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However (and my knowledge of shaders is limited), wouldn't that bit of shader code be called the same number of times even if it were a smaller bitmap stretched to 1024x768?


No, not if you use a smaller render target. The pixel shader is executed once for each texel in the render target. A6 then uses that render target as texture for rendering the view entity or panel, so it will do texture lookups for every screen pixel that is occupied by the view entity/panel (which happens to be 1024x768 if it is screen-alligned) from the previously created texture.

If your entity is screen alligned, several screen pixels will lookup from the same texel, so you will get blocks of screen pixels with the same color unless you use linear interpolation for your sampler (which is the default).

shader tutorial