diff --git a/clang/docs/LanguageExtensions.rst b/clang/docs/LanguageExtensions.rst --- a/clang/docs/LanguageExtensions.rst +++ b/clang/docs/LanguageExtensions.rst @@ -13,6 +13,7 @@ BlockLanguageSpec Block-ABI-Apple AutomaticReferenceCounting + MatrixSupport Introduction ============ @@ -492,6 +493,12 @@ 'select', they operate somewhat differently. OpenCL selects based on signedness of the condition operands, but GCC vectors use normal bool conversions (that is, != 0). +Matrixes +======== + +Clang provides a matrix extension, which is currently being implemented. See +:ref:`matrixsupport` for more details. + Half-Precision Floating Point ============================= diff --git a/clang/docs/MatrixSupport.rst b/clang/docs/MatrixSupport.rst new file mode 100644 --- /dev/null +++ b/clang/docs/MatrixSupport.rst @@ -0,0 +1,300 @@ +================== +Matrix Support +================== + +.. contents:: + :local: + +.. _matrixsupport: + +Clang provides a language extension that allows users to express high-level +matrix math on the C/C++ level. The draft specification can be found :ref:`below `. + +Note that the implementation is currently in progress. + +.. _matrixsupport-draftspec: + +Draft Specification +=================== + +Matrix Type Attribute +--------------------- + +The *attribute-token* ``matrix_type`` is used to declare a matrix type. It shall +appear at most once in each *attribute-list*. The attribute shall only appertain +to a *typedef-name* of a typedef of a non-volatile type that is a *signed +integer type*, an *unsigned integer type*, or a *floating-point type*. The +element type must be unqualified and qualifiers are applied to the matrix type +directly. An *attribute-argument-clause* must be present and it shall have the +form: + +``(constant-expression, constant-expression)`` + +Both *constant-expressions* shall be a positive non-zero integral constant +expressions. The maximum of the product of the constants is implementation +defined. If that implementation defined limit is exceeded, the program is +ill-formed. + +An *attribute* of the form ``matrix_type(R, C)`` forms a matrix type with an +element type of the cv-qualified type the attribute appertains to and *R* rows +and *C* columns. + +If a declaration of a *typedef-name* has a ``matrix_type`` attribute, then all +declaration of that *typedef-name* shall have a matrix_type attribute with the +same element type, number of rows, and number of columns. + +Matrix Type +----------- + +A matrix type has an underlying *element type*, a constant number of rows, and +a constant number of columns. Matrix types with the same element type, rows, +and columns are the same type. A value of a matrix type contains ``rows * +columns`` values of the *element type* laid out in column-major order without +padding in a way compatible with an array of at least that many elements of the +underlying *element type*. + +A matrix type is a *scalar type* and its alignment is implementation defined. + +TODO: Does it make sense to allow M::element_type, M::rows, and M::columns +where M is a matrix type? We don’t support this anywhere else, but it’s +convenient. The alternative is using template deduction to extract this +information. Also add spelling for C. + +TODO: Specify how matrix values are passed to functions. + +Future Work: Initialization syntax. + +Standard Conversions +-------------------- + +The standard conversions are extended as follows. + +For integral promotions, floating-point promotion, integral conversions, +floating-point conversions, and floating-integral conversions: apply the rules +to the underlying type of the matrix type. The resulting type is a matrix type +with that underlying element type. If the number of rows or columns differ +between the original and resulting type, the program is ill-formed. Otherwise +the resulting value is as follows: + +* If the original value was of matrix type, each element is converted element + by element. +* If the original value was not of matrix type, each element takes the value of + the original value. + +Arithmetic Conversions +---------------------- + +The usual arithmetic conversions are extended as follows. + +Insert at the start: + +* If either operand is of matrix type, apply the usual arithmetic conversions + using its underlying element type. The resulting type is a matrix type with + that underlying element type. + +Matrix Type Element Access Operator +----------------------------------- + +An expression of the form ``postfix-expression [expression][expression]`` where +the ``postfix-expression`` is of matrix type is a matrix element access +expression. ``expression`` shall not be a comma expression, and shall be a +prvalue of unscoped enumeration or integral type. Given the expression +``E1[E2][E3]`` the result is an lvalue of the same type as the underlying +element type of the matrix that refers to the value at E2 row and E3 column in +the matrix. The expression E1 is sequenced before E2 and E3. The expressions +E2 and E3 are unsequenced. + +**Note**: We considered providing an expression of the form +``postfix-expression [expression]`` to access columns of a matrix. We think +that such an expression would be problematic once both column and row major +matrixes are supported: depending on the memory layout, either accessing columns +or rows can be done efficiently, but not both. Instead, we propose to provide +builtins to extract rows and columns from a matrix. This makes the operations +more explicit. + +Matrix Type Binary Operators +---------------------------- + +Each matrix type supports the following binary operators: ``+``, ``-`` and ``*``. The ``*`` +operator provides matrix multiplication, while ``+`` and ``-`` are performed +element-wise. There are also scalar versions of the operators, which take a +matrix type and the underlying element type. The operation is applied to all +elements of the matrix using the scalar value. + +The operands of ``+``, ``-`` and ``*`` shall have either matrix type, arithmetic or +unscoped enumeration type. At least one of the operands shall be of matrix type. + +For ``BIN_OP`` in ``+``, ``-``, ``*`` given the expression ``M1 BIN_OP M2`` where, for +``*``, one of M1 or M2 is of arithmetic type: + +* The usual arithmetic conversions are applied to M1 and M2. [ Note: if M1 or + M2 are of arithmetic type, they are broadcast to matrices here. — end note ] +* The matrix types of M1 and M2 shall have the same number of rows and columns. +* The result is equivalent to Res in the following where col is the number of + columns and row is the number of rows in the matrix type: + +.. code-block:: c++ + + decltype(M1) Res; + for (int C = 0; C < col; ++C) + for (int R = 0; R < row; ++R) + Res[R][C] = M1[R][C] BIN_OP M2[R][C]; + +Given the expression ``M1 * M2`` where ``M1`` and ``M2`` are of matrix type: + +* The usual arithmetic conversions are applied to ``M1`` and ``M2``. +* The type of ``M1`` shall have the same number of columns as the type of ``M2`` has + rows. +* The resulting type, ``MTy``, is the result of applying the usual arithmetic + conversions to ``M1`` and ``M2``, but with the same number of rows as M1’s matrix + type and the same number of columns as M2’s matrix type. +* The result is equivalent to ``Res`` in the following where ``EltTy`` is the + element type of ``MTy``, ``col`` is the number of columns and ``row`` is the + number of rows in ``MTy``: + +.. code-block:: c++ + + MTy Res; + for (int C = 0; C < col; ++C) { + for (int R = 0; R < row; ++R) { + EltTy Elt = 0; + for (int K = 0; K < inner; ++K) { + Elt += M1[R][K] * M2[K][C]; + } + Res[R][C] = Elt; + } + +All operations on matrix types match the behavior of the underlying element +type with respect to signed overflows. + +With respect to rounding errors, the the ``*`` operator preserves the behavior of +the separate multiply and add operations by default. We propose to provide a +Clang option to override this behavior and allow contraction of those +operations (e.g. *-ffp-contract=matrix*). + +Matrix Type builtin Operations +------------------------------ + +Each matrix type supports a collection of builtin expressions that look like +function calls but do not form an overload set. Here they are described as +function declarations with rules for how to construct the argument list types +and return type and the library description elements from +[library.description.structure.specifications]/3 in the C++ standard. + +Definitions: + +* *M*, *M1*, *M2*, *M3* - Matrix types +* *T* - Element type +* *row*, *col* - Row and column arguments respectively. + + +``M2 __builtin_matrix_transpose(M1 matrix)`` + +**Remarks**: The return type is a cv-unqualified matrix type that has the same +element type as ``M1`` and has the the same number of rows as ``M1`` has columns and +the same number of columns as ``M1`` has rows. + +**Returns**: A matrix ``Res`` equivalent to the code below, where ``col`` refers to the +number of columns of ``M``, and ``row`` to the number of rows of ``M``. + +**Effects**: Equivalent to: + +.. code-block:: c++ + + M Res; + for (int C = 0; C < col; ++C) + for (int R = 0; R < row; ++R) + Res[C][R] = matrix[R][C]; + + +``M __builtin_matrix_column_load(T *ptr, int row, int col, int stride)`` + +**Mandates**: ``row`` and ``col`` shall be integral constants greater than 0. + +**Preconditions**: ``stride >= row``. + +**Remarks**: The return type is a cv-unqualified matrix type with an element +type of the cv-unqualified version of ``T`` and a number of rows and columns equal +to ``row`` and ``col`` respectively. + +**Returns**: A matrix ``Res`` equivalent to: + +.. code-block:: c++ + + M Res; + for (int C = 0; C < col; ++C) { + for (int R = 0; R < row; ++K) + Res[R][C] = ptr[R]; + ptr += stride + } + + +``void __builtin_matrix_column_store(M matrix, T *ptr, int stride)`` + +**Preconditions**: ``stride`` is greater than or equal to the number of rows in ``M``. + +**Effects**: Equivalent to: + +.. code-block:: c++ + + for (int C = 0; C < columns in M; ++C) { + for (int R = 0; R < rows in M; ++K) + ptr[R] = matrix[R][C]; + ptr += stride + } + +**Remarks**: The type ``T`` is the const-unqualified version of the matrix +argument’s element type. + +Example +======= + +This code performs a matrix-multiply of two 4x4 *float* matrixes followed by an matrix addition: + +.. code-block:: c++ + + typedef float m4x4_t __attribute__((matrix_type(4, 4))); + + void f(m4x4_t *a, m4x4_t *b, m4x4_t *c, m4x4_t *r) { + *r = *a + (*b * *c); + } + + +This will get lowered by Clang to the LLVM IR below. In our current +implementation, we use LLVM’s array type as storage type for the matrix +data. Before accessing the data, we cast the array to a vector type. This +allows us to use the element width as alignment, without running into issues +with LLVM’s large default alignment for vector types, which is problematic in +structs. + +.. code:: + + define void @f([16 x float]* %a, [16 x float]* %b, [16 x float]* %c, [16 x float]* %r) #0 { + entry: + %a.addr = alloca [16 x float]*, align 8 + %b.addr = alloca [16 x float]*, align 8 + %c.addr = alloca [16 x float]*, align 8 + %r.addr = alloca [16 x float]*, align 8 + store [16 x float]* %a, [16 x float]** %a.addr, align 8 + store [16 x float]* %b, [16 x float]** %b.addr, align 8 + store [16 x float]* %c, [16 x float]** %c.addr, align 8 + store [16 x float]* %r, [16 x float]** %r.addr, align 8 + %0 = load [16 x float]*, [16 x float]** %a.addr, align 8 + %1 = bitcast [16 x float]* %0 to <16 x float>* + %2 = load <16 x float>, <16 x float>* %1, align 4 + %3 = load [16 x float]*, [16 x float]** %b.addr, align 8 + %4 = bitcast [16 x float]* %3 to <16 x float>* + %5 = load <16 x float>, <16 x float>* %4, align 4 + %6 = call <16 x float> @llvm.matrix.multiply.v16f32.v16f32.v16f32(<16 x float> %2, <16 x float> %5, i32 4, i32 4, i32 4) + %7 = load [16 x float]*, [16 x float]** %c.addr, align 8 + %8 = bitcast [16 x float]* %7 to <16 x float>* + %9 = load <16 x float>, <16 x float>* %8, align 4 + %10 = fadd <16 x float> %6, %9 + %11 = load [16 x float]*, [16 x float]** %r.addr, align 8 + %12 = bitcast [16 x float]* %11 to <16 x float>* + store <16 x float> %10, <16 x float>* %12, align 4 + ret void + } + ; Function Attrs: nounwind readnone speculatable willreturn + declare <16 x float> @llvm.matrix.multiply.v16f32.v16f32.v16f32(<16 x float>, <16 x floa +