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problem ： Enter a 16bit Number of , Now ask it to divide by 3 Obtained quotient and remainder ? How to optimize ?
See this topic , The first way to think of is the most traditional subtraction 3, Shangjia 1, Judgment remainder , Then keep decreasing , Keep adding , Until the last remainder is less than 3, This method is the stupidest and most intuitive . Use this method to realize it first .
module divid( input clk, input rst_n, input [15:0] din, output reg [1:0]
y_dout, output reg[15:0] s_dout ); reg [15:0] temp_data; reg end_flag; always @
(posedge clk or negedge rst_n) begin if(!rst_n) begin temp_data <= din; end else
begin temp_data<= temp_data - 2'd3; end end always @ (posedge clk or negedge
rst_n) begin if(!rst_n) begin end_flag <= 1'b0; end else if(temp_data <= 2'd3)
begin end_flag <= 1'b1; end else begin end_flag <= 1'b0; end end reg [15:0]
cnt; always @ (posedge clk or negedge rst_n) begin if(!rst_n) begin cnt <= 16'd0
; end else if(end_flag) begin cnt <= 16'd0; end else begin cnt <= cnt + 1'b1;
end end always @(posedge clk or negedge rst_n) begin if(!rst_n) begin y_dout <=
2'd0; end else if(temp_data <= 2'd3) begin y_dout <= temp_data[1:0]; end end
always @(posedge clk or negedge rst_n) begin if(!rst_n) begin s_dout <= 16'd0;
end else if(temp_data <= 2'd3) begin s_dout <= cnt; end end endmodule
Next, this is a more optimized approach ：
This practice refers to other people's articles , Divide by at one time 3 In operation , Only three sequences need to be considered , that is 11,100,101. What is this ? This law can be found from the following formula ：
Just sort it out , Arrange the divisor from high to low , Look from front to back 11,100,101 These three sequences , A sequence of these three numbers was encountered , Business write 1, Otherwise, I will write 0. Remove this sequence when done . If encountered 100, take 3’b100-2’b11
=
1’b1 Insert to the highest bit of the original sequence ; encounter 101, Then insert 2’b10, encounter 11, No operation . When actually writing code , Enter the divisor bit by bit from high to low , The quotient can be shifted to the left one at a time , In this way, after the complete sequence, the quotient calculated at the beginning will reach the high position , Avoid using register index .
A counter is required to control the number of state transitions , In theory, just count to the bit width of the divisor -1 that will do , But in practice, in order to avoid the final return IDLE The problem of making the remainder incorrect , Count it to the bit width of the divisor . Finally, quotient and remainder are obtained . The remainder is the binary number represented by the next state at the end of the counter .
module divide_by_three #( parameter DATAWIDTH = 16 )( input clk, input rst_n,
input vld_in, input[DATAWIDTH-1:0] data_in, output reg [DATAWIDTH-1:0]
quotient, output reg[1:0] reminder, output reg vld_out ); reg [1:0] c_state; reg
[1:0] n_state; reg [$clog2(DATAWIDTH):0] cnt; reg [DATAWIDTH-1:0] data_reg;
parameter IDLE= 2'b11; always @ (posedge clk or negedge rst_n) begin if(!rst_n)
begin c_state <= IDLE; end else begin c_state <= n_state; end end always @ (*)
begin case(c_state) IDLE : if(vld_in) n_state = 2'b00; else n_state = IDLE; 2
'b00 : if(cnt==DATAWIDTH) n_state = IDLE; else if(data_reg[DATAWIDTH-1])
n_state = 2'b01; else n_state = 2'b00; 2'b01 : if(cnt==DATAWIDTH) n_state = IDLE
; else if(data_reg[DATAWIDTH-1]) n_state = 2'b00; else n_state = 2'b10; 2'b10 :
if(cnt==DATAWIDTH) n_state = IDLE; else if(data_reg[DATAWIDTH-1]) n_state = 2'
b10; else n_state = 2'b01; default : n_state = IDLE; endcase end always @
(posedge clk or negedge rst_n) begin if(!rst_n) begin
{cnt,data_reg,reminder,quotient,vld_out} <= 0; end else begin case(c_state)
IDLE : begin {vld_out,cnt} <= 0; if(vld_in) begin data_reg <= data_in; end else
begin data_reg <= data_reg; end end 2'b00,2'b01,2'b10 : begin if(cnt==
DATAWIDTH-1) begin cnt <= cnt + 1; reminder <= n_state; vld_out <= 1; end else
begin cnt<= cnt + 1; vld_out <= 0; data_reg <= {data_reg[DATAWIDTH-2:0],1'b0};
end if(data_reg[DATAWIDTH-1]) begin quotient <= {quotient[DATAWIDTH-2:0],c_state
[1]|c_state[0]}; end else begin quotient <= {quotient[DATAWIDTH-2:0],c_state[1]}
; end end endcase end end endmodule
The third paragraph of this code is about quotient , Why do you want to shift the state value of the current state to the left ? The specific reason depends on the state machine above , When the maximum is 1 When , Now this one's business is 1, Only occurs in the state S01 And status S10, When the highest is not 1 When , If in state S10 When , Now for 100, Consult 1, Take the highest position , If in S01 State time , Now for 010, Now Shang Wei 1, Consult 0.（ That's probably the explanation , Take a closer look ）
And the counter counts to 16 Question of , Actually 0 reach 15 That's enough , however 16 Just to get it back to IDLE.
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