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@@ -382,6 +382,8 @@ Doing so may require special handling of certain matrix operations:
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row/column becomes SPIR-V matrix column/row. If elements in a row/column are
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packed together, they should be loaded into a column/row correspondingly.
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+See `Appendix A. Matrix Representation`_ for further explanation regarding these design choices.
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+
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Structs
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-------
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@@ -2468,3 +2470,76 @@ either because of no Vulkan equivalents at the moment, or because of deprecation
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will emit an warning and ignore it.
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* ``:packoffset()``: Not supported right now. The compiler will emit an warning
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and ignore it.
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+
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+Appendix
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+==========
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+
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+Appendix A. Matrix Representation
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+---------------------------------
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+Consider a matrix in HLSL defined as ``float2x3 m;``. Conceptually, this is a matrix with 2 rows and 3 columns.
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+This means that you can access its elements via expressions such as ``m[i][j]``, where ``i`` can be ``{0, 1}`` and ``j`` can be ``{1, 2, 3}``.
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+
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+Now let's look how matrices are defined in SPIR-V:
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+
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+.. code:: spirv
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+
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+ %columnType = OpTypeVector %float <number of rows>
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+ %matType = OpTypeMatrix %columnType <number of columns>
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+
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+As you can see, SPIR-V conceptually represents matrices as a collection of vectors where each vector is a *column*.
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+
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+Now, let's represent our float2x3 matrix in SPIR-V. If we choose a naive translation (3 columns, each of which is a vector of size 2), we get:
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+
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+.. code:: spirv
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+
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+ %v2float = OpTypeVector %float 2
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+ %mat3v2float = OpTypeMatrix %v2float 3
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+
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+Now, let's use this naive translation to access into the matrix (e.g. ``m[0][2]``). This is evaluated by first finding ``n = m[0]``, and then finding ``n[2]``.
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+Notice that in HLSL, ``m[0]`` represents a row, which is a vector of size 3. But accessing the first dimension of the SPIR-V matrix give us
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+the first column which is a vector of size 2.
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+
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+.. code:: spirv
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+
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+ ; n is a vector of size 2
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+ %n = OpAccessChain %v2float %m %int_0
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+
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+Notice that in HLSL access ``m[i][j]``, ``i`` can be ``{0, 1}`` and ``j`` can be ``{0, 1, 2}``.
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+But in SPIR-V OpAccessChain access, the first index (``i``) can be ``{0, 1, 2}`` and the second index (``j``) can be ``{1, 0}``.
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+Therefore, the naive translation does not work well with indexing.
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+
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+As a result, we must translate a given HLSL float2x3 matrix (with 2 rows and 3 columns) as a SPIR-V matrix with 3 rows and 2 columns:
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+
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+.. code:: spirv
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+
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+ %v3float = OpTypeVector %float 3
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+ %mat2v3float = OpTypeMatrix %v3float 2
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+
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+This way, all accesses into the matrix can be naturally handled correctly.
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+
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+Packing
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+~~~~~~~
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+The HLSL ``row_major`` and ``column_major`` type modifiers change the way packing is done.
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+The following table provides an example which should make our translation more clear:
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+
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++------------------+---------------------------+---------------------------+-----------------------------+-------------------+
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+| Host CPU Data | HLSL Variable | GPU (HLSL Representation) | GPU (SPIR-V Representation) | SPIR-V Decoration |
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++==================+===========================+===========================+=============================+===================+
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+|``{1,2,3,4,5,6}`` | ``float2x3`` | ``[1 3 5]`` | ``[1 2]`` | |
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+| | | | | |
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+| | | ``[2 4 6]`` | ``[3 4]`` | ``RowMajor`` |
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+| | | | | |
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+| | | | ``[5 6]`` | |
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++------------------+---------------------------+---------------------------+-----------------------------+-------------------+
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+|``{1,2,3,4,5,6}`` | ``column_major float2x3`` | ``[1 3 5]`` | ``[1 2]`` | |
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+| | | | | |
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+| | | ``[2 4 6]`` | ``[3 4]`` | ``RowMajor`` |
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+| | | | | |
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+| | | | ``[5 6]`` | |
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++------------------+---------------------------+---------------------------+-----------------------------+-------------------+
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+|``{1,2,3,4,5,6}`` | ``row_major float2x3`` | ``[1 2 3]`` | ``[1 4]`` | |
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+| | | | | |
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+| | | ``[4 5 6]`` | ``[2 5]`` | ``ColMajor`` |
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+| | | | | |
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+| | | | ``[3 6]`` | |
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++------------------+---------------------------+---------------------------+-----------------------------+-------------------+
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Ehsan