core/ambidefs.cpp

   1
   2 #include "config.h"
   3
   4 #include "ambidefs.h"
   5
   6 #include "alnumbers.h"
   7
   8
   9 namespace {
  10
  11 using AmbiChannelFloatArray = std::array<float,MaxAmbiChannels>;
  12
  13 constexpr auto inv_sqrt3f = static_cast<float>(1.0/al::numbers::sqrt3);
  14
  15
  16 /* These HF gains are derived from the same 32-point speaker array. The scale
  17  * factor between orders represents the same scale factors for any (regular)
  18  * speaker array decoder. e.g. Given a first-order source and second-order
  19  * output, applying an HF scale of HFScales[1][0] / HFScales[2][0] to channel 0
  20  * will result in that channel being subsequently decoded for second-order as
  21  * if it was a first-order decoder for that same speaker array.
  22  */
  23 constexpr std::array HFScales{
  24     std::array{4.000000000e+00f, 2.309401077e+00f, 1.192569588e+00f, 7.189495850e-01f},
  25     std::array{4.000000000e+00f, 2.309401077e+00f, 1.192569588e+00f, 7.189495850e-01f},
  26     std::array{2.981423970e+00f, 2.309401077e+00f, 1.192569588e+00f, 7.189495850e-01f},
  27     std::array{2.359168820e+00f, 2.031565936e+00f, 1.444598386e+00f, 7.189495850e-01f},
  28     /*std::array{1.947005434e+00f, 1.764337084e+00f, 1.424707344e+00f, 9.755104127e-01f, 4.784482742e-01f}, */
  29 };
  30
  31 /* Same as above, but using a 10-point horizontal-only speaker array. Should
  32  * only be used when the device is mixing in 2D B-Format for horizontal-only
  33  * output.
  34  */
  35 constexpr std::array HFScales2D{
  36     std::array{2.236067977e+00f, 1.581138830e+00f, 9.128709292e-01f, 6.050756345e-01f},
  37     std::array{2.236067977e+00f, 1.581138830e+00f, 9.128709292e-01f, 6.050756345e-01f},
  38     std::array{1.825741858e+00f, 1.581138830e+00f, 9.128709292e-01f, 6.050756345e-01f},
  39     std::array{1.581138830e+00f, 1.460781803e+00f, 1.118033989e+00f, 6.050756345e-01f},
  40     /*std::array{1.414213562e+00f, 1.344997024e+00f, 1.144122806e+00f, 8.312538756e-01f, 4.370160244e-01f}, */
  41 };
  42
  43
  44 /* This calculates a first-order "upsampler" matrix. It combines a first-order
  45  * decoder matrix with a max-order encoder matrix, creating a matrix that
  46  * behaves as if the B-Format input signal is first decoded to a speaker array
  47  * at first-order, then those speaker feeds are encoded to a higher-order
  48  * signal. While not perfect, this should accurately encode a lower-order
  49  * signal into a higher-order signal.
  50  */
  51 constexpr std::array FirstOrderDecoder{
  52     std::array{1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f},
  53     std::array{1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f},
  54     std::array{1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f},
  55     std::array{1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f},
  56     std::array{1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f},
  57     std::array{1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f},
  58     std::array{1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f},
  59     std::array{1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f},
  60 };
  61 constexpr std::array FirstOrderEncoder{
  62     CalcAmbiCoeffs( inv_sqrt3f,  inv_sqrt3f,  inv_sqrt3f),
  63     CalcAmbiCoeffs( inv_sqrt3f,  inv_sqrt3f, -inv_sqrt3f),
  64     CalcAmbiCoeffs(-inv_sqrt3f,  inv_sqrt3f,  inv_sqrt3f),
  65     CalcAmbiCoeffs(-inv_sqrt3f,  inv_sqrt3f, -inv_sqrt3f),
  66     CalcAmbiCoeffs( inv_sqrt3f, -inv_sqrt3f,  inv_sqrt3f),
  67     CalcAmbiCoeffs( inv_sqrt3f, -inv_sqrt3f, -inv_sqrt3f),
  68     CalcAmbiCoeffs(-inv_sqrt3f, -inv_sqrt3f,  inv_sqrt3f),
  69     CalcAmbiCoeffs(-inv_sqrt3f, -inv_sqrt3f, -inv_sqrt3f),
  70 };
  71 static_assert(FirstOrderDecoder.size() == FirstOrderEncoder.size(), "First-order mismatch");
  72
  73 /* This calculates a 2D first-order "upsampler" matrix. Same as the first-order
  74  * matrix, just using a more optimized speaker array for horizontal-only
  75  * content.
  76  */
  77 constexpr std::array FirstOrder2DDecoder{
  78     std::array{1.666666667e-01f, -9.622504486e-02f, 0.0f,  1.666666667e-01f},
  79     std::array{1.666666667e-01f, -1.924500897e-01f, 0.0f,  0.000000000e+00f},
  80     std::array{1.666666667e-01f, -9.622504486e-02f, 0.0f, -1.666666667e-01f},
  81     std::array{1.666666667e-01f,  9.622504486e-02f, 0.0f, -1.666666667e-01f},
  82     std::array{1.666666667e-01f,  1.924500897e-01f, 0.0f,  0.000000000e+00f},
  83     std::array{1.666666667e-01f,  9.622504486e-02f, 0.0f,  1.666666667e-01f},
  84 };
  85 constexpr std::array FirstOrder2DEncoder{
  86     CalcAmbiCoeffs(-0.50000000000f, 0.0f,  0.86602540379f),
  87     CalcAmbiCoeffs(-1.00000000000f, 0.0f,  0.00000000000f),
  88     CalcAmbiCoeffs(-0.50000000000f, 0.0f, -0.86602540379f),
  89     CalcAmbiCoeffs( 0.50000000000f, 0.0f, -0.86602540379f),
  90     CalcAmbiCoeffs( 1.00000000000f, 0.0f,  0.00000000000f),
  91     CalcAmbiCoeffs( 0.50000000000f, 0.0f,  0.86602540379f),
  92 };
  93 static_assert(FirstOrder2DDecoder.size() == FirstOrder2DEncoder.size(), "First-order 2D mismatch");
  94
  95
  96 /* This calculates a second-order "upsampler" matrix. Same as the first-order
  97  * matrix, just using a slightly more dense speaker array suitable for second-
  98  * order content.
  99  */
 100 constexpr std::array SecondOrderDecoder{
 101     std::array{8.333333333e-02f,  0.000000000e+00f, -7.588274978e-02f,  1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f, -1.591525047e-02f, -1.443375673e-01f,  1.167715449e-01f},
 102     std::array{8.333333333e-02f, -1.227808683e-01f,  0.000000000e+00f,  7.588274978e-02f, -1.443375673e-01f,  0.000000000e+00f, -9.316949906e-02f,  0.000000000e+00f, -7.216878365e-02f},
 103     std::array{8.333333333e-02f, -7.588274978e-02f,  1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f, -1.443375673e-01f,  1.090847495e-01f,  0.000000000e+00f, -4.460276122e-02f},
 104     std::array{8.333333333e-02f,  0.000000000e+00f,  7.588274978e-02f,  1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f, -1.591525047e-02f,  1.443375673e-01f,  1.167715449e-01f},
 105     std::array{8.333333333e-02f, -1.227808683e-01f,  0.000000000e+00f, -7.588274978e-02f,  1.443375673e-01f,  0.000000000e+00f, -9.316949906e-02f,  0.000000000e+00f, -7.216878365e-02f},
 106     std::array{8.333333333e-02f,  7.588274978e-02f, -1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f, -1.443375673e-01f,  1.090847495e-01f,  0.000000000e+00f, -4.460276122e-02f},
 107     std::array{8.333333333e-02f,  0.000000000e+00f, -7.588274978e-02f, -1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f, -1.591525047e-02f,  1.443375673e-01f,  1.167715449e-01f},
 108     std::array{8.333333333e-02f,  1.227808683e-01f,  0.000000000e+00f, -7.588274978e-02f, -1.443375673e-01f,  0.000000000e+00f, -9.316949906e-02f,  0.000000000e+00f, -7.216878365e-02f},
 109     std::array{8.333333333e-02f,  7.588274978e-02f,  1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f,  1.443375673e-01f,  1.090847495e-01f,  0.000000000e+00f, -4.460276122e-02f},
 110     std::array{8.333333333e-02f,  0.000000000e+00f,  7.588274978e-02f, -1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f, -1.591525047e-02f, -1.443375673e-01f,  1.167715449e-01f},
 111     std::array{8.333333333e-02f,  1.227808683e-01f,  0.000000000e+00f,  7.588274978e-02f,  1.443375673e-01f,  0.000000000e+00f, -9.316949906e-02f,  0.000000000e+00f, -7.216878365e-02f},
 112     std::array{8.333333333e-02f, -7.588274978e-02f, -1.227808683e-01f,  0.000000000e+00f,  0.000000000e+00f,  1.443375673e-01f,  1.090847495e-01f,  0.000000000e+00f, -4.460276122e-02f},
 113 };
 114 constexpr std::array SecondOrderEncoder{
 115     CalcAmbiCoeffs( 0.000000000e+00f, -5.257311121e-01f,  8.506508084e-01f),
 116     CalcAmbiCoeffs(-8.506508084e-01f,  0.000000000e+00f,  5.257311121e-01f),
 117     CalcAmbiCoeffs(-5.257311121e-01f,  8.506508084e-01f,  0.000000000e+00f),
 118     CalcAmbiCoeffs( 0.000000000e+00f,  5.257311121e-01f,  8.506508084e-01f),
 119     CalcAmbiCoeffs(-8.506508084e-01f,  0.000000000e+00f, -5.257311121e-01f),
 120     CalcAmbiCoeffs( 5.257311121e-01f, -8.506508084e-01f,  0.000000000e+00f),
 121     CalcAmbiCoeffs( 0.000000000e+00f, -5.257311121e-01f, -8.506508084e-01f),
 122     CalcAmbiCoeffs( 8.506508084e-01f,  0.000000000e+00f, -5.257311121e-01f),
 123     CalcAmbiCoeffs( 5.257311121e-01f,  8.506508084e-01f,  0.000000000e+00f),
 124     CalcAmbiCoeffs( 0.000000000e+00f,  5.257311121e-01f, -8.506508084e-01f),
 125     CalcAmbiCoeffs( 8.506508084e-01f,  0.000000000e+00f,  5.257311121e-01f),
 126     CalcAmbiCoeffs(-5.257311121e-01f, -8.506508084e-01f,  0.000000000e+00f),
 127 };
 128 static_assert(SecondOrderDecoder.size() == SecondOrderEncoder.size(), "Second-order mismatch");
 129
 130 /* This calculates a 2D second-order "upsampler" matrix. Same as the second-
 131  * order matrix, just using a more optimized speaker array for horizontal-only
 132  * content.
 133  */
 134 constexpr std::array SecondOrder2DDecoder{
 135     std::array{1.666666667e-01f, -9.622504486e-02f, 0.0f,  1.666666667e-01f, -1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f},
 136     std::array{1.666666667e-01f, -1.924500897e-01f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, -1.721325932e-01f},
 137     std::array{1.666666667e-01f, -9.622504486e-02f, 0.0f, -1.666666667e-01f,  1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f},
 138     std::array{1.666666667e-01f,  9.622504486e-02f, 0.0f, -1.666666667e-01f, -1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f},
 139     std::array{1.666666667e-01f,  1.924500897e-01f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, -1.721325932e-01f},
 140     std::array{1.666666667e-01f,  9.622504486e-02f, 0.0f,  1.666666667e-01f,  1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f},
 141 };
 142 constexpr std::array SecondOrder2DEncoder{
 143     CalcAmbiCoeffs(-0.50000000000f, 0.0f,  0.86602540379f),
 144     CalcAmbiCoeffs(-1.00000000000f, 0.0f,  0.00000000000f),
 145     CalcAmbiCoeffs(-0.50000000000f, 0.0f, -0.86602540379f),
 146     CalcAmbiCoeffs( 0.50000000000f, 0.0f, -0.86602540379f),
 147     CalcAmbiCoeffs( 1.00000000000f, 0.0f,  0.00000000000f),
 148     CalcAmbiCoeffs( 0.50000000000f, 0.0f,  0.86602540379f),
 149 };
 150 static_assert(SecondOrder2DDecoder.size() == SecondOrder2DEncoder.size(),
 151     "Second-order 2D mismatch");
 152
 153
 154 /* This calculates a third-order "upsampler" matrix. Same as the first-order
 155  * matrix, just using a more dense speaker array suitable for third-order
 156  * content.
 157  */
 158 constexpr std::array ThirdOrderDecoder{
 159     std::array{5.000000000e-02f,  3.090169944e-02f,  8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f,  6.454972244e-02f,  9.045084972e-02f,  0.000000000e+00f, -1.232790000e-02f, -1.256118221e-01f,  0.000000000e+00f,  1.126112056e-01f,  7.944389175e-02f,  0.000000000e+00f,  2.421151497e-02f,  0.000000000e+00f},
 160     std::array{5.000000000e-02f, -3.090169944e-02f,  8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f, -6.454972244e-02f,  9.045084972e-02f,  0.000000000e+00f, -1.232790000e-02f,  1.256118221e-01f,  0.000000000e+00f, -1.126112056e-01f,  7.944389175e-02f,  0.000000000e+00f,  2.421151497e-02f,  0.000000000e+00f},
 161     std::array{5.000000000e-02f,  3.090169944e-02f, -8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f, -6.454972244e-02f,  9.045084972e-02f,  0.000000000e+00f, -1.232790000e-02f, -1.256118221e-01f,  0.000000000e+00f,  1.126112056e-01f, -7.944389175e-02f,  0.000000000e+00f, -2.421151497e-02f,  0.000000000e+00f},
 162     std::array{5.000000000e-02f, -3.090169944e-02f, -8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f,  6.454972244e-02f,  9.045084972e-02f,  0.000000000e+00f, -1.232790000e-02f,  1.256118221e-01f,  0.000000000e+00f, -1.126112056e-01f, -7.944389175e-02f,  0.000000000e+00f, -2.421151497e-02f,  0.000000000e+00f},
 163     std::array{5.000000000e-02f,  8.090169944e-02f,  0.000000000e+00f,  3.090169944e-02f,  6.454972244e-02f,  0.000000000e+00f, -5.590169944e-02f,  0.000000000e+00f, -7.216878365e-02f, -7.763237543e-02f,  0.000000000e+00f, -2.950836627e-02f,  0.000000000e+00f, -1.497759251e-01f,  0.000000000e+00f, -7.763237543e-02f},
 164     std::array{5.000000000e-02f,  8.090169944e-02f,  0.000000000e+00f, -3.090169944e-02f, -6.454972244e-02f,  0.000000000e+00f, -5.590169944e-02f,  0.000000000e+00f, -7.216878365e-02f, -7.763237543e-02f,  0.000000000e+00f, -2.950836627e-02f,  0.000000000e+00f,  1.497759251e-01f,  0.000000000e+00f,  7.763237543e-02f},
 165     std::array{5.000000000e-02f, -8.090169944e-02f,  0.000000000e+00f,  3.090169944e-02f, -6.454972244e-02f,  0.000000000e+00f, -5.590169944e-02f,  0.000000000e+00f, -7.216878365e-02f,  7.763237543e-02f,  0.000000000e+00f,  2.950836627e-02f,  0.000000000e+00f, -1.497759251e-01f,  0.000000000e+00f, -7.763237543e-02f},
 166     std::array{5.000000000e-02f, -8.090169944e-02f,  0.000000000e+00f, -3.090169944e-02f,  6.454972244e-02f,  0.000000000e+00f, -5.590169944e-02f,  0.000000000e+00f, -7.216878365e-02f,  7.763237543e-02f,  0.000000000e+00f,  2.950836627e-02f,  0.000000000e+00f,  1.497759251e-01f,  0.000000000e+00f,  7.763237543e-02f},
 167     std::array{5.000000000e-02f,  0.000000000e+00f,  3.090169944e-02f,  8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f, -3.454915028e-02f,  6.454972244e-02f,  8.449668365e-02f,  0.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f,  3.034486645e-02f, -6.779013272e-02f,  1.659481923e-01f,  4.797944664e-02f},
 168     std::array{5.000000000e-02f,  0.000000000e+00f,  3.090169944e-02f, -8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f, -3.454915028e-02f, -6.454972244e-02f,  8.449668365e-02f,  0.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f,  3.034486645e-02f,  6.779013272e-02f,  1.659481923e-01f, -4.797944664e-02f},
 169     std::array{5.000000000e-02f,  0.000000000e+00f, -3.090169944e-02f,  8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f, -3.454915028e-02f, -6.454972244e-02f,  8.449668365e-02f,  0.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f, -3.034486645e-02f, -6.779013272e-02f, -1.659481923e-01f,  4.797944664e-02f},
 170     std::array{5.000000000e-02f,  0.000000000e+00f, -3.090169944e-02f, -8.090169944e-02f,  0.000000000e+00f,  0.000000000e+00f, -3.454915028e-02f,  6.454972244e-02f,  8.449668365e-02f,  0.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f, -3.034486645e-02f,  6.779013272e-02f, -1.659481923e-01f, -4.797944664e-02f},
 171     std::array{5.000000000e-02f,  5.000000000e-02f,  5.000000000e-02f,  5.000000000e-02f,  6.454972244e-02f,  6.454972244e-02f,  0.000000000e+00f,  6.454972244e-02f,  0.000000000e+00f,  1.016220987e-01f,  6.338656910e-02f, -1.092600649e-02f, -7.364853795e-02f,  1.011266756e-01f, -7.086833869e-02f, -1.482646439e-02f},
 172     std::array{5.000000000e-02f,  5.000000000e-02f,  5.000000000e-02f, -5.000000000e-02f, -6.454972244e-02f,  6.454972244e-02f,  0.000000000e+00f, -6.454972244e-02f,  0.000000000e+00f,  1.016220987e-01f, -6.338656910e-02f, -1.092600649e-02f, -7.364853795e-02f, -1.011266756e-01f, -7.086833869e-02f,  1.482646439e-02f},
 173     std::array{5.000000000e-02f, -5.000000000e-02f,  5.000000000e-02f,  5.000000000e-02f, -6.454972244e-02f, -6.454972244e-02f,  0.000000000e+00f,  6.454972244e-02f,  0.000000000e+00f, -1.016220987e-01f, -6.338656910e-02f,  1.092600649e-02f, -7.364853795e-02f,  1.011266756e-01f, -7.086833869e-02f, -1.482646439e-02f},
 174     std::array{5.000000000e-02f, -5.000000000e-02f,  5.000000000e-02f, -5.000000000e-02f,  6.454972244e-02f, -6.454972244e-02f,  0.000000000e+00f, -6.454972244e-02f,  0.000000000e+00f, -1.016220987e-01f,  6.338656910e-02f,  1.092600649e-02f, -7.364853795e-02f, -1.011266756e-01f, -7.086833869e-02f,  1.482646439e-02f},
 175     std::array{5.000000000e-02f,  5.000000000e-02f, -5.000000000e-02f,  5.000000000e-02f,  6.454972244e-02f, -6.454972244e-02f,  0.000000000e+00f, -6.454972244e-02f,  0.000000000e+00f,  1.016220987e-01f, -6.338656910e-02f, -1.092600649e-02f,  7.364853795e-02f,  1.011266756e-01f,  7.086833869e-02f, -1.482646439e-02f},
 176     std::array{5.000000000e-02f,  5.000000000e-02f, -5.000000000e-02f, -5.000000000e-02f, -6.454972244e-02f, -6.454972244e-02f,  0.000000000e+00f,  6.454972244e-02f,  0.000000000e+00f,  1.016220987e-01f,  6.338656910e-02f, -1.092600649e-02f,  7.364853795e-02f, -1.011266756e-01f,  7.086833869e-02f,  1.482646439e-02f},
 177     std::array{5.000000000e-02f, -5.000000000e-02f, -5.000000000e-02f,  5.000000000e-02f, -6.454972244e-02f,  6.454972244e-02f,  0.000000000e+00f, -6.454972244e-02f,  0.000000000e+00f, -1.016220987e-01f,  6.338656910e-02f,  1.092600649e-02f,  7.364853795e-02f,  1.011266756e-01f,  7.086833869e-02f, -1.482646439e-02f},
 178     std::array{5.000000000e-02f, -5.000000000e-02f, -5.000000000e-02f, -5.000000000e-02f,  6.454972244e-02f,  6.454972244e-02f,  0.000000000e+00f,  6.454972244e-02f,  0.000000000e+00f, -1.016220987e-01f, -6.338656910e-02f,  1.092600649e-02f,  7.364853795e-02f, -1.011266756e-01f,  7.086833869e-02f,  1.482646439e-02f},
 179 };
 180 constexpr std::array ThirdOrderEncoder{
 181     CalcAmbiCoeffs( 0.35682208976f,  0.93417235897f,  0.00000000000f),
 182     CalcAmbiCoeffs(-0.35682208976f,  0.93417235897f,  0.00000000000f),
 183     CalcAmbiCoeffs( 0.35682208976f, -0.93417235897f,  0.00000000000f),
 184     CalcAmbiCoeffs(-0.35682208976f, -0.93417235897f,  0.00000000000f),
 185     CalcAmbiCoeffs( 0.93417235897f,  0.00000000000f,  0.35682208976f),
 186     CalcAmbiCoeffs( 0.93417235897f,  0.00000000000f, -0.35682208976f),
 187     CalcAmbiCoeffs(-0.93417235897f,  0.00000000000f,  0.35682208976f),
 188     CalcAmbiCoeffs(-0.93417235897f,  0.00000000000f, -0.35682208976f),
 189     CalcAmbiCoeffs( 0.00000000000f,  0.35682208976f,  0.93417235897f),
 190     CalcAmbiCoeffs( 0.00000000000f,  0.35682208976f, -0.93417235897f),
 191     CalcAmbiCoeffs( 0.00000000000f, -0.35682208976f,  0.93417235897f),
 192     CalcAmbiCoeffs( 0.00000000000f, -0.35682208976f, -0.93417235897f),
 193     CalcAmbiCoeffs(     inv_sqrt3f,      inv_sqrt3f,      inv_sqrt3f),
 194     CalcAmbiCoeffs(     inv_sqrt3f,      inv_sqrt3f,     -inv_sqrt3f),
 195     CalcAmbiCoeffs(    -inv_sqrt3f,      inv_sqrt3f,      inv_sqrt3f),
 196     CalcAmbiCoeffs(    -inv_sqrt3f,      inv_sqrt3f,     -inv_sqrt3f),
 197     CalcAmbiCoeffs(     inv_sqrt3f,     -inv_sqrt3f,      inv_sqrt3f),
 198     CalcAmbiCoeffs(     inv_sqrt3f,     -inv_sqrt3f,     -inv_sqrt3f),
 199     CalcAmbiCoeffs(    -inv_sqrt3f,     -inv_sqrt3f,      inv_sqrt3f),
 200     CalcAmbiCoeffs(    -inv_sqrt3f,     -inv_sqrt3f,     -inv_sqrt3f),
 201 };
 202 static_assert(ThirdOrderDecoder.size() == ThirdOrderEncoder.size(), "Third-order mismatch");
 203
 204 /* This calculates a 2D third-order "upsampler" matrix. Same as the third-order
 205  * matrix, just using a more optimized speaker array for horizontal-only
 206  * content.
 207  */
 208 constexpr std::array ThirdOrder2DDecoder{
 209     std::array{1.250000000e-01f, -5.523559567e-02f, 0.0f,  1.333505242e-01f, -9.128709292e-02f, 0.0f, 0.0f, 0.0f,  9.128709292e-02f, -1.104247249e-01f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  4.573941867e-02f},
 210     std::array{1.250000000e-01f, -1.333505242e-01f, 0.0f,  5.523559567e-02f, -9.128709292e-02f, 0.0f, 0.0f, 0.0f, -9.128709292e-02f,  4.573941867e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -1.104247249e-01f},
 211     std::array{1.250000000e-01f, -1.333505242e-01f, 0.0f, -5.523559567e-02f,  9.128709292e-02f, 0.0f, 0.0f, 0.0f, -9.128709292e-02f,  4.573941867e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  1.104247249e-01f},
 212     std::array{1.250000000e-01f, -5.523559567e-02f, 0.0f, -1.333505242e-01f,  9.128709292e-02f, 0.0f, 0.0f, 0.0f,  9.128709292e-02f, -1.104247249e-01f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -4.573941867e-02f},
 213     std::array{1.250000000e-01f,  5.523559567e-02f, 0.0f, -1.333505242e-01f, -9.128709292e-02f, 0.0f, 0.0f, 0.0f,  9.128709292e-02f,  1.104247249e-01f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -4.573941867e-02f},
 214     std::array{1.250000000e-01f,  1.333505242e-01f, 0.0f, -5.523559567e-02f, -9.128709292e-02f, 0.0f, 0.0f, 0.0f, -9.128709292e-02f, -4.573941867e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  1.104247249e-01f},
 215     std::array{1.250000000e-01f,  1.333505242e-01f, 0.0f,  5.523559567e-02f,  9.128709292e-02f, 0.0f, 0.0f, 0.0f, -9.128709292e-02f, -4.573941867e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -1.104247249e-01f},
 216     std::array{1.250000000e-01f,  5.523559567e-02f, 0.0f,  1.333505242e-01f,  9.128709292e-02f, 0.0f, 0.0f, 0.0f,  9.128709292e-02f,  1.104247249e-01f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  4.573941867e-02f},
 217 };
 218 constexpr std::array ThirdOrder2DEncoder{
 219     CalcAmbiCoeffs(-0.38268343237f, 0.0f,  0.92387953251f),
 220     CalcAmbiCoeffs(-0.92387953251f, 0.0f,  0.38268343237f),
 221     CalcAmbiCoeffs(-0.92387953251f, 0.0f, -0.38268343237f),
 222     CalcAmbiCoeffs(-0.38268343237f, 0.0f, -0.92387953251f),
 223     CalcAmbiCoeffs( 0.38268343237f, 0.0f, -0.92387953251f),
 224     CalcAmbiCoeffs( 0.92387953251f, 0.0f, -0.38268343237f),
 225     CalcAmbiCoeffs( 0.92387953251f, 0.0f,  0.38268343237f),
 226     CalcAmbiCoeffs( 0.38268343237f, 0.0f,  0.92387953251f),
 227 };
 228 static_assert(ThirdOrder2DDecoder.size() == ThirdOrder2DEncoder.size(), "Third-order 2D mismatch");
 229
 230
 231 /* This calculates a 2D fourth-order "upsampler" matrix. There is no 3D fourth-
 232  * order upsampler since fourth-order is the max order we'll be supporting for
 233  * the foreseeable future. This is only necessary for mixing horizontal-only
 234  * fourth-order content to 3D.
 235  */
 236 constexpr std::array FourthOrder2DDecoder{
 237     std::array{1.000000000e-01f,  3.568220898e-02f, 0.0f,  1.098185471e-01f,  6.070619982e-02f, 0.0f, 0.0f, 0.0f,  8.355491589e-02f,  7.735682057e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  5.620301997e-02f,  8.573754253e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  2.785781628e-02f},
 238     std::array{1.000000000e-01f,  9.341723590e-02f, 0.0f,  6.787159473e-02f,  9.822469464e-02f, 0.0f, 0.0f, 0.0f, -3.191513794e-02f,  2.954767620e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -9.093839659e-02f, -5.298871540e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -7.293270986e-02f},
 239     std::array{1.000000000e-01f,  1.154700538e-01f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, -1.032795559e-01f, -9.561828875e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  9.014978717e-02f},
 240     std::array{1.000000000e-01f,  9.341723590e-02f, 0.0f, -6.787159473e-02f, -9.822469464e-02f, 0.0f, 0.0f, 0.0f, -3.191513794e-02f,  2.954767620e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  9.093839659e-02f,  5.298871540e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -7.293270986e-02f},
 241     std::array{1.000000000e-01f,  3.568220898e-02f, 0.0f, -1.098185471e-01f, -6.070619982e-02f, 0.0f, 0.0f, 0.0f,  8.355491589e-02f,  7.735682057e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -5.620301997e-02f, -8.573754253e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  2.785781628e-02f},
 242     std::array{1.000000000e-01f, -3.568220898e-02f, 0.0f, -1.098185471e-01f,  6.070619982e-02f, 0.0f, 0.0f, 0.0f,  8.355491589e-02f, -7.735682057e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -5.620301997e-02f,  8.573754253e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  2.785781628e-02f},
 243     std::array{1.000000000e-01f, -9.341723590e-02f, 0.0f, -6.787159473e-02f,  9.822469464e-02f, 0.0f, 0.0f, 0.0f, -3.191513794e-02f, -2.954767620e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  9.093839659e-02f, -5.298871540e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -7.293270986e-02f},
 244     std::array{1.000000000e-01f, -1.154700538e-01f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, -1.032795559e-01f,  9.561828875e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  9.014978717e-02f},
 245     std::array{1.000000000e-01f, -9.341723590e-02f, 0.0f,  6.787159473e-02f, -9.822469464e-02f, 0.0f, 0.0f, 0.0f, -3.191513794e-02f, -2.954767620e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -9.093839659e-02f,  5.298871540e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -7.293270986e-02f},
 246     std::array{1.000000000e-01f, -3.568220898e-02f, 0.0f,  1.098185471e-01f, -6.070619982e-02f, 0.0f, 0.0f, 0.0f,  8.355491589e-02f, -7.735682057e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  5.620301997e-02f, -8.573754253e-02f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,  2.785781628e-02f},
 247 };
 248 constexpr std::array FourthOrder2DEncoder{
 249     CalcAmbiCoeffs( 3.090169944e-01f,  0.000000000e+00f,  9.510565163e-01f),
 250     CalcAmbiCoeffs( 8.090169944e-01f,  0.000000000e+00f,  5.877852523e-01f),
 251     CalcAmbiCoeffs( 1.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f),
 252     CalcAmbiCoeffs( 8.090169944e-01f,  0.000000000e+00f, -5.877852523e-01f),
 253     CalcAmbiCoeffs( 3.090169944e-01f,  0.000000000e+00f, -9.510565163e-01f),
 254     CalcAmbiCoeffs(-3.090169944e-01f,  0.000000000e+00f, -9.510565163e-01f),
 255     CalcAmbiCoeffs(-8.090169944e-01f,  0.000000000e+00f, -5.877852523e-01f),
 256     CalcAmbiCoeffs(-1.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f),
 257     CalcAmbiCoeffs(-8.090169944e-01f,  0.000000000e+00f,  5.877852523e-01f),
 258     CalcAmbiCoeffs(-3.090169944e-01f,  0.000000000e+00f,  9.510565163e-01f),
 259 };
 260 static_assert(FourthOrder2DDecoder.size() == FourthOrder2DEncoder.size(), "Fourth-order 2D mismatch");
 261
 262
 263 template<size_t N, size_t M>
 264 constexpr auto CalcAmbiUpsampler(const std::array<std::array<float,N>,M> &decoder,
 265     const std::array<AmbiChannelFloatArray,M> &encoder)
 266 {
 267     std::array<AmbiChannelFloatArray,N> res{};
 268
 269     for(size_t i{0};i < decoder[0].size();++i)
 270     {
 271         for(size_t j{0};j < encoder[0].size();++j)
 272         {
 273             double sum{0.0};
 274             for(size_t k{0};k < decoder.size();++k)
 275                 sum += double{decoder[k][i]} * encoder[k][j];
 276             res[i][j] = static_cast<float>(sum);
 277         }
 278     }
 279
 280     return res;
 281 }
 282
 283 } // namespace
 284
 285 const std::array<std::array<float,MaxAmbiChannels>,4> AmbiScale::FirstOrderUp{CalcAmbiUpsampler(FirstOrderDecoder, FirstOrderEncoder)};
 286 const std::array<std::array<float,MaxAmbiChannels>,4> AmbiScale::FirstOrder2DUp{CalcAmbiUpsampler(FirstOrder2DDecoder, FirstOrder2DEncoder)};
 287 const std::array<std::array<float,MaxAmbiChannels>,9> AmbiScale::SecondOrderUp{CalcAmbiUpsampler(SecondOrderDecoder, SecondOrderEncoder)};
 288 const std::array<std::array<float,MaxAmbiChannels>,9> AmbiScale::SecondOrder2DUp{CalcAmbiUpsampler(SecondOrder2DDecoder, SecondOrder2DEncoder)};
 289 const std::array<std::array<float,MaxAmbiChannels>,16> AmbiScale::ThirdOrderUp{CalcAmbiUpsampler(ThirdOrderDecoder, ThirdOrderEncoder)};
 290 const std::array<std::array<float,MaxAmbiChannels>,16> AmbiScale::ThirdOrder2DUp{CalcAmbiUpsampler(ThirdOrder2DDecoder, ThirdOrder2DEncoder)};
 291 const std::array<std::array<float,MaxAmbiChannels>,25> AmbiScale::FourthOrder2DUp{CalcAmbiUpsampler(FourthOrder2DDecoder, FourthOrder2DEncoder)};
 292
 293
 294 std::array<float,MaxAmbiOrder+1> AmbiScale::GetHFOrderScales(const uint src_order,
 295     const uint dev_order, const bool horizontalOnly) noexcept
 296 {
 297     std::array<float,MaxAmbiOrder+1> res{};
 298
 299     if(!horizontalOnly)
 300     {
 301         for(size_t i{0};i < MaxAmbiOrder+1;++i)
 302             res[i] = HFScales[src_order][i] / HFScales[dev_order][i];
 303     }
 304     else
 305     {
 306         for(size_t i{0};i < MaxAmbiOrder+1;++i)
 307             res[i] = HFScales2D[src_order][i] / HFScales2D[dev_order][i];
 308     }
 309
 310     return res;
 311 }