恢复余数除法器

恢复余数除法器

算法描述

恢复余数除法器是一种常用的除法器,过程与手算除法的方法很类似,过程为

  1. 将除数向左位移直到比被除数大
  2. 执行被除数减除数操作,得余数,并将商向左移位1位,空位补1
  3. 若余数大于0,除数向右移位1位。如余数小于0,余数加当前除数,商最后一位置0,除数向右移位1位
  4. 重复到2,只到除数比最初的除数小

RTL代码

RTL代码就是使用了大量的if语句完成了以上的算法描述,其中

  • 为了使移位后的除数确保大于被除数,直接将除数放到一个位宽WIDTH*3的寄存器的前WIDTH位
  • divisor_move >= '{divisor_lock}用于当移位除数小于原除数时停止
  • (divisor_move > '{remainder_r}) && (dout == 'b0)用于当出现第一个1时才开始保存结果
module restore_divider #(
    parameter WIDTH = 4
)(
    input clk,    // Clock
    input rst_n,  // Asynchronous reset active low

    input [WIDTH * 2 - 1:0]dividend,
    input [WIDTH - 1:0]divisor,

    input din_valid,

    output reg [2 * WIDTH - 1:0]dout,
    output [WIDTH - 1:0]remainder
);

reg [2 * WIDTH:0]remainder_r;
reg [3 * WIDTH - 1:0]divisor_move;
reg [WIDTH - 1:0]divisor_lock;
always @ (posedge clk or negedge rst_n) begin
    if(~rst_n) begin
        //初始化
        {remainder_r,divisor_lock,divisor_move,dout} <= 'b0;
    end else begin
        if(din_valid == 1'b1) begin 
            //锁存输入,3倍WIDTH的宽度用于保证移位后的除数大于被除数
            remainder_r[WIDTH * 2 - 1:0] <= dividend;
            remainder_r[2 * WIDTH] <= 'b0;
            divisor_move[3 * WIDTH - 1:2 * WIDTH] <= divisor;
            divisor_move[2 * WIDTH - 1:0] <= 'b0;
            divisor_lock <= divisor;
            dout <= 'b0;
        end else if((divisor_move > '{remainder_r}) && (dout == 'b0)) begin
            //开始条件
             remainder_r <= remainder_r;
            dout <= 'b0;
            divisor_move <= divisor_move >> 1;
            divisor_lock <= divisor_lock;
        end else if(divisor_move >= '{divisor_lock}) begin
            if(remainder_r[2 * WIDTH] == 1'b0) begin //执行减法
                remainder_r <= remainder_r - divisor_move;
                dout <= {dout[2 * WIDTH - 2:0],1'b1};
                // divisor_move <= divisor_move >> 1;
                divisor_lock <= divisor_lock;
                if(remainder_r >= divisor_move) begin
                    divisor_move <= divisor_move >> 1;
                end else begin
                    divisor_move <= divisor_move;
                end
            end else begin  //恢复余数
                remainder_r <= remainder_r + divisor_move;
                dout <= {dout[2 * WIDTH - 1:1],1'b0};
                divisor_move <= divisor_move >> 1;
                divisor_lock <= divisor_lock;
            end
        end else begin
            remainder_r <= remainder_r;
            divisor_lock <= divisor_lock;
            divisor_move <= divisor_move;
            dout <= dout;
        end
    end
end

assign remainder = remainder_r[WIDTH - 1:0];

endmodule

测试平台

测试平台复用了shiftsub除法器的平台,增加了“遇错停止”的功能

module tb_divider (
);

parameter WIDTH = 4;

logic clk;    // Clock
logic rst_n;  // Asynchronous reset active low
logic [2 * WIDTH - 1:0]dividend;
logic [WIDTH - 1:0]divisor;

logic din_valid;

logic [2 * WIDTH - 1:0]dout;
logic [WIDTH - 1:0]remainder;

restore_divider #(
    .WIDTH(WIDTH)
) dut (
    .clk(clk),    // Clock
    .rst_n(rst_n),  // Asynchronous reset active low

    .dividend(dividend),
    .divisor(divisor),

    .din_valid(din_valid),

    .dout(dout),
    .remainder(remainder)
);

initial begin
    clk = 'b0;
    forever begin
        #50 clk = ~clk;
    end
end

initial begin
    rst_n = 1'b1;
    # 5 rst_n = 'b0;
    #10 rst_n = 1'b1;
end

logic [2 * WIDTH - 1:0]dout_exp;
logic [WIDTH - 1:0]remainder_exp;
initial begin
    {dividend,divisor,din_valid} = 'b0;
    forever begin
        @(negedge clk);
        dividend = (2 * WIDTH)'($urandom_range(0,2 ** (2 * WIDTH)));
        divisor = (WIDTH)'($urandom_range(1,2 ** WIDTH - 1));
        din_valid = 1'b1;

        remainder_exp = dividend % divisor;
        dout_exp = (dividend - remainder_exp) / divisor;

        repeat(5 * WIDTH) begin
            @(negedge clk);
            din_valid = 'b0;
        end
        if((remainder == remainder_exp) && (dout_exp == dout)) begin
            $display("successfully");
        end else begin
            $display("failed");
            $stop;
        end
    end
end

endmodule

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