Module core 

Core tropical GEMM algorithms using BLIS-style blocking.

This module provides the portable implementation of tropical matrix multiplication, optimized for cache efficiency using the BLIS framework.

BLIS Algorithm Overview

The BLIS (BLAS-like Library Instantiation Software) approach achieves near-optimal performance through hierarchical cache blocking:

┌─────────────────────────────────────────────────────────────────┐
│ Loop 5: for jc in 0..N step NC    (partition columns of B)     │
│   Loop 4: for pc in 0..K step KC  (partition depth)            │
│     Pack B[pc:KC, jc:NC] → B̃  (fits in L3 cache)               │
│     Loop 3: for ic in 0..M step MC  (partition rows of A)      │
│       Pack A[ic:MC, pc:KC] → Ã  (fits in L2 cache)             │
│       Loop 2: for jr in 0..NC step NR  (register blocking)     │
│         Loop 1: for ir in 0..MC step MR  (microkernel)         │
│           microkernel(Ã[ir], B̃[jr], C[ic+ir, jc+jr])           │
└─────────────────────────────────────────────────────────────────┘

Cache Tiling Parameters

The TilingParams struct controls blocking sizes:

Parameter	Purpose	Typical Value (f32 AVX2)
MC	Rows per L2 block	256
NC	Columns per L3 block	256
KC	Depth per block	512
MR	Microkernel rows	8
NR	Microkernel columns	8

Packing

Before computation, matrices are packed into contiguous buffers:

• pack_a: Packs an MC×KC block of A for sequential microkernel access
• pack_b: Packs a KC×NC block of B for efficient broadcasting

Packing eliminates TLB misses and enables SIMD vectorization.

Microkernel

The innermost loop executes an MR×NR tile computation:

for each k in packed_k:
    C[0:MR, 0:NR] = C ⊕ (A_col[0:MR] ⊗ B_row[0:NR])

The Microkernel trait abstracts over portable and SIMD implementations.

Module Contents

• gemm: The main GEMM algorithm with blocking loops
• kernel: Microkernel trait and portable implementation
• packing: Matrix packing utilities
• tiling: Cache tiling parameters and iterators
• argmax: Argmax tracking for backpropagation

Structs

BlockIterator

Iterator over blocks for the outer loop.

GemmWithArgmax

Result of GEMM with argmax tracking.

GemmWorkspace

Reusable CPU packing storage, shared by sequential calls through an exclusive borrow.

PortableMicrokernel

Portable (non-SIMD) microkernel implementation.

TilingParams

Tiling parameters for BLIS-style GEMM blocking.

Enums

Layout

Matrix layout enumeration.

Transpose

Transpose specification.

Traits

Microkernel

Trait for GEMM microkernels.

MicrokernelWithArgmax

Trait for microkernels that track argmax during computation.

Functions

pack_a^⚠

Pack a panel of matrix A into a contiguous buffer.

pack_b^⚠

Pack a panel of matrix B into a contiguous buffer.

packed_a_size

Calculate packed buffer size for A.

packed_b_size

Calculate packed buffer size for B.

tropical_gemm_inner^⚠

Tropical GEMM with custom kernel and tiling parameters.

tropical_gemm_inner_with_workspace^⚠

GEMM using reusable packing buffers.

tropical_gemm_portable^⚠

Tropical GEMM: C = A ⊗ B

tropical_gemm_with_argmax_inner^⚠

Tropical GEMM with argmax tracking and custom kernel.

tropical_gemm_with_argmax_inner_with_workspace^⚠

GEMM using reusable packing buffers.

tropical_gemm_with_argmax_portable^⚠

Tropical GEMM with argmax tracking.