基于迭代单元的恢复余数开方器
基本算法
该开方器的算法与“手算”(以前并不知道开方还有这种手算的方法)算法相似,使用迭代解决,文字描述如下
- 将0为余数的初值
a
,0作为结果初值b
- 将被开方数前两位
{I(2m + 1),I(2m)}
取出,与01比较大小。若前两位大,则{I(2m + 1),I(2m)} - 01
为输出余数(a(m)
),输出结果1(b(m)
),否则{I(2m + 1),I(2m)}
为输出余数(a(m)
),输出结果0(b(m)
)
- 将被开方数的从高位数第3,4位
{I(2m - 1),I(2m - 2)}
取出,比较{a(m),I(2m - 1),I(2m - 2)}
和{b(m),2'b01}
的大小,若前一项大,则输出余数a(m - 1)
为前一项减后一项,输出结果b(m - 1)
为{b(m),1}
;否则,输出余数为前一项(直接输出),输出结果b(m - 1)
为{b(m),0}
- …
- 直到计算完被开方数结束
迭代单元
算法
迭代单元的算法比较简单,描述如下:
- 组合输入余数和当前开方数的两位
{b,I(i),I(i - 1)}
,组合输入结果和01为{a,2'b01}
- 比较大小,若组合余数大则输出余数为组合余数减去组合结果,输出结果
{a,1}
;否则余数输出组合余数,结果输出{a,0}
RTL代码
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| module square_cell #( parameter WIDTH = 4, parameter STEP = 0 )( input clk, input rst_n,
input [2 * WIDTH - 1:0]radicand, input [WIDTH - 1:0]last_dout, input [2 * WIDTH - 1:0]remainder_din,
output reg [WIDTH - 1:0]this_dout, output reg [2 * WIDTH - 1:0]remainder_dout );
wire [2 * WIDTH - 1:0]target_data = {remainder_din[2 * WIDTH - 3:0],radicand[2 * STEP +:2]}; wire [2 * WIDTH - 1:0]try_data = {last_dout,2'b01};
always @(posedge clk or negedge rst_n) begin if(~rst_n) begin {this_dout,remainder_dout} <= 'b0; end else begin if(target_data >= try_data) begin this_dout <= {last_dout[WIDTH - 2:0],1'b1}; remainder_dout <= target_data - try_data; end else begin this_dout <= {last_dout[WIDTH - 2:0],1'b0}; remainder_dout <= target_data; end end end endmodule
|
顶层与Testbench
顶层单元
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| module square_extractor #( parameter WIDTH = 4 )( input clk, input rst_n,
input [2 * WIDTH - 1:0]radicand,
output [WIDTH - 1:0]dout, output [2 * WIDTH - 1:0]remainder );
genvar i; generate for (i = WIDTH - 1; i >= 0; i = i - 1) begin:square wire [2 * WIDTH - 1:0]remainder_dout,remainder_din; wire [WIDTH - 1:0]this_dout,last_dout; if(i == WIDTH - 1) begin assign remainder_din = 'b0; assign last_dout = 'b0; end else begin assign remainder_din = square[i + 1].remainder_dout; assign last_dout = square[i + 1].this_dout; end square_cell #( .WIDTH(WIDTH), .STEP(i) ) u_square_cell ( .clk(clk), .rst_n(rst_n),
.radicand(radicand), .last_dout(last_dout), .remainder_din(remainder_din),
.this_dout(this_dout), .remainder_dout(remainder_dout) ); end endgenerate
assign dout = square[0].this_dout; assign remainder = square[0].remainder_dout;
endmodule
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TestBench
Testbench输入随机的输入后,等待完成,完成后取结果和余数看是否能恢复出正确的输入
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| module tb_square ( );
parameter WIDTH = 4;
logic clk; logic rst_n;
logic [2 * WIDTH - 1:0]radicand;
logic [WIDTH - 1:0]dout; logic [2 * WIDTH - 1:0]remainder;
square_extractor #( .WIDTH(WIDTH) ) dut ( .clk(clk), .rst_n(rst_n),
.radicand(radicand),
.dout(dout), .remainder(remainder) );
initial begin clk = 0; forever begin #50 clk = ~clk; end end
initial begin rst_n = 1'b1; #5 rst_n = 1'b0; #10 rst_n = 1'b1; end
logic [2 * WIDTH - 1:0]act; logic [2 * WIDTH - 1:0]dout_ex; initial begin radicand = 'b0; forever begin @(negedge clk); radicand = (2 * WIDTH)'($urandom_range(0,2 ** (2 * WIDTH))); repeat(4 * WIDTH) begin @(negedge clk); end dout_ex = '{dout}; act = dout_ex * dout_ex + remainder; if(act != radicand) begin $stop; end end end
endmodule
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