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 Devesh Bhaskaran
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tt_um_db_MAC (
    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
);

reg [7:0] reg_a,reg_b;
wire [15:0] W,Sum;
reg [15:0] Out;


assign uio_oe = clk ? 8'hFF : 8'h00;
  
always @(posedge clk or negedge rst_n) begin
      
        if (!rst_n) begin
            reg_a <= 0;
				reg_b <= 0;
        end else begin
            reg_a<=ui_in;
				reg_b<=uio_in;
        end
    end

vedic_8bit_multiplier m1(reg_a, reg_b, W);
reversible_16bit_adder a1 (
    .A(Out),
    .B(W),
    .Cin(1'b0),      // Assuming the adder has a carry-in input
    .Sum(Sum)     // Assuming the adder has a carry-out output
);

always @(negedge clk or negedge rst_n) begin
	     
        if (!rst_n) begin
            Out<=0;
        end else begin
            Out<=Sum;
        end
    end

	 assign {uio_out,uo_out}= Out;
	 
wire _unused = &{ena, 1'b0};
   
endmodule


module BVPPG_gate (
    input  wire A,   
    input  wire B,  
    input  wire C,
	 input  wire D,
	 input  wire E,
    output reg P,
	 output reg Q, 
	 output reg R,
	 output reg S,
	 output reg T
);

wire [1:0]X;

buf b1(P, A);
buf b2(Q, B);
and a1(X[0], A, B);
xor x1(R, X[0], C);
buf b3(S, D);
and a2(X[1], A, D);
xor x3(T, X[1], E);

   
endmodule


module feynman_gate (
    input  wire A,   
    input  wire B,    
    output reg P,
	 output reg Q 
);

buf b1(P, A);
xor x1(Q, A, B);
   
endmodule


module peres_gate (
    input  wire A,   
    input  wire B,  
    input  wire C,   
    output reg P,
	 output reg Q, 
	 output reg R     
);

wire X;

buf b1(P, A);
xor x1(Q, A, B);
and a1(X, A, B);
xor x2(R, X, C);

   
endmodule

module reversible_12bit_adder (
    input  wire [11:0] A,   // 12-bit input A
    input  wire [11:0] B,   // 12-bit input B
    input  wire [11:0] C,   // 12-bit input C
    output      [11:0] Sum  // 12-bit Sum
);

// Intermediate wires for full adders
wire [11:0] sum1, carry1;
wire [2:0] carry2;

// First stage of full adders
reversible_full_adder fa[11:0](A[11:0], B[11:0], C[11:0], 1'b0, sum1[11:0], carry1[11:0]);

assign Sum[0] = sum1[0];


// Second stage of full adders
    reversible_6bit_adder fa13(sum1[6:1], carry1[5:0], 6'b0, Sum[6:1], carry2[0]);
    reversible_6bit_adder fa14({1'b0, sum1[11:7]}, carry1[11:6], {5'b0,carry2[0]}, {carry2[2], Sum[11:7]}, carry2[1]);

    wire _unused = &{carry2[2:1]};
endmodule


module reversible_16bit_adder (
    input  wire [15:0] A,   // 6-bit input A
    input  wire [15:0] B,   // 6-bit input B
    input  wire        Cin,   // 6-bit input C
    output reg [15:0] Sum
);

// Intermediate wires for full adders
    wire [3:0]C;

// First stge of full adders
    reversible_4bit_adder fa[3:0](A[15:0], B[15:0], {C[2:0], Cin}, Sum[15:0], {C[3:0]});

    wire _unused = &{C[3]};
endmodule


module reversible_4bit_adder (
    input  wire [3:0] A,   // 6-bit input A
    input  wire [3:0] B,   // 6-bit input B
    input  wire       Cin,   // 6-bit input C
    output reg [3:0] Sum, // 6-bit Sum
    output reg       Carry // 6-bit Carry
);

// Intermediate wires for full adders
wire [2:0] C;

// Instantiation of reversible full adders
    reversible_full_adder fa0 (A[0], B[0], Cin,  1'b0, Sum[0], C[0]);
    reversible_full_adder fa1 (A[1], B[1], C[0], 1'b0, Sum[1], C[1]);
    reversible_full_adder fa2 (A[2], B[2], C[1], 1'b0, Sum[2], C[2]);
    reversible_full_adder fa3 (A[3], B[3], C[2], 1'b0, Sum[3], Carry);

endmodule



module reversible_6bit_adder (
    input  wire [5:0] A,   // 6-bit input A
    input  wire [5:0] B,   // 6-bit input B
    input  wire [5:0] C,   // 6-bit input C
    output      [5:0] Sum, // 6-bit Sum
    output            Carry
);

// Intermediate wires for full adders
wire [5:0] sum1, carry1;
wire [5:0] carry2;


// First stage of full adders
reversible_full_adder fa0(A[0], B[0], C[0], 1'b0, sum1[0], carry1[0]);
reversible_full_adder fa1(A[1], B[1], C[1], 1'b0, sum1[1], carry1[1]);
reversible_full_adder fa2(A[2], B[2], C[2], 1'b0, sum1[2], carry1[2]);
reversible_full_adder fa3(A[3], B[3], C[3], 1'b0, sum1[3], carry1[3]);
reversible_full_adder fa4(A[4], B[4], C[4], 1'b0, sum1[4], carry1[4]);
reversible_full_adder fa5(A[5], B[5], C[5], 1'b0, sum1[5], carry1[5]);

buf b1(Sum[0], sum1[0]);

// Second stage of full adders
reversible_full_adder fa7(sum1[1], carry1[0], 1'b0, 1'b0, Sum[1], carry2[0]);
reversible_full_adder fa8(sum1[2], carry1[1], carry2[0], 1'b0, Sum[2], carry2[1]);
reversible_full_adder fa9(sum1[3], carry1[2], carry2[1], 1'b0, Sum[3], carry2[2]);
reversible_full_adder fa10(sum1[4], carry1[3], carry2[2], 1'b0, Sum[4], carry2[3]);
reversible_full_adder fa11(sum1[5], carry1[4], carry2[3], 1'b0, Sum[5], carry2[4]);
reversible_full_adder fa12(1'b0, carry1[5], carry2[4], 1'b0,  Carry, carry2[5]);

	wire _unused = &{carry2[5]};
endmodule


// Reversible full adder
module reversible_full_adder (
    input  wire A,     // Input A
    input  wire B,     // Input B
    input  wire Cin,   // Carry-in
	 input  wire Ctrl,
    output reg S,     // Sum
    output reg Cout   // Carry-out
);

wire [1:0]g;
wire [1:0]n;

peres_gate p1(A, B, Ctrl, g[0], n[0], n[1]);
peres_gate p2(n[0], Cin,  n[1], g[1], S, Cout);

wire _unused = &{g[1:0]};


endmodule


module vedic_2bit_multiplier(
    input wire [1:0] A, B,
    output reg [3:0] P
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



// 4x4 Vedic Multiplier used for partial products
module vedic_4bit_multiplier (
    input  wire [3:0] A, // 4-bit input A
    input  wire [3:0] B, // 4-bit input B
    output  [7:0] P  // 8-bit output product
);

    // Intermediate partial products
    wire [3:0] P1, P2, P3;
    wire [3:2] P0;
    wire temp;

    // 2x2 Vedic Multipliers for 4x4 multiplication
    vedic_2bit_multiplier U0 (A[1:0], B[1:0], {P0[3:2], P[1:0]});
    vedic_2bit_multiplier U1 (A[1:0], B[3:2], P1[3:0]);
    vedic_2bit_multiplier U2 (A[3:2], B[1:0], P2[3:0]);
    vedic_2bit_multiplier U3 (A[3:2], B[3:2], P3[3:0]);
    
    reversible_6bit_adder a1({P3, P0[3:2]}, {2'b0, P2}, {2'b0, P1}, P[7:2], temp);
    
    wire _unused = &{temp};

endmodule


module vedic_8bit_multiplier (
    input  wire [7:0] A, // 8-bit input A
    input  wire [7:0] B, // 8-bit input B
    output  [15:0] P // 16-bit output product
);

    // Intermediate partial products
	wire [7:0]  P1, P2, P3;
	wire [7:4]  P0;

    // 4x4 multipliers for partial products
    vedic_4bit_multiplier U0 (A[3:0], B[3:0], {P0[7:4], P[3:0]});
    vedic_4bit_multiplier U1 (A[3:0], B[7:4], P1[7:0]);
    vedic_4bit_multiplier U2 (A[7:4], B[3:0], P2[7:0]);
    vedic_4bit_multiplier U3 (A[7:4], B[7:4], P3[7:0]);

	 
	 reversible_12bit_adder a1({P3, P0[7:4]}, {4'b0, P2}, {4'b0, P1}, P[15:4]);

endmodule


Reference solution:
rtl/generated.v: 
	wire [4:0]g;
	wire [3:1]i;
	wire [3:0]a;
	 
	 BVPPG_gate b1(A[0], B[0], 1'b0, B[1], 1'b0, g[0], i[1], P[0], i[2], a[0]);
	 peres_gate p1(A[1], i[1], 1'b0, i[3], g[1], a[1]);
	 peres_gate p2(i[3], i[2], 1'b0, g[2], g[3], a[2]);
	 peres_gate p3(a[0], a[1], 1'b0, g[4], P[1], a[3]);
	 feynman_gate f1(a[3], a[2], P[3], P[2]);

	wire _unused = &{g[4:0]};