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_sqrt2f = static_cast<float>(1.0/al::numbers::sqrt2);
  14 constexpr auto inv_sqrt3f = static_cast<float>(1.0/al::numbers::sqrt3);
  15
  16
  17 /* These HF gains are derived from the same 32-point speaker array. The scale
  18  * factor between orders represents the same scale factors for any (regular)
  19  * speaker array decoder. e.g. Given a first-order source and second-order
  20  * output, applying an HF scale of HFScales[1][0] / HFScales[2][0] to channel 0
  21  * will result in that channel being subsequently decoded for second-order as
  22  * if it was a first-order decoder for that same speaker array.
  23  */
  24 constexpr std::array<std::array<float,MaxAmbiOrder+1>,MaxAmbiOrder+1> HFScales{{
  25     {{ 4.000000000e+00f, 2.309401077e+00f, 1.192569588e+00f, 7.189495850e-01f }},
  26     {{ 4.000000000e+00f, 2.309401077e+00f, 1.192569588e+00f, 7.189495850e-01f }},
  27     {{ 2.981423970e+00f, 2.309401077e+00f, 1.192569588e+00f, 7.189495850e-01f }},
  28     {{ 2.359168820e+00f, 2.031565936e+00f, 1.444598386e+00f, 7.189495850e-01f }},
  29     /* 1.947005434e+00f, 1.764337084e+00f, 1.424707344e+00f, 9.755104127e-01f, 4.784482742e-01f */
  30 }};
  31
  32 /* Same as above, but using a 10-point horizontal-only speaker array. Should
  33  * only be used when the device is mixing in 2D B-Format for horizontal-only
  34  * output.
  35  */
  36 constexpr std::array<std::array<float,MaxAmbiOrder+1>,MaxAmbiOrder+1> HFScales2D{{
  37     {{ 2.236067977e+00f, 1.581138830e+00f, 9.128709292e-01f, 6.050756345e-01f }},
  38     {{ 2.236067977e+00f, 1.581138830e+00f, 9.128709292e-01f, 6.050756345e-01f }},
  39     {{ 1.825741858e+00f, 1.581138830e+00f, 9.128709292e-01f, 6.050756345e-01f }},
  40     {{ 1.581138830e+00f, 1.460781803e+00f, 1.118033989e+00f, 6.050756345e-01f }},
  41     /* 1.414213562e+00f, 1.344997024e+00f, 1.144122806e+00f, 8.312538756e-01f, 4.370160244e-01f */
  42 }};
  43
  44
  45 /* This calculates a first-order "upsampler" matrix. It combines a first-order
  46  * decoder matrix with a max-order encoder matrix, creating a matrix that
  47  * behaves as if the B-Format input signal is first decoded to a speaker array
  48  * at first-order, then those speaker feeds are encoded to a higher-order
  49  * signal. While not perfect, this should accurately encode a lower-order
  50  * signal into a higher-order signal.
  51  */
  52 constexpr std::array<std::array<float,4>,8> FirstOrderDecoder{{
  53     {{ 1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f, }},
  54     {{ 1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f, }},
  55     {{ 1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f,  1.250000000e-01f, }},
  56     {{ 1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f, }},
  57     {{ 1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f, }},
  58     {{ 1.250000000e-01f,  1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f, }},
  59     {{ 1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f,  1.250000000e-01f, }},
  60     {{ 1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f, -1.250000000e-01f, }},
  61 }};
  62 constexpr std::array<AmbiChannelFloatArray,8> FirstOrderEncoder{{
  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     CalcAmbiCoeffs(-inv_sqrt3f, -inv_sqrt3f, -inv_sqrt3f),
  71 }};
  72 static_assert(FirstOrderDecoder.size() == FirstOrderEncoder.size(), "First-order mismatch");
  73
  74 /* This calculates a 2D first-order "upsampler" matrix. Same as the first-order
  75  * matrix, just using a more optimized speaker array for horizontal-only
  76  * content.
  77  */
  78 constexpr std::array<std::array<float,4>,4> FirstOrder2DDecoder{{
  79     {{ 2.500000000e-01f,  2.041241452e-01f, 0.0f,  2.041241452e-01f, }},
  80     {{ 2.500000000e-01f,  2.041241452e-01f, 0.0f, -2.041241452e-01f, }},
  81     {{ 2.500000000e-01f, -2.041241452e-01f, 0.0f,  2.041241452e-01f, }},
  82     {{ 2.500000000e-01f, -2.041241452e-01f, 0.0f, -2.041241452e-01f, }},
  83 }};
  84 constexpr std::array<AmbiChannelFloatArray,4> FirstOrder2DEncoder{{
  85     CalcAmbiCoeffs( inv_sqrt2f, 0.0f,  inv_sqrt2f),
  86     CalcAmbiCoeffs( inv_sqrt2f, 0.0f, -inv_sqrt2f),
  87     CalcAmbiCoeffs(-inv_sqrt2f, 0.0f,  inv_sqrt2f),
  88     CalcAmbiCoeffs(-inv_sqrt2f, 0.0f, -inv_sqrt2f),
  89 }};
  90 static_assert(FirstOrder2DDecoder.size() == FirstOrder2DEncoder.size(), "First-order 2D mismatch");
  91
  92
  93 /* This calculates a second-order "upsampler" matrix. Same as the first-order
  94  * matrix, just using a slightly more dense speaker array suitable for second-
  95  * order content.
  96  */
  97 constexpr std::array<std::array<float,9>,12> SecondOrderDecoder{{
  98     {{ 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, }},
  99     {{ 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, }},
 100     {{ 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, }},
 101     {{ 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     {{ 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     {{ 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     {{ 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     {{ 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     {{ 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     {{ 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     {{ 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     {{ 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 }};
 111 constexpr std::array<AmbiChannelFloatArray,12> SecondOrderEncoder{{
 112     CalcAmbiCoeffs( 0.000000000e+00f, -5.257311121e-01f,  8.506508084e-01f),
 113     CalcAmbiCoeffs(-8.506508084e-01f,  0.000000000e+00f,  5.257311121e-01f),
 114     CalcAmbiCoeffs(-5.257311121e-01f,  8.506508084e-01f,  0.000000000e+00f),
 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 }};
 125 static_assert(SecondOrderDecoder.size() == SecondOrderEncoder.size(), "Second-order mismatch");
 126
 127 /* This calculates a 2D second-order "upsampler" matrix. Same as the second-
 128  * order matrix, just using a more optimized speaker array for horizontal-only
 129  * content.
 130  */
 131 constexpr std::array<std::array<float,9>,6> SecondOrder2DDecoder{{
 132     {{ 1.666666667e-01f, -9.622504486e-02f, 0.0f,  1.666666667e-01f, -1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f, }},
 133     {{ 1.666666667e-01f, -1.924500897e-01f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, -1.721325932e-01f, }},
 134     {{ 1.666666667e-01f, -9.622504486e-02f, 0.0f, -1.666666667e-01f,  1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f, }},
 135     {{ 1.666666667e-01f,  9.622504486e-02f, 0.0f, -1.666666667e-01f, -1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f, }},
 136     {{ 1.666666667e-01f,  1.924500897e-01f, 0.0f,  0.000000000e+00f,  0.000000000e+00f, 0.0f, 0.0f, 0.0f, -1.721325932e-01f, }},
 137     {{ 1.666666667e-01f,  9.622504486e-02f, 0.0f,  1.666666667e-01f,  1.490711985e-01f, 0.0f, 0.0f, 0.0f,  8.606629658e-02f, }},
 138 }};
 139 constexpr std::array<AmbiChannelFloatArray,6> SecondOrder2DEncoder{{
 140     CalcAmbiCoeffs(-0.50000000000f, 0.0f,  0.86602540379f),
 141     CalcAmbiCoeffs(-1.00000000000f, 0.0f,  0.00000000000f),
 142     CalcAmbiCoeffs(-0.50000000000f, 0.0f, -0.86602540379f),
 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 }};
 147 static_assert(SecondOrder2DDecoder.size() == SecondOrder2DEncoder.size(),
 148     "Second-order 2D mismatch");
 149
 150
 151 /* This calculates a third-order "upsampler" matrix. Same as the first-order
 152  * matrix, just using a more dense speaker array suitable for third-order
 153  * content.
 154  */
 155 constexpr std::array<std::array<float,16>,20> ThirdOrderDecoder{{
 156     {{ 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, }},
 157     {{ 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, }},
 158     {{ 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, }},
 159     {{ 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     {{ 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, }},
 161     {{ 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, }},
 162     {{ 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, }},
 163     {{ 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     {{ 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, }},
 165     {{ 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, }},
 166     {{ 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, }},
 167     {{ 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     {{ 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, }},
 169     {{ 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, }},
 170     {{ 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, }},
 171     {{ 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     {{ 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     {{ 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     {{ 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     {{ 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 }};
 177 constexpr std::array<AmbiChannelFloatArray,20> ThirdOrderEncoder{{
 178     CalcAmbiCoeffs( 0.35682208976f,  0.93417235897f,  0.00000000000f),
 179     CalcAmbiCoeffs(-0.35682208976f,  0.93417235897f,  0.00000000000f),
 180     CalcAmbiCoeffs( 0.35682208976f, -0.93417235897f,  0.00000000000f),
 181     CalcAmbiCoeffs(-0.35682208976f, -0.93417235897f,  0.00000000000f),
 182     CalcAmbiCoeffs( 0.93417235897f,  0.00000000000f,  0.35682208976f),
 183     CalcAmbiCoeffs( 0.93417235897f,  0.00000000000f, -0.35682208976f),
 184     CalcAmbiCoeffs(-0.93417235897f,  0.00000000000f,  0.35682208976f),
 185     CalcAmbiCoeffs(-0.93417235897f,  0.00000000000f, -0.35682208976f),
 186     CalcAmbiCoeffs( 0.00000000000f,  0.35682208976f,  0.93417235897f),
 187     CalcAmbiCoeffs( 0.00000000000f,  0.35682208976f, -0.93417235897f),
 188     CalcAmbiCoeffs( 0.00000000000f, -0.35682208976f,  0.93417235897f),
 189     CalcAmbiCoeffs( 0.00000000000f, -0.35682208976f, -0.93417235897f),
 190     CalcAmbiCoeffs(     inv_sqrt3f,      inv_sqrt3f,      inv_sqrt3f),
 191     CalcAmbiCoeffs(     inv_sqrt3f,      inv_sqrt3f,     -inv_sqrt3f),
 192     CalcAmbiCoeffs(    -inv_sqrt3f,      inv_sqrt3f,      inv_sqrt3f),
 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 }};
 199 static_assert(ThirdOrderDecoder.size() == ThirdOrderEncoder.size(), "Third-order mismatch");
 200
 201 /* This calculates a 2D third-order "upsampler" matrix. Same as the third-order
 202  * matrix, just using a more optimized speaker array for horizontal-only
 203  * content.
 204  */
 205 constexpr std::array<std::array<float,16>,8> ThirdOrder2DDecoder{{
 206     {{ 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, }},
 207     {{ 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, }},
 208     {{ 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, }},
 209     {{ 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     {{ 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, }},
 211     {{ 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     {{ 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, }},
 213     {{ 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 }};
 215 constexpr std::array<AmbiChannelFloatArray,8> ThirdOrder2DEncoder{{
 216     CalcAmbiCoeffs(-0.38268343237f, 0.0f,  0.92387953251f),
 217     CalcAmbiCoeffs(-0.92387953251f, 0.0f,  0.38268343237f),
 218     CalcAmbiCoeffs(-0.92387953251f, 0.0f, -0.38268343237f),
 219     CalcAmbiCoeffs(-0.38268343237f, 0.0f, -0.92387953251f),
 220     CalcAmbiCoeffs( 0.38268343237f, 0.0f, -0.92387953251f),
 221     CalcAmbiCoeffs( 0.92387953251f, 0.0f, -0.38268343237f),
 222     CalcAmbiCoeffs( 0.92387953251f, 0.0f,  0.38268343237f),
 223     CalcAmbiCoeffs( 0.38268343237f, 0.0f,  0.92387953251f),
 224 }};
 225 static_assert(ThirdOrder2DDecoder.size() == ThirdOrder2DEncoder.size(), "Third-order 2D mismatch");
 226
 227
 228 /* This calculates a 2D fourth-order "upsampler" matrix. There is no 3D fourth-
 229  * order upsampler since fourth-order is the max order we'll be supporting for
 230  * the foreseeable future. This is only necessary for mixing horizontal-only
 231  * fourth-order content to 3D.
 232  */
 233 constexpr std::array<std::array<float,25>,10> FourthOrder2DDecoder{{
 234     {{ 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, }},
 235     {{ 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, }},
 236     {{ 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, }},
 237     {{ 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, }},
 238     {{ 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, }},
 239     {{ 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, }},
 240     {{ 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     {{ 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, }},
 242     {{ 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, }},
 243     {{ 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, }},
 244 }};
 245 constexpr std::array<AmbiChannelFloatArray,10> FourthOrder2DEncoder{{
 246     CalcAmbiCoeffs( 3.090169944e-01f,  0.000000000e+00f,  9.510565163e-01f),
 247     CalcAmbiCoeffs( 8.090169944e-01f,  0.000000000e+00f,  5.877852523e-01f),
 248     CalcAmbiCoeffs( 1.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f),
 249     CalcAmbiCoeffs( 8.090169944e-01f,  0.000000000e+00f, -5.877852523e-01f),
 250     CalcAmbiCoeffs( 3.090169944e-01f,  0.000000000e+00f, -9.510565163e-01f),
 251     CalcAmbiCoeffs(-3.090169944e-01f,  0.000000000e+00f, -9.510565163e-01f),
 252     CalcAmbiCoeffs(-8.090169944e-01f,  0.000000000e+00f, -5.877852523e-01f),
 253     CalcAmbiCoeffs(-1.000000000e+00f,  0.000000000e+00f,  0.000000000e+00f),
 254     CalcAmbiCoeffs(-8.090169944e-01f,  0.000000000e+00f,  5.877852523e-01f),
 255     CalcAmbiCoeffs(-3.090169944e-01f,  0.000000000e+00f,  9.510565163e-01f),
 256 }};
 257 static_assert(FourthOrder2DDecoder.size() == FourthOrder2DEncoder.size(), "Fourth-order 2D mismatch");
 258
 259
 260 template<size_t N, size_t M>
 261 auto CalcAmbiUpsampler(const std::array<std::array<float,N>,M> &decoder,
 262     const std::array<AmbiChannelFloatArray,M> &encoder)
 263 {
 264     std::array<AmbiChannelFloatArray,N> res{};
 265
 266     for(size_t i{0};i < decoder[0].size();++i)
 267     {
 268         for(size_t j{0};j < encoder[0].size();++j)
 269         {
 270             double sum{0.0};
 271             for(size_t k{0};k < decoder.size();++k)
 272                 sum += double{decoder[k][i]} * encoder[k][j];
 273             res[i][j] = static_cast<float>(sum);
 274         }
 275     }
 276
 277     return res;
 278 }
 279
 280 } // namespace
 281
 282 const std::array<AmbiChannelFloatArray,4> AmbiScale::FirstOrderUp{CalcAmbiUpsampler(FirstOrderDecoder, FirstOrderEncoder)};
 283 const std::array<AmbiChannelFloatArray,4> AmbiScale::FirstOrder2DUp{CalcAmbiUpsampler(FirstOrder2DDecoder, FirstOrder2DEncoder)};
 284 const std::array<AmbiChannelFloatArray,9> AmbiScale::SecondOrderUp{CalcAmbiUpsampler(SecondOrderDecoder, SecondOrderEncoder)};
 285 const std::array<AmbiChannelFloatArray,9> AmbiScale::SecondOrder2DUp{CalcAmbiUpsampler(SecondOrder2DDecoder, SecondOrder2DEncoder)};
 286 const std::array<AmbiChannelFloatArray,16> AmbiScale::ThirdOrderUp{CalcAmbiUpsampler(ThirdOrderDecoder, ThirdOrderEncoder)};
 287 const std::array<AmbiChannelFloatArray,16> AmbiScale::ThirdOrder2DUp{CalcAmbiUpsampler(ThirdOrder2DDecoder, ThirdOrder2DEncoder)};
 288 const std::array<AmbiChannelFloatArray,25> AmbiScale::FourthOrder2DUp{CalcAmbiUpsampler(FourthOrder2DDecoder, FourthOrder2DEncoder)};
 289
 290
 291 std::array<float,MaxAmbiOrder+1> AmbiScale::GetHFOrderScales(const uint src_order,
 292     const uint dev_order, const bool horizontalOnly) noexcept
 293 {
 294     std::array<float,MaxAmbiOrder+1> res{};
 295
 296     if(!horizontalOnly)
 297     {
 298         for(size_t i{0};i < MaxAmbiOrder+1;++i)
 299             res[i] = HFScales[src_order][i] / HFScales[dev_order][i];
 300     }
 301     else
 302     {
 303         for(size_t i{0};i < MaxAmbiOrder+1;++i)
 304             res[i] = HFScales2D[src_order][i] / HFScales2D[dev_order][i];
 305     }
 306
 307     return res;
 308 }