不恢复余数除法器

不恢复余数除法器

基本算法

不恢复余数除法器的基本算法来自于恢复余数除法器，区别在于当余数变负时不停下恢复余数而是继续运行迭代，并在迭代中加上移位后除数而不是减去移位后除数，基本算法如下所示

1. 将除数向左移位到恰好大于被除数
2. 若余数为正：余数减去移位后除数；若余数为负：余数加上移位后除数；
3. 若现余数为正，该位结果为1，否则为0，将除数向右移位一位
4. 重复2,3，知道移位后除数小于原除数

RTL代码

module norestore_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
);

// parameter JUDGE = 2 ** (2 * WIDTH);

reg [2 * WIDTH:0]remainder_r;
reg [3 * WIDTH - 1:0]divisor_move;
reg [WIDTH - 1:0]divisor_lock;
reg [2 * WIDTH:0]judge;
always @ (*) begin
    if(remainder_r[2 * WIDTH] == 1'b0) begin
        judge = remainder_r - divisor_move;
    end else begin
        judge = remainder_r + divisor_move;
    end
end

always @ (posedge clk or negedge rst_n) begin
    if(~rst_n) begin
        {remainder_r,divisor_lock,divisor_move,dout} <= 'b0;
    end else begin
        if(din_valid == 1'b1) begin //lock input data
            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
         //开始运算条件
            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
                remainder_r <= judge;
                if(judge[2 * WIDTH] == 'b0) begin
                    dout <= {dout[2 * WIDTH - 2:0],1'b1};
                end else begin
                    dout <= {dout[2 * WIDTH - 2:0],1'b0};
                end
            end else begin
                remainder_r <= judge;
                if(judge[2 * WIDTH] == 'b0) begin
                    dout <= {dout[2 * WIDTH - 2:0],1'b1};
                end else begin
                    dout <= {dout[2 * WIDTH - 2:0],1'b0};
                end
            end
            divisor_move <= divisor_move >> 1;
            divisor_lock <= divisor_lock;
        end else if(remainder_r[2 * WIDTH - 1] == 1'b1) begin
         //调整余数
            remainder_r <= remainder_r + divisor_lock;
            dout <= dout;
            divisor_lock <= divisor_lock;
            divisor_move <= divisor_move;
        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

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;

norestore_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