMENTATION(__m128 Vsine_pi_over_eight;)                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vsine_pi_over_eight;)
    67. 

  67. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Scosine_pi_over_eight;)     ENABLE_SSE_IMPLEMENTATION(__m128 Vcosine_pi_over_eight;)                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vcosine_pi_over_eight;)
    68. 

  68. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sone_half;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vone_half;)                                              ENABLE_AVX_IMPLEMENTATION(__m256 Vone_half;)
    69. 

  69. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sone;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vone;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vone;)
    70. 

  70. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stiny_number;)              ENABLE_SSE_IMPLEMENTATION(__m128 Vtiny_number;)                                           ENABLE_AVX_IMPLEMENTATION(__m256 Vtiny_number;)
    71. 

  71. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ssmall_number;)             ENABLE_SSE_IMPLEMENTATION(__m128 Vsmall_number;)                                          ENABLE_AVX_IMPLEMENTATION(__m256 Vsmall_number;)
    72. 

  72. 

  73. ENABLE_SCALAR_IMPLEMENTATION(Sfour_gamma_squared.f=Four_Gamma_Squared;)                   ENABLE_SSE_IMPLEMENTATION(Vfour_gamma_squared=_mm_set1_ps(Four_Gamma_Squared);)           ENABLE_AVX_IMPLEMENTATION(Vfour_gamma_squared=_mm256_set1_ps(Four_Gamma_Squared);)
    74. 

  74. ENABLE_SCALAR_IMPLEMENTATION(Ssine_pi_over_eight.f=Sine_Pi_Over_Eight;)                   ENABLE_SSE_IMPLEMENTATION(Vsine_pi_over_eight=_mm_set1_ps(Sine_Pi_Over_Eight);)           ENABLE_AVX_IMPLEMENTATION(Vsine_pi_over_eight=_mm256_set1_ps(Sine_Pi_Over_Eight);)
    75. 

  75. ENABLE_SCALAR_IMPLEMENTATION(Scosine_pi_over_eight.f=Cosine_Pi_Over_Eight;)               ENABLE_SSE_IMPLEMENTATION(Vcosine_pi_over_eight=_mm_set1_ps(Cosine_Pi_Over_Eight);)       ENABLE_AVX_IMPLEMENTATION(Vcosine_pi_over_eight=_mm256_set1_ps(Cosine_Pi_Over_Eight);)
    76. 

  76. ENABLE_SCALAR_IMPLEMENTATION(Sone_half.f=.5;)                                             ENABLE_SSE_IMPLEMENTATION(Vone_half=_mm_set1_ps(.5);)                                     ENABLE_AVX_IMPLEMENTATION(Vone_half=_mm256_set1_ps(.5);)
    77. 

  77. ENABLE_SCALAR_IMPLEMENTATION(Sone.f=1.;)                                                  ENABLE_SSE_IMPLEMENTATION(Vone=_mm_set1_ps(1.);)                                          ENABLE_AVX_IMPLEMENTATION(Vone=_mm256_set1_ps(1.);)
    78. 

  78. ENABLE_SCALAR_IMPLEMENTATION(Stiny_number.f=1.e-20;)                                      ENABLE_SSE_IMPLEMENTATION(Vtiny_number=_mm_set1_ps(1.e-20);)                              ENABLE_AVX_IMPLEMENTATION(Vtiny_number=_mm256_set1_ps(1.e-20);)
    79. 

  79. ENABLE_SCALAR_IMPLEMENTATION(Ssmall_number.f=1.e-12;)                                     ENABLE_SSE_IMPLEMENTATION(Vsmall_number=_mm_set1_ps(1.e-12);)                             ENABLE_AVX_IMPLEMENTATION(Vsmall_number=_mm256_set1_ps(1.e-12);)
    80. 

  80. 

  81. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa11;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va11;)
    82. 

  82. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa21;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va21;)
    83. 

  83. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa31;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va31;)
    84. 

  84. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa12;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va12;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va12;)
    85. 

  85. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa22;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va22;)
    86. 

  86. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa32;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va32;)
    87. 

  87. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa13;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va13;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va13;)
    88. 

  88. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa23;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va23;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va23;)
    89. 

  89. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa33;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va33;)
    90. 

  90. 

  91. #ifdef COMPUTE_V_AS_MATRIX
    92. 

  92. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv11;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv11;)
    93. 

  93. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv21;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv21;)
    94. 

  94. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv31;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv31;)
    95. 

  95. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv12;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv12;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv12;)
    96. 

  96. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv22;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv22;)
    97. 

  97. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv32;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv32;)
    98. 

  98. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv13;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv13;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv13;)
    99. 

  99. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv23;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv23;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv23;)
    100. 

  100. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv33;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv33;)
    101. 

  101. #endif
    102. 

  102. 

  103. #ifdef COMPUTE_V_AS_QUATERNION
    104. 

  104. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvs;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vqvs;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vqvs;)
    105. 

  105. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvx;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvx;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvx;)
    106. 

  106. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvy;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvy;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvy;)
    107. 

  107. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvz;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvz;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvz;)
    108. 

  108. #endif
    109. 

  109. 

  110. #ifdef COMPUTE_U_AS_MATRIX
    111. 

  111. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su11;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu11;)
    112. 

  112. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su21;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu21;)
    113. 

  113. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su31;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu31;)
    114. 

  114. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su12;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu12;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu12;)
    115. 

  115. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su22;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu22;)
    116. 

  116. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su32;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu32;)
    117. 

  117. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su13;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu13;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu13;)
    118. 

  118. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su23;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu23;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu23;)
    119. 

  119. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su33;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu33;)
    120. 

  120. #endif
    121. 

  121. 

  122. #ifdef COMPUTE_U_AS_QUATERNION
    123. 

  123. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squs;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vqus;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vqus;)
    124. 

  124. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squvx;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vquvx;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vquvx;)
    125. 

  125. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squvy;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vquvy;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vquvy;)
    126. 

  126. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squvz;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vquvz;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vquvz;)
    127. 

  127. #endif
    128. 

  128. 

  129. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sc;)                        ENABLE_SSE_IMPLEMENTATION(__m128 Vc;)                                                     ENABLE_AVX_IMPLEMENTATION(__m256 Vc;)
    130. 

  130. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss;)                        ENABLE_SSE_IMPLEMENTATION(__m128 Vs;)                                                     ENABLE_AVX_IMPLEMENTATION(__m256 Vs;)
    131. 

  131. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sch;)                       ENABLE_SSE_IMPLEMENTATION(__m128 Vch;)                                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vch;)
    132. 

  132. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ssh;)                       ENABLE_SSE_IMPLEMENTATION(__m128 Vsh;)                                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vsh;)
    133. 

  133. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp1;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp1;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp1;)
    134. 

  134. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp2;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp2;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp2;)
    135. 

  135. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp3;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp3;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp3;)
    136. 

  136. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp4;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp4;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp4;)
    137. 

  137. ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp5;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp5;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp5;)
    138.