What exactly does code in Canny do?

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Hi,

I'm trying to modify the Canny function to output both edges and also a mask which flags each edge pixel with 1,2,3,4 (corresponding to the 4 edge directions used by Canny). I've found the code which I belive to be responsible for this, however I need some help understanding this code:

Here is a bit of code from modules/gpu/src/cuda/canny.cu in the the function calcMapKernel:

__global__ void calcMapKernel(const PtrStepSzi dx, const PtrStepi dy, PtrStepi map, const float low_thresh, const float high_thresh)
{
    const int CANNY_SHIFT = 15;
    //0.4142135623730950488016887242097 = tan(pi/8), this is the angles
    const int TG22 = (int)(0.4142135623730950488016887242097*(1<<CANNY_SHIFT) + 0.5);

    const int x = blockIdx.x * blockDim.x + threadIdx.x;
    const int y = blockIdx.y * blockDim.y + threadIdx.y;

    if (x == 0 || x >= dx.cols - 1 || y == 0 || y >= dx.rows - 1)
        return;

    int dxVal = dx(y, x);
    int dyVal = dy(y, x);

    const int s = (dxVal ^ dyVal) < 0 ? -1 : 1;
    const float m = tex2D(tex_mag, x, y);

    dxVal = ::abs(dxVal);
    dyVal = ::abs(dyVal);

    // 0 - the pixel can not belong to an edge
    // 1 - the pixel might belong to an edge
    // 2 - the pixel does belong to an edge
    int edge_type = 0;

    if (m > low_thresh)
    {
        //what do these 2 lines do?
        const int tg22x = dxVal * TG22;
        const int tg67x = tg22x + ((dxVal + dxVal) << CANNY_SHIFT);

        dyVal <<= CANNY_SHIFT;

        //I guess these if blocks determine where the pixel is part of a edge using it's direction
        if (dyVal < tg22x)
        {
            if (m > tex2D(tex_mag, x - 1, y) && m >= tex2D(tex_mag, x + 1, y))
                edge_type = 1 + (int)(m > high_thresh);
        }
        else if(dyVal > tg67x)
        {
            if (m > tex2D(tex_mag, x, y - 1) && m >= tex2D(tex_mag, x, y + 1))
                edge_type = 1 + (int)(m > high_thresh);
        }
        else
        {
            if (m > tex2D(tex_mag, x - s, y - 1) && m >= tex2D(tex_mag, x + s, y + 1))
                edge_type = 1 + (int)(m > high_thresh);
        }
    }

    map(y, x) = edge_type;
}

What exactly are these lines doing? :

const int tg22x = dxVal * TG22;
const int tg67x = tg22x + ((dxVal + dxVal) << CANNY_SHIFT);

Thanks!