import { ddAddDd, ddDiffDd, ddMultBy2, ddMultDouble2, ddMultByNeg2, ddMultBy4, twoDiff, ddMultDd } from "double-double";

// We *have* to do the below to improve performance with bundlers❗ The assignee is a getter❗ The assigned is a pure function❗
const td  = twoDiff;
const qaq = ddAddDd;
const qmd = ddMultDouble2;
const qmq = ddMultDd;
const qm2 = ddMultBy2;
const qm4 = ddMultBy4;
const qdq = ddDiffDd;


/**
 * Returns the polynomial whose roots are all the `t` values on the given bezier 
 * curve such that the line from the given point to the point on the bezier 
 * evaluated at `t` is tangent to the bezier curve at `t`.
 * 
 * * intermediate calculations are done (and the final result returned in)
 * double-double precision
 * 
 * @param ps an order 3 bezier curve given as an ordered array of its
 * control point coordinates, e.g. `[[0,0], [1,1], [2,1], [2,0]]`
 * @param p a point, e.g. `[1,2]`
 * 
 * @internal
 */
function getFootpointPoly3Dd(
        ps: number[][], p: number[]): [number[], number[], number[], number[], number[], number[]] {

    //const [[x0, y0], [x1, y1], [x2, y2], [x3, y3]] = ps;
    const p0 = ps[0];
    const p1 = ps[1];
    const p2 = ps[2];
    const p3 = ps[3];
    const x0 = p0[0];
    const y0 = p0[1];
    const x1 = p1[0];
    const y1 = p1[1];
    const x2 = p2[0];
    const y2 = p2[1];
    const x3 = p3[0];
    const y3 = p3[1];

    const [x,y] = p;

    const xx0 = td(x0,x);  // exact
    const xx1 = td(x1,x);  // exact
    const xx2 = td(x2,x);  // exact
    const xx3 = td(x3,x);  // exact
    const yy0 = td(y0,y);  // exact
    const yy1 = td(y1,y);  // exact
    const yy2 = td(y2,y);  // exact
    const yy3 = td(y3,y);  // exact

    const x00 = qmq(xx0,xx0);
    const x01 = qmd(6,qmq(xx0,xx1))
    const x02 = qmd(6,qmq(xx0,xx2))
    const x03 = qm2(qmq(xx0,xx3))
    const x11 = qmd(9,qmq(xx1,xx1))
    const x12 = qmd(18,qmq(xx1,xx2))
    const x13 = qmd(6,qmq(xx1,xx3))
    const x22 = qmd(9,qmq(xx2,xx2))
    const x23 = qmd(6,qmq(xx2,xx3))
    const x33 = qmq(xx3,xx3);

    const y00 = qmq(yy0,yy0);
    const y01 = qmd(6,qmq(yy0,yy1))
    const y02 = qmd(6,qmq(yy0,yy2))
    const y03 = qm2(qmq(yy0,yy3))
    const y11 = qmd(9,qmq(yy1,yy1))
    const y12 = qmd(18,qmq(yy1,yy2))
    const y13 = qmd(6,qmq(yy1,yy3))
    const y22 = qmd(9,qmq(yy2,yy2))
    const y23 = qmd(6,qmq(yy2,yy3))
    const y33 = qmq(yy3,yy3);

    const q1 = qaq(x13,x22);
    const q2 = qaq(x03,x12);
    const q3 = qaq(x02,x11);
    const r1 = qaq(y13,y22);
    const r2 = qaq(y03,y12);
    const r3 = qaq(y02,y11);

    // const t5 = 6*(((((x33 - x23) + (x00 - x01)) + q1) + (q3 - q2)) + 
    //               ((((y33 - y23) + (y00 - y01)) + r1) + (r3 - r2)));
    const t5 = qmd(
        6,
        qaq(
            qaq(qaq(qaq(qdq(x33,x23),qdq(x00,x01)),q1),qdq(q3,q2)),
            qaq(qaq(qaq(qdq(y33,y23),qdq(y00,y01)),r1),qdq(r3,r2))
        )
    );

    
    //const t4 = 5*((((x23 + 5*x01) + 3*q2) - 2*(q1 + 2*q3 + 3*x00)) +
    //              (((y23 + 5*y01) + 3*r2) - 2*(r1 + 2*r3 + 3*y00)));
    const t4 = qmd(
        5,
        qaq(
            qdq(qaq(qaq(x23,qmd(5,x01)),qmd(3,q2)),qm2(qaq(qaq(q1,qm2(q3)),qmd(3,x00)))),
            qdq(qaq(qaq(y23,qmd(5,y01)),qmd(3,r2)),qm2(qaq(qaq(r1,qm2(r3)),qmd(3,y00))))
        )
    );

    //const t3 = 4*(((q1 - 3*(q2 - 2*q3)) - 5*(2*x01 - 3*x00)) +
    //              ((r1 - 3*(r2 - 2*r3)) - 5*(2*y01 - 3*y00)));
    const t3 = qm4(qaq(
        qdq(qdq(q1,qmd(3,(qdq(q2,qm2(q3))))),qmd(5,qdq(qm2(x01),qmd(3,x00)))),
        qdq(qdq(r1,qmd(3,(qdq(r2,qm2(r3))))),qmd(5,qdq(qm2(y01),qmd(3,y00))))
    ));

    //const t2 = 3*((q2 - 2*(2*q3 - 5*(x01 - 2*x00))) +
    //              (r2 - 2*(2*r3 - 5*(y01 - 2*y00))));
    const t2 = qmd(
        3,
        qaq(
            qdq(q2,qm2(qdq(qm2(q3),qmd(5,qdq(x01,qm2(x00)))))),
            qdq(r2,qm2(qdq(qm2(r3),qmd(5,qdq(y01,qm2(y00))))))
        )
    );

    //const t1 = 2*((q3 - 5*(x01 - 3*x00)) +
    //              (r3 - 5*(y01 - 3*y00)));
    const t1 = qm2(qaq(
        qdq(q3,qmd(5,(qdq(x01,qmd(3,x00))))),
        qdq(r3,qmd(5,(qdq(y01,qmd(3,y00)))))
    ));

    //const t0 = ((x01 - 6*x00) +
    //            (y01 - 6*y00));
    const t0 = qaq(
        qdq(x01,qmd(6,x00)),
        qdq(y01,qmd(6,y00))
    );


    return [t5,t4,t3,t2,t1,t0];
}


export { getFootpointPoly3Dd }