Systems and methods for downloading algorithmic elements to a coprocessor and corresponding processing and communication techniques are provided. For an improved graphics pipeline, the invention provides a class of co-processing device, such as a graphics processor unit (GPU), providing improved capabilities for an abstract or virtual machine for performing graphics calculations and rendering. The invention allows for runtime-predicated flow control of programs downloaded to coprocessors, enables coprocessors to include indexable arrays of on-chip storage elements that are readable and writable during execution of programs, provides native support for textures and texture maps and corresponding operations in a vertex shader, provides frequency division of vertex streams input to a vertex shader with optional support for a stream modulo value, provides a register storage element on a pixel shader and associated interfaces for storage associated with representing the “face” of a pixel, provides vertex shaders and pixel shaders with more on-chip register storage and the ability to receive larger programs than any existing vertex or pixel shaders and provides 32 bit float number support in both vertex and pixel shaders.