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.

`ifndef HVSYNC_GENERATOR_H
`define HVSYNC_GENERATOR_H

/*
Video sync generator, used to drive a VGA monitor.
Timing from: https://en.wikipedia.org/wiki/Video_Graphics_Array
To use:
- Wire the hsync and vsync signals to top level outputs
- Add a 3-bit (or more) "rgb" output to the top level
*/

module hvsync_generator(clk, reset, hsync, vsync, display_on, hpos, vpos);

  input clk;
  input reset;
  output reg hsync, vsync;
  output display_on;
  output reg [9:0] hpos;
  output reg [9:0] vpos;

  // declarations for TV-simulator sync parameters
  // horizontal constants
  parameter H_DISPLAY       = 640; // horizontal display width
  parameter H_BACK          =  48; // horizontal left border (back porch)
  parameter H_FRONT         =  16; // horizontal right border (front porch)
  parameter H_SYNC          =  96; // horizontal sync width
  // vertical constants
  parameter V_DISPLAY       = 480; // vertical display height
  parameter V_TOP           =  33; // vertical top border
  parameter V_BOTTOM        =  10; // vertical bottom border
  parameter V_SYNC          =   2; // vertical sync # lines
  // derived constants
  parameter H_SYNC_START    = H_DISPLAY + H_FRONT;
  parameter H_SYNC_END      = H_DISPLAY + H_FRONT + H_SYNC - 1;
  parameter H_MAX           = H_DISPLAY + H_BACK + H_FRONT + H_SYNC - 1;
  parameter V_SYNC_START    = V_DISPLAY + V_BOTTOM;
  parameter V_SYNC_END      = V_DISPLAY + V_BOTTOM + V_SYNC - 1;
  parameter V_MAX           = V_DISPLAY + V_TOP + V_BOTTOM + V_SYNC - 1;

  wire hmaxxed = (hpos == H_MAX) || reset;	// set when hpos is maximum
  wire vmaxxed = (vpos == V_MAX) || reset;	// set when vpos is maximum
  
  // horizontal position counter
  always @(posedge clk)
  begin
    hsync <= (hpos>=H_SYNC_START && hpos<=H_SYNC_END);
    if(hmaxxed)
      hpos <= 0;
    else
      hpos <= hpos + 1;
  end

  // vertical position counter
  always @(posedge clk)
  begin
    vsync <= (vpos>=V_SYNC_START && vpos<=V_SYNC_END);
    if(hmaxxed)
      if (vmaxxed)
        vpos <= 0;
      else
        vpos <= vpos + 1;
  end
  
  // display_on is set when beam is in "safe" visible frame
  assign display_on = (hpos<H_DISPLAY) && (vpos<V_DISPLAY);

endmodule

`endif



`default_nettype none

module scale_rom(
        input  wire [3:0] note_in,
        output wire [15:0] freq_out
);
  reg  [15:0] rom_content[12];
  initial begin
    rom_content[1] = 16'h0000;
    rom_content[0] = 16'h205E;
    rom_content[2] = 16'h267D;
    rom_content[3] = 16'h2B34;
    rom_content[4] = 16'h307E;
    rom_content[5] = 16'h39AC;
    rom_content[6] = 16'h40BC;
    rom_content[7] = 16'h4CFB;
    rom_content[8] = 16'h5669;
    rom_content[9] = 16'h60FD;
    rom_content[10] = 16'h7358;
    rom_content[11] = 16'h8178;
  end
  assign freq_out = rom_content[note_in];
endmodule


/*
 * Copyright (c) 2024 Konrad Beckmann
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tria(
    input  wire [7:0] val_in, 
    output wire [7:0] val_out);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



/*
* Copyright (c) 2024 Konrad Beckmann
* Copyright (c) 2024 Linus Mårtensson
* SPDX-License-Identifier: Apache-2.0
*/

`default_nettype none

module tt_um_top(
`ifdef VERILATOR
  // Extra signals for web simulator
  output wire        audio_en , // Audio Enabled. Set to false to enable video rendering
  output wire [15:0] audio_out, // Audio sample output
  output wire [31:0] clk_hz,    // clk frequency in Hz. Output consumed by simulator to adjust sampling rate (when to consume audio_out)
`endif

  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
);

// ------------------------------
// Audio signals
wire audio_pdm;
wire audio_sample;

`ifdef VERILATOR
  assign audio_en = 1'b0;
  assign audio_out = {audio_sample, 15'b000000000000000};
  assign clk_hz = 25000000; // This is reality
`endif

// ------------------------------
// VGA signals
wire hsync;
wire vsync;
wire [1:0] R;
wire [1:0] G;
wire [1:0] B;
wire video_active;
wire [9:0] pix_x;
wire [9:0] pix_y;

// TinyVGA PMOD
assign uo_out = {hsync, B[0], G[0], R[0], vsync, B[1], G[1], R[1]};

// Audio PMOD
`ifdef ULX3S
// Expose video_active to ULX3S
assign uio_out = {audio_pdm, video_active, 6'b000000};
`else
assign uio_out = {audio_pdm, 7'b0000000};
`endif
assign uio_oe = 8'b10000000;

// Suppress unused signals warning
wire _unused_ok = &{ena, ui_in, uio_in, video_active};

// ------------------------------
// Audio start

assign audio_pdm = audio_sample;

`define ENABLE_AUDIO
`ifdef ENABLE_AUDIO
  reg [24:0] ctr_audio;
  reg [7:0] ctr_clkdiv25;
  reg pulse_1MHz;

  always @(posedge clk) begin
    if (~rst_n) begin
      ctr_clkdiv25 <= 0;
      ctr_audio <= 0;
      pulse_1MHz <= 0;
    end else begin
      ctr_clkdiv25 <= ctr_clkdiv25 + 1;
      if (ctr_clkdiv25 == 25) begin
        ctr_clkdiv25 <= 0;
        ctr_audio <= ctr_audio + 1;
        pulse_1MHz <= 1'b1;
      end else begin
        pulse_1MHz <= 1'b0;
      end
    end
  end

  wire [ 3:0] note_in;
  wire [15:0] freq_out;

  assign note_in = 
      {3'b000, ctr_audio[17]}
    + {3'b000, ctr_audio[19]}
    + (
        (
          ctr_audio[21] +
          ctr_audio[17] - 
          ctr_audio[22]
        ) == 2 ? 1 : 0
    )
    + (
        (
          ctr_audio[21] + 
          ctr_audio[22] + 
          ctr_audio[23]
        ) == 3 ? 4 : 0
    )
    + (
        (
          ctr_audio[21] + 
          ctr_audio[22]
        ) == 2 ? 2 : 0
    );

  scale_rom scale_rom_instance(
    .note_in(note_in),
    .freq_out(freq_out)
  );

  wire voice1;
  wire [11:0] pulsewidth = (1<<9) + {3'b000, ctr_audio[18:10]} + {1'b0, ctr_audio[23], 10'b0000000000};

  voice #()
      Voice1(
          .clk(clk),
          .rst_n(rst_n),
          .en(pulse_1MHz),
          .frequency((freq_out >> 3)),
          .pulsewidth(pulsewidth),
          .voice(voice1)
  );

  assign audio_sample = voice1;

// Audio end
`else
  assign audio_sample = 0;
`endif

// ------------------------------
// VGA start
hvsync_generator hvsync_gen(
    .clk(clk),
    .reset(~rst_n),
    .hsync(hsync),
    .vsync(vsync),
    .display_on(video_active),
    .hpos(pix_x),
    .vpos(pix_y)
);

reg  [11:0] counter;
wire [23:0] VAL;
reg   [7:0] r, g, b;
reg   [5:0] LFSR = 1;
reg  [12:0] yq, yqo, xq, xqo;

wire [7:0] tria1_in = tmp2[7:0];
wire [7:0] tria1_out;

wire [7:0] tria2_in = pix_x[9:2] - 80;
wire [7:0] tria2_out;

wire [7:0] tria3_in = tmp1[7:0];
wire [7:0] tria3_out;

wire [7:0] tria4_in = tmp4[7:0];
wire [7:0] tria4_out;

tria tria1(
    .val_in(tria1_in),
    .val_out(tria1_out)
);

tria tria2(
    .val_in(tria2_in),
    .val_out(tria2_out)
);

tria tria3(
    .val_in(tria3_in),
    .val_out(tria3_out)
);

tria tria4(
    .val_in(tria4_in),
    .val_out(tria4_out)
);

assign VAL[7:0]   = r;
assign VAL[15:8]  = g;
assign VAL[23:16] = b;

wire [11:0] tmp1 = (
                {2'b0, pix_x} 
                + (counter<<3)
              ) >> 4;

wire [12:0] tmp2 = ((xq>>4) - (yq>>5));
wire [11:0] tmp3 = (
        {4'b0, tria1_out}
        + (
          {2'b0,
            (pix_x>>2) + (pix_y>>3)
          }
        )
        - 20
      );
wire [11:0] tmp4 = (
                {2'b0, pix_y}
                + (counter << 2)
              ) >> 1;

wire _unused_truncate = &{tmp1, tmp2, tmp3, tmp4};

always @(posedge clk) begin
  if(~rst_n) begin
    LFSR <= 1;
    yq <= 0;
    yqo <= 0;
    xq <= 0;
    xqo <= 0;
    r <= 0;
    g <= 0;
    b <= 0;
  end else begin

    r <= tria2_out < 32 ? tmp3[7:0] : 0;
    g <= r + {3'b0, pix_y[8:4]};
    b <= g + {3'b0, pix_y[8:4]};    
    
    xq <= xqo 
      + (
        {5'b0, tria3_out >> 4}
      )
      + 22;
    xqo <= xq;
    if (hsync) begin
      yq <= yqo
        + {5'b0, tria4_out >> 2}
        - 22;
      xq <= 0;
    end else begin
      yqo <= yq;
    end
    if (vsync) begin
      LFSR <= 1;
      yq <= 0;
      yqo <= 0;
    end else begin
      LFSR[5:1] <= LFSR[4:0];
      LFSR[0]   <= LFSR[2] ^ LFSR[1];
    end
  end
end

assign R = video_active ? (
        (VAL[7:6]) + (LFSR[5:0] < VAL[5:0])
    ) : 2'b00;
assign G = video_active ? (
        (VAL[15:14]) + (LFSR[5:0] < VAL[13:8])
    ) : 2'b00;
assign B = video_active ? (
        (VAL[23:22]) + (LFSR[5:0] < VAL[21:16])
    ) : 2'b00;

always @(posedge vsync) begin
    if (~rst_n) begin
        counter <= 0;
    end else begin
        counter <= counter + 1;
    end
end

// VGA end

endmodule


`default_nettype none

module voice(
    input  wire        clk,
    input  wire        rst_n,
    input  wire        en,          // enable signal, when high, calculation is done.
    input  wire [15:0] frequency,   // frequency, but it's not Hz...
    input  wire [11:0] pulsewidth,  // pulse width %. 0 = 0%, 1<<11 = 50%, (1<<12)-1 = 100%
    output wire        voice        // waveform data out.
);

parameter                 ACC_WIDTH = 24;
parameter                 ADD_WIDTH = 16;
reg       [ACC_WIDTH-1:0] accumulator;
wire      [ADD_WIDTH-1:0] add_value;
reg                       pulse       = 0;

assign voice = pulse;
assign add_value = en ? frequency : 0;

always @(posedge clk)
begin
    if (~rst_n)
    begin
        pulse <= 0;
    end
    else begin
        if (en) begin
            accumulator <= accumulator + {8'b00000000, add_value};
            if (accumulator[23:12] >= pulsewidth[11:0])
                pulse <= 1;
            else
                pulse <= 0;
        end
    end
end

endmodule


Reference solution:
rtl/generated.v: 
    assign val_out = val_in > 127 ? 255 - val_in : val_in;