#pragma once
#if LUPWD

Preprocessed Scalar
der6x_upwd(in ScalarField vertex)
{
    Scalar inv_ds = AC_inv_dsx;

    return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
                    (-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
                     Scalar(15.0) * (vertex[vertexIdx.x + 1, vertexIdx.y, vertexIdx.z] +
                                     vertex[vertexIdx.x - 1, vertexIdx.y, vertexIdx.z]) -
                     Scalar(6.0) * (vertex[vertexIdx.x + 2, vertexIdx.y, vertexIdx.z] +
                                    vertex[vertexIdx.x - 2, vertexIdx.y, vertexIdx.z]) +
                     vertex[vertexIdx.x + 3, vertexIdx.y, vertexIdx.z] +
                     vertex[vertexIdx.x - 3, vertexIdx.y, vertexIdx.z])};
}

Preprocessed Scalar
der6y_upwd(in ScalarField vertex)
{
    Scalar inv_ds = AC_inv_dsy;

    return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
                    (-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
                     Scalar(15.0) * (vertex[vertexIdx.x, vertexIdx.y + 1, vertexIdx.z] +
                                     vertex[vertexIdx.x, vertexIdx.y - 1, vertexIdx.z]) -
                     Scalar(6.0) * (vertex[vertexIdx.x, vertexIdx.y + 2, vertexIdx.z] +
                                    vertex[vertexIdx.x, vertexIdx.y - 2, vertexIdx.z]) +
                     vertex[vertexIdx.x, vertexIdx.y + 3, vertexIdx.z] +
                     vertex[vertexIdx.x, vertexIdx.y - 3, vertexIdx.z])};
}

Preprocessed Scalar
der6z_upwd(in ScalarField vertex)
{
    Scalar inv_ds = AC_inv_dsz;

    return (Scalar){Scalar(1.0 / 60.0) * inv_ds *
                    (-Scalar(20.0) * vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z] +
                     Scalar(15.0) * (vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 1] +
                                     vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 1]) -
                     Scalar(6.0) * (vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 2] +
                                    vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 2]) +
                     vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z + 3] +
                     vertex[vertexIdx.x, vertexIdx.y, vertexIdx.z - 3])};
}

#endif