Systolic Gauss-Jordan

This folder contains the current RTL for the systolic Gauss-Jordan path in rtl/systolic_gauss_jordan/.

Role

This subsystem implements the available GF(2) elimination kernel introduced on the project homepage. It streams rows of the augmented system [A | B] through a lifted trapezoidal mesh whose processing elements perform pivot detection, row updates, and reduction using only local state and nearest-neighbor communication.

Available surface

The reference top solves A x = B by streaming rows of [A | B] into the mesh. The only architectural output exposed by the reference top is the bottom boundary trace data_bottom_o.

Why systolic

The design uses a systolic organization because the target computation is dominated by regular GF(2) row operations with predictable communication patterns. This makes the array suitable for FPGA-oriented studies in which throughput, locality, and control simplicity matter as much as arithmetic count.

RTL overview

Row r begins at global column r. The first active cell on that row is a pe_diag instance, and every active cell to its right is a pe_col instance. Data enters from the top edge and moves downward within a global column. Opcodes enter each row at the diagonal cell and move rightward across the active region.

The available path is intentionally small:

input.sv reads A/B rows, applies the stagger schedule, and feeds the mesh
controller.sv owns the run window and reduce pulse
pe_diag.sv, pe_col.sv, and trapeziod_mesh.sv implement the array
mem.sv, delay_line.sv, and gj_pkg.sv provide the supporting primitives

Resource scaling

Because the architecture is regular and parameterized, its resource cost can be studied as a function of matrix dimensions, mesh shape, and scheduling strategy. This makes the module useful both as an implementation vehicle and as a platform for exploring hardware-performance tradeoffs in decoder design.

Module map

Source file	Documentation page	Role in the subsystem
`rtl/systolic_gauss_jordan/gj_pkg.sv`	Shared package	Canonical home for opcode definitions and shared data types
`rtl/systolic_gauss_jordan/delay_line.sv`	Delay line	Small reusable timing primitive used by feeders and wrappers
`rtl/systolic_gauss_jordan/mem.sv`	Memory	Simple synchronous storage block for experiments and examples
`rtl/systolic_gauss_jordan/input.sv`	Minimal input pipeline	Collapsed reference feeder from A/B RAMs to the staggered mesh ingress
`rtl/systolic_gauss_jordan/controller.sv`	Bottom-trace top	Minimal reference top that exposes only the bottom architectural trace
`rtl/systolic_gauss_jordan/pe_diag.sv`	Diagonal PE	Left-edge pivot cell that generates or forwards row control
`rtl/systolic_gauss_jordan/pe_col.sv`	Column PE	Interior/right processing cell that applies the diagonal opcode
`rtl/systolic_gauss_jordan/trapeziod_mesh.sv`	Trapezoidal mesh	Structural mesh tying the lifted array together

How to test this now

The matching cocotb suite is documented in Test: Systolic Gauss-Jordan. The fastest useful commands are:

make -C test/systolic_gauss_jordan TEST=pe_diag
make -C test/systolic_gauss_jordan TEST=pe_col
make -C test/systolic_gauss_jordan TEST=trapeziod_mesh
make -C test/systolic_gauss_jordan TEST=trapeziod_full_trace_reduce