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.

/*
 * Copyright (c) 2024 Dmitri Lyalikov
 * SPDX-License-Identifier: Apache-2.0
 */

`define default_netname none

  /** 
    | Behavior                    | A   | B    | C   | D   |
    | --------------------------- | --- | ---- | --- | --- |
   0| RS (Regular Spiking)        | .02 | .02  | -65 | 8   |
   1| IB (Intrinsically Bursting) | .02 | .02  | -55 | 4   |
   2| CH (Chattering)             | .02 | .02  | -50 | 2   |
   3| FS (Fast Spiking)           | 0.1 | 0.2  | -65 | 2   |
   4| TC (Thalamo-Cortical)       | .02 | 0.25 | -65 | .05 |
   5| RZ (Resonator)              | 0.1 | 0.25 | -65 | 2   |
   6| LTS (Low Threshold Spiking) | .02 | 0.25 | -65 | 2   |
  */

// Top Level Module
module tt_um_exai_izhikevich_neuron (
    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,      // will go high when the design is enabled
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);
  assign uio_out = uio_in;      // We do not use second output pin, assign so Verilator doesn't yell at us
  assign uio_oe  = 0;           // Config uio_in output enable to 0: Input mode
  
  reg         [3:0]  a, b;         
  reg  signed [17:0] v1, u1;
  wire signed [17:0] u1reset, v1new, u1new, du1;
  wire signed [17:0] v1xv1, v1xb;
  wire signed [17:0] p, c14;
  reg  signed [17:0] c, d;
  wire signed [17:0] I;  // uio_in[3:0];

  assign p = 18'sh0_4CCC;   // 30
  assign c14 = 18'sh1_6666; // 1.4

  // 8-bit signed integer precision of input current 
  assign I = {1'b0, ui_in[4:0], 12'h0}; 

  // Update logic 
  always @ (posedge clk)
  begin 
    if (!rst_n)          // Reset state
    begin
      v1 <= 18'sh3_4CCD;     // -0.7v 
      u1 <= 18'sh3_CCCD;     // -0.2
      a <= 1;                // .02
      b <= 1;                // .02             
      c <= 18'sh3_A666;      // -.065
      d <= 18'sh0_147A;      // .08
      // Switch case for different neuron types
      case (uio_in[2:0])
        // RS (Regular Spiking) a = 0.02, b = 0.02, c = -.065, d = .08
        3'b000: begin
          a <= 1;            // .02
          b <= 1;            // .02             
          c <= 18'sh3_A666;  // -.065
          d <= 18'sh0_147A;  // .08
        end 
        // IB (Intrinsically Bursting) a = 0.02, b = 0.02, c = -.055, d = .04
        3'b001: begin
          a <= 1;            // .02
          b <= 1;            // .02             
          c <= 18'sh3_8CCC;  // -.055
          d <= 18'sh0_0A3D;  // .04
        end
        // CH (Chattering) a = 0.02, b = 0.02, c = -.050, d = .02
        3'b010: begin
          a <= 1;            // .02
          b <= 1;            // .02             
          c <= 18'sh3_8000;  // -.050
          d <= 18'sh0_051E;  // .02
        end
        // FS (Fast Spiking) a = 0.1, b = 0.2, c = -.065, d = .02
        3'b011: begin
          a <= 2;            // .1
          b <= 4;            // .2             
          c <= 18'sh3_A666;  // -.065
          d <= 18'sh0_051E;  // .02
        end
        // TC (Thalamo-Cortical) a = 0.02, b = 0.25, c = -.065, d = .05
        3'b100: begin
          a <= 1;            // .02
          b <= 4;            // .25             
          c <= 18'sh3_A666;  // -.065
          d <= 18'sh0_0020;  // .05
        end
        // RZ (Resonator) a = 0.1, b = 0.25, c = -.065, d = .02
        3'b101: begin
          a <= 2;            // .1
          b <= 4;            // .25             
          c <= 18'sh3_A666;  // -.065
          d <= 18'sh0_051E;  // .02
        end
        // LTS (Low Threshold Spiking) a = 0.02, b = 0.25, c = -.065, d = .02
        3'b110: begin
          a <= 1;            // .02
          b <= 4;            // .25             
          c <= 18'sh3_A666;  // -.065
          d <= 18'sh0_051E;  // .02
        end
        3'b111: begin
          a <= {uio_in[3], ui_in[7:5]};
          b <= uio_in[7:4];
        end
        default: begin
          a <= 1;           // .02
          b <= 1;           // .02             
          c <= 18'sh3_A666; // -.065
          d <= 18'sh0_147A; // .08
        end
    endcase
    end
    else
    if (ena)
    begin
      if ((v1 > p))      // This is a spike above threshold (30mv)
      begin
        v1 <= c;
        u1 <= u1reset;
      end
      else
      begin             
        v1 <= v1new;
        u1 <= u1new;
      end
    end
  end
  // Push out signed 8-bit integer to output pin (membrane voltage)
  assign uo_out = v1[17:10]; 

	// v1(n+1) = v1(n) + (v1(n)^2) + 5/4*v1(n) +1.40/4 - u1(n)/4 + I/4)/4
	signed_mult v1sq(v1xv1, v1, v1);
	assign v1new = v1 + ((v1xv1 + v1+(v1>>>2) + (c14>>>2) - (u1>>>2) + (I>>>2))>>>2);
	
	// u1(n+1) = u1 + dt*a*(b*v1(n) - u1(n))
	assign v1xb = v1>>>b;         //mult (v1xb, v1, b);
	assign du1 = (v1xb-u1)>>>a ;  //mult (du1, (v1xb-u1), a);
	assign u1new = u1 + (du1>>>4) ; 
	assign u1reset = u1 + d ;
  
endmodule


// signed mult of 2.16 format 2'comp
module signed_mult (out, a, b);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule






Reference solution:
rtl/generated.v: 
	output 		[17:0]	out;
	input 	signed	[17:0] 	a;
	input 	signed	[17:0] 	b;
	
	wire	signed	[17:0]	out;
  /* verilator lint_off UNUSEDSIGNAL */
	wire 	signed	[35:0]	mult_out;

  // Remove linter warning of unused bits
	assign mult_out = a * b;
	//assign out = mult_out[33:17];
	assign out = {mult_out[35], mult_out[32:16]};