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 CL-123-abc
 * SPDX-License-Identifier: Apache-2.0
 */

/* Module name: tt_um_stochastic_integrator_tt9_CL123abc
 * Module description: 
 * Stochastic integrator using Euler's method of integration, so the result is a gradually acculumating integration. 
 * No auto reset, so have to manually reset.
 * References in docs.
 * More details on the submodules are found after this module below.
 * INPUTS: 
 * ui_in[0] for serial input of input a
 * ui_in[1] for serial input of input b
 * OUTPUTS:
 * uo_out[0] for serial output of sequential integrators' integrator a value
 * uo_out[1] for serial output of sequential integrators' integrator b value
 * uo_out[2] for serial output of sequential integrators' integrator c value
 * uo_out[3] for serial output of system integrators' integrator a value
 * uo_out[4] for serial output of system integrators' integrator b value
 * uo_out[5] for serial output of ODE integrators' integrator a value
 * uo_out[6] for serial output of ODE integrators' integrator b value
 * uo_out[7] for output of seq integrator c sn bitstream
 */

`default_nettype none

module tt_um_stochastic_integrator_tt9_CL123abc(
    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
);
	
wire [8:0] input_value_a, input_value_b;
reg [17:0] clk_counter; // synchronizes all the timers in the module, it is 18 bits because I copied the other code, will update but shouldn't matter as long as its large enough
reg [8:0] integrator_a_output_value, integrator_b_output_value, integrator_c_output_value;
reg [8:0] system_integrator_a_output_value, system_integrator_b_output_value;
reg [8:0] test_integrator_a_output_value, test_integrator_b_output_value;
wire [30:0] lfsr_output;
wire [8:0] integrator_a_counter_value, integrator_b_counter_value, integrator_c_counter_value;
wire [8:0] system_integrator_a_counter_value, system_integrator_b_counter_value;
wire [8:0] test_integrator_a_counter_value, test_integrator_b_counter_value;
wire input_sn_bit_a, input_sn_bit_b, input_sn_bit_half1, input_sn_bit_half2;
wire integrator_a_sn_bit, integrator_b_sn_bit, integrator_c_sn_bit;
wire system_integrator_a_sn_bit, system_integrator_b_sn_bit;
wire test_integrator_a_sn_bit, test_integrator_b_sn_bit;
wire uo_out_wire_0, uo_out_wire_1, uo_out_wire_2, uo_out_wire_3, uo_out_wire_4, uo_out_wire_5, uo_out_wire_6;
parameter MAX_COUNTER = 9'd511;
parameter HALF_COUNTER = 9'd256;
parameter SET_INTERVAL = 18'd16;

//Convert serial input to values
serial_to_value_input serial_input(.clk(clk), .clk_counter(clk_counter), .rst_n(rst_n), 
		.input_bit_1(ui_in[0]), .output_bitseq_1(input_value_a), .input_bit_2(ui_in[1]), .output_bitseq_2(input_value_b));

//LFSR generates the psuedorandom numbers (must be 9bits to compare) 
lfsr my_lfsr(.clk(clk), .rst_n(rst_n), .lfsr(lfsr_output));

// Three Integrators In sequence \\
// While input b (dec) is 0, generates the equations t, (t^2)/2, (t^3)/6
// Generating input SC bitstreams
		
comparator input_a_sng_comparator(.bits_a(input_value_a), .bits_b(lfsr_output[8:0]), .bit_out(input_sn_bit_a));  
comparator input_b_sng_comparator(.bits_a(input_value_b), .bits_b({lfsr_output[5:0], lfsr_output[18:16]}), .bit_out(input_sn_bit_b)); 
comparator input_halfprob1_sng_comparator(.bits_a(HALF_COUNTER), .bits_b({lfsr_output[11:5],lfsr_output[25:24]}), .bit_out(input_sn_bit_half1));
comparator input_halfprob2_sng_comparator(.bits_a(HALF_COUNTER), .bits_b({lfsr_output[22:20],lfsr_output[30:25]}), .bit_out(input_sn_bit_half2));
		
// Generating t value and corresponding SC bitstream
counter integrator_a_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(input_sn_bit_a), 
                           .sn_bit_dec(input_sn_bit_b), .value_output(integrator_a_counter_value));  
comparator integrator_a_sng_comparator(.bits_a(integrator_a_counter_value), .bits_b(lfsr_output[30:22]), .bit_out(integrator_a_sn_bit));
		
// Generating (t^2)/2 value and corresponding SC bitstream
counter integrator_b_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(integrator_a_sn_bit), 
                               .sn_bit_dec(input_sn_bit_b), .value_output(integrator_b_counter_value));  
comparator integrator_b_sng_comparator(.bits_a(integrator_b_counter_value), .bits_b({lfsr_output[15:13],lfsr_output[6:1]}), 
                                         .bit_out(integrator_b_sn_bit));  
		
// Generating (t^3)/6 value and corresponding SC bitstream
counter integrator_c_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(integrator_b_sn_bit), 
                           .sn_bit_dec(input_sn_bit_b), .value_output(integrator_c_counter_value));  
comparator integrator_c_sng_comparator(.bits_a(integrator_c_counter_value), .bits_b({lfsr_output[24:19],lfsr_output[14:12]}), 
                            .bit_out(integrator_c_sn_bit));  
	
// Systems of ODEs \\
// Solving dy1/dt = y2 - 0.5, dy2/dt = 0.5 - y1
modified_counter system_integrator_a_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(system_integrator_b_sn_bit), .sn_bit_dec(input_sn_bit_half1), 
.inc_mul(9'b1), .dec_mul(9'b1), .initial_value(9'b0), .value_output(system_integrator_a_counter_value)); 
comparator system_integrator_a_sng_comparator(.bits_a(system_integrator_a_counter_value), .bits_b(lfsr_output[30:22]), 
                 .bit_out(system_integrator_a_sn_bit));
modified_counter system_integrator_b_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(input_sn_bit_half2), .sn_bit_dec(system_integrator_a_sn_bit), 
 .inc_mul(9'b1), .dec_mul(9'b1), .initial_value(HALF_COUNTER), .value_output(system_integrator_b_counter_value)); 
comparator system_integrator_b_sng_comparator(.bits_a(system_integrator_b_counter_value), .bits_b({lfsr_output[15:13],lfsr_output[6:1]}), 
                 .bit_out(system_integrator_b_sn_bit));

// Second order ODE \\
// Solving a stochastic ODE with equation d2y/dt2 + 2 dy/dt + y = 0
// Generates first integration, z(t) = (t+1)*e^-t
modified_counter test_integrator_a_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(!(test_integrator_b_sn_bit)), .sn_bit_dec(input_sn_bit_a), 
.inc_mul(9'b1), .dec_mul(9'b1), .initial_value(MAX_COUNTER), .value_output(test_integrator_a_counter_value)); 
comparator test_integrator_a_sng_comparator(.bits_a(test_integrator_a_counter_value), .bits_b(lfsr_output[30:22]), 
                 .bit_out(test_integrator_a_sn_bit));
		
// Using modified counter, generates second integration, y(t) = t*e^-t
modified_counter test_integrator_b_counter(.clk(clk), .rst_n(rst_n), .sn_bit_inc(test_integrator_a_sn_bit), 
.sn_bit_dec(test_integrator_b_sn_bit), .inc_mul(9'b1), .dec_mul(9'b10), .initial_value(9'd0), .value_output(test_integrator_b_counter_value));  
comparator test_integrator_b_sng_comparator(.bits_a(test_integrator_b_counter_value), .bits_b({lfsr_output[15:13],lfsr_output[6:1]}), .bit_out(test_integrator_b_sn_bit));

//Serial outputs
value_to_serial_output integrator_a_output(.clk(clk), .rst_n(rst_n), .input_bits(integrator_a_output_value), .output_bit(uo_out_wire_0));
value_to_serial_output integrator_b_output(.clk(clk), .rst_n(rst_n), .input_bits(integrator_b_output_value), .output_bit(uo_out_wire_1));
value_to_serial_output integrator_c_output(.clk(clk), .rst_n(rst_n), .input_bits(integrator_c_output_value), .output_bit(uo_out_wire_2));
value_to_serial_output system_integrator_a_output(.clk(clk), .rst_n(rst_n), .input_bits(system_integrator_a_output_value), .output_bit(uo_out_wire_3));
value_to_serial_output system_integrator_b_output(.clk(clk), .rst_n(rst_n), .input_bits(system_integrator_b_output_value), .output_bit(uo_out_wire_4));
value_to_serial_output test_integrator_a_output(.clk(clk), .rst_n(rst_n), .input_bits(test_integrator_a_output_value), .output_bit(uo_out_wire_5));
value_to_serial_output test_integrator_b_output(.clk(clk), .rst_n(rst_n), .input_bits(test_integrator_b_output_value), .output_bit(uo_out_wire_6));

// Clock Sequential Block
always@(posedge clk or posedge rst_n) begin
    if (rst_n) begin
        clk_counter <= 0;
    end
    else begin
        clk_counter <= clk_counter + 1'b1;
    end
end
	
// Output Sequential Block
always@(posedge clk or posedge rst_n)begin
    if (rst_n) begin
        integrator_a_output_value <= 0;
        integrator_b_output_value <= 0;
        integrator_c_output_value <= 0;
        
        system_integrator_a_output_value <= 0;
        system_integrator_b_output_value <= 0;
        
        test_integrator_a_output_value <= 0;
        test_integrator_b_output_value <= 0;
    end
	else if ((clk_counter%(SET_INTERVAL)) == 0) begin // see the integration result after SET_INTERVAL
        integrator_a_output_value <= integrator_a_counter_value; 
        integrator_b_output_value <= integrator_b_counter_value;
        integrator_c_output_value <= integrator_c_counter_value;
        
        system_integrator_a_output_value <= system_integrator_a_counter_value;
        system_integrator_b_output_value <= system_integrator_b_counter_value;
        
        test_integrator_a_output_value <= test_integrator_a_counter_value;
        test_integrator_b_output_value <= test_integrator_b_counter_value;
    end
end

  // PIN LAYOUT
  // All output pins must be assigned. If not used, assign to 0.

	assign uo_out[0] = uo_out_wire_0;
	assign uo_out[1] = uo_out_wire_1; 
	assign uo_out[2] = uo_out_wire_2;
	assign uo_out[3] = uo_out_wire_3;
	assign uo_out[4] = uo_out_wire_4;
	assign uo_out[5] = uo_out_wire_5;
	assign uo_out[6] = uo_out_wire_6;
	assign uo_out[7] = integrator_c_sn_bit; 
    assign uio_out[7:0] = 0;    
    assign uio_oe[7:0]  = 0;
  
  // List all unused inputs to prevent warnings
    wire _unused = &{ena, ui_in[7:2], uio_in, 1'b0}; 
endmodule

/* SUBMODULES:
     *
     * /////////////////////////////////////////////////////////////////////////////
	 * SUBMODULE NAME:
	 * serial_to_value_input (.clk(), .clk_counter(), .rst_n(), 
	    					  .input_bit_1(), .output_bitseq_1(), 
	    					  .input_bit_2(), .output_bitseq_2());
     * SUBMODULE DESCRIPTION: 
     * Takes in serial input (10bit) carrying the 9bit probability 
	 * and gives the 9bit value as output. The last bit in the 10 is the dummy bit.
     * INPUTS:
     * .clk() takes in the clk of the whole circuit.
	 * .clk_counter() takes in the global clock counter that is controlled by the main code.
     * .rst_n() takes in the reset of the whole circuit.
	 * .input_bit_1() takes in the serial bitstream of input 1, 1 bit per clk cycle. 
     * .input_bit_2() takes in the serial bitstream of input 2, 1 bit per clk cycle. 
     * OUTPUTS:
     * .output_bitseq_1() outputs the 9bit value of input 1.
	 * .output_bitseq_2() outputs the 9bit value of input 1.
     * \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	 *
	 * /////////////////////////////////////////////////////////////////////////////
	 * SUBMODULE NAME:
     * lfsr (.clk(), .rst_n(), .lfsr());
     * SUBMODULE DESCRIPTION:
	 * Generates and runs the LFSR, which is 31 bits long and has a seed of 31'd134995 in this code.
     * INPUTS:
     * .clk() takes in the clk of the whole circuit.
	 * .rst_n() takes in the reset of the whole circuit.
     * OUTPUTS:
	 * .lfsr() outputs the entire LFSR contents in 31-bit.
     * \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	 *
     * /////////////////////////////////////////////////////////////////////////////
	 * SUBMODULE NAME:
     * comparator(bits_a, bits_b, bit_out)
	 * SUBMODULE DESCRIPTION:
     * Takes in the 9-bit values of a and b and outputs 1 when a>b.
     * INPUTS:
     * .bits_a() takes in a 9-bit value.
	 * .bits_b() takes in a 9-bit value.
     * OUTPUTS:
	 * .bit_out() outputs the 1-bit value that makes the sn bitstream.
     * \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	 * /////////////////////////////////////////////////////////////////////////////
	 * SUBMODULE NAME:
     * counter(clk, rst_n, sn_bit_inc, sn_bit_dec, value_output)
	 * SUBMODULE DESCRIPTION:
     * The integrator counter that can increment and decrement. When the inc == dec, no change in value.
	 * As a default, it can only inc and dec by 1 per input and always starts at 0.
     * INPUTS:
	 * .clk() takes in the clk of the whole circuit.
	 * .rst_n() takes in the reset of the whole circuit.
     * .sn_bit_inc() takes in a 1 bit input, if inc == 1 and dec == 0, counter increments
     * .sn_bit_dec() takes in a 1 bit input, if inc == 0 and dec == 1, counter decrements
     * OUTPUTS:
	 * .value_output() outputs the current value of the counter
     * \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	 * /////////////////////////////////////////////////////////////////////////////
	 * SUBMODULE NAME:
     * modified_counter(clk, rst_n, sn_bit_inc, sn_bit_dec, inc_mul, dec_mul, initial_value, value_output)
	 * The integrator counter that can increment and decrement. When the inc == dec, no change in value.
	 * Can set the value of inc/dec and the initial value of the counter.
	 * INPUTS:
     * .clk() takes in the clk of the whole circuit.
	 * .rst_n() takes in the reset of the whole circuit.
     * .sn_bit_inc() takes in a 1 bit input, if inc == 1 and dec == 0, counter increments.
     * .sn_bit_dec() takes in a 1 bit input, if inc == 0 and dec == 1, counter decrements.
	 * .inc_mul() takes in a 9-bit value and sets the value for each increment.
     * .dec_mul() takes in a 9-bit value and sets the value for each decrement.
	 * .initial_value() takes in a 9-bit value and sets the counter's value at reset.
     * OUTPUTS:
	 * .value_output() outputs the current value of the counter.
     * \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	 *
     * /////////////////////////////////////////////////////////////////////////////
	 * SUBMODULE NAME:
     * value_to_serial_output(.clk(), .rst_n(), .input_bits(), .output_bit());
     * SUBMODULE DESCRIPTION:
	 * Outputs each bit in the 9bit input as a serial bitstream with an added 10th bit as 0 as a dummy bit.
     * INPUTS:
     * .clk() takes in the clk of the whole circuit.
     * .rst_n() takes in the rst_n of the whole circuit.
	 * .input_bits() takes in a 9bit value, here that is the probability of 1s in the SN bitstream.
     * OUTPUTS:
	 * .output_bit() outputs each bit in the 9bit value and then outputs 0 for the 10th bit.
     * \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	 *
 
*/

module serial_to_value_input(clk, clk_counter, rst_n, input_bit_1, output_bitseq_1, input_bit_2, output_bitseq_2);
input wire [17:0] clk_counter;
input wire clk, rst_n, input_bit_1, input_bit_2;
output reg [8:0] output_bitseq_1, output_bitseq_2; 
reg [8:0] output_bitcounter_1, output_bitcounter_2;
reg loop; 
reg [3:0] output_case;
reg [4:0] adjustment;
	
parameter MAX_CLK_CYCLES = 18'd131072;

	always @(posedge clk or posedge rst_n) begin
    	if(rst_n) begin 
    		output_bitseq_1 <= 9'd0;
    		output_bitseq_2 <= 9'b0;
    		output_bitcounter_1 <= 9'd0;
    		output_bitcounter_2 <= 9'b0;
    		loop <= 1'b0;
			output_case <= 4'b0;
    		adjustment <= 5'd9;
    	end
    	else begin
			if (loop == 0) begin
				if (clk_counter == 0) begin
					case (output_case)
                    4'd0: adjustment <= 5'd9;
                    4'd1: adjustment <= 5'd16;
                    4'd2: adjustment <= 5'd13;
                    4'd3: adjustment <= 5'd10; 
                    4'd4: adjustment <= 5'd17; 
                    4'd5: adjustment <= 5'd14;
                    4'd6: adjustment <= 5'd11;   
                    4'd7: adjustment <= 5'd18;   
                    4'd8: adjustment <= 5'd17; 
                    4'd9: adjustment <= 5'd12;   
                    default:;
					endcase
				end
				output_bitcounter_1 <= (output_bitcounter_1 >> 1);
				output_bitcounter_1[8] <= input_bit_1;
				output_bitcounter_2 <= (output_bitcounter_2 >> 1);
				output_bitcounter_2[8] <= input_bit_2;
				if(clk_counter[4:0] == adjustment) begin
					output_bitseq_1 <= output_bitcounter_1;
					output_bitseq_2 <= output_bitcounter_2;
					loop <= 1;
				end
			end
			else if (loop == 1) begin
				if (clk_counter == MAX_CLK_CYCLES) begin
					if(output_case == 4'd9)
						output_case <= 4'd0;
					else 
						output_case <= output_case + 4'd1;
				loop <= 0;
				end
			end
		end
	end
endmodule

module lfsr(clk, rst_n, lfsr);
input wire clk, rst_n;
output reg [30:0] lfsr;

    always@(posedge clk or posedge rst_n) begin
        if (rst_n)
            lfsr <= 31'd134995;
        else begin
            lfsr[0] <= lfsr[27] ^ lfsr[30];
            lfsr[30:1] <= lfsr[29:0];
            end
        end
endmodule


module comparator(bits_a, bits_b, bit_out);
input wire [8:0] bits_a, bits_b;
output wire bit_out;

assign bit_out = (bits_a > bits_b);
endmodule

module counter(clk, rst_n, sn_bit_inc, sn_bit_dec, value_output);
input wire clk, rst_n, sn_bit_inc, sn_bit_dec;
output reg [8:0] value_output; 
//This value will change with every input, 
//so to store the integration result, need to capture the result somewhere else, timed to clk_counter

parameter MAX_LIMIT = 9'd511;
parameter MIN_LIMIT = 9'd0;
    
    always@(posedge clk or posedge rst_n) begin
        if (rst_n) begin
            value_output <= 0; 
        end
        else begin
            if (sn_bit_dec == 1 && sn_bit_inc == 0) begin
                if (value_output == MIN_LIMIT) begin //min limit
                    //stay at min limit
                end 
                else begin
                    value_output <= value_output - 1'b1;
                end
            end
            else if (sn_bit_dec == 0 && sn_bit_inc == 1) begin
                if (value_output == MAX_LIMIT) begin //max limit
                    //stay at max limit
                end
                else begin
                    value_output <= value_output + 1'b1;
                end
            end
            // If sn_bit_dec == sn_bit_inc == (0 or 1) then no change
            // Add reset?
        end
    end
endmodule

module modified_counter(clk, rst_n, sn_bit_inc, sn_bit_dec, inc_mul, dec_mul, initial_value, value_output);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



module value_to_serial_output(clk, rst_n, input_bits, output_bit);
input wire clk, rst_n;
input wire [8:0] input_bits;
reg [8:0] bitseq;
reg [3:0] counter;
output reg output_bit;
parameter NUMBER_OF_BITS = 4'd9;

	always@(posedge clk or posedge rst_n) begin
		if(rst_n) begin
            bitseq <= 0;
            counter <= 0;
            output_bit <= 0;
        end
        else begin
			case(counter)
			0: begin
				output_bit <= input_bits[0];
                bitseq <= input_bits >> 1;
                counter <= counter + 1;
			end
			NUMBER_OF_BITS: begin
				output_bit <= 0;
                counter <= 0;
			end
			default: begin
				bitseq <= bitseq >> 1;
                output_bit <= bitseq[0];
                counter <= counter + 1;
			end
			endcase
         end
    end
endmodule


Reference solution:
rtl/generated.v: input wire clk, rst_n, sn_bit_inc, sn_bit_dec;
input wire [8:0] inc_mul, dec_mul;
input wire [8:0] initial_value;
output reg [8:0] value_output; 
reg init_flag; // I would just use initial value for the async reset because the initial value is set and isn't going to change but
			   // theres a warning so I am using a init flag instead.

parameter MAX_LIMIT = 9'd511;
parameter MIN_LIMIT = 9'd0;
            // If sn_bit_dec == sn_bit_inc == (0 or 1) then no change
            // Add reset?
	
    always@(posedge clk or posedge rst_n) begin
        if (rst_n) begin
            value_output <= 0;
			init_flag <= 1;
        end
        else begin
			if (init_flag == 1) begin
            	if (sn_bit_dec == 1 && sn_bit_inc == 0) begin
					if (initial_value == MIN_LIMIT) begin //min limit
                    	//stay at min limit
						value_output <= initial_value;
                	end 
                	else begin
                    	value_output <= initial_value - dec_mul;
                	end
            	end
            	else if (sn_bit_dec == 0 && sn_bit_inc == 1) begin
					if (initial_value == MAX_LIMIT) begin //max limit
                    	//stay at max limit
						value_output <= initial_value;
                	end
                	else begin
                    	value_output <= initial_value + inc_mul;
                	end
            	end
				init_flag <= 0;
			end
			else begin //How to keep in limit when dec_mul/inc_mul is changeable and can jump over limit?
				if (sn_bit_dec == 1 && sn_bit_inc == 0) begin
					if (value_output == MIN_LIMIT) begin //min limit
                    	//stay at min limit
                	end 
					else begin 
                    	value_output <= value_output - dec_mul;
                	end
            	end
            	else if (sn_bit_dec == 0 && sn_bit_inc == 1) begin
					if (value_output == MAX_LIMIT) begin //max limit
                    	//stay at max limit
                	end
                	else begin
                    	value_output <= value_output + inc_mul;
                	end
            	end
			end
        end
    end