Automating Custom Precision Function Evaluation for Embedded Processors
[IEEE International COnference on Compilers, Architectures and 
Synthesis for Embedded Systems (CASES), San Francisco, Sept. 2005]

abstract.
Due to resource and power constraints, embedded processors
often cannot aord dedicated floating-point units. For instance, 
the IBM PowerPC processor embedded in Xilinx Virtex-II Pro FPGAs 
only supports emulated floating-point arithmetic, which leads to 
slow operation when floating-point arithmetic is desired. This 
paper presents a customizable mathematical library using fixed-point 
arithmetic for elementary function evaluation. We approximate 
functions via polynomial or rational approximations depending on the
user-defined accuracy requirements. The data representation for the 
inputs and outputs are compatible with IEEE single-precision and 
double-precision floating-point formats. Results show that our 
32-bit polynomial method achieves over 80 times speedup over the 
single-precision mathematical library from Xilinx, while our 64-bit 
polynomial method achieves over 30 times speedup.