A three-dimensional API for communicating with hardware implementations of vertex shaders and pixel shaders having local registers. With respect to vertex shaders, API communications are provided that may make use of an on-chip register index and API communications are also provided for a specialized function, implemented on-chip at a register level, that outputs the fractional portion(s) of input(s). With respect to pixel shaders, API communications are provided for a specialized function, implemented on-chip at a register level, that performs a linear interpolation function and API communications are provided for specialized modifiers, also implemented on-chip at a register level, that perform modification functions including negating, complementing, remapping, stick biasing, scaling and saturating. Advantageously, these API communications expose these very useful on-chip graphical algorithmic elements to a developer while hiding the details of the operation of the vertex shader and pixel shader chips from the developer.