√ 开方器

// Square Root - 逐位试探法
// 从MSB到LSB逐位试探，检查 root^2 <= radicand
module sqrt_newton(
    input  wire clk,
    input  wire rst,
    input  wire start,
    input  wire [15:0] radicand,
    output reg  [7:0]  sqrt_out,
    output reg  done
);

reg [7:0]  root;
reg [3:0]  bit_pos;
reg running;
reg [15:0] rad_reg;

wire [7:0]  trial_root = root | (8'd1 << bit_pos[2:0]);
wire [15:0] trial_sq   = trial_root * trial_root;
wire        can_set    = (rad_reg >= trial_sq);

always @(posedge clk or posedge rst) begin
    if (rst) begin
        sqrt_out <= 8'd0;
        done     <= 1'b0;
        root     <= 8'd0;
        bit_pos  <= 4'd0;
        running  <= 1'b0;
        rad_reg  <= 16'd0;
    end else begin
        done <= 1'b0;
        
        if (start && !running) begin
            root    <= 8'd0;
            bit_pos <= 4'd7;
            running <= 1'b1;
            rad_reg <= radicand;
        end
        
        if (running) begin
            if (can_set)
                root <= trial_root;
            
            if (bit_pos == 4'd0) begin
                // Output the final trial_root (including this step's bit)
                sqrt_out <= can_set ? trial_root : root;
                done     <= 1'b1;
                running  <= 1'b0;
            end else begin
                bit_pos <= bit_pos - 4'd1;
            end
        end
    end
end

endmodule