// Write a CORDIC algorithm to calculate the sine and cosine of an angle.
/*
The CORDIC (Coordinate Rotation Digital Computer) algorithm is a numerical method used to calculate various mathematical functions, including sine, cosine, and tangent, using only simple shift and addition operations. It's particularly useful in digital signal processing and other applications where speed and efficiency are crucial.
Here's a simplified explanation of the CORDIC algorithm for calculating sine and cosine:
1. **Initialization**:
   - Start with an initial angle (θ) and an initial vector (x, y) set to (1, 0).
   - The angle is typically represented in radians.
   - The vector (x, y) represents the coordinates of a point on the unit circle.
   2. **Rotation**:
   - For each iteration, you rotate the vector (x, y) by a fixed angle (α) towards the target angle (θ).
   - The rotation angle (α) is determined by the current angle (θ) and the desired precision.
   - The rotation is done using the following formulas:
   - x' = x - (y * α)
   - y' = y + (x * α)
   - The rotation is done in a specific direction based on the sign of the angle (θ).
   3. **Iteration**:
   - Repeat the rotation process for a certain number of iterations, typically determined by the desired precision.
   - Each iteration reduces the error between the current angle and the target angle.
   4. **Final Calculations**:
   - After the iterations, the final values of x and y represent the sine and cosine of the angle (θ).
   - The sine is the y-coordinate (y), and the cosine is the x-coordinate (x).
   - The tangent can be calculated as sine divided by cosine.
   - The CORDIC algorithm is efficient because it uses only simple shift and addition operations, making it suitable for hardware implementation.
   - The number of iterations required for a given precision depends on the desired accuracy.
   - The algorithm can be extended to calculate other functions like hyperbolic sine and cosine, as well as inverse trigonometric functions.
   - The CORDIC algorithm is widely used in various applications, including digital signal processing, navigation systems, and robotics.
*/
module cordic(
    input wire [7:0] angle,
    output wire [7:0] sine,
    output wire [7:0] cosine
);
    // Constants for rotation angles
    parameter alpha =
    8'b00100101; // 0.6072529350088812561694
    parameter beta =
    8'b00010010; // 0.3035240759005697976353
    parameter gamma =
    8'b00001001; // 0.1517620449196624368329
    parameter delta =
    8'b00000100; // 0.0758810224598312184164
    parameter epsilon =
    8'b00000010; // 0.0379405112299156092082
    parameter zeta =
    8'b00000001; // 0.0189702556149578046041
    // Internal registers
    reg [7:0] x = 8'b10000000; // Initial x-coordinate
    reg [7:0] y = 8'b00000000; // Initial y-coordinate
    reg [7:0] angle_reg = 0; // Current angle
    // Iterate for the number of iterations
    always @(posedge clk) begin
        for (int i = 0; i < 8; i++) begin
            if (angle_reg[i]) begin
                if (angle_reg[i] == 1'b1) begin
                    x <= x - (y >> i);
                    y <= y + (x >> i);
                end
            end
            angle_reg <= angle_reg - (alpha >> i);
        end
        end
        // Output assignments
        assign sine = y;
        assign cosine = x;
        odule
