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`include "inc.v"

/* add two points on the elliptic curve $y^2=x^3-x+1$ over a Galois field GF(3^M)

 * whose irreducible polynomial is $x^97 + x^12 + 2$. */

/* $P3(x3,y3) == P1 + P2$ for any points $P1(x1,y1),P2(x2,y2)$ */

module point_add(clk, reset, x1, y1, zero1, x2, y2, zero2, done, x3, y3, zero3);

    input clk, reset;

    input [`WIDTH:0] x1, y1, x2, y2;

    input zero1; // asserted if P1 == 0

    input zero2; // asserted if P2 == 0

    output reg done;

    output reg [`WIDTH:0] x3, y3;

    output reg zero3; // asserted if P3 == 0

    wire [`WIDTH:0] x3a, x3b, y3a, y3b;

    wire zero3a,

         use1,  // asserted if $ins1$ do work

         done2; // asserted if $ins2$ finished

    assign use1 = zero1 | zero2;

    func9

        ins9 (x1, y1, zero1, x2, y2, zero2, x3a, y3a, zero3a);

    func10

        ins10 (clk, reset, x1, y1, x2, y2, done2, x3b, y3b);

    always @ (posedge clk)

        zero3 <= use1 & zero3a;

    always @ (posedge clk)

        if (reset)

            done <= 0;

        else

            done <= use1 ? 1 : done2;

    always @ (posedge clk)

        if (reset)

          begin

            x3 <= 0; y3 <= 0;

          end

        else

          begin

            x3 <= use1 ? x3a : x3b;

            y3 <= use1 ? y3a : y3b;

          end

endmodule

/* $P1$ and/or $P2$ is the infinite point */

module func9(x1, y1, zero1, x2, y2, zero2, x3, y3, zero3);

    input [`WIDTH:0] x1, y1, x2, y2;

    input zero1; // asserted if P1 == 0

    input zero2; // asserted if P2 == 0

    output [`WIDTH:0] x3, y3;

    output zero3; // asserted if P3 == 0

    assign zero3 = zero1 & zero2;

    genvar i;

    generate

        for (i=0; i<=`WIDTH; i=i+1)

          begin:label

            assign x3[i] = (x1[i] & zero1) | (x2[i] & zero2);

            assign y3[i] = (y1[i] & zero1) | (y2[i] & zero2);

          end

    endgenerate

endmodule

/* $P1$ or $P2$ is not the infinite point */

module func10(clk, reset, x1, y1, x2, y2, done, x3, y3);

    input clk, reset;

    input [`WIDTH:0] x1, y1, x2, y2;

    output done;

    output [`WIDTH:0] x3, y3;

    assign x3 = x1;

    assign y3 = y1;

    assign done = 1;

endmodule