Symbolic Algorithms for Embedded System Design a Dissertation Submitted to the Department of Electrical Engineering and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

The growing market of multi-media applications requires development of complex embedded systems with significant data-path portions. However, current hardware synthesis and software optimizations tools and methodologies do not support arithmeticlevel optimizations necessary for data intensive applications. In particular, most highlevel synthesis tools cannot automatically synthesize data paths such that complex arithmetic library blocks are intelligently used. Thus, the data paths of such circuits are often manually designed and mapped to pre-optimized library elements. Similarly, current compilers and software optimization methods are frequently incapable of optimizations required by multi-media software designers. Namely, most high-level arithmetic optimizations and the use of complex instructions and pre-optimized embedded library functions are left to the designers’ ingenuity. In this thesis, results from symbolic polynomial manipulation techniques are used to develop algorithms for high-level data-path hardware synthesis, embedded-software optimization, and automated application specific embedded processor design. Polynomials are chosen to abstract data-intensive software/hardware library elements and high-level specifications. Two new arithmetic-level symbolic polynomial decomposition algorithms are proposed. These algorithms map a specification to an implementation with minimum number of library elements or minimal delay. The decomposition algorithms are applied to high-level synthesis of data intensive circuits by the tool SymSyn. SymSyn performs arithmetic optimization on dataflow descriptions and automatically maps them into data paths using complex arithmetic library components. SymSyn is capable of finding the minimal component mapping and the minimal critical-path delay mapping of the given dataflow. SymSyn is used in