Vignette filter: precompute more values, simplify math, cleanup code

 * limitations under the License.

 */

static float2 scale;

static float2 center, dimensions;

static float range, inv_max_dist, shade, slope;

static float2 overDimensions;

static float2 neg_center, axis_scale, inv_dimensions;

static float sloped_neg_range, sloped_inv_max_dist, shade, opp_shade;

void init_vignette(uint32_t dim_x, uint32_t dim_y, float center_x, float center_y,

        float desired_scale, float desired_shade, float desired_slope) {

    center.x = center_x;

    center.y = center_y;

    dimensions.x = (float)dim_x;

    dimensions.y = (float)dim_y;

    neg_center.x = -center_x;

    neg_center.y = -center_y;

    inv_dimensions.x = 1.f / (float)dim_x;

    inv_dimensions.y = 1.f / (float)dim_y;

    axis_scale = (float2)1.f;

    if (dim_x > dim_y)

        axis_scale.y = (float)dim_y / (float)dim_x;

    else

        axis_scale.x = (float)dim_x / (float)dim_y;

    const float max_dist = 0.5 * length(axis_scale);

    sloped_inv_max_dist = desired_slope * 1.f/max_dist;

    float max_dist = 0.5;

    if (dim_x > dim_y) {

        scale.x = 1.0;

        scale.y = dimensions.y / dimensions.x;

        max_dist *= sqrt(scale.y*scale.y + 1);

    } else {

        scale.x = dimensions.x / dimensions.y;

        scale.y = 1.0;

        max_dist *= sqrt(scale.x*scale.x + 1);

    }

    inv_max_dist = 1.0/max_dist;

    // Range needs to be between 1.3 to 0.6. When scale is zero then range is

    // 1.3 which means no vignette at all because the luminousity difference is

    // less than 1/256.  Expect input scale to be between 0.0 and 1.0.

    range = 1.3 - 0.7*sqrt(desired_scale);

    shade = desired_shade;

    slope = desired_slope;

    const float neg_range = 0.7*sqrt(desired_scale) - 1.3;

    sloped_neg_range = exp(neg_range * desired_slope);

    overDimensions = ((float2)1.f) / dimensions;

    shade = desired_shade;

    opp_shade = 1.f - desired_shade;

}

void root(const uchar4 *in, uchar4 *out, uint32_t x, uint32_t y) {

    // Convert x and y to floating point coordinates with center as origin

    const float4 fin = convert_float4(*in);

    float2 coord = {(float)x, (float)y};

    coord *= overDimensions;

    coord -= center;

    const float dist = length(scale * coord);

    const float lumen = shade / (1.0 + exp((dist * inv_max_dist - range) * slope)) + (1.0 - shade);

    const float2 inCoord = {(float)x, (float)y};

    const float2 coord = mad(inCoord, inv_dimensions, neg_center);

    const float sloped_dist_ratio = length(axis_scale * coord)  * sloped_inv_max_dist;

    const float lumen = opp_shade + shade / ( 1.0 + sloped_neg_range * exp(sloped_dist_ratio) );

    float4 fout;

    fout.rgb = fin.rgb * lumen;

    fout.w = fin.w;