[Proposal] Add Matrix Multiplication (MatMul) as a Tensor-Level Abstraction in XLS IR

## Motivation

XLS currently operates primarily at a scalar level, where computations are expressed as fine-grained operations in IR. While this design is powerful for general computation, it is not optimal for emerging machine learning workloads, which rely heavily on tensor-level operations such as matrix multiplication.

Introducing a matrix multiplication (MatMul) abstraction at the IR level would allow XLS to better support hardware-efficient generation of ML accelerators.

---

## Problem

Currently, matrix multiplication must be manually expressed as a combination of scalar operations, which:

- Increases IR complexity
- Limits optimization opportunities
- Prevents the compiler from making tensor-level scheduling and architectural decisions
- Leads to suboptimal hardware in terms of area, timing, and power (PPA)

---

## Proposed Solution

I propose introducing a `MatMul` (or equivalent) tensor-level operation in XLS IR, along with multiple lowering strategies.

### 1. IR-Level Abstraction

- Define a `MatMul` operation in IR
- Represent matrix multiplication as a first-class operation instead of scalar expansion

---

### 2. Lowering Strategies

Implement multiple lowering paths:

#### (a) Combinational Expansion
- Fully unrolled scalar multiplications
- High area, low latency

#### (b) Pipelined MAC Tree
- Reduces critical path
- Improves timing performance

#### (c) Systolic Array Mapping (if possible)
- Hardware-efficient for ML workloads
- Enables scalable parallelism

---

### 3. Integration with Scheduling

- Allow the XLS scheduler to exploit MatMul-level knowledge
- Improve pipeline balancing and resource sharing

---

### 4. OpenROAD Integration

After RTL generation, use OpenROAD flow to:

- Evaluate Area
- Evaluate Timing
- Evaluate Power
- Evaluate Routability

This enables a feedback loop:

Compiler → RTL → Physical Design → PPA Metrics → Compiler Optimization

---

## Expected Outcomes

- Introduction of tensor-level abstraction in XLS
- Multiple hardware-efficient lowering strategies
- Improved PPA compared to scalar-expanded implementations
- A reproducible flow combining compiler + physical design tools

---

## Why this matters

This work bridges the gap between:

- Compiler design
- Hardware generation
- Physical design evaluation

It aligns with modern ML accelerator design trends and enables XLS to generate optimized hardware for real-world workloads.

---

## Status

I am currently exploring the XLS codebase and have successfully set up the environment and started contributing via documentation improvements.

I am interested in implementing this proposal incrementally through further contributions.