Design of a low-cost floating-point programmable vertex processor for mobile graphics applications based on hybrid number system

Recent OpenGL ES 2.0 API Specification for embedded systems graphics operations requires programmable vertex shader and fragment shader to process vertex and pixel data. Calculation of dot-product for two vectors and transcendental functions for a scalar are two fundamental arithmetic operations in the vertex processing. Since some complicated arithmetic operations in binary number system (BNS) turn into simple operations of addition and/or multiplication in the logarithmic number system (LNS), we present a low-cost design of a floating-point programmable vertex processor based on hybrid BNS and LNS. The proposed design achieves at least the same (or even higher) precision with much lower cost compared with recent similar implementations.