This repository contains HLSL implementations of matrix operations, specifically focusing on GEMM (General Matrix Multiply) operations with various implementation approaches.

A GEMM (General Matrix Multiply) operation is one of the most fundamental and computationally intensive operations in linear algebra and machine learning. Here's a comprehensive description:

GEMM performs the operation: C = α × A × B + β × C

Where:

• A is an M×K matrix (M rows, K columns)
• B is a K×N matrix (K rows, N columns)
• C is an M×N matrix (M rows, N columns)
• α (alpha) and β (beta) are scalars

The fundamental computation for each element C[i,j] is:

C[i,j] = Σ(k=0 to K-1) A[i,k] × B[k,j]

This means each element in the result matrix C is the dot product of a row from matrix A and a column from matrix B.

Dimensions:

• Input A: M × K
• Input B: K × N
• Output C: M × N
• The inner dimension K must match between A and B

Computational Complexity: O(M × N × K) operations

Memory Access Patterns:

• A is accessed row-wise
• B is accessed column-wise
• C is accessed in various patterns depending on algorithm

This repository demonstrates different approaches based on feature availability:

• gemm.hlsl: Basic tiling with shared memory tiles to improve cache locality
• linalg-wave.hlsl: Hardware-accelerated manually tiled using Wave-scope linalg::Matrix objects
• linalg-threadgroup.hlsl: Hardware-accelerated driver tiled using ThreadGroup-scope linalg::Matrix objects

All implementations support configurable M, N, and K dimensions:

• M: Number of rows in matrix A and C
• N: Number of columns in matrix B and C
• K: Number of columns in matrix A and rows in matrix B

To modify matrix sizes, edit the #define statements at the top of each shader file:

#define M 2048    // Rows in A and C
#define N 1024    // Columns in B and C  
#define K 512     // Columns in A, rows in B