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 Thorsten Knoll
 * SPDX-License-Identifier: Apache-2.0
 */

`timescale 1ns/1ps 

`define default_netname none

module tt_um_thorkn_audiochip_v2 (
    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
);

  wire  pwm_1_out;
  wire  pwm_2_out;
  wire  [11:0] frequency;
  wire 	reset;
  
  assign reset = !rst_n;
  assign frequency = {uio_in[7:4],ui_in[7:0]};

  PWMaudio pwm_audio (
    .io_pwm_1           (pwm_1_out                ), //o
    .io_pwm_2           (pwm_2_out                ), //o
    .io_frequency       (frequency                ), //i
    .io_adsr_switch     (uio_in[3]                ), //i
    .io_adsr_choice     (uio_in[2:0]              ), //i
    .clk                (clk                      ), //i
    .reset              (reset                    )  //i
  );

  // All output pins must be assigned. If not used, assign to 0.
  assign uo_out = {6'b0000_00, pwm_2_out, pwm_1_out}; 
  assign uio_out = 8'b0000_0000;
  assign uio_oe = 8'b0000_0000;

endmodule

module PWMaudio (
  output              io_pwm_1,
  output              io_pwm_2,
  input      [11:0]   io_frequency,
  input               io_adsr_switch,
  input      [2:0]    io_adsr_choice,
  input               clk,
  input               reset
);
  localparam fsm_adsr_enumDef_BOOT = 3'd0;
  localparam fsm_adsr_enumDef_stateEntry = 3'd1;
  localparam fsm_adsr_enumDef_stateAttack = 3'd2;
  localparam fsm_adsr_enumDef_stateDelay = 3'd3;
  localparam fsm_adsr_enumDef_stateSustain = 3'd4;
  localparam fsm_adsr_enumDef_stateRelease = 3'd5;

  wire       [11:0]   pwm_ctrl_io_freq;
  reg        [7:0]    pwm_ctrl_io_level;
  wire                pwm_ctrl_io_pwm_1;
  wire                pwm_ctrl_io_pwm_2;
  reg        [23:0]   adsr1;
  reg        [23:0]   adsr2;
  reg        [23:0]   adsr3;
  reg        [23:0]   adsr4;
  wire       [2:0]    switch_PWMaudio_l25;
  wire                fsm_adsr_wantExit;
  reg                 fsm_adsr_wantStart;
  wire                fsm_adsr_wantKill;
  reg        [23:0]   fsm_adsr_counter;
  reg        [7:0]    fsm_adsr_level_adsr;
  reg        [2:0]    fsm_adsr_stateReg;
  reg        [2:0]    fsm_adsr_stateNext;
  wire                when_PWMaudio_l110;
  wire                when_PWMaudio_l114;
  wire                when_PWMaudio_l124;
  wire                when_PWMaudio_l128;
  wire                when_PWMaudio_l139;
  wire                when_PWMaudio_l149;
  wire                when_PWMaudio_l153;
  wire                when_StateMachine_l238;
  wire                when_StateMachine_l238_1;
  wire                when_StateMachine_l238_2;
  wire                when_StateMachine_l238_3;
  `ifndef SYNTHESIS
  reg [95:0] fsm_adsr_stateReg_string;
  reg [95:0] fsm_adsr_stateNext_string;
  `endif


  PWMctrl pwm_ctrl (
    .io_freq     (pwm_ctrl_io_freq[11:0]  ), //i
    .io_level    (pwm_ctrl_io_level[7:0]  ), //i
    .io_pwm_1    (pwm_ctrl_io_pwm_1       ), //o
    .io_pwm_2    (pwm_ctrl_io_pwm_2       ), //o
    .clk         (clk                     ), //i
    .reset       (reset                   )  //i
  );
  `ifndef SYNTHESIS
  always @(*) begin
    case(fsm_adsr_stateReg)
      fsm_adsr_enumDef_BOOT : fsm_adsr_stateReg_string = "BOOT        ";
      fsm_adsr_enumDef_stateEntry : fsm_adsr_stateReg_string = "stateEntry  ";
      fsm_adsr_enumDef_stateAttack : fsm_adsr_stateReg_string = "stateAttack ";
      fsm_adsr_enumDef_stateDelay : fsm_adsr_stateReg_string = "stateDelay  ";
      fsm_adsr_enumDef_stateSustain : fsm_adsr_stateReg_string = "stateSustain";
      fsm_adsr_enumDef_stateRelease : fsm_adsr_stateReg_string = "stateRelease";
      default : fsm_adsr_stateReg_string = "????????????";
    endcase
  end
  always @(*) begin
    case(fsm_adsr_stateNext)
      fsm_adsr_enumDef_BOOT : fsm_adsr_stateNext_string = "BOOT        ";
      fsm_adsr_enumDef_stateEntry : fsm_adsr_stateNext_string = "stateEntry  ";
      fsm_adsr_enumDef_stateAttack : fsm_adsr_stateNext_string = "stateAttack ";
      fsm_adsr_enumDef_stateDelay : fsm_adsr_stateNext_string = "stateDelay  ";
      fsm_adsr_enumDef_stateSustain : fsm_adsr_stateNext_string = "stateSustain";
      fsm_adsr_enumDef_stateRelease : fsm_adsr_stateNext_string = "stateRelease";
      default : fsm_adsr_stateNext_string = "????????????";
    endcase
  end
  `endif

  assign switch_PWMaudio_l25 = io_adsr_choice;
  always @(*) begin
    case(switch_PWMaudio_l25)
      3'b000 : begin
        adsr1 = 24'h000032;
      end
      3'b001 : begin
        adsr1 = 24'h000032;
      end
      3'b010 : begin
        adsr1 = 24'h00000a;
      end
      3'b011 : begin
        adsr1 = 24'h00000a;
      end
      3'b100 : begin
        adsr1 = 24'h0003e8;
      end
      3'b101 : begin
        adsr1 = 24'h0003e8;
      end
      3'b110 : begin
        adsr1 = 24'h001388;
      end
      default : begin
        adsr1 = 24'h001388;
      end
    endcase
  end

  always @(*) begin
    case(switch_PWMaudio_l25)
      3'b000 : begin
        adsr2 = 24'h000064;
      end
      3'b001 : begin
        adsr2 = 24'h0001f4;
      end
      3'b010 : begin
        adsr2 = 24'h0005dc;
      end
      3'b011 : begin
        adsr2 = 24'h0007d0;
      end
      3'b100 : begin
        adsr2 = 24'h000064;
      end
      3'b101 : begin
        adsr2 = 24'h0007d0;
      end
      3'b110 : begin
        adsr2 = 24'h0003e8;
      end
      default : begin
        adsr2 = 24'h001388;
      end
    endcase
  end

  always @(*) begin
    case(switch_PWMaudio_l25)
      3'b000 : begin
        adsr3 = 24'h0001f4;
      end
      3'b001 : begin
        adsr3 = 24'h0001f4;
      end
      3'b010 : begin
        adsr3 = 24'h0003e8;
      end
      3'b011 : begin
        adsr3 = 24'h0005dc;
      end
      3'b100 : begin
        adsr3 = 24'h0007d0;
      end
      3'b101 : begin
        adsr3 = 24'h0007d0;
      end
      3'b110 : begin
        adsr3 = 24'h0001f4;
      end
      default : begin
        adsr3 = 24'h0003e8;
      end
    endcase
  end

  always @(*) begin
    case(switch_PWMaudio_l25)
      3'b000 : begin
        adsr4 = 24'h000064;
      end
      3'b001 : begin
        adsr4 = 24'h000064;
      end
      3'b010 : begin
        adsr4 = 24'h000190;
      end
      3'b011 : begin
        adsr4 = 24'h000190;
      end
      3'b100 : begin
        adsr4 = 24'h000190;
      end
      3'b101 : begin
        adsr4 = 24'h0003e8;
      end
      3'b110 : begin
        adsr4 = 24'h000190;
      end
      default : begin
        adsr4 = 24'h002710;
      end
    endcase
  end

  assign io_pwm_1 = pwm_ctrl_io_pwm_1;
  assign io_pwm_2 = pwm_ctrl_io_pwm_2;
  assign pwm_ctrl_io_freq = io_frequency;
  assign fsm_adsr_wantExit = 1'b0;
  always @(*) begin
    fsm_adsr_wantStart = 1'b0;
    case(fsm_adsr_stateReg)
      fsm_adsr_enumDef_stateEntry : begin
      end
      fsm_adsr_enumDef_stateAttack : begin
      end
      fsm_adsr_enumDef_stateDelay : begin
      end
      fsm_adsr_enumDef_stateSustain : begin
      end
      fsm_adsr_enumDef_stateRelease : begin
      end
      default : begin
        fsm_adsr_wantStart = 1'b1;
      end
    endcase
  end

  assign fsm_adsr_wantKill = 1'b0;
  always @(*) begin
    if(io_adsr_switch) begin
      pwm_ctrl_io_level = fsm_adsr_level_adsr;
    end else begin
      pwm_ctrl_io_level = 8'hff;
    end
  end

  always @(*) begin
    fsm_adsr_stateNext = fsm_adsr_stateReg;
    case(fsm_adsr_stateReg)
      fsm_adsr_enumDef_stateEntry : begin
        fsm_adsr_stateNext = fsm_adsr_enumDef_stateAttack;
      end
      fsm_adsr_enumDef_stateAttack : begin
        if(when_PWMaudio_l114) begin
          fsm_adsr_stateNext = fsm_adsr_enumDef_stateDelay;
        end
      end
      fsm_adsr_enumDef_stateDelay : begin
        if(when_PWMaudio_l128) begin
          fsm_adsr_stateNext = fsm_adsr_enumDef_stateSustain;
        end
      end
      fsm_adsr_enumDef_stateSustain : begin
        if(when_PWMaudio_l139) begin
          fsm_adsr_stateNext = fsm_adsr_enumDef_stateRelease;
        end
      end
      fsm_adsr_enumDef_stateRelease : begin
        if(when_PWMaudio_l153) begin
          fsm_adsr_stateNext = fsm_adsr_enumDef_stateEntry;
        end
      end
      default : begin
      end
    endcase
    if(fsm_adsr_wantStart) begin
      fsm_adsr_stateNext = fsm_adsr_enumDef_stateEntry;
    end
    if(fsm_adsr_wantKill) begin
      fsm_adsr_stateNext = fsm_adsr_enumDef_BOOT;
    end
  end

  assign when_PWMaudio_l110 = (adsr1 <= fsm_adsr_counter);
  assign when_PWMaudio_l114 = (fsm_adsr_level_adsr == 8'hff);
  assign when_PWMaudio_l124 = (adsr2 <= fsm_adsr_counter);
  assign when_PWMaudio_l128 = (fsm_adsr_level_adsr == 8'h7f);
  assign when_PWMaudio_l139 = (adsr3 <= fsm_adsr_counter);
  assign when_PWMaudio_l149 = (adsr4 <= fsm_adsr_counter);
  assign when_PWMaudio_l153 = (fsm_adsr_level_adsr == 8'h0);
  assign when_StateMachine_l238 = ((! (fsm_adsr_stateReg == fsm_adsr_enumDef_stateAttack)) && (fsm_adsr_stateNext == fsm_adsr_enumDef_stateAttack));
  assign when_StateMachine_l238_1 = ((! (fsm_adsr_stateReg == fsm_adsr_enumDef_stateDelay)) && (fsm_adsr_stateNext == fsm_adsr_enumDef_stateDelay));
  assign when_StateMachine_l238_2 = ((! (fsm_adsr_stateReg == fsm_adsr_enumDef_stateSustain)) && (fsm_adsr_stateNext == fsm_adsr_enumDef_stateSustain));
  assign when_StateMachine_l238_3 = ((! (fsm_adsr_stateReg == fsm_adsr_enumDef_stateRelease)) && (fsm_adsr_stateNext == fsm_adsr_enumDef_stateRelease));
  always @(posedge clk or posedge reset) begin
    if(reset) begin
      fsm_adsr_counter <= 24'h0;
      fsm_adsr_level_adsr <= 8'h0;
      fsm_adsr_stateReg <= fsm_adsr_enumDef_BOOT;
    end else begin
      fsm_adsr_stateReg <= fsm_adsr_stateNext;
      case(fsm_adsr_stateReg)
        fsm_adsr_enumDef_stateEntry : begin
        end
        fsm_adsr_enumDef_stateAttack : begin
          fsm_adsr_counter <= (fsm_adsr_counter + 24'h000001);
          if(when_PWMaudio_l110) begin
            fsm_adsr_level_adsr <= (fsm_adsr_level_adsr + 8'h01);
            fsm_adsr_counter <= 24'h0;
          end
        end
        fsm_adsr_enumDef_stateDelay : begin
          fsm_adsr_counter <= (fsm_adsr_counter + 24'h000001);
          if(when_PWMaudio_l124) begin
            fsm_adsr_level_adsr <= (fsm_adsr_level_adsr - 8'h01);
            fsm_adsr_counter <= 24'h0;
          end
        end
        fsm_adsr_enumDef_stateSustain : begin
          fsm_adsr_counter <= (fsm_adsr_counter + 24'h000001);
          fsm_adsr_level_adsr <= 8'h7f;
        end
        fsm_adsr_enumDef_stateRelease : begin
          fsm_adsr_counter <= (fsm_adsr_counter + 24'h000001);
          if(when_PWMaudio_l149) begin
            fsm_adsr_level_adsr <= (fsm_adsr_level_adsr - 8'h01);
            fsm_adsr_counter <= 24'h0;
          end
        end
        default : begin
        end
      endcase
      if(when_StateMachine_l238) begin
        fsm_adsr_counter <= 24'h0;
      end
      if(when_StateMachine_l238_1) begin
        fsm_adsr_counter <= 24'h0;
      end
      if(when_StateMachine_l238_2) begin
        fsm_adsr_counter <= 24'h0;
      end
      if(when_StateMachine_l238_3) begin
        fsm_adsr_counter <= 24'h0;
      end
    end
  end


endmodule

module PWMctrl (
  input      [11:0]   io_freq,
  input      [7:0]    io_level,
  output              io_pwm_1,
  output              io_pwm_2,
  input               clk,
  input               reset
);

  wire                pwmdriver_1_1_io_pwm;
  wire                pwmdriver_2_io_pwm;
  wire       [11:0]   _zz_freq_counter_valueNext;
  wire       [0:0]    _zz_freq_counter_valueNext_1;
  wire       [7:0]    _zz_pwm_steps_counter_valueNext;
  wire       [0:0]    _zz_pwm_steps_counter_valueNext_1;
  reg                 freq_counter_willIncrement;
  reg                 freq_counter_willClear;
  reg        [11:0]   freq_counter_valueNext;
  reg        [11:0]   freq_counter_value;
  wire                freq_counter_willOverflowIfInc;
  wire                freq_counter_willOverflow;
  reg                 pwm_steps_counter_willIncrement;
  wire                pwm_steps_counter_willClear;
  reg        [7:0]    pwm_steps_counter_valueNext;
  reg        [7:0]    pwm_steps_counter_value;
  wire                pwm_steps_counter_willOverflowIfInc;
  wire                pwm_steps_counter_willOverflow;
  reg        [7:0]    duty_cycle_1;
  wire                when_PWMctrl_l23;
  wire                when_PWMctrl_l29;
  function  zz_freq_counter_willIncrement(input dummy);
    begin
      zz_freq_counter_willIncrement = 1'b0;
      zz_freq_counter_willIncrement = 1'b1;
    end
  endfunction
  wire  _zz_1;

  assign _zz_freq_counter_valueNext_1 = freq_counter_willIncrement;
  assign _zz_freq_counter_valueNext = {11'd0, _zz_freq_counter_valueNext_1};
  assign _zz_pwm_steps_counter_valueNext_1 = pwm_steps_counter_willIncrement;
  assign _zz_pwm_steps_counter_valueNext = {7'd0, _zz_pwm_steps_counter_valueNext_1};
  PWMdriver pwmdriver_1_1 (
    .io_dutyCycle    (duty_cycle_1[7:0]     ), //i
    .io_pwm          (pwmdriver_1_1_io_pwm  ), //o
    .clk             (clk                   ), //i
    .reset           (reset                 )  //i
  );
  PWMdriver pwmdriver_2 (
    .io_dutyCycle    (pwm_steps_counter_value[7:0]  ), //i
    .io_pwm          (pwmdriver_2_io_pwm            ), //o
    .clk             (clk                           ), //i
    .reset           (reset                         )  //i
  );
  assign _zz_1 = zz_freq_counter_willIncrement(1'b0);
  always @(*) freq_counter_willIncrement = _zz_1;
  always @(*) begin
    freq_counter_willClear = 1'b0;
    if(when_PWMctrl_l23) begin
      freq_counter_willClear = 1'b1;
    end
  end

  assign freq_counter_willOverflowIfInc = (freq_counter_value == 12'hfff);
  assign freq_counter_willOverflow = (freq_counter_willOverflowIfInc && freq_counter_willIncrement);
  always @(*) begin
    freq_counter_valueNext = (freq_counter_value + _zz_freq_counter_valueNext);
    if(freq_counter_willClear) begin
      freq_counter_valueNext = 12'h0;
    end
  end

  always @(*) begin
    pwm_steps_counter_willIncrement = 1'b0;
    if(when_PWMctrl_l23) begin
      pwm_steps_counter_willIncrement = 1'b1;
    end
  end

  assign pwm_steps_counter_willClear = 1'b0;
  assign pwm_steps_counter_willOverflowIfInc = (pwm_steps_counter_value == 8'hff);
  assign pwm_steps_counter_willOverflow = (pwm_steps_counter_willOverflowIfInc && pwm_steps_counter_willIncrement);
  always @(*) begin
    pwm_steps_counter_valueNext = (pwm_steps_counter_value + _zz_pwm_steps_counter_valueNext);
    if(pwm_steps_counter_willClear) begin
      pwm_steps_counter_valueNext = 8'h0;
    end
  end

  assign io_pwm_1 = pwmdriver_1_1_io_pwm;
  assign when_PWMctrl_l23 = (freq_counter_value == io_freq);
  assign when_PWMctrl_l29 = (pwm_steps_counter_value < 8'h7f);
  always @(*) begin
    if(when_PWMctrl_l29) begin
      duty_cycle_1 = 8'h0;
    end else begin
      duty_cycle_1 = io_level;
    end
  end

  assign io_pwm_2 = pwmdriver_2_io_pwm;
  always @(posedge clk or posedge reset) begin
    if(reset) begin
      freq_counter_value <= 12'h0;
      pwm_steps_counter_value <= 8'h0;
    end else begin
      freq_counter_value <= freq_counter_valueNext;
      pwm_steps_counter_value <= pwm_steps_counter_valueNext;
    end
  end


endmodule

//PWMdriver replaced by PWMdriver

module PWMdriver (
  input      [7:0]    io_dutyCycle,
  output              io_pwm,
  input               clk,
  input               reset
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




Reference solution:
rtl/generated.v: 
  wire       [7:0]    _zz_counter_valueNext;
  wire       [0:0]    _zz_counter_valueNext_1;
  reg                 counter_willIncrement;
  wire                counter_willClear;
  reg        [7:0]    counter_valueNext;
  reg        [7:0]    counter_value;
  wire                counter_willOverflowIfInc;
  wire                counter_willOverflow;
  function  zz_counter_willIncrement(input dummy);
    begin
      zz_counter_willIncrement = 1'b0;
      zz_counter_willIncrement = 1'b1;
    end
  endfunction
  wire  _zz_1;

  assign _zz_counter_valueNext_1 = counter_willIncrement;
  assign _zz_counter_valueNext = {7'd0, _zz_counter_valueNext_1};
  assign _zz_1 = zz_counter_willIncrement(1'b0);
  always @(*) counter_willIncrement = _zz_1;
  assign counter_willClear = 1'b0;
  assign counter_willOverflowIfInc = (counter_value == 8'hff);
  assign counter_willOverflow = (counter_willOverflowIfInc && counter_willIncrement);
  always @(*) begin
    counter_valueNext = (counter_value + _zz_counter_valueNext);
    if(counter_willClear) begin
      counter_valueNext = 8'h0;
    end
  end

  assign io_pwm = (counter_value < io_dutyCycle);
  always @(posedge clk or posedge reset) begin
    if(reset) begin
      counter_value <= 8'h0;
    end else begin
      counter_value <= counter_valueNext;
    end
  end