Symbolic Differentiation in GPU Shaders

Brian Guenter, John Rapp, Mark Finch
Microsoft Research
Microsoft Research TechReport MSR-TR-2011-31, 2011


   title={Symbolic Differentiation in GPU Shaders},

   author={Guenter, B. and Rapp, J. and Finch, M.},



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Derivatives arise frequently in graphics and scientific computation applications. As GPU’s become more widely used for scientific computation the need for derivatives can be expected to increase. To meet this need we have added symbolic differentiation as a built in language feature in the HLSL shading language. The symbolic derivative is computed at compile time so it is available in all types of shaders (geometry, pixel, vertex, etc.). The algorithm for computing the symbolic derivative is simple and has reasonable compilation and run time overhead.
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