For the complete documentation index, see llms.txt. Markdown versions of all pages are available by appending .md to any URL (e.g. /max/get-started.md).

Mojo function

matmul_kernel_naive

def matmul_kernel_naive[c_type: DType, a_type: DType, b_type: DType, c_layout_type: TensorLayout, a_layout_type: TensorLayout, b_layout_type: TensorLayout, BLOCK_DIM: Int, transpose_b: Bool = False, elementwise_lambda_fn: Optional[def[dtype: DType, width: SIMDLength, *, alignment: Int = Int(1)](IndexList[Int(2)], SIMD[dtype, width]) capturing thin -> None] = None, s_type: DType = get_accum_type[c_type](), c_storage: TensorStorage = PointerStorage, a_storage: TensorStorage = PointerStorage, b_storage: TensorStorage = PointerStorage](c: TileTensor[c_type, c_layout_type, MutAnyOrigin, Storage=c_storage], a: TileTensor[a_type, a_layout_type, ImmutAnyOrigin, Storage=a_storage], b: TileTensor[b_type, b_layout_type, ImmutAnyOrigin, Storage=b_storage], m: Int, n: Int, k: Int)

Computes one output element of a matrix multiply per thread by iterating over the K dimension.

Each thread maps to a single (x, y) coordinate of c and accumulates the dot product of the corresponding row of a and column of b (or row of b when transpose_b is set). When elementwise_lambda_fn is supplied the accumulated value is passed through it instead of being stored directly.

Parameters:

c_type (DType): DType of the output tile c elements.
a_type (DType): DType of the input tile a elements.
b_type (DType): DType of the input tile b elements.
c_layout_type (TensorLayout): Tensor layout of the output tile c.
a_layout_type (TensorLayout): Tensor layout of the input tile a.
b_layout_type (TensorLayout): Tensor layout of the input tile b.
BLOCK_DIM (Int): Thread-block dimension used when launching the kernel.
transpose_b (Bool): Whether b is accessed transposed, so its row y is read as b[y, i] instead of b[i, y] (defaults to False).
elementwise_lambda_fn (Optional[def[dtype: DType, width: SIMDLength, *, alignment: Int = Int(1)](IndexList[Int(2)], SIMD[dtype, width]) capturing thin -> None]): Optional epilogue applied to the accumulated value before it is stored to c (defaults to None, which stores the raw accumulation).
s_type (DType): DType used for the inner accumulation (defaults to the accumulator type for c_type).
c_storage (TensorStorage): Storage type of the output tile c (defaults to PointerStorage[element_width=1]).
a_storage (TensorStorage): Storage type of the input tile a (defaults to PointerStorage[element_width=1]).
b_storage (TensorStorage): Storage type of the input tile b (defaults to PointerStorage[element_width=1]).

Args:

c (TileTensor[c_type, c_layout_type, MutAnyOrigin, Storage=c_storage]): Output tile of shape (m, n).
a (TileTensor[a_type, a_layout_type, ImmutAnyOrigin, Storage=a_storage]): Input tile of shape (m, k).
b (TileTensor[b_type, b_layout_type, ImmutAnyOrigin, Storage=b_storage]): Input tile of shape (k, n), or (n, k) when transpose_b is set.
m (Int): Number of rows of a and c.
n (Int): Number of columns of c.
k (Int): Contraction dimension shared by a and b.