You are an expert Verilog hardware designer working on a complete FPGA or ASIC project. You are given the full source code of a Verilog project. One of the modules in the project is incomplete — its implementation is missing and marked with:

// >>> Module Implementation Begin

// <<< Module Implementation End

Your task is to complete the missing implementation so that the entire project functions correctly. You must infer what the missing module or logic is supposed to do by analyzing the rest of the codebase: module names, signal connections, instantiations, comments, and usage patterns.

Follow these rules:

1. Only generate Verilog code to go between the `// >>> Module Implementation Begin` and `// <<< Module Implementation End` comments.
2. Use Verilog-2001 syntax. Ensure the code is synthesizable.
3. Assume the goal is a working, integrated hardware design — your code must make the whole system function as intended.
4. Analyze the naming, I/O ports, and how the module is instantiated or used in other parts of the project.
5. Implement correct behavior based on design context. Do not guess randomly — reason it out.
6. Avoid vendor-specific features unless explicitly required.
7. Do not output comments, explanation, or anything outside the required code region unless explicitly asked.

Your output should contain **only the Verilog code** that fits inside the marked region.

`default_nettype none

module tt_um_delta_liafn (
    input  wire [7:0] ui_in,    // Dedicated inputs
    output wire [7:0] uo_out,   // Dedicated outputs
    input  wire [7:0] uio_in,   // IOs: Input path
    output wire [7:0] uio_out,  // IOs: Output path
    output wire [7:0] uio_oe,   // IOs: Enable path (active high: 0=input, 1=output)
    input  wire       ena,      // always 1 when the design is powered, so you can ignore it
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);

  // All output pins must be assigned. If not used, assign to 0.
  assign uio_oe = 8'b11111111;

  // List all unused inputs to prevent warnings
  wire _unused = &{ena, uio_in, 1'b0};

  // Delta threshold for spiking
  wire [7:0] delta_threshold = 8'd50;

  // Implement Beta value for leaky integration later
  // This value will be multiplied by the state and added to the input current to update the state of the lif
  //wire [7:0] beta = 8'd128; 

  // Intermediate signals
  wire [7:0] state;
  wire [7:0] prev_state;
  wire signed [8:0] diff;         // 9-bit to handle overflow
  wire [8:0] abs_diff;
  wire [7:0] difference;
  wire spike;

  // TOP MODULE LOGIC
  // flow output of lif into reg to update current state
  lif lif_inst (.current(ui_in), .clk(clk), .reset_n(rst_n), .spike(spike), .state(state));

  // Instantiate the register to hold the previous state
  reg_state_store store (.state(state), .clk(clk), .reset_n(rst_n), .prev_state(prev_state));

  // Compare the previous and current states
  assign diff = state - prev_state;

  // Get absolute difference since it is signed
  assign abs_diff = (diff < 0) ? -diff : diff;

  // Check if difference exceeds delta threshold and set spike if it does
  assign spike = (abs_diff >= {1'b0, delta_threshold});

  // Output the difference if there is a spike, else pass zero
  assign difference = spike ? abs_diff[7:0] : 8'b00000000;

  // Connect outputs for testing and debugging
  assign uio_out = difference; // Output the difference on uio_out
  assign uo_out = state;       // Output the current state on uo_out

endmodule


`default_nettype none

module lif(
    input wire [7:0] current,  // Input current to the neuron
    input wire clk,            // Clock signal
    input wire reset_n,        // Active-low reset signal
    input wire spike,          // Spike signal used for controlling reset of the state
    output reg [7:0] state     // Current state of the neuron
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




`default_nettype none

module reg_state_store(
    input wire [7:0]    state,
    input wire          clk,
    input wire          reset_n,
    output reg [7:0]    prev_state
);

    always @(posedge clk) begin
        if (!reset_n) begin
            prev_state <= 0; // Reset previous state to 0
        end else begin
            prev_state <= state; // Update previous state to current state
        end
    end

endmodule


Reference solution:
rtl/generated.v: 
    wire [7:0] next_state;            // Wire for next state calculation
    // following the equation next_state = beta*state + I_in
    reg [7:0] beta;                   // Scaling factor for leaky integration beta
    wire [15:0] scaled_state;         // 16-bit wire for the scaled state calculation

    always @(posedge clk) begin
        if (!reset_n) begin
            state <= 8'd0;            // Reset state to zero
            beta <= 8'd128;           // Initialize beta to 128 (approx. 0.5 scaling when right-shifted by 8)
        end else begin
            state <= next_state;      // Update state with next state value
        end
    end

    // Calculate the scaled state: state * beta (using 16 bits to prevent overflow)
    assign scaled_state = state * beta;

    // Next state and reset state logic
    // When spike is 0, update the state with leaky integrate formula: next_state = (scaled_state >> 8) + current
    // When spike is 1, reset the state to just the input current value
    assign next_state = spike ? current : (scaled_state[15:8]) + current;