FX-SCORE: A Framework for Fixed-Point Compilation of SPICE Device Models Using Gappa++

Abstract

Automated, offline precision-analysis of dataflow computation containing elementary functions (e.g. exp) and if-then-else control flow operations enables accurate fixed-point FPGA implementation of SPICE device equations. We perform interval analysis of these equations using Gappa++ to statically compare error bounds of fixed-point and double-precision implementations. This is possible due to the limited dynamic range of physical voltage, current and conductance quantities in a SPICE simulation of real-world circuits. In contrast to previous custom-precision SPICE device mappings, our fixed-point implementation has the same accuracy as double-precision implementation when compared to ideal arithmetic (reals). To deliver these implementations we develop FX-SCORE, a high-level framework based on the SCORE streaming FPGA framework, that automatically generates Gappa++ scripts and AutoESL circuits to explore the cost-quality tradeoffs of Fixed-point FPGA implementations. Using our methodology, we can determine whether fixed-point is always better than a double-precision implementation at the same relative error. We demonstrate 35% geometric mean area improvement for different SPICE device models such as Diode, Level-1 MOSFET and an Approximate MOSFET when comparing custom fixed-point implementations with standard double-precision realizations.