phi_arithmetic.v

// ============================================================================
// φ-ARITHMETIC UNIT — Zero-DSP48 Multiplication using φ² = φ + 1
// ============================================================================
//
// Key identities:
//   φ × x = x + x_prev    (ONE ADDER, 0 DSP48!)
//   φ² × x = x + φ×x      (TWO ADDERS, 0 DSP48!)
//   φⁿ × x = n adders     (ZERO DSP48 for any power!)
//
// Generated by TRI sacred-const phi-arith
// φ² + 1/φ² = 3 = TRINITY
//
// ============================================================================

`default_nettype none

module phi_arithmetic_unit #(
    parameter WIDTH = 25
)(
    input  wire clk,
    input  wire rst,
    input  wire [WIDTH-1:0] x_in,
    input  wire [WIDTH-1:0] x_prev,     // Previous value (Fibonacci sequence)
    input  wire valid_in,
    output wire [WIDTH-1:0] phi_x,      // φ × x
    output wire [WIDTH-1:0] phi2_x,     // φ² × x
    output reg valid_out
);

    // φ × x = x + x_prev (ONE ADDER!)
    wire [WIDTH-1:0] phi_x_wire = x_in + x_prev;

    // φ² × x = x + φ×x (TWO ADDERS!)
    reg [WIDTH-1:0] phi_x_reg;
    reg [WIDTH-1:0] phi2_x_reg;

    always @(posedge clk) begin
        if (rst) begin
            phi_x_reg <= 0;
            phi2_x_reg <= 0;
            valid_out <= 1'b0;
        end else begin
            phi_x_reg <= phi_x_wire;
            phi2_x_reg <= x_in + phi_x_wire;  // x + (x + x_prev) = 2x + x_prev
            valid_out <= valid_in;
        end
    end

    assign phi_x = phi_x_reg;
    assign phi2_x = phi2_x_reg;

endmodule

`default_nettype wire