// This module generates random 32-bit sequences using the
// simple pseudorandom number generator where each random number
// is computed as 69069 * (previous random number) + 1.
// This sequence will iterate through all 2^32 possible values
// before repeating itself.
//
// The circuit avoids multiplication through adding shifted values;
// note that 69069 = 2^16 + 2^12 - 2^9 - 2^6 + 2^4 - 2^2 + 1,
module Sequence (Clock, Result);
    input Clock;
    output [31:0] Result;
    reg [31:0] Result;
    wire [31:0] Next;

    // Note that the next value will begin to be computed as soon as the
    // current result changes. This allows for immediate update
    // of the sequence as soon as the clock goes from 0 to 1.
    assign Next = (Result << 16) + (Result << 12) - (Result << 9)
        - (Result << 6) + (Result << 4) - (Result << 2) + Result + 1;

    initial begin
        Result = 32'hE4E4E4E4;
    end

    always @(posedge Clock) begin
        Result = Next;
    end
endmodule