8.1 Introduction to TileTensor

Mojo's layout package provides a number of APIs for working with dense multidimensional arrays, which simplify writing algorithms for handling linear algebra.

This section discusses the TileTensor abstraction and its related types:

• TileTensor is a flexible tensor type that combines a tile_layout.Layout and a pointer to data.
• The tile_layout.Layout struct describes an arrangement of data in memory. A layout is a function that maps a set of logical coordinates (like (x, y) in a two-dimensional array) to a linear index value (such as an offset into a memory buffer). Layouts can describe simple row-major or column-major matrices, but also more complex organizations, like a matrix subdivided into tiles.

• Coord is a tuple-like container for storing integer coordinates that supports both compile-time and run-time values. It's used for defining logical coordinates and layout shapes, among other things.

The layout package also includes the older LayoutTensor type, and its associated IntTuple-based layout type, layout.Layout. TileTensor is essentially a new version of LayoutTensor that addresses several of the shortcomings of that type. Most of the concepts are the same for both the old and new types. However, TileTensor doesn't yet implement all the features supported by LayoutTensor. Here are some guidelines for when to use each type:

• Use TileTensor when you need layouts with run-time dimensions, nested layouts, or when working with the newer Coord-based layout system. The Coord-based layout system minimizes the memory footprint of the layout struct, which can help reduce register pressure on GPUs.

• Use LayoutTensor when you need established operations like copy_dma, collective_load, or compatibility with existing code using IntTuple-based layouts.

You can convert a TileTensor into a LayoutTensor, so you can use both types if necessary. Likewise, you can easily convert a Coord-based layout into an IntTuple-based layout.

For more information on LayoutTensor, see the pages on IntTuple-based layouts and LayoutTensor.

Adapted from the Mojo Manual, part of the Modular Platform repository (github.com/modular/modular), Copyright (c) Modular Inc., licensed under the Apache License v2.0 with LLVM Exceptions. Changes were made: reformatted as an accessible XYZ web edition with build-verified example outputs. Mojo is a trademark of Modular Inc.; this edition is not affiliated with or endorsed by Modular. License: Apache-2.0 WITH LLVM-exception.